ALBERT

Description: In this study, we present a new synthesis of GPS velocities for tectonic deformation within the Tibetan Plateau and its surrounding areas, a combined data set of ~1854 GPS-derived horizontal velocity vectors. Assuming that crustal deformation is localized along major faults, a block modelling approach is employed to interpret the GPS velocity field. We construct a 30-element block model to describe present-day deformation in western China, with half of them located within the Tibetan Plateau, and the remainder located in its surrounding areas. We model the GPS velocities simultaneously for the effects of block rotations and elastic strain induced by the bounding faults. Our model yields a good fit to the GPS data with a mean residual of 1.08 mm a –1 compared to the mean uncertainty of 1.36 mm a –1 for each velocity component, indicating a good agreement between the predicted and observed velocities. The major strike-slip faults such as the Altyn Tagh, Xianshuihe, Kunlun and Haiyuan faults have relatively uniform slip rates in a range of 5–12 mm a –1 along most of their segments, and the estimated fault slip rates agree well with previous geologic and geodetic results. Blocks having significant residuals are located at the southern and southeastern Tibetan Plateau, suggesting complex tectonic settings and further refinement of accurate definition of block geometry in these regions.

Description: By introducing two types of zenith troposphere delay (ZTD) products in precise point positioning (PPP), we developed the ZTD-corrected PPP and the ZTD-constrained PPP, both of them reduced the PPP convergence time. Both enhanced PPP methods are examined by global empirical ZTD models and regional ZTD corrections. For global ZTD models, we verified that ZTD-corrected PPP will deviate the positioning results, while ZTD-constrained PPP could produce unbiased estimations. Therefore, the latter is utilized to study the performance of global ZTD models (ITG, GPT2w, GZTD and UNB3m). After numerous experiments, we found that the performance of ZTD models was positively related to the real ZTD accuracy, and we proposed a universal tropospheric stochastic model 2SQR(9rms) which denotes double the square of nine times ZTD rms, to constrain ZTD in PPP. The proposed model subsequently was validated by real-time static and kinematic ZTD-constrained PPP on the premise that the ZTD rms on every station was known. Compared with traditional PPP, in static PPP, the number of improved stations is increased by 15.5 per cent (ITG), 14.4 per cent (GPT2w), 11.1 per cent (GZTD) and 8.3 per cent (UNB3m). For kinematic PPP, PPP constrained by ITG model still had the best performance, the number of improved stations is increased by 14.4 per cent, after 30 min of initialization time, 13.4 cm east, 13.4 cm north and 11.7 cm up positioning accuracy was obtained, compared with 15.3 cm east, 15.3 cm north and 14.3 cm up accuracy by traditional PPP. In addition, experiments using regional ZTD corrections to enhance real-time PPP showed that both ZTD-corrected PPP and ZTD-constrained PPP can notably reduce the convergence time on the vertical component (within 15 cm).

Description: Using an up-to-date global plate rotation model, applied to the endpoints of preserved major spreading ridge isochrons, we have calculated the explicitly reconstructable length-weighted mean global half-spreading rate (HSR), ridge length and area production as a function of time since the end of the Cretaceous Normal Superchron at 83.0 Ma. Our calculations integrate uncertainties in rotation parameters and chron boundary ages with the partial sampling uncertainties arising from progressive subduction of older oceanic lithosphere and its preserved spreading record. This record of directly reconstructable oceanic ridge production provides a well-constrained baseline that can be compared to reconstructions that include the largely unconstrained extrapolated histories of entirely subducted oceanic plates. The directly reconstructable global mean HSR has not varied by more than ±15 per cent about an average rate of 28.4 ± 4.6 mm a –1 since 83 Ma. No long-term secular trend is evident: a maximum global mean half-rate of 32 ± 6 mm a –1 occurred from 33.1 Ma to about 25.8 Ma, with minima of 26 ± 5 mm a –1 between about 56 and 40.2 Ma, and 24 ± 1 mm a –1 since 3.2 Ma. Only this most recent interval has a rate that differs significantly (at ±2) from the long-term mean. The global, reconstructable ridge length at 56 Ma decreases by less than 15 per cent relative to the modern ridge system; by 83 Ma it has decreased by 38 per cent. These relatively high preserved ridge fractions mean that the estimated uncertainty due to partial sampling stays roughly equivalent to the estimated rotation model uncertainties, allowing long-term spreading rate variations of 〉20 per cent since the Late Cretaceous to be ruled out. In contrast, prior to 83 Ma too little oceanic lithosphere is preserved to reliably reconstruct global spreading rates.

Description: We study fluctuations in the degree-2 zonal spherical harmonic coefficient of the Earth's gravity potential, C 20 , over the period 2003–2015. This coefficient is related to the Earth's oblateness and studying its temporal variations, C 20 , can be used to monitor large-scale mass movements between high and low latitude regions. We examine C 20 inferred from six different sources, including satellite laser ranging (SLR), GRACE and global geophysical fluids models. We further include estimates that we derive from measured variations in the length-of-day (LOD), from the inversion of global crustal displacements as measured by GPS, as well as from the combination of GRACE and the output of an ocean model as described by Sun et al. We apply a sequence of trend and seasonal moving average filters to the different time-series in order to decompose them into an interannual, a seasonal and an intraseasonal component. We then perform a comparison analysis for each component, and we further estimate the noise level contained in the different series using an extended version of the three-cornered-hat method. For the seasonal component, we generally obtain a very good agreement between the different sources, and except for the LOD-derived series, we find that over 90 per cent of the variance in the seasonal components can be explained by the sum of an annual and semiannual oscillation of constant amplitudes and phases, indicating that the seasonal pattern is stable over the considered time period. High consistency between the different estimates is also observed for the intraseasonal component, except for the solution from GRACE, which is known to be affected by a strong tide-like alias with a period of about 161 d. Estimated interannual components from the different sources are generally in agreement with each other, although estimates from GRACE and LOD present some discrepancies. Slight deviations are further observed for the estimate from the geophysical models, likely to be related to the omission of polar ice and groundwater changes in the model combination we use. On the other hand, these processes do not seem to play an important role at seasonal and shorter timescales, as the sum of modelled atmospheric, oceanic and hydrological effects effectively explains the observed C 20 variations at those scales. We generally obtain very good results for the solution from SLR, and we confirm that this well-established technique accurately tracks changes in C 20 . Good agreement is further observed for the estimate from the GPS inversion, showing that this indirect method is successful in capturing fluctuations in C 20 on scales ranging from intra- to interannual. Obtaining accurate estimates from LOD, however, remains a challenging task and more reliable models of atmospheric wind fields are needed in order to obtain high-quality C 20 , in particular at the seasonal scale. The combination of GRACE data and the output of an ocean model appears to be a promising approach, particularly since corresponding C 20 is not affected by tide-like aliases, and generally gives better results than the solution from GRACE, which still seems to be of rather poor quality.

Description: We explore thermal convection of a fluid with a temperature-dependent viscosity in a basally heated 3-D spherical shell using linear stability analyses and numerical experiments, while considering the application of our results to terrestrial planets. The inner to outer radius ratio of the shell f assumed in the linear stability analyses is in the range of 0.11–0.88. The critical Rayleigh number R c for the onset of thermal convection decreases by two orders of magnitude as f increases from 0.11 to 0.88, when the viscosity depends sensitively on the temperature, as is the case for real mantle materials. Numerical simulations carried out in the range of f  = 0.11–0.55 show that a thermal boundary layer (TBL) develops both along the surface and bottom boundaries to induce cold and hot plumes, respectively, when f is 0.33 or larger. However, for smaller f values, a TBL develops only on the bottom boundary. Convection occurs in the stagnant-lid regime where the root mean square velocity on the surface boundary is less than 1 per cent of its maximum at depth, when the ratio of the viscosity at the surface boundary to that at the bottom boundary exceeds a threshold that depends on f . The threshold decreases from 10 6.5 at f  = 0.11 to 10 4 at f  = 0.55. If the viscosity at the base of the convecting mantle is 10 20 –10 21  Pa s, the Rayleigh number exceeds R c for Mars, Venus and the Earth, but does not for the Moon and Mercury; convection is unlikely to occur in the latter planets unless the mantle viscosity is much lower than 10 20  Pa s and/or the mantle contains a strong internal heat source.

Description: Subducting oceanic lithosphere is an example of a thin sheet-like object whose characteristic lateral dimension greatly exceeds its thickness. Here we exploit this property to derive a new hybrid boundary-integral/thin sheet (BITS) representation of subduction that combines in a single equation all the forces acting on the sheet: gravity, internal resistance to bending and stretching, and the tractions exerted by the ambient mantle. For simplicity, we limit ourselves to 2-D. We solve the BITS equations using a discrete Lagrangian approach in which the sheet is represented by a set of vertices connected by edges. Instantaneous solutions for the sinking speed of a slab attached to a trailing flat sheet obey a scaling law of the form V / V Stokes  = fct(St), where V Stokes is a characteristic Stokes sinking speed and St is the sheet's flexural stiffness. Time-dependent solutions for the evolution of the sheet's shape and thickness show that these are controlled by the viscosity ratio between the sheet and its surroundings. An important advantage of the BITS approach is the possibility of generalizing the sheet's rheology, either to a viscosity that varies along the sheet or to a non-Newtonian shear-thinning rheology.

Description: The aftershock distribution of the 1933 Sanriku-oki outer trench earthquake is estimated by using modern relocation methods and a newly developed velocity structure to examine the spatial extent of the source-fault and the possibility of a triggered interplate seismicity. In this study, we first examined the regional data quality of the 1933 earthquake based on smoked-paper records and then relocated the earthquakes by using the 3-D velocity structure and double-difference method. The improvements of hypocentre locations using these methods were confirmed by the examination of recent earthquakes that are accurately located based on ocean bottom seismometer data. The results show that the 1933 aftershocks occurred under both the outer- and inner-trench-slope regions. In the outer-trench-slope region, aftershocks are distributed in a ~280-km-long area and their depths are shallower than 50 km. Although we could not constrain the fault geometry from the hypocentre distribution, the depth distribution suggests the whole lithosphere is probably not under deviatoric tension at the time of the 1933 earthquake. The occurrence of aftershocks under the inner trench slope was also confirmed by an investigation of waveform frequency difference between outer and inner trench earthquakes as recorded at Mizusawa. The earthquakes under the inner trench slope were shallow (depth less double equals30 km) and the waveforms show a low-frequency character similar to the waveforms of recent, precisely located earthquakes in the same area. They are also located where recent activity of interplate thrust earthquakes is high. These suggest that the 1933 outer-trench-slope main shock triggered interplate earthquakes, which is an unusual case in the order of occurrence in contrast with the more common pairing of a large initial interplate shock with subsequent outer-slope earthquakes. The off-trench earthquakes are distributed about 80 km width in the trench perpendicular direction. This wide width cannot be explained from a single high-angle fault confined at a shallow depth (depth less double equals50 km). The upward motion of the 1933 tsunami waveform records observed at Sanriku coast also cannot be explained from a single high-angle west-dipping normal fault. If we consider additional fault, involvement of high-angle, east-dipping normal faults can better explain the tsunami first motion and triggering of the aftershock in a wide area under the outer trench slope. Therefore multiple off-trench normal faults may have activated during the 1933 earthquake. We also relocated recent (2001–2012) seismicity by the same method. The results show that the present seismicity in the outer-trench-slope region can be divided into several groups along the trench. Comparison of the 1933 rupture dimensions based on our aftershock relocations with the morphologies of fault scarps in the outer trench slope suggest that the rupture was limited to the region where fault scarps are largely trench parallel and cross cut the seafloor spreading fabric. These findings imply that bending geometry and structural segmentation of the incoming plate largely controls the spatial extent of the 1933 seismogenic faulting. In this shallow rupture model for this largest outer trench earthquake, triggered seismicity in the forearc and structural control of faulting represent an important deformation styles for off-trench and shallow megathrust zones.

Description: Geodetic, geologic and palaeomagnetic data reveal that Oregon (western USA) rotates clockwise at 0.3 to 1.0° Ma –1 (relative to North America) about an axis near the Idaho–Oregon–Washington border, while northeast Washington is relatively fixed. This rotation has been going on for at least 15 Ma. The Yakima fold and thrust belt (YFTB) forms the boundary between northern Oregon and central Washington where convergence of the clockwise-rotating Oregon block is apparently accommodated. North–south shortening across the YFTB has been thought to occur in a fan-like manner, increasing in rate to the west. We obtained high-accuracy, high-density geodetic GPS measurements in 2012–2014 that are used with earlier GPS measurements from the 1990s to characterize YFTB kinematics. The new results show that the deformation associated with the YFTB starts at the Blue Mountains Anticline in northern Oregon and extends north beyond the Frenchman Hills in Washington, past the epicentre of the 1872 M w 7.0 Entiat earthquake to 49°N. The north–south strain rate across the region is 2 to 3 x 10 –9 yr –1 between the volcanic arc and the eastern edge of the YFTB (241.0°E); east of there it drops to about 10 –9 yr –1 . At the eastern boundary of the YFTB, faults and earthquake activity are truncated by a north-trending, narrow zone of deformation that runs along the Pasco Basin and Moses Lake regions near 240.9°E. This zone, abutting the Department of Energy Hanford Nuclear Reservation, accommodates about 0.5 mm yr –1 of east to northeast shortening. A similar zone of N-trending transpression is seen along 239.9°E where there is a change in the strike of the Yakima folds. The modern deformation of the YFTB is about 600 km wide from south to north and internally may be controlled by pre-existing crustal structure.

Description: The Central Anatolian orogenic plateau is represented by young volcanism, rapid plateau uplift and distinctive (past and active) tectonic deformation. In this study, we consider observational data in terms of regional present-day geodynamics in the region. The residual topography of Central Anatolia was derived to define the regional isostatic conditions according to Airy isostasy and infer the potential role of ‘dynamic topography’. 2-D thermomechanical forward models for coupled mantle-lithosphere flow/deformation were conducted along an N–S directional profile through the region (e.g. northern/Pontides, interior and southern/Taurides). These models were based on seismic tomography data that provide estimates about the present-day mantle thermal structure beneath the Anatolian plate. We compare the modelling results with calculated residual topography and independent data sets of geological deformation, gravity and high surface heat flow/widespread geothermal activity. Model results suggest that there is ~1 km of mantle flow induced dynamic topography associated with the sublithospheric flow driven by the seismically inferred mantle structure. The uprising mantle may have also driven the asthenospheric source of volcanism in the north (e.g. Galatia volcanic province) and the Cappadocia volcanic province in the south while elevating the surface in the last 10 Myr. Our dynamic topography calculations emphasize the role of vertical forcing under other orogenic plateaux underlain by relatively thin crust and low-density asthenospheric mantle.

Description: In many geological systems, inversion of density stratification sets in Rayleigh–Taylor (RT) instabilities, leading to an ascent of relatively low-density materials through the high-density overburden in the form of diapirs. These diapirs often originate from dipping low-density layers. This study aims to show how the initial tilt of such source layers can control the ascent behaviour of diapirs initiated by RT instabilities. Using two-layer viscous models we produced RT instabilities in physical experiments, and investigated the effects of source-layer tilts ( β ). Our experiments suggest that these diapirs ascend with contrasting lateral spreading rates in the up and down slope directions, resulting in their axi-asymmetric geometry. However, their heads retain a circular outline on the horizontal top surface, where the upwelling axis is located away from their geometric centre in the upslope direction. In this paper, we present a series of experimental models to demonstrate the spectrum of axi-symmetric to -asymmetric geometrical transitions with increasing β . Our experiments also reveal that when β is large (〉4°) the diapirs become unstable, resulting in a continuous migration of their stems in the upslope direction. Using the volume of fluid method we ran computational fluid dynamic (CFD) simulations to study the underlying hydrodynamics of axi-asymmetric diapiric growth. The CFD simulations show that β 〉 0° conditions develop stronger flow vortices on the downslope side of an ascending diapir, leading to a pressure difference between the up- and downslope flanks. Such a differential pressure causes the diapir head to spread at a faster rate in the tilt direction. An estimate of the asymmetric spreading rates is given as a function of β . Our present study provides a fundamental understanding of the hydrodynamic flow structure responsible for the asymmetric growth of RT instabilities on tilted source layers, as applicable to a wide range of large-scale geological settings, such as sedimentary basins and subduction zones.

Description: The geomechanical analysis of a highly compartmentalized reservoir is performed to simulate the seafloor subsidence due to gas production. The available observations over the hydrocarbon reservoir consist of bathymetric surveys carried out before and at the end of a 10-yr production life. The main goal is the calibration of the reservoir compressibility c M , that is, the main geomechanical parameter controlling the surface response. Two conceptual models are considered: in one (i) c M varies only with the depth and the vertical effective stress (heterogeneity due to lithostratigraphic variability); in another (ii) c M varies also in the horizontal plane, that is, it is spatially distributed within the reservoir stratigraphic units. The latter hypothesis accounts for a possible partitioning of the reservoir due to the presence of sealing faults and thrusts that suggests the idea of a block heterogeneous system with the number of reservoir blocks equal to the number of uncertain parameters. The method applied here relies on an ensemble-based data assimilation (DA) algorithm (i.e. the ensemble smoother, ES), which incorporates the information from the bathymetric measurements into the geomechanical model response to infer and reduce the uncertainty of the parameter c M . The outcome from conceptual model (i) indicates that DA is effective in reducing the c M uncertainty. However, the maximum settlement still remains underestimated, while the areal extent of the subsidence bowl is overestimated. We demonstrate that the selection of the heterogeneous conceptual model (ii) allows to reproduce much better the observations thus removing a clear bias of the model structure. DA allows significantly reducing the c M uncertainty in the five blocks (out of the seven) characterized by large volume and large pressure decline. Conversely, the assimilation of land displacements only partially constrains the prior c M uncertainty in the reservoir blocks marginally contributing to the cumulative seafloor subsidence, that is, blocks with low pressure.

Description: The geocentre motion is the motion of the centre of mass of the entire Earth, considered an isolated system, in a terrestrial system of reference. We first derive a formula relating the harmonic degree-1 Lagrangian variation of the gravity at a station to both the harmonic degree-1 vertical displacement of the station and the displacement of the whole Earth's centre of mass. The relationship is independent of the nature of the Earth deformation and is valid for any source of deformation. We impose no constraint on the system of reference, except that its origin must initially coincide with the centre of mass of the spherically symmetric Earth model. Next, we consider the geocentre motion caused by surface loading. In a system of reference whose origin is the centre of mass of the solid Earth, we obtain a specific relationship between the gravity variation at the surface, the geocentre displacement and the load Love number $h^{\prime }_1$ , which demands the Earth's structure and rheological behaviour be known. For various networks of real or fictitious stations, we invert synthetic signals of surface gravity variations caused by atmospheric loading to retrieve the degree-1 variation of gravity. We then select six well-distributed stations of the Global Geodynamics Project, which is a world network of superconducting gravimeters, to invert actual gravity data for the degree-1 variations and determine the geocentre displacement between the end of 2004 and the beginning of 2012, assuming it to be due to surface loading. We find annual and semi-annual displacements with amplitude 0.5–2.3 mm.

Description: This work aims to explore the ongoing tectonic activity of structures in the outermost sector of the Northern Apennines, which represents the active leading edge of the thrust belt and is dominated by compressive deformation. We have applied the Persistent Scatterer Interferometry (PSI) technique to obtain new insights into the present-day deformation pattern of the frontal area of the Northern Apennine. PSI has proved to be effective in detecting surface deformation of wide regions involved in low tectonic movements. We used 34 Envisat images in descending geometry over the period of time between 2004 and 2010, performing about 300 interferometric pairs. The analysis of the velocity maps and of the PSI time-series has allowed to observe ground deformation over the sector of the Po Plain between Piacenza and Reggio Emilia. The time-series of permanent GPS stations located in the study area, validated the results of the PSI technique, showing a good correlation with the PS time-series. The PS analysis reveals the occurrence of a well-known subsidence area on the rear of the Ferrara arc, mostly connected to the exploitation of water resources. In some instances, the PS velocity pattern reveals ground uplift (with mean velocities ranging from 1 to 2.8 mm yr –1 ) above active thrust-related anticlines of the Emilia and Ferrara folds, and part of the Pede-Apennine margin. We hypothesize a correlation between the observed uplift deformation pattern and the growth of the thrust-related anticlines. As the uplift pattern corresponds to known geological features, it can be used to constrain the seismo-tectonic setting, and a working hypothesis may involve that the active Emilia and Ferrara thrust folds would be characterized by interseismic periods possibly dominated by aseismic creep.

Description: In Europe, common input data types for seismic hazard evaluation include earthquake catalogues, seismic zonation models and ground motion models, all with well-constrained epistemic uncertainties. In contrast, neotectonic deformation models and their related uncertainties are rarely considered in earthquake forecasting and seismic hazard studies. In this study, for the first time in Europe, we developed a seismic hazard model based exclusively on active fault and geodynamic deformation models. We applied it to the External Dinarides, a slow-deforming fold-and-thrust belt in the Central Mediterranean. The two deformation models furnish consistent long-term earthquake rates above the M w 4.7 threshold on a latitude/longitude grid with 0.2° spacing. Results suggest that the use of deformation models is a valid alternative to empirical-statistical approaches in earthquake forecasting in slow-deforming regions of Europe. Furthermore, we show that the variability of different deformation models has a comparable effect on the peak ground motion acceleration uncertainty as do the ground motion prediction equations.

Description: We review the theory of the Earth's elastic and gravitational response to a surface disk load. The solutions for displacement of the surface and the geoid are developed using expansions of Legendre polynomials, their derivatives and the load Love numbers. We provide a matlab  function called diskload that computes the solutions for both uncompensated and compensated disk loads. In order to numerically implement the Legendre expansions, it is necessary to choose a harmonic degree, n max , at which to truncate the series used to construct the solutions. We present a rule of thumb (ROT) for choosing an appropriate value of n max , describe the consequences of truncating the expansions prematurely and provide a means to judiciously violate the ROT when that becomes a practical necessity.

Description: Two types of signals are clearly visible in continuous GPS (cGPS) time-series in Iceland, in particular in the vertical component. The first one is a yearly seasonal cycle, usually sinusoid-like with a minimum in the spring and a maximum in the fall. The second one is a trend of uplift, with higher values the closer the cGPS stations are to the centre of Iceland and ice caps. Here, we study the seasonal cycle signal by deriving its average at 71 GPS sites in Iceland. We estimate the annual and semi-annual components of the cycle in their horizontal and vertical components using a least-squares adjustment. The peak-to-peak amplitude of the cycle of the vertical component at the studied sites ranges from 4 mm near the coastline up to 27 mm at the centre of the Vatnajökull, the largest ice cap in Iceland. The minimum of the seasonal cycle occurs earlier in low lying areas than in the central part of Iceland, consistent with snow load having a large influence on seasonal deformation. Modelling shows that the seasonal cycle is well explained by accounting for elastically induced surface displacements due to snow, atmosphere, reservoir lake and ocean variations. Model displacement fields are derived considering surface loads on a multilayered isotropic spherical Earth. Through forward and inverse modelling, we were able to reproduce a priori information on the average seasonal cycle of known loads (atmosphere, snow in non-glaciated areas and lake reservoir) and get an estimation of other loads (glacier mass balance and ocean). The seasonal glacier mass balance cycle in glaciated areas and snow load in non-glaciated areas are the main contributions to the seasonal deformation. For these loads, induced seasonal vertical displacements range from a few millimetres far from the loads in Iceland, to more than 20 mm at their centres. Lake reservoir load also has to be taken into account on local scale as it can generate up to 20 mm of vertical deformation. Atmosphere load and ocean load are observable and generate vertical displacements in the order of a few millimetres. Inversion results also shows that the Iceland crust is less rigid than the world average. Interannual deviation from the GPS seasonal cycle can occur and are caused by unusual weather conditions over extended period of time.

Description: An important real world application of doublet flow occurs in well design of both geothermal and hydrocarbon reservoirs. A guiding principle for fluid management of injection and extraction wells is that mass balance is commonly assumed between the injected and produced fluid. Because the doublets are considered closed loops, the injection fluid is assumed to eventually reach the producer well and all the produced fluid ideally comes from stream tubes connected to the injector of the well pair making up the doublet. We show that when an aquifer background flow occurs, doublets will rarely retain closed loops of fluid recirculation. When the far-field flow rate increases relative to the doublet's strength, the area occupied by the doublet will diminish and eventually vanishes. Alternatively, rather than using a single injector (source) and single producer (sink), a linear array of multiple injectors separated by some distance from a parallel array of producers can be used in geothermal energy projects as well as in waterflooding of hydrocarbon reservoirs. Fluid flow in such an arrangement of parallel source-sink arrays is shown to be macroscopically equivalent to that of a line doublet. Again, any far-field flow that is strong enough will breach through the line doublet, which then splits into two vortices. Apart from fundamental insight into elementary flow dynamics, our new results provide practical clues that may contribute to improve the planning and design of doublets and direct line drives commonly used for flow management of groundwater, geothermal and hydrocarbon reservoirs.

Description: Seismic waves produced by fault ruptures give rise to gravity perturbations. So far, these perturbations have either been modelled as permanent coseismic gravity change in a half-space or spherical Earth model, or as full time-domain model in infinite space. In this paper, we present the explicit solution of gravity perturbations in time domain produced by a double-couple buried in a homogeneous half-space. This result is especially suited to study gravity perturbations up to a few hundreds of kilometres from the epicentre. It facilitates detailed parametric studies of gravity perturbations from fault rupture, and predicts gravity perturbations of real earthquakes with greatly improved accuracy. The results may serve to develop first designs of gravity-assisted earthquake early-warning systems, made possible by a new generation of ultrasensitive gravity gradiometers, which is currently under development.

Description: In November 2010, intense seismic activity including 29 events with a magnitude above 5.0, started in the western part of the Gulf of Aden, where the structure of the oceanic spreading ridge is characterized by a series of N115°-trending slow-spreading segments set within an EW-trending rift. Using signals recorded by permanent and temporary networks in Djibouti and Yemen, we located 1122 earthquakes, with a magnitude ranging from 2.1 to 5.6 from 2010 November 1 to 2011 March 31. By looking in detail at the space–time distribution of the overall seismicity, and both the frequency and the moment tensor of large earthquakes, we re-examine the chronology of this episode. In addition, we also interpret the origin of the activity using high-resolution bathymetric data, as well as from observations of seafloor cable damage caused by high temperatures and lava flows. The analysis allows us to identify distinct active areas. First, we interpret that this episode is mainly related to a diking event along a specific ridge segment, located at E044°. In light of previous diking episodes in nearby subaerial rift segments, for which field constraints and both seismic and geodetic data exist, we interpret the space–time evolution of the seismicity of the first few days. Migration of earthquakes suggests initial magma ascent below the segment centre. This is followed by a southeastward dike propagation below the rift immediately followed by a northwestward dike propagation below the rift ending below the northern ridge wall. The cumulative seismic moment associated with this sequence reaches 9.1 x 10 17 Nm, and taking into account a very low seismic versus geodetic moment, we estimate a horizontal opening of ~0.58–2.9 m. The seismic activity that followed occurred through several bursts of earthquakes aligned along the segment axis, which are interpreted as short dike intrusions implying fast replenishment of the crustal magma reservoir feeding the dikes. Over the whole period, the opening is estimated to be ~1.76–8.8 m across the segment. A striking feature of this episode is that the seismicity remained confined within one individual segment, whereas the adjacent en-echelon segments were totally quiescent, suggesting that the magma supply system of one segment is disconnected from those of the neighbouring segments. Second, we identify activity induced by the first intrusion with epicentres aligned along an N035°E-trending, ~30 km long at the northwestern end of the active opening segment. This group encompasses more than seven earthquakes with magnitude larger than 5.0, and with strike-slip focal mechanisms consistent with the faults identified in the bathymetry and the structural pattern of the area. We propose that a transform fault is currently in formation which indicates an early stage of the ridge segmentation, at the locus of the trend change of the spreading ridge, which also corresponds to the boundary between a clear oceanic lithosphere and the zone of transform between continental and oceanic crust.

Description: Continuous gravimetric observations have been made with three successive generations of superconducting gravimeter over 20 yr at Syowa Station ( $39.6\deg$ E, $69.0\deg$ S), East Antarctica. The third-generation instrument, OSG#058, was installed in January 2010 and was calibrated by an absolute gravimeter during January and February, 2010. The estimated scale factor was –73.823 ± 0.053 μGal V –1 (1 μGal = 10 –8 m s –2 ). The first 5 yr of OSG#058 data from 2010 January 7 to 2015 January 10 were decomposed into tidal waves (M3 to Ssa) and other non-tidal components by applying the Bayesian tidal analysis program BAYTAP. Long-term non-tidal gravity residuals, which were obtained by subtracting annual and 18.6 year tidal waves and the predicted gravity response to the Earth's variable rotation, showed significant correlation with the accumulated snow depth measured at Syowa Station. The greatest correlation occurred when the gravity variations lagged the accumulated snow depth by 21 d. To estimate the gravitational effect of the accumulated snow mass, we inferred a conversion factor of 3.13 ± 0.08 μGal m –1 from this relation. The accumulated snow depth at Syowa Station was found to represent an extensive terrestrial water storage (the snow accumulation) around Syowa Station, which was estimated from the Gravity Recovery and Climate Experiment satellite gravity data. The snow accumulation around Syowa Station was detectable by the superconducting gravimeter.

Description: We challenge the perspective that seismicity could contribute to polar motion by arguing quantitatively that, in first approximation and on the average, interseismic deformations can compensate for it. This point is important because what we must simulate and observe in Earth Orientation Parameter time-series over intermediate timescales of decades or centuries is the residual polar motion resulting from the two opposing processes of coseismic and interseismic deformations. In this framework, we first simulate the polar motion caused by only coseismic deformations during the longest period available of instrumental seismicity, from 1900 to present, using both the CMT and ISC-GEM catalogues. The instrumental seismicity covering a little longer than one century does not represent yet the average seismicity that we should expect on the long term. Indeed, although the simulation shows a tendency to move the Earth rotation pole towards 133°E at the average rate of 16.5 mm yr –1 , this trend is still sensitive to individual megathrust earthquakes, particularly to the 1960 Chile and 1964 Alaska earthquakes. In order to further investigate this issue, we develop a global seismicity model (GSM) that is independent from any earthquake catalogue and that describes the average seismicity along plate boundaries on the long term by combining information about present-day plate kinematics with the Anderson theory of faulting, the seismic moment conservation principle and a few other assumptions. Within this framework, we obtain a secular polar motion of 8 mm yr –1 towards 112.5°E that is comparable with that estimated from 1900 to present using the earthquake catalogues, although smaller by a factor of 2 in amplitude and different by 20° in direction. Afterwards, in order to reconcile the idea of a secular polar motion caused by earthquakes with our simplest understanding of the seismic cycle, we adapt the GSM in order to account for interseismic deformations and we use it to quantify, for the first time ever, their contribution to polar motion. Taken together, coseismic and interseismic deformations make the rotation pole wander around the north pole with maximum polar excursions of about 1 m. In particular, the rotation pole moves towards about Newfoundland when the interseismic contribution dominates over the coseismic ones (i.e. during phases of low seismicity or, equivalently, when most of the fault system associated with plate boundaries is locked). When megathrust earthquakes occur, instead, the rotation pole is suddenly shifted in an almost opposite direction, towards about 133°E.

Description: The new release AIUB-RL02 of monthly gravity models from GRACE GPS and K-Band range-rate data is based on reprocessed satellite orbits referring to the reference frame IGb08. The release is consistent with the IERS2010 conventions. Improvements with respect to its predecessor AIUB-RL01 include the use of reprocessed (RL02) GRACE observations, new atmosphere and ocean dealiasing products (RL05), an upgraded ocean tide model (EOT11A), and the interpolation of shallow ocean tides (admittances). The stochastic parametrization of AIUB-RL02 was adapted to include daily accelerometer scale factors, which drastically reduces spurious signal at the 161 d period in C 20 and at other low degree and order gravity field coefficients. Moreover, the correlation between the noise in the monthly gravity models and solar activity is considerably reduced in the new release. The signal and the noise content of the new AIUB-RL02 monthly gravity fields are studied and calibrated errors are derived from their non-secular and non-seasonal variability. The short-period time-variable signal over the oceans, mostly representing noise, is reduced by 50 per cent with respect to AIUB-RL01. Compared to the official GFZ-RL05a and CSR-RL05 monthly models, the AIUB-RL02 stands out by its low noise at high degrees, a fact emerging from the estimation of seasonal variations for selected river basins and of mass trends in polar regions. Two versions of the monthly AIUB-RL02 gravity models, with spherical harmonics resolution of degree and order 60 and 90, respectively, are available for the time period from March 2003 to March 2014 at the International Center for Global Earth Models or from ftp://ftp.unibe.ch/aiub/GRAVITY/GRACE (last accessed 22 March 2016).

Description: While elasticity is a defining characteristic of the Earth's lithosphere, it is often ignored in numerical models of long-term tectonic processes in favour of a simpler viscoplastic description. Here we assess the consequences of this assumption on a well-studied geodynamic problem: the growth of normal faults at an extensional plate boundary. We conduct 2-D numerical simulations of extension in elastoplastic and viscoplastic layers using a finite difference, particle-in-cell numerical approach. Our models simulate a range of faulted layer thicknesses and extension rates, allowing us to quantify the role of elasticity on three key observables: fault-induced topography, fault rotation, and fault life span. In agreement with earlier studies, simulations carried out in elastoplastic layers produce rate-independent lithospheric flexure accompanied by rapid fault rotation and an inverse relationship between fault life span and faulted layer thickness. By contrast, models carried out with a viscoplastic lithosphere produce results that may qualitatively resemble the elastoplastic case, but depend strongly on the product of extension rate and layer viscosity U x L . When this product is high, fault growth initially generates little deformation of the footwall and hanging wall blocks, resulting in unrealistic, rigid block-offset in topography across the fault. This configuration progressively transitions into a regime where topographic decay associated with flexure is fully accommodated within the numerical domain. In addition, high U x L favours the sequential growth of multiple short-offset faults as opposed to a large-offset detachment. We interpret these results by comparing them to an analytical model for the fault-induced flexure of a thin viscous plate. The key to understanding the viscoplastic model results lies in the rate-dependence of the flexural wavelength of a viscous plate, and the strain rate dependence of the force increase associated with footwall and hanging wall bending. This behaviour produces unrealistic deformation patterns that can hinder the geological relevance of long-term rifting models that assume a viscoplastic rheology.

Description: We document two kinds of traveling ionospheric disturbances, namely, CTIDs (Co-tsunami-Traveling-Ionospheric-disturbances) and ATIDs (Ahead-of-Tsunami-Traveling-Ionospheric-disturbances) related to the Tohoku-Oki tsunami of 2011 March 11. They are referred to the disturbances that remain behind and ahead of the principal tsunami wave front, respectively. We first note their presence in a numerical experiment performed using a simulation code coupling the tsunami, atmosphere and ionosphere. This code uses the tsunami wavefield as an input and simulates acoustic-gravity waves (AGWs) in the atmosphere and TIDs, in the form of total electron content (TEC) disturbance, in the ionosphere. The simulated TEC reveals the excitation of CTIDs (at about 2 TECU) and ATIDs (at about 1 TECU), representing up to 5 per cent disturbance over the ambient electron density, and they arise from the dissipation of AGWs in the thermosphere. A novel outcome is that during the tsunami passage between ~6° and 12° of epicentral distance, strong ATIDs arrive ~20–60 min ahead of the tsunami wave front covering ~3°–10° of distance from the tsunami location. Simulation results are compared with the far-field observations using GNSS satellites and confirm that ATIDs are the first detected TEC maximum, occurring 20–60 min ahead of the tsunami arrival. Our simulation also confirms the presence of largest TEC maximum representing CTIDs, 10–20 min after the first tsunami wave. ATIDs reported in this study have characteristics that can be potentially used for the early warning of the tsunami.

Description: Apparent acceleration in Gravity Recovery and Climate Experiment (GRACE) Antarctic ice mass time-series may reflect both ice discharge and surface mass balance contributions. However, a recent study suggests there is also contamination from errors in atmospheric pressure de-aliasing fields [European Center for Medium-Range Weather Forecast (ECMWF) operational products] used during GRACE data processing. To further examine this question, we compare GRACE atmospheric pressure de-aliasing (GAA) fields with in situ surface pressure data from coastal and inland stations. Differences between the two are likely due to GAA errors, and provide a measure of error in GRACE solutions. Time-series of differences at individual weather stations are fit to four presumed error components: annual sinusoids, a linear trend, an acceleration term and jumps at times of known ECMWF model changes. Using data from inland stations, we estimate that atmospheric pressure error causes an acceleration error of about +7.0 Gt yr –2 , which is large relative to prior GRACE estimates of Antarctic ice mass acceleration in the range of –12 to –14 Gt yr –2 . We also estimate apparent acceleration rates from other barometric pressure (reanalysis) fields, including ERA-Interim, MERRA and NCEP/DOE. When integrated over East Antarctica, the four mass acceleration estimates (from GAA and the three reanalysis fields) vary considerably (by ~2–16 Gt yr –2 ). This shows the need for further effort to improve atmospheric mass estimates in this region of sparse in situ observations, in order to use GRACE observations to measure ice mass acceleration and related sea level change.

Description: In the context of the 2014 realization of the International Terrestrial Reference Frame, the International DORIS (Doppler Orbitography Radiopositioning Integrated by Satellite) Service (IDS) has delivered to the IERS a set of 1140 weekly SINEX files including station coordinates and Earth orientation parameters, covering the time period from 1993.0 to 2015.0. From this set of weekly SINEX files, the IDS combination centre estimated a cumulative DORIS position and velocity solution to obtain mean horizontal and vertical motion of 160 stations at 71 DORIS sites. The main objective of this study is to validate the velocities of the DORIS sites by comparison with external models or time-series. Horizontal velocities are compared with two recent global plate models (GEODVEL 2010 and NNR-MORVEL56). Prior to the comparisons, DORIS horizontal velocities were corrected for Global Isostatic Adjustment from the ICE-6G (VM5a) model. For more than half of the sites, the DORIS horizontal velocities differ from the global plate models by less than 2–3 mm yr –1 . For five of the sites (Arequipa, Dionysos/Gavdos, Manila and Santiago) with horizontal velocity differences with respect to these models larger than 10 mm yr –1 , comparisons with GNSS estimates show the veracity of the DORIS motions. Vertical motions from the DORIS cumulative solution are compared with the vertical velocities derived from the latest GPS cumulative solution over the time span 1995.0–2014.0 from the University of La Rochelle solution at 31 co-located DORIS-GPS sites. These two sets of vertical velocities show a correlation coefficient of 0.83. Vertical differences are larger than 2 mm yr –1 at 23 percent of the sites. At Thule, the disagreement is explained by fine-tuned DORIS discontinuities in line with the mass variations of outlet glaciers. Furthermore, the time evolution of the vertical time-series from the DORIS station in Thule show similar trends to the GRACE equivalent water height.

Description: We have used ensemble averages of satellite-derived free-air gravity anomaly data, together with inverse modelling techniques, to determine the effective elastic thickness, T e , of circum-Pacific subducting oceanic lithosphere and its relationship to plate age. Synthetic modelling tests show that T e can be recovered best using gravity anomaly, rather than bathymetry, data and profiles that are at least 750 km long. Inverse modelling based on a uniform T e elastic plate suggests that T e increases with age of the subducting oceanic lithosphere and is given approximately by the depth to the 390 ± 10 °C oceanic isotherm based on a cooling plate model. Misfits between the observed and calculated gravity anomalies are significantly improved if a mechanically weak zone is included between the trench axis and the outer rise. This weak zone is coincident with observations of bend-faulting and seismicity. Inverse modelling shows that T e landward of the outer rise is generally 40–65 per cent less than the T e seaward of the outer rise. Both landward and seaward T e increases with age of the lithosphere and are given by the depth to the 342–349 °C and 671–714 °C oceanic isotherm, respectively. A dependence of T e on age is consistent with models for the cooling of oceanic lithosphere as it moves away from a mid-ocean ridge and the temperature-dependent ductile creep of oceanic lithospheric minerals such as olivine. By comparing the observed T e to the predicted T e based on laboratory-derived yield strength envelopes and an assumption of elastic-perfectly plastic deformation, we have attempted to constrain the rheology of oceanic lithosphere. Regardless of the assumed friction coefficient, the dry-olivine low-temperature plasticity flow laws of Goetze, Evans & Goetze, Raterron et al . and Mei et al . all provide quite a good fit to the observed T e at circum-Pacific subduction zones. This result contrasts with the Hawaiian Islands, where these flow laws are generally too strong to fit the observations. The discrepancy in rheology within Pacific plate may be caused by differences in the timescale of loading and therefore the amount of viscoelastic stress relaxation that has occurred. Other possibilities include thermal rejuvenation and magma-assisted flexure at the Hawaiian Islands.

Description: The long-wavelength gravity field contains information about processes in the sublithospheric mantle. As satellite-derived gravity models now provide the long to medium-wavelength gravity field at unprecedented accuracy, techniques used to process gravity data need to be updated. We show that when determining these long-wavelengths, the treatment of topographic-isostatic effect (TIE) and isostatic effects (IE) is a likely source of error. We constructed a global isostatic model and calculated global TIE and IE. These calculations were done for ground stations as well as stations at satellite height. We considered both gravity and gravity gradients. Using these results, we determined how much of the gravity signal comes from distant sources. We find that a significant long-wavelength bias is introduced if far-field effects on the topographic effect are neglected. However, due to isostatic compensation far-field effects of the topographic effect are to a large degree compensated by the far-field IE. This means that far-field effects can be reduced effectively by always considering topographic masses together with their compensating isostatic masses. We show that to correctly represent the ultra-long wavelengths, a global background model should be used. This is demonstrated both globally and for a continental-scale case area in North America. In the case of regional modelling, where the ultra-long wavelengths are not of prime importance, gravity gradients can be used to help minimize correction errors caused by far-field effects.

Description: Large gaps and inconsistencies remain in published estimates of Nubia–Somalia plate motion based on reconstructions of seafloor spreading data around Africa. Herein, we use newly available reconstructions of the Southwest Indian Ridge at ~1-Myr intervals since 20 Ma to estimate Nubia–Somalia plate motion farther back in time than previously achieved and with an unprecedented degree of temporal resolution. At the northern end of the East African rift, our new estimates of Nubia–Somalia motion for six times from 0.78 Ma to 5.2 Ma differ by only 2 per cent from the rift-normal component of motion that is extrapolated from a recently estimated GPS angular velocity. The rate of rift-normal extension thus appears to have remained steady since at least 5.2 Ma. Our new rotations indicate that the two plates have moved relative to each other since at least 16 Ma and possibly longer. Motion has either been steady since at least 16 Ma or accelerated modestly between 6 and 5.2 Ma. Our Nubia–Somalia rotations predict 42.5 ± 3.8 km of rift-normal extension since 10.6 Ma across the well-studied, northern segment of the Main Ethiopian Rift, consistent with 40–50 km estimates for extension since 10.6 Myr based on seismological surveys of this narrow part of the plate boundary. Nubia–Somalia rotations are also derived by combining newly estimated Somalia–Arabia rotations that reconstruct the post-20-Ma opening of the Gulf of Aden with Nubia–Arabia rotations estimated via a probabilistic analysis of plausible opening scenarios for the Red Sea. These rotations predict Nubia–Somalia motion since 5.2 Myr that is consistent with that determined from Southwest Indian Ridge data and also predict 40 ± 3 km of rift-normal extension since 10.6 Ma across the Main Ethiopian Rift, consistent with our 42.5 ± 3.8 km Southwest Indian Ridge estimate. Our new rotations exclude at high confidence level previous estimates of 12 ± 13 and 123 ± 14 km for rift-normal extensions across the Main Ethiopian Rift since 10.6 Ma based on reconstructions of Chron 5n.2 along the Southwest Indian Ridge. Sparse coverage of magnetic reversals older than 16 Ma along the western third of the Southwest Indian Ridge precludes reliable determinations of Nubia–Somalia plate motion before 16 Ma, leaving unanswered the key question of when the motion between the two plates began.

Description: The TAMMAR segment of the Mid-Atlantic Ridge forms a classic propagating system centred about two degrees south of the Kane Fracture Zone. The segment is propagating to the south at a rate of 14 mm yr –1 , 15 per cent faster than the half-spreading rate. Here, we use seismic refraction data across the propagating rift, sheared zone and failed rift to investigate the crustal structure of the system. Inversion of the seismic data agrees remarkably well with crustal thicknesses determined from gravity modelling. We show that the crust is thickened beneath the highly magmatic propagating rift, reaching a maximum thickness of almost 8 km along the seismic line and an inferred (from gravity) thickness of about 9 km at its centre. In contrast, the crust in the sheared zone is mostly 4.5–6.5 km thick, averaging over 1 km thinner than normal oceanic crust, and reaching a minimum thickness of only 3.5 km in its NW corner. Along the seismic line, it reaches a minimum thickness of under 5 km. The PmP reflection beneath the sheared zone and failed rift is very weak or absent, suggesting serpentinisation beneath the Moho, and thus effective transport of water through the sheared zone crust. We ascribe this increased porosity in the sheared zone to extensive fracturing and faulting during deformation. We show that a bookshelf-faulting kinematic model predicts significantly more crustal thinning than is observed, suggesting that an additional mechanism of deformation is required. We therefore propose that deformation is partitioned between bookshelf faulting and simple shear, with no more than 60 per cent taken up by bookshelf faulting.

Description: Constraining laterally varying structures in planetary interiors is important for understanding both the composition and the internal dynamics of a planet. Recognizing that seismic imaging technique is currently only viable for studying the Earth's interior structures, methods that can be supported by advanced space geodetic techniques may become alternatives to ‘image’ the interiors of other planets. The method of tidal tomography is one possibility, and it relies on high precision measurement of the response of a planet to its body tide. However, it is essential to develop an efficient analytical tool that computes the dependence of tidal response to 3-D interior structures. In this paper, we present a complete formulation of such an analytical tool, which calculates to high accuracy the tidal response of a terrestrial planet with lateral heterogeneities in its elastic and density structures. We treat the lateral heterogeneities as small perturbations and derive the governing equations based on the perturbation theory. In a spherical harmonic representation, equations at each order of perturbation are reduced into multiple matrix equations at harmonics that are allowed by mode couplings, and the total response equals the sum of all those single-harmonic responses, which can be solved semi-analytically. We test our perturbation method by applying it to the Moon with a harmonic degree-1 mantle structure for which the perturbation solutions of the tidal response are compared with those from a fully numerical method. The remarkable agreement between results from these two methods validates the perturbation method. As an example, we then use the perturbation method to evaluate the impact of lunar crustal thickness variations on tidal response of the Moon. We find that lunar crust produces much smaller degree-3 tidal responses than a relatively weak degree-1 structure in the deep lunar mantle. Our calculations show that degree-3 tidal response measurements may hold key constraints on possible degree-1 mantle structure of the Moon, as suggested from previous modelling results.

Description: Seismic data are primarily used in studies of the Earth's lithospheric structure including the Moho geometry. In regions, where seismic data are sparse or completely absent, gravimetric or combined gravimetric-seismic methods could be applied to determine the Moho depth. In this study, we derive and present generalized expressions for solving the Vening Meinesz–Moritz's (VMM) inverse problem of isostasy for a Moho depth determination from gravity and vertical gravity-gradient data. By solving the (non-linear) Fredholm's integral equation of the first kind, the linearized observation equations, which functionally relate the (given) gravity/gravity-gradient data to the (unknown) Moho depth, are derived in the spectral domain. The VMM gravimetric results are validated by using available seismic and gravimetric Moho models. Our results show that the VMM Moho solutions obtained by solving the VMM problem for gravity and gravity-gradient data are almost the same. This finding indicates that in global applications, using the global gravity/gravity-gradient data coverage, the spherical harmonic expressions for the gravimetric forward and inverse modelling yield (theoretically) the same results. Globally, these gravimetric solutions have also a relatively good agreement with the CRUST1.0 and GEMMA GOCE models in terms of their rms Moho differences (4.7 km and 4.1 km, respectively).

Description: Geophysical techniques are widely used to monitor volcanic unrest. A number of studies have also demonstrated that hydrological processes can produce or trigger geophysical signals. Hydrologically induced gravity signals have previously been recorded by specifically designed gravity surveys as well as, inadvertently, by volcano monitoring studies. Water table corrections of microgravity surveys are commonplace. However, the fluctuations of the water table beneath survey locations are often poorly known, and such a correction fails to account for changes in water-mass storage in the unsaturated zone. Here, we combine 2-D axis-symmetrical numerical fluid-flow models with an axis-symmetric, distributed-mass, gravity calculation to model gravity changes in response to fluctuating hydrological recharge. Flow simulations are based on tropical volcanic settings where high surface permeabilities promote thick unsaturated zones. Our study highlights that mass storage (saturation) changes within the unsaturated zone beneath a survey point can generate recordable gravity changes. We show that for a tropical climate, recharge variations can generate gravity variations of over 150 μGal; although, we demonstrate that for the scenarios investigated here, the probability of recording such large signals is low. Our modelling results indicate that microgravity survey corrections based on water table elevation may result in errors of up to 100 μGal. The effect of inter-annual recharge fluctuations dominate over seasonal cycles which makes prediction and correction of the hydrological contribution more difficult. Spatial hydrogeological heterogeneity can also impact on the accuracy of relative gravity surveys, and can even result in the introduction of additional survey errors. The loading fluctuations associated with saturation variations in the unsaturated zone may also have implications for other geophysical monitoring techniques, such as geodetic monitoring of ground deformation.

Description: Several attempts have been made to obtain a radiographic image inside volcanoes using cosmic-ray muons (muography). Muography is expected to resolve highly heterogeneous density profiles near the surface of volcanoes. However, several prior works have failed to make clear observations due to contamination by background noise. The background contamination leads to an overestimation of the muon flux and consequently a significant underestimation of the density in the target mountains. To investigate the origin of the background noise, we performed a Monte Carlo simulation. The main components of the background noise in muography are found to be low-energy protons, electrons and muons in case of detectors without particle identification and with energy thresholds below 1 GeV. This result was confirmed by comparisons with actual observations of nuclear emulsions. This result will be useful for detector design in future works, and in addition some previous works of muography should be reviewed from the view point of background contamination.

Description: Essential to understanding sea level change and its causes during the last interglacial (LIG) is the quantification of uncertainties. In order to estimate the uncertainties, we develop a statistical framework for the comparison of palaeoclimatic sea level index points and GIA model predictions. For the investigation of uncertainties, as well as to generate better model predictions, we implement a massive ensemble approach by applying a data assimilation scheme based on particle filter methods. The different runs are distinguished through varying ice sheet reconstructions based on oxygen-isotope curves and different parameter selections within the GIA model. This framework has several advantages over earlier work, such as the ability to examine either the contribution of individual observations to the results or the probability of specific input parameters. This exploration of input parameters and data leads to a larger range of estimates than previously published work. We illustrate how the assumptions that enter into the statistical analysis, such as the existence of outliers in the observational database or the initial ice volume history, can introduce large variations to the estimate of the maximum highstand. Thus, caution is required to avoid overinterpreting results. We conclude that there are reasonable doubts whether the data sets previously used in statistical analyses are able to tightly constrain the value of maximum highstand during the LIG.

Description: A 3-D density model of the crust and upper mantle beneath the Karoo basin is presented here. The model is constrained using potential field, borehole and seismic data. Uplift of the basin by the end of the Cretaceous has resulted in an unusually high plateau (〉1000 m) covering a large portion of South Africa. Isostatic studies show the topography is largely compensated by changes in Moho depths (~35 km on-craton and 〉45 km off-craton) and changes in lithospheric mantle densities between the Kaapvaal Craton and surrounding regions (~50 kg m –3 increase from on- to off-craton). This density contrast is determined by inverted satellite gravity and gravity gradient data. The highest topography along the edge of the plateau (〉1200 m) and a strong Bouguer gravity low over Lesotho, however, can only be explained by a buoyant asthenosphere with a density decrease of around 40 kg m –3 .

Description: A Neogene magmatic reactivation of the Manihiki Plateau, a large igneous province (LIP) in the central Pacific, is studied using seismic reflection data. Igneous diapirs have been identified exclusively within a narrow WNW–ESE striking corridor in the southern High Plateau (HP), which is parallel to the Neogene Pacific Plate motion and overlaps with an extrapolation of the Society Islands Hotspot (SIH) path. The igneous diapirs are characterized by a narrow width (〉5 km), penetration of the Neogene sediments, and they become progressively younger towards the East (23–10 Ma). The magmatic source appears to be of small lateral extent, which leads to the conclusion that the diapirs represent Neogene hotspot volcanism within a LIP, and thus may be an older, previously unknown extension of the SIH track (〉4.5 Ma). Comparing hotspot volcanism within oceanic and continental lithosphere, we further conclude that hotspot volcanism within LIP crust has similarities to tectonically faulted continental crust.

Description: A method to estimate the rotation change in the orientation of the centre-of-figure (CF) frame caused by earthquakes is proposed for the first time. This method involves using the point dislocation theory based on a spherical, non-rotating, perfectly elastic and isotropic (SNREI) Earth. The rotation change in the orientation is related solely to the toroidal displacements of degree one induced by the vertical dip slip dislocation, and the spheroidal displacements induced by an earthquake have no contribution. The effects of two recent large earthquakes, the 2004 Sumatra and the 2011 Tohoku-Oki, are studied. Results showed that the Sumatra and Tohoku-Oki earthquakes both caused the CF frame to rotate by at least tens of μas (micro-arc-second). Although the visible co-seismic displacements are identified and removed from the coordinate time-series, the rotation change due to the unidentified ones and errors in removal is non-negligible. Therefore, the rotation change in the orientation of the CF frame due to seismic deformation should be taken into account in the future in reference frame and geodesy applications.

Description: Many mechanisms control the state of stress within Earth plates. First-order well-known mechanisms include stresses induced by lateral variations of lithospheric density structure, sublithospheric tractions, ridge push and subduction pull. In this study, we attempt to quantify the influence of these mechanisms to understand the origin of stresses in the lithosphere, choosing the African plate (TAP) as an example. A finite-element based suite, Proshell, was developed to combine several data sets, to estimate the gravitational potential energy (GPE) of the lithosphere and to calculate stresses acting on the real (non-planar) geometry of TAP. We introduce several quantitative parameters to measure the degree of fit between the model and observations. Our modelling strategy involves nine series of numerical experiments. We start with the simplest possible model and then, step by step, build it up to be a more physically realistic model, all the while discussing the influence of each additional component. The starting (oversimplified) model series (1) is based on the CRUST2 data set for the crust and a half-space-cooling approximation of the lithospheric mantle. We then describe models (series 2–5) that account for lithospheric mantle density heterogeneities to build a more reliable GPE model. The consecutive series involve basal traction from the convective mantle (series A, C) and the rheological heterogeneity of the TAP via variations in its effective elastic thickness (series B, C). The model quality reflects the increase in complexity between series with an improving match to observed stress regimes and directions. The most complex model (series D) also accounts for the bending stresses in the elastic lithosphere and achieves a remarkably good fit to observations. All of our experiments were based on the iteration of controlling parameters in order to achieve the best fit between modelled and observed stresses, always considering physically feasible values. This gives us confidence that our methodology appropriately models the stress pattern of Africa, and that it may be further applied to other plates on Earth. Our modelling approach allows us to quantify several important features controlling the lithospheric stress pattern. Even though the initial oversimplified model does not fit the observations satisfactorily, it shows how ridge push may create significant compressive stresses in the lithosphere. More complex models show the importance of the density structure of the lithosphere, specifically in the subcrustal lithosphere. The stress regime within the TAP mainly results from a global balance of masses and mass moments between continental and oceanic parts of the plate. The orientation of stresses, in turn, is influenced more by local features expressed by topographic and crustal density variations, whereas existent subcrustal density variations appear to be smoothed by the crust above. The models show that accounting separately for either basal tractions or rheological heterogeneities brings moderate improvement, but the combination of these two mechanisms results in a substantially better match between model and observations. The bending stresses caused by isostatical re-adjustment improve the model match, but they have to be analysed with caution because of their depth-dependent nature.

Description: The Red Sea and Gulf of Aden represent two young basins that formed between Africa and Arabia since the early Oligocene, floored by oceanic crust or by transitional and thinned continental crust. While in the easternmost Gulf of Aden, the rift–drift transition can be dated chron C6 (~20.1 Ma), here we show that in the Red Sea the first pulse of seafloor spreading occurred during chron C3n.2n (~4.6 Ma) around ~17.1°N (present-day coordinates) and propagated southwards from this location, separating the Danakil microplate from Arabia. It is also shown that seafloor spreading between Arabia and Nubia started later, around chron 2A (~2.58 Ma), and propagated northwards. At present, there is no magnetic evidence for the existence of a linear spreading centre in the northern Red Sea at latitudes higher than ~24°N and in the southern Red Sea below ~14.8°N. The present-day plate kinematics of this region can be described with high accuracy by a network of five interacting plates (Nubia, Arabia, Somalia, Sinai and Danakil) and six triple junctions. For times older than anomaly 2A (~2.58 Ma) and up to anomaly 3, the absence of marine magnetic anomalies between Arabia and Nubia prevents a rigorous kinematic description of the five-plates system. However, there is strong evidence that the unique changes in plate motions during the last 5 Myr were a dramatic slowdown at chron C2 (~1.77 Ma) in the spreading or extension rates along the ridge and rift axes, thereby a good representation of the real plate motions can be obtained anyway by backward extension of the oldest Arabia–Nubia and Arabia–Danakil stage rotations determined on the basis of marine magnetic anomalies, respectively, C2–C2A and C2A–C3. The proposed kinematic reconstructions are accompanied by a geodynamic explanation for the genesis of large continent–continent fracture zones at the rift–drift transition and by an analysis of the strain associated with plate motions in Afar, northeastern Egypt and Sinai.

Description: On 2016 February 6 the South Taiwan earthquake ( M w 6.4) occurred in the Meinong District of Kaohsiung, southern Taiwan, at a depth of 17 km. It caused 117 fatalities and widespread damage to infrastructures, especially in the Tainan city. To clarify the generating mechanism of this damaging earthquake, we determined high-resolution 3-D images of P - and S -wave velocity ( V P , V S ) and Poisson's ratio ( ) in the epicentral area. We used 105 712 P - and 61 250 S -wave arrival times of 8279 local earthquakes (1.5 ≤ M ≤ 6.4) recorded at 41 seismic stations in South Taiwan during 2000–2011. In the upper crust (depth ≤ 10 km), the most remarkable feature is low- V P , low- V S and high- anomalies in areas with known active faults in the southwestern and easternmost parts of Taiwan. In contrast, high- V P , high- V S and low- anomalies become dominant in the lower crust. The hypocentre of the 2016 South Taiwan earthquake is located in a boundary zone where seismic velocity and Poisson's ratio change drastically in both the horizontal and vertical directions. Furthermore, the hypocentre is underlain by a vertically elongated high- anomaly at depths of 23–40 km, which may reflect ascending fluids from the upper (or uppermost) mantle. The low- V and high- anomalies in the upper crust coincide with areas of low heat flow, negative Bouguer gravity anomaly, and low magnetotelluric resistivity, which may reflect crustal fluids contained in the young fold-and-thrust belt. These results suggest that the 2016 South Taiwan earthquake was triggered by ascending fluids from dehydration of the subducting Eurasian slab, invading into active faults with a high loading rate.

Description: In this study, we propose an approach for determining the geopotential difference using high-frequency-stability microwave links between satellite and ground station based on Doppler cancellation system. Suppose a satellite and a ground station are equipped with precise optical-atomic clocks (OACs) and oscillators. The ground oscillator emits a signal with frequency f a towards the satellite and the satellite receiver (connected with the satellite oscillator) receives this signal with frequency f b which contains the gravitational frequency shift effect and other signals and noises. After receiving this signal, the satellite oscillator transmits and emits, respectively, two signals with frequencies f b and f c towards the ground station. Via Doppler cancellation technique, the geopotential difference between the satellite and the ground station can be determined based on gravitational frequency shift equation by a combination of these three frequencies. For arbitrary two stations on ground, based on similar procedures as described above, we may determine the geopotential difference between these two stations via a satellite. Our analysis shows that the accuracy can reach 1 m 2 s – 2 based on the clocks’ inaccuracy of about 10 –17 (s s –1 ) level. Since OACs with instability around 10 –18 in several hours and inaccuracy around 10 –18 level have been generated in laboratory, the proposed approach may have prospective applications in geoscience, and especially, based on this approach a unified world height system could be realized with one-centimetre level accuracy in the near future.

Description: Crystallization experiments in the dendritic regime have been carried out in hypergravity conditions (from 1 to 1300 g) from an ammonium chloride solution (NH 4 Cl and H 2 O). A commercial centrifuge was equipped with a slip ring so that electric power (needed for a Peltier device and a heating element), temperature and ultrasonic signals could be transmitted between the experimental setup and the laboratory. Ultrasound measurements (2–6 MHz) were used to detect the position of the front of the mushy zone and to determine attenuation in the mush. Temperature measurements were used to control a Peltier element extracting heat from the bottom of the setup and to monitor the evolution of crystallization in the mush and in the liquid. A significant increase of solid fraction and attenuation in the mush is observed as gravity is increased. Kinetic undercooling is significant in our experiments and has been included in a macroscopic mush model. The other ingredients of the model are conservation of energy and chemical species, along with heat/species transfer between the mush and the liquid phase: boundary-layer exchanges at the top of the mush and bulk convection within the mush (formation of chimneys). The outputs of the model compare well with our experiments. We have then run the model in a range of parameters suitable for the Earth's inner core. This has shown the role of bulk mush convection for the inner core and the reason why a solid fraction very close to unity should be expected. We have also run melting experiments: after crystallization of a mush, the liquid has been heated from above until the mush started to melt, while the bottom cold temperature was maintained. These melting experiments were motivated by the possible local melting at the inner core boundary that has been invoked to explain the formation of the anomalously slow F-layer at the bottom of the outer core or inner core hemispherical asymmetry. Oddly, the consequences of melting are an increase in solid fraction and a decrease in attenuation. It is hence possible that surface seismic velocity and attenuation of the inner core are strongly affected by melting.

Description: The coupling that exists between surface processes and deformation within both the shallow crust and the deeper mantle-lithosphere has stimulated the development of computational geodynamic models that incorporate a free surface boundary condition. We introduce a treatment of this boundary condition that is suitable for staggered grid, finite difference schemes employing a structured Eulerian mesh. Our interface capturing treatment discretizes the free surface boundary condition via an interface that conforms with the edges of control volumes (e.g. a ‘staircase’ representation) and requires only local stencil modifications to be performed. Comparisons with analytic solutions verify that the method is first-order accurate. Additional intermodel comparisons are performed between known reference models to further validate our free surface approximation. Lastly, we demonstrate the applicability of a multigrid solver to our free surface methodology and demonstrate that the local stencil modifications do not strongly influence the convergence of the iterative solver.

Description: Ellesmere Island in Arctic Canada displays a complex geological evolution. The region was affected by two distinct orogenies, the Palaeozoic Ellesmerian orogeny (the Caledonian equivalent in Arctic Canada and Northern Greenland) and the Palaeogene Eurekan orogeny, related to the opening of Baffin Bay and the consequent convergence of the Greenland plate. The details of this complex evolution and the present-day deep structure are poorly constrained in this remote area and deep geophysical data are sparse. Receiver function analysis of seven temporary broad-band seismometers of the Ellesmere Island Lithosphere Experiment complemented by two permanent stations provides important data on the crustal velocity structure of Ellesmere Island. The crustal expression of the northernmost tectonic block of Ellesmere Island (~82°–83°N), Pearya, which was accreted during the Ellesmerian orogeny, is similar to that at the southernmost part, which is part of the Precambrian Laurentian (North America-Greenland) craton. Both segments have thick crystalline crust (~35–36 km) and comparable velocity–depth profiles. In contrast, crustal thickness in central Ellesmere Island decreases from ~24–30 km in the Eurekan fold and thrust belt (~79.7°–80.6°N) to ~16–20 km in the Hazen Stable Block (HSB; ~80.6°–81.4°N) and is covered by a thick succession of metasediments. A deep crustal root (~48 km) at ~79.6°N is interpreted as cratonic crust flexed beneath the Eurekan fold and thrust belt. The Carboniferous to Palaeogene sedimentary succession of the Sverdrup Basin is inferred to be up to 1–4 km thick, comparable to geologically-based estimates, near the western margin of the HSB.

Description: Joint analysis of the seismic velocities and geoid, gravity and gravity gradients are used to constrain the viscosity profile within the mantle as well as the lateral density variations. Recent ESA's Gravity field and steady-state Ocean Circulation Explorer measurements of the second-order derivatives of the Earth's gravity potential give new possibilities to determine these mantle properties. Using a simple mantle model and seismic tomography results, we investigate how the gravitational potential, the three components of the gravity vector and the gravity gradients can bring information on the radial viscosity profile and on the mantle mass anomalies. We start with lateral density variations in the Earth's mantle based either on slab history or deduced from seismic tomography. The main uncertainties are: for the latter case, the relationship between seismic velocity and density—the so-called density/velocity scaling factor—and for the former case, the variation with depth of the density contrast between the cold slabs and the surrounding mantle. We perform a Monte Carlo search for the viscosity and the density/velocity scaling factor profiles within the mantle, which allows to fit the observed geoid, gravity and gradients of gravity. We compute the posterior probability distribution of the unknown parameters, and find that the gravity gradients improve the estimate of the scaling factor within the upper mantle, because of their sensitivity to the masses within the upper mantle, whereas the geoid and the gravity better constrain the scaling factor in the lower mantle. In the upper mantle, it is less than 0.02 in the upper part and about 0.08–0.14 in the lower part, and it is significantly larger for depths greater than 1200 km (about 0.32–0.34). In any case, the density/velocity scaling factor between 670 and 1150 km depth is not well constrained. We show that the viscosity of the upper part of the mantle is strongly correlated with the viscosity of the lower part of the mantle and that the viscosity profile is characterized by a decrease in the lower part of the upper mantle (about 10 20 –2  x  10 20 Pa s) and by an increase (about 10 23 –2  x  10 23 Pa s) at the top of the lower mantle (between 670 and 1150 km). The viscosity of the mantle below 1150 km depth is well estimated in our Monte Carlo search and is about 10 22 –4  x  10 22 Pa s.

Description: A sequence of large earthquakes occurred along the North Anatolian fault in the 20th century. These earthquakes, including the 1999 Izmit/Düzce earthquakes, generally propagated westward towards the Marmara Sea, defining the Main Marmara fault as a potential seismic gap. It is important to conduct a detailed assessment of the seismic hazards along the main Marmara fault because the megacity Istanbul lies only approximately 10 km north of the eastern segment of the Main Marmara fault, which is referred to as the Princes’ Islands Fault segment (PIF). Here, we study the locking status of this fault segment to evaluate the seismic hazard potential. For the first time, combined ascending and descending Interferometric Synthetic Aperture Radar and Global Positioning System observations were used to investigate the crustal deformation associated with the PIF. After careful corrections of the estimated ground velocity, a deformation pattern relating to fault locking near the Princes’ Islands was identified. The modeling results revealed that the slip rate and locking depth of the fault segment show a clear trade-off, which were estimated as 18.9 ± 7.2 mm yr –1 and 12.1 ± 7.0 km, respectively. With a moment accumulation rate of 1.7 ± 0.4  x  10 17 Nm yr –1 (proportional to the product of slip rate and locking depth), our results imply a build-up of a geodetic moment on the PIF and therefore a potential for earthquake hazards in the vicinity of the Istanbul megacity.

Description: Large-scale topography may be due to several causes, including (1) variations in crustal thickness and density structure, (2) oceanic lithosphere age differences, (3) subcrustal density variations in the continental lithosphere and (4) convective flow in the mantle beneath the lithosphere. The last contribution in particular may change with time and be responsible for continental inundations; distinguishing between these contributions is therefore important for linking Earth's history to its observed geological record. As a step towards this goal, this paper aims at such distinction for the present-day topography: the approach taken is deriving a ‘model’ topography due to contributions (3) and (4), along with a model geoid, using a geodynamic mantle flow model. Both lithosphere thickness and density anomalies beneath the lithosphere are inferred from seismic tomography. Density anomalies within the continental lithosphere are uncertain, because they are probably due to variations in composition and temperature, making a simple scaling from seismic to density anomalies inappropriate. Therefore, we test a number of different assumptions regarding these. As a reality check, model topography is compared, in terms of both correlation and amplitude ratio, to ‘residual’ topography, which follows from observed topography after subtracting contributions (1) and (2). The model geoid is compared to observations as well. Comparatively good agreement is found if there is either an excess density of 0.2 per cent in the lithosphere above 150 km depth, with anomalies below as inferred from tomography, or if the excess density is 0.4 per cent in the entire lithosphere. Further, a good fit is found for viscosity 10 20 Pa s in the asthenosphere, increasing to 10 23 Pa s in the lower mantle above D'. Results are quite dependent on which tomography models they are based on; for some recent ones, topography correlation is 0.6, many smaller scale features are matched, topography amplitude is less than 30 per cent too large, while geoid variance reduction exceeds 70 per cent—overall a considerable improvement compared to previous models. Correlation becomes less if smaller scale features (corresponding to spherical harmonic degrees 15 and higher), which are probably largely due to anomalies in the lithosphere, are also considered. Comparison of results with different viscosity structures, and a regional comparison of amplitude ratios, indicates that lateral viscosity variations can be quite strong, but only leading to moderate variations in model topography of a factor probably less than two.

Description: We present a distributed slip model for the 1999 M w 6.3 Chamoli earthquake of north India using interferometric synthetic aperture radar (InSAR) data from both ascending and descending orbits and Bayesian estimation of confidence levels and trade-offs of the model geometry parameters. The results of fault-slip inversion in an elastic half-space show that the earthquake ruptured a $9 _{ - 2.2}^{\circ + 3.4}$ northeast-dipping plane with a maximum slip of ~1 m. The fault plane is located at a depth of ~ $15.9_{ - 3.0}^{ + 1.1}$ km and is ~120 km north of the Main Frontal Thrust, implying that the rupture plane was on the northernmost detachment near the mid-crustal ramp of the Main Himalayan Thrust. The InSAR-determined moment is 3.35 x 10 18 Nm with a shear modulus of 30 GPa, equivalent to M w 6.3, which is smaller than the seismic moment estimates of M w 6.4–6.6. Possible reasons for this discrepancy include the trade-off between moment and depth, uncertainties in seismic moment tensor components for shallow dip-slip earthquakes and the role of earth structure models in the inversions. The released seismic energy from recent earthquakes in the Garhwal region is far less than the accumulated strain energy since the 1803 M s 7.5 earthquake, implying substantial hazard of future great earthquakes.

Description: We use a Bayesian formalism combined with a grid node discretization for the linear inversion of gravimetric data in terms of 3-D density distribution. The forward modelling and the inversion method are derived from seismological inversion techniques in order to facilitate joint inversion or interpretation of density and seismic velocity models. The Bayesian formulation introduces covariance matrices on model parameters to regularize the ill-posed problem and reduce the non-uniqueness of the solution. This formalism favours smooth solutions and allows us to specify a spatial correlation length and to perform inversions at multiple scales. We also extract resolution parameters from the resolution matrix to discuss how well our density models are resolved. This method is applied to the inversion of data from the volcanic island of Basse-Terre in Guadeloupe, Lesser Antilles. A series of synthetic tests are performed to investigate advantages and limitations of the methodology in this context. This study results in the first 3-D density models of the island of Basse-Terre for which we identify: (i) a southward decrease of densities parallel to the migration of volcanic activity within the island, (ii) three dense anomalies beneath Petite Plaine Valley, Beaugendre Valley and the Grande-Découverte-Carmichaël-Soufrière Complex that may reflect the trace of former major volcanic feeding systems, (iii) shallow low-density anomalies in the southern part of Basse-Terre, especially around La Soufrière active volcano, Piton de Bouillante edifice and along the western coast, reflecting the presence of hydrothermal systems and fractured and altered rocks.

Description: Oblique convergence across Tibet leads to slip partitioning with the coexistence of strike-slip, normal and thrust motion on major fault systems. A key point is to understand and model how faults interact and accumulate strain at depth. Here, we extract ground deformation across the Haiyuan Fault restraining bend, at the northeastern boundary of the Tibetan plateau, from Envisat radar data spanning the 2001–2011 period. We show that the complexity of the surface displacement field can be explained by the partitioning of a uniform deep-seated convergence. Mountains and sand dunes in the study area make the radar data processing challenging and require the latest developments in processing procedures for Synthetic Aperture Radar interferometry. The processing strategy is based on a small baseline approach. Before unwrapping, we correct for atmospheric phase delays from global atmospheric models and digital elevation model errors. A series of filtering steps is applied to improve the signal-to-noise ratio across high ranges of the Tibetan plateau and the phase unwrapping capability across the fault, required for reliable estimate of fault movement. We then jointly invert our InSAR time-series together with published GPS displacements to test a proposed long-term slip-partitioning model between the Haiyuan and Gulang left-lateral Faults and the Qilian Shan thrusts. We explore the geometry of the fault system at depth and associated slip rates using a Bayesian approach and test the consistency of present-day geodetic surface displacements with a long-term tectonic model. We determine a uniform convergence rate of 10 [8.6–11.5] mm yr –1 with an N89 [81–97]°E across the whole fault system, with a variable partitioning west and east of a major extensional fault-jog (the Tianzhu pull-apart basin). Our 2-D model of two profiles perpendicular to the fault system gives a quantitative understanding of how crustal deformation is accommodated by the various branches of this thrust/strike-slip fault system and demonstrates how the geometry of the Haiyuan fault system controls the partitioning of the deep secular motion.

Description: In this paper, we study stability of the rate, state and temperature friction (RSTF) model. The Segall and Rice approach is used to model heat transfer at the sliding interface with its surroundings. The effect of pore pressure is not considered in the model to avoid the complex expression for critical stiffness. Linear stability analysis of the spring-mass sliding system is carried out with the ageing law under the quasistatic conditions in order to determine the critical stiffness above which sliding behaviour changes from unstable to stable or vice versa. Our numerical simulations establish that critical stiffness of the heated surface may increase or decrease from corresponding to the critical stiffness of the unheated surface depending on the relative values of two contradictory parameters related with velocity effect and temperature effect. Parametric studies are also carried out to understand shear velocity and temperature of the sliding surface dependence of steady friction. The RSTF model is also used to study the gravity induced failure of a creeping rock slope and the results are justified.

Description: We compute the gravimetric factor at the Chandler wobble (CW) frequency using time-series from superconducting gravimeters (SG) longer than a decade. We first individually process the polar motion and data at each individual gravity station to estimate the gravimetric factor amplitude and phase, then we make a global analysis by applying a stacking method to different subsets of up to seven SG stations. The stacking is an efficient way of getting rid of local effects and improving the signal-to-noise ratio of the combined data sets. Using the stacking method, we find a gravimetric factor amplitude and phase of 1.118 ± 0.016 and –0.45 ± 0.66 deg, respectively, which is smaller in amplitude than expected. The sources of error are then carefully considered. For both local and global analyses, the uncertainties on our results are reliably constrained by computing the standard deviation of the estimates of the gravimetric factor amplitude and phase for increasing length of the time-series. Constraints on the CW anelastic dissipation can be set since any departure of the gravimetric factor from its elastic value may provide some insights into the dissipative processes that occur at the CW period. In particular, assuming given rheological models for the Earth's mantle enables us to make the link between the gravimetric factor phase and the CW quality factor.

Description: Analysing independent 1-yr data sets of 10 European superconducting gravimeters (SG) reveals statistically significant temporal variations of M2 tidal parameters. Both common short-term (〈2 yr) and long-term (〉2 yr) features are identified in all SG time-series but one. The averaged variations of the amplitude factor are about 0.2. The path of load vector variations equivalent to the temporal changes of tidal parameters suggests the presence of an 8.85 yr modulation (lunar perigee). The tidal waves having the potential to modulate M2 with this period belong to the 3rd degree constituents. Their amplitude factors turn out to be much closer to body tide model predictions than that of the main 2nd degree M2, which indicates ocean loading for 3rd degree waves to be less prominent than for 2nd degree waves within the M2 group. These two different responses to the loading suggest that the observed modulation is more due to insufficient frequency resolution of limited time-series rather than to time variable loading. Presently, SG gravity time-series are still too short to prove if time variable loading processes are involved too as in case of the annual M2 modulation known to appear for analysis intervals of less than 1 yr. Whatever the variations are caused by, they provide the upper accuracy limit for earth model validation and permit estimating the temporal stability of SG scale factors and assessing the quality of gravity time-series.

Description: A sequence of large earthquakes occurred along the North Anatolian fault in the 20th century. These earthquakes, including the 1999 Izmit/Düzce earthquakes, generally propagated westward towards the Marmara Sea, defining the Main Marmara fault as a potential seismic gap. It is important to conduct a detailed assessment of the seismic hazards along the main Marmara fault because the megacity Istanbul lies only approximately 10 km north of the eastern segment of the Main Marmara fault, which is referred to as the Princes’ Islands Fault segment (PIF). Here, we study the locking status of this fault segment to evaluate the seismic hazard potential. For the first time, combined ascending and descending Interferometric Synthetic Aperture Radar and Global Positioning System observations were used to investigate the crustal deformation associated with the PIF. After careful corrections of the estimated ground velocity, a deformation pattern relating to fault locking near the Princes’ Islands was identified. The modeling results revealed that the slip rate and locking depth of the fault segment show a clear trade-off, which were estimated as 18.9 ± 7.2 mm yr –1 and 12.1 ± 7.0 km, respectively. With a moment accumulation rate of 1.7 ± 0.4  x  10 17 Nm yr –1 (proportional to the product of slip rate and locking depth), our results imply a build-up of a geodetic moment on the PIF and therefore a potential for earthquake hazards in the vicinity of the Istanbul megacity.

Description: Deformation analysis in general and strain analysis in particular using permanent GPS networks require proper analysis of time-series in which all functional effects are taken into consideration and all stochastic effects are captured using an appropriate noise model. This contribution addresses both issues when considering the strain parameters of a GPS network. Estimates of spatial correlation, time correlated noise, and multivariate power spectrum for daily position time-series of the Southern California Integrated GPS Network (SCIGN) stations collected between 1996 and 2011 are obtained. Significant signals with periods of 13.63 d and those related to the GPS draconitic year are identified in these time-series. We aim to assess the effect of a realistic noise model of the series on the uncertainties of the strain parameters including displacements, normal and shear strains, and rotations. For the SCIGN network considered, the following results are highlighted. Contrary to the common belief, the uncertainties of the displacements parameters become smaller when taking a realistic noise model into account. This however was not the case when assessing the noise characteristics of the normal and shear strain, and rotation parameters. The uncertainties increase nearly by a factor of two, in agreement to what is expected. Some of the significant deformation parameters of the white noise model become less significant in case of the realistic noise model.

Description: The Siple Coast region of Antarctica contains a number of fast-flowing ice streams, which control the dynamics and mass balance of the region. These ice streams are known to undergo stagnation and reactivation cycles, which lead to ice thickness changes that may be sufficient to excite a viscous solid Earth response (glacial isostatic adjustment; GIA). This study aims to quantify Siple Coast ice thickness changes during the last 2000 yr in order to determine the degree to which they might contribute to GIA and associated present-day bedrock uplift rates. This is important because accurate modelling of GIA is necessary to determine the rate of present-day ice-mass change from satellite gravimetry. Recently-published reconstructions of ice-stream variability were used to create a suite of kinematic models for the stagnation-related thickening of Kamb Ice Stream since ~1850 AD, and a GIA model was used to predict present-day deformation rates in response to this thickening. A number of longer-term loading scenarios, which include the stagnation and reactivation of ice streams across the Siple Coast over the past 2000 yr, were also constructed, and used to investigate the longer term GIA signal in the region. Uplift rates for each of the ice loading histories, based on a range of earth models, were compared with regional GPS-observed uplift rates and an empirical GIA estimate. We estimate Kamb Ice Stream to have thickened by 70–130 m since stagnation ~165 years ago. Modelled present-day vertical motion in response to this load increase peaks at –17 mm yr –1 (i.e. 17 mm yr –1 subsidence) for the weakest earth models tested here. Comparison of the solid Earth response to ice load changes throughout the last glacial cycle, including ice stream stagnation and reactivation across the Siple Coast during the last 2000 yr, with an empirical GIA estimate suggests that the upper mantle viscosity of the region is greater than 1 x 10 20 Pa s. When upper mantle viscosity values of 1 x 10 20  Pa s or smaller are combined with our suite of ice-load scenarios we predict uplift rates across Siple Coast that are at least 4 mm yr –1 smaller than those predicted by the empirical GIA estimate. GPS data are unable to further constrain model parameters due to the distance of the GPS sites from the study area. Our results demonstrate that Late Holocene ice load changes related to the stagnation and reactivation of ice streams on the Siple Coast may play a dominant role in defining the present-day uplift signal. However, both the detailed Earth structure and deglacial history of the region need to be better constrained in order to reduce uncertainties associated with the GIA signal of this region.

Description: We have extended backwards from 2001 to 1979 the current release 05 (RL05) of the Gravity Recovery and Climate Experiment (GRACE) Atmospheric and Oceanic De-aliasing Level-1B (AOD1B) product and studied the impact of this and a previous release 04 (RL04) of the AOD1B product on precise orbits of five altimetry satellites (ERS-1, ERS-2, TOPEX/Poseidon, Envisat and Jason-1) for the time span 1991–2012, as compared to the case when no AOD1B product is used. We have found that using AOD1B RL05 product reduces root mean square (RMS) fits of satellite laser ranging (SLR) observations by about 1.0–6.4 per cent, 2-d arc overlaps in radial, cross-track and along-track directions by about 1.3–12.0, 0.3–10.0 and 2.0–10.0 per cent, respectively, for various satellites tested, as compared to the case without AOD1B product. Using AOD1B RL05 product instead of RL04 one reduces SLR RMS fits by 0.1–0.7 per cent, 2-d arc overlaps in radial, cross-track and along-track directions by 0.1–0.6, 0.1–1.3 and 0.2–1.2 per cent, respectively, for the satellite orbits tested. The multi-mission crossover analysis shows that the application of an AOD1B product reduces the scatter of radial errors by 0.4–2.8 per cent for the satellite missions studied. At the regions with the most pronounced changes the use of the AOD1B products improves the consistency between the sea level as measured by the TOPEX and ERS-2 missions and by the Jason-1 and Envisat missions by 5 to 10 per cent (globally by about 2 per cent). The results of our study show that extended AOD1B RL05 product performs better than the AOD1B RL04 and improves orbits of altimetry satellites and consistency of sea level products.

Description: A new analytical method for the computation of a truncated series of solid spherical harmonic coefficients (HCs) from data on a spheroid (i.e. an oblate ellipsoid of revolution) is derived, using a transformation between surface and solid spherical HCs. A two-step procedure is derived to extend this transformation beyond degree and order (d/o) 520. The method is compared to the Hotine–Jekeli transformation in a numerical study based on the EGM2008 global gravity model. Both methods are shown to achieve submicrometre precision in terms of height anomalies for a model to d/o 2239. However, both methods result in spherical harmonic models that are different by up to 7.6 mm in height anomalies and 2.5 mGal in gravity disturbances due to the different coordinate system used. While the Hotine–Jekeli transformation requires the use of an ellipsoidal coordinate system, the new method uses only spherical polar coordinates. The Hotine–Jekeli transformation is numerically more efficient, but the new method can more easily be extended to cases where (a linear combination of) normal derivatives of the function under consideration are given on the surface of the spheroid. It therefore provides a solution to many types of ellipsoidal boundary-value problems in the spectral domain.

Description: The thickness and equivalent global sea level contribution of an improved model of the central and northern Laurentide Ice Sheet is constrained by 24 relative sea level histories and 18 present-day GPS-measured vertical land motion rates. The final model, termed Laur16, is derived from the ICE-5G model by holding the timing history constant and iteratively adjusting the thickness history, in four regions of northern Canada. In the final model, the last glacial maximum (LGM) thickness of the Laurentide Ice Sheet west of Hudson Bay was ~3.4–3.6 km. Conversely, east of Hudson Bay, peak ice thicknesses reached ~4 km. The ice model thicknesses inferred for these two regions represent, respectively, a ~30 per cent decrease and an average ~20–25 per cent increase to the load thickness relative to the ICE-5G reconstruction, which is generally consistent with other recent studies that have focussed on Laurentide Ice Sheet history. The final model also features peak ice thicknesses of 1.2–1.3 km in the Baffin Island region, a modest reduction relative to ICE-5G and unchanged thicknesses for a region in the central Canadian Arctic Archipelago west of Baffin Island. Vertical land motion predictions of the final model fit observed crustal uplift rates well, after an adjustment is made for the elastic crustal response to present-day ice mass changes of regional ice cover. The new Laur16 model provides more than a factor of two improvement of the fit to the RSL data ( 2 measure of misfit) and a factor of nine improvement to the fit of the GPS data (mean squared error measure of fit), compared to the ICE-5G starting model. Laur16 also fits the regional RSL data better by a factor of two and gives a slightly better fit to GPS uplift rates than the recent ICE-6G model. The volume history of the Laur16 reconstruction corresponds to an up to 8 m reduction in global sea level equivalent compared to ICE-5G at LGM.

Description: We explore Earth's elastic deformation response to ocean tidal loading (OTL) using kinematic Global Positioning System (GPS) observations and forward-modelled predictions across South America. Harmonic coefficients are extracted from up to 14 yr of GPS-inferred receiver locations, which we estimate at 5 min intervals using precise point positioning. We compare the observed OTL-induced surface displacements against predictions derived from spherically symmetric, non-rotating, elastic and isotropic (SNREI) Earth models. We also compare sets of modelled predictions directly for various ocean-tide and Earth-model combinations. The vector differences between predicted displacements computed using separate ocean-tide models reveal uniform-displacement components common to all stations in the South America network. Removal of the network-mean OTL-induced displacements from each site substantially reduces the vector differences between observed and predicted displacements. We focus on the dominant astronomical tidal harmonics from three distinct frequency bands: semidiurnal (M 2 ), diurnal (O 1 ) and fortnightly (M f ). In each band, the observed OTL-induced surface displacements strongly resemble the modelled displacement-response patterns, and the residuals agree to about 0.3 mm or better. Even with the submillimetre correspondence between observations and predictions, we detect regional-scale spatial coherency in the final set of residuals, most notably for the M 2 harmonic. The spatial coherency appears relatively insensitive to the specific choice of ocean-tide or SNREI-Earth model. Varying the load model or 1-D elastic structure yields predicted OTL-induced displacement differences of order 0.1 mm or less for the network. Furthermore, estimates of the observational uncertainty place the noise level below the magnitude of the residual displacements for most stations, supporting our interpretation that random errors cannot account for the entire misfit. Therefore, the spatially coherent residuals may reveal deficiencies in the a priori SNREI Earth models. In particular, the residuals may indicate sensitivity to regional deviations from standard globally averaged Earth structure due to the presence of the South American craton.

Description: The 2011 October 23 M W 7.1 Van earthquake in eastern Turkey caused ~600 deaths and caused widespread damage and economic loss. The seismogenic rupture was restricted to 10–25 km in depth, but aseismic surface creep, coincident with outcrop fault exposures, was observed in the hours to months after the earthquake. We combine observations from radar interferometry, seismology, geomorphology and Quaternary dating to investigate the geological slip rate and seismotectonic context of the Van earthquake, and assess the implications for continuing seismic hazard in the region. Transient post-seismic slip on the upper Van fault started immediately following the earthquake, and decayed over a period of weeks; it may not fully account for our long-term surface slip-rate estimate of ≥0.5 mm yr –1 . Post-seismic slip on the Bostanici splay fault initiated several days to weeks after the main shock, and we infer that it may have followed the M W  5.9 aftershock on the 9th November. The Van earthquake shows that updip segmentation can be important in arresting seismic ruptures on dip-slip faults. Two large, shallow aftershocks show that the upper 10 km of crust can sustain significant earthquakes, and significant slip is observed to have reached the surface in the late Quaternary, so there may be a continuing seismic hazard from the upper Van fault and the associated splay. The wavelength of folding in the hanging wall of the Van fault is dominated by the structure in the upper 10 km of the crust, masking the effect of deeper seismogenic structures. Thus, models of subsurface faulting based solely on surface folding and faulting in regions of reverse faulting may underestimate the full depth extent of seismogenic structures in the region. In measuring the cumulative post-seismic offsets to anthropogenic structures, we show that Structure-from-Motion can be rapidly deployed to create snapshots of post-seismic displacement. We also demonstrate the utility of declassified Corona mission imagery (1960s–1970s) for geomorphic mapping in areas where recent urbanization has concealed the geomorphic markers.

Description: Within a slab experiencing present-day lateral break-off, a particular type of earthquakes is expected to cluster at the detachment horizon tip: namely, events generated by reverse faulting, with the approximately horizontal compression involved acting along the strike of the slab. Such a cluster of moderate magnitude earthquakes (4.7 ≤  m b ≤ 5.0) was identified in this study at the 160–175 km depth range of the Vrancea seismogenic body, in the Southeast Carpathians mountains collision environment. The corresponding cluster epicentres were systematically positioned at the boundary between a region being subject ( cf. published GPS records), to present-day upward movements, and another one that underwent present-day subsidence. Such an overall setting seems to suggest that a lateral break-off is currently developing at the indicated depth within the Vrancea slab, leading to topographic uplift above the already detached slab section, and to enhanced subsidence above the section to which the gravitational slab pull was being transferred. In addition, by taking into account some systematic time correspondence which we documented between moderate magnitude events of the 160–175 km depth cluster and the subsequent strong Vrancea shocks ( M w ≥ 6.9), it appears that the latter, although occurring at much shallower depths (roughly, in the 80–140 km range), were also controlled by the break-off progress.

Description: Bajada del Diablo is located in the Northern Patagonian Massif, Chubut, Argentina. The study area includes several circular structures found in Miocene olivine basalts of the Quiñelaf Eruptive Complex and in the Late Pliocene/Early Pleistocene Pampa Sastre conglomerates. An impact origin has been proposed for these circular structures. With the aim of further investigate the proposed impact origin, topographic, gravimetric, magnetic, resistivity, palaeomagnetic and electromagnetic surveys in two circular structures (‘8’ and ‘G’) located in Pampa Sastre conglomerates and in basalts of the Quiñelaf Eruptive Complex were carried out. The new geophysical results support the hypothesis of an impact origin. However, the confirmation of such an origin through the findings of shock metamorphism evidences and/or the recovery of meteorites remains elusive.

Description: Planar faults are widely adopted during inversions to determine slip distributions and fault geometries using geodetic observations; however, little research has been conducted with respect to curved faults. We attribute this to the lack of an appropriate parameterized modelling method. In this paper, we present a curved-fault modelling method (CFMM) that describes a curved fault according to specific parameters, and we also develop a corresponding hybrid iterative inversion algorithm (HIIA) to perform inversions for parametric curved-fault geometries and slips. The results of the strike-component and dip-component synthetic tests show that a complex S-shaped fault surface and a circular slip distribution are successfully recovered, indicating the strong performance of the CFMM and HIIA methods. In addition, we describe and verify a scenario for determining the number of necessary geometrical parameters for the HIIA and examine the case study of the Wenchuan earthquake, which occurred on a complex listric fault surface. During the iteration process of the HIIA, both the fault geometry and slip distribution of the Beichuan and Pengguan faults converge to optimal values, indicating a Beichuan fault (BCF) model with a continuous listric shape and gradual steepening from the southwest to the northeast, which is highly consistent with geological survey results. Both the synthetic and real-world case studies show that the HIIA and the CMFF are superior to the conventional fault modelling method based on rectangular planes and that these models have the potential for use in more integrated research involving inversion studies, such as joint slip/curved-fault-geometry inversions that take into account data resolving power.

Description: Estimating in situ stress based on hydraulic fracturing data typically depends on interpretation of the breakdown, secondary breakdown (‘reopening’) and shut-in pressure. While it has been recognized that the near-wellbore stress field should be taken into account and that the compressibility of the injection system and the viscous flow of the fluid can diminish the accuracy of stress estimates, these issues have not been well quantified. A coupled numerical model that includes the compressibility of the injection system and the flow of a viscous fluid in a plane-strain hydraulic fracture extending from a wellbore, in an impermeable rock, and in the presence of a non-isotropic in situ stress field provides a basic tool for estimating the order of the error associated with hydraulic fracturing stress measurements under non-ideal conditions. The main findings of this work are model-based guidelines on the values of relevant dimensionless parameter groups to ensure sufficient accuracy of stress estimates that use idealized models. When these guidelines cannot be met under field conditions, the model can be further applied to obtain first-order corrections that account for compressibility, viscosity and near-wellbore effects.

Description: We consider the problem of seismic velocity change estimation using ambient noise recordings. Motivated by Zhan et al. , we study how the velocity change estimation is affected by seasonal fluctuations in the noise sources. More precisely, we consider a numerical model and introduce spatio-temporal seasonal fluctuations in the noise sources. We show that indeed, as pointed out by Zhan et al. , the stretching method is affected by these fluctuations and produces misleading apparent velocity variations which reduce dramatically the signal to noise ratio of the method. We also show that these apparent velocity variations can be eliminated by an adequate normalization of the cross-correlation functions. Theoretically we expect our approach to work as long as the seasonal fluctuations in the noise sources are uniform, an assumption which holds for closely located seismic stations. We illustrate with numerical simulations in homogeneous and scattering media that the proposed normalization significantly improves the accuracy of the velocity change estimation. Similar behaviour is also observed with real data recorded in the Aegean volcanic arc. We study in particular the volcano of Santorini during the seismic unrest of 2011–2012 and observe a decrease in the velocity of seismic waves which is correlated with GPS measured elevation.

Description: Globally gridded estimates of monthly-mean anomalies of terrestrial water storage (TWS) are estimated from the most recent GRACE release 05a of GFZ Potsdam in order to provide non-geodetic users a convenient access to state-of-the-art GRACE monitoring data. We use an ensemble of five global land model simulations with different physics and different atmospheric forcing to obtain reliable gridded scaling factors required to correct for spatial leakage introduced during data processing. To allow for the application of this data-set for large-scale monitoring tasks, model validation efforts, and subsequently also data assimilation experiments, globally gridded estimates of TWS uncertainties that include (i) measurement, (ii) leakage and (iii) re-scaling errors are provided as well. The results are generally consistent with the gridded data provided by Tellus, but deviate in some basins which are largely affected by the uncertainties of the model information required for re-scaling, where the approach based on the median of a small ensemble of global land models introduced in this paper leads to more robust results.

Description: Passive seismic experiment was carried out at the SW contact of the Dinarides and Pannonian basin to determine the crustal structure and velocity discontinuities. The aim of the experiment was to define the relationship between the Adriatic microplate and the Pannonian segment as a part of the European plate. Most of the temporary seismic stations were deployed in Croatia along the Alp07 profile—a part of the active-source ALP 2002 project. About 300-km-long profile stretches from Istra peninsula to the Drava river, in a WSW–ESE direction. Teleseismic events recorded on 13 temporary seismic stations along the profile were analysed by P -receiver function method. Two types of characteristic receiver functions (RF) have been identified, belonging to Dinaridic and Pannonian crusts as defined on the Alp07 profile, while in transitional zone there are both types. Three major crustal discontinuities can be identified for the Dinaridic type: sedimentary basement, intracrustal discontinuity and Mohorovičić discontinuity, whereas the Pannonian type revealed only two discontinuities. The intracrustal discontinuity was not observed in the Pannonian type, thus pointing to a single-layered crust in the Pannonian basin. Two interpretation methods were applied: forward modelling of the receiver functions and H – stacking method, and the results were compared with the active-source seismic data at deep refraction profile Alp07. The receiver function modelling has given reliable results of the Moho depths that are in accordance with the seismic refraction results at the end of the Alp07 profile, that is in the area of Pannonian crust characterized by simple crustal structure and low seismic velocities ( Vp between 5.9 and 6.2 km s –1 ). In the Dinarides and its peripheral parts, receiver function modelling regularly gives greater Moho depths, up to +15 per cent, due to more complex crustal structure. The depths of the Moho calculated by the H – stacking method vary within wide limits (±13 km), due to band limited data of short-period stations. The results at five stations have to be rejected because of huge deviations in comparison with all previous results, while at the other seven stations the Moho depths vary within ±15 per cent around the Moho discontinuity of the Alp07 profile.

Description: Megathrust earthquakes of magnitude close to 9 are followed by large-scale (thousands of km) and long-lasting (decades), significant crustal and mantle deformation. This deformation can be observed at the surface and quantified with GPS measurements. Here we report on deformation observed during the 5 yr time span after the 2010 M w 8.8 Maule Megathrust Earthquake (2010 February 27) over the whole South American continent. With the first 2 yr of those data, we use finite element modelling (FEM) to relate this deformation to slip on the plate interface and relaxation in the mantle, using a realistic layered Earth model and Burgers rheologies. Slip alone on the interface, even up to large depths, is unable to provide a satisfactory fit simultaneously to horizontal and vertical displacements. The horizontal deformation pattern requires relaxation both in the asthenosphere and in a low-viscosity channel along the deepest part of the plate interface and no additional low-viscosity wedge is required by the data. The vertical velocity pattern (intense and quick uplift over the Cordillera) is well fitted only when the channel extends deeper than 100 km. Additionally, viscoelastic relaxation alone cannot explain the characteristics and amplitude of displacements over the first 200 km from the trench and aseismic slip on the fault plane is needed. This aseismic slip on the interface generates stresses, which induce additional relaxation in the mantle. In the final model, all three components (relaxation due to the coseismic slip, aseismic slip on the fault plane and relaxation due to aseismic slip) are taken into account. Our best-fit model uses slip at shallow depths on the subduction interface decreasing as function of time and includes (i) an asthenosphere extending down to 200 km, with a steady-state Maxwell viscosity of 4.75 x 10 18 Pa s; and (ii) a low-viscosity channel along the plate interface extending from depths of 55–135 km with viscosities below 10 18 Pa s.

Description: We provide an updated present-day stress map for the Italian territory. Following the World Stress Map (WSM) Project guidelines, we list the different stress indicators, explaining the criteria used to select data. We discuss the data, which will also be included in the 2016 release of the WSM, highlighting the areas for which we have added stress information. Our map displays the minimum horizontal stress orientations inferred from crustal stress indicators down to 40 km depth using data of A–C quality, updated for earthquakes until December 2015. We have completely reviewed all data, and the data set now contains 855 entries, in contrast to the previous 715. The number of data with A–C quality of 630 corresponds to an increase of 26 per cent relative to the previous data set. In particular, the new data set contains the results of the analysis of borehole breakouts, critically reviewed data from earthquake focal mechanisms, data concerning active faults, formal inversions of focal mechanisms of seismic sequences or of restricted areas and one stress determination from overcoring. The new data set defines the stress field in areas not well covered by the previous data: the region north to the Po Plain and the central Adriatic sea, both characterized by a thrust- and strike-faulting regime, the northern Sicilian belt with a prevailing normal-faulting regime, and the Ionian sea with a strike-slip regime.

Description: Measurements of the velocity field associated with plumes rising through a viscous fluid are performed using stereoscopic Particle-Image Velocimetry in the Rayleigh number range 4.4 x 10 5 –6.4 x 10 5 . The experimental model is analogous to a mantle plume rising from the core–mantle boundary to the base of the lithosphere. The behaviour of the plume is studied throughout its life cycle, which is broken up into four stages; the Formation Stage, when the plume forms; the Rising Stage, when the plume rises through the fluid; the Spreading Stage, when the plume reaches the surface and spreads; and finally the Declining Stage, when the heat source has been removed and the plume weakens. The latter three stages are examined in terms of the Finite-Time Lyapunov Exponent fields and the advection of passive tracers throughout the flow. The temperature at the heater and near the fluid surface are measured using thermocouples to infer how the presence of a mantle plume would produce excess temperature near the lithosphere throughout the various stages of its life cycle. In all experiments, a time lag is observed between the removal of the heat source and the decline in the excess temperature near the surface, which is proportional to the rise time. A simple analytical model is presented, which suggests that under mantle conditions (i.e. negligible thermal diffusion), the relationship between the time lag and the rise time is robust and independent of the Rayleigh number; however, the constant of proportionality is closer to unity in the absence of diffusion. Once the heat source is removed, the excess temperature near the surface declines exponentially at a rate that is inversely proportional to the rise time. The implications of this result are discussed in terms of the decline in volcanism in the Louisville hotspot chain over the past 20 Ma. The rise velocity of material in the plume is examined; the rise velocity is found to vary significantly with the plume height in a manner that is inconsistent with many of the common semi-analytical models of thermal plumes in the literature. It is also argued that this height dependency will cause estimates of the rise velocity based on the decay series of uranium isotopes to significantly underestimate the true value.

Description: Regional recovery of the disturbing gravitational potential in the area of Central Europe from satellite gravitational gradients data is discussed in this contribution. The disturbing gravitational potential is obtained by inverting surface integral formulas which transform the disturbing gravitational potential onto disturbing gravitational gradients in the spherical local north-oriented frame. Two numerical approaches that solve the inverse problem are considered. In the first approach, the integral formulas are rigorously decomposed into two parts, that is, the effects of the gradient data within near and distant zones. While the effect of the near zone data is sought as an inverse problem, the effect of the distant zone data is synthesized from the global gravitational model GGM05S using spectral weights given by truncation error coefficients up to the degree 150. In the second approach, a reference gravitational field up to the degree 180 is applied to reduce and smooth measured gravitational gradients. In both cases we recovered the disturbing gravitational potential from each of the four well-measured gravitational gradients of the GOCE satellite separately as well as from their combination. Obtained results are compared with the EGM2008, DIR-r2, TIM-r2 and SPW-r2 global gravitational models. The best fit was achieved for EGM2008 and the second approach combining all four well-measured gravitational gradients with rms of 1.231 m 2  s –2 .

Description: The Makran subduction zone is one of the last convergent margins to be investigated using space-based geodesy. While there is a lack of historical and modern instrumentation in the region, a sparse sampling of continuous and campaign measurements over the past decade has allowed us to make the first estimates of convergence rates. We combine GPS measurements from 20 stations located in Iran, Pakistan and Oman along with hypocentral locations from the International Seismological Centre to create a preliminary 3-D estimate of the geometry of the megathrust, along with a preliminary fault-coupling model for the Makran subduction zone. Using a convergence rate which is strongly constrained by measurements from the incoming Arabia plate along with the backslip method of Savage, we find the Makran subduction zone appears to be locked to a depth of at least 38 km and accumulating strain.We also find evidence for a segmentation of plate coupling, with a 300 km long section of reduced plate coupling. The range of acceptable locking depths from our modelling and the 900 km along-strike length for the megathrust, makes the Makran subduction zone capable of earthquakes up to M w  = 8.8. In addition, we find evidence for slow-slip-like transient deformation events on two GPS stations. These observations are suggestive of transient deformation events observed in Cascadia, Japan and elsewhere.

Description: We present efficient Fourier-domain algorithms for modelling gravity effects due to topographic masses. The well-known Parker's formula originally based on the standard fast Fourier transform (FFT) algorithm is modified by applying the Gauss–FFT method instead. Numerical precision of the forward and inverse Fourier transforms embedded in Parker's formula and its extended forms are significantly improved by the Gauss–FFT method. The topographic model is composed of two major aspects, the geometry and the density. Versatile geometric representations, including the mass line model, the mass prism model, the polyhedron model and smoother topographic models interpolated from discrete data sets using high-order splines or pre-defined by analytical functions, in combination with density distributions that vary both laterally and vertically in rather arbitrary ways following exponential or general polynomial functions, now can be treated in a consistent framework by applying the Gauss–FFT method. The method presented has been numerically checked by space-domain analytical and hybrid analytical/numerical solutions already established in the literature. Synthetic and real model tests show that both the Gauss–FFT method and the standard FFT method run much faster than space-domain solutions, with the Gauss–FFT method being superior in numerical accuracy. When truncation errors are negligible, the Gauss–FFT method can provide forward results almost identical to space-domain analytical or semi-numerical solutions in much less time.

Description: The gravity gradient tensor (GGT) has been increasingly used in practical applications, but the advantages and the disadvantages of the analysis of GGT components versus the analysis of the vertical component of the gravity field are still debated. We analyse the performance of joint inversion of GGT components versus separate inversion of the gravity field alone, or of one tensor component. We perform our analysis by inspection of the Picard Plot, a Singular Value Decomposition tool, and analyse both synthetic data and gradiometer measurements carried out at the Vredefort structure, South Africa. We show that the main factors controlling the reliability of the inversion are algebraic ambiguity (the difference between the number of unknowns and the number of available data points) and signal-to-noise ratio. Provided that algebraic ambiguity is kept low and the noise level is small enough so that a sufficient number of SVD components can be included in the regularized solution, we find that: (i) the choice of tensor components involved in the inversion is not crucial to the overall reliability of the reconstructions; (ii) GGT inversion can yield the same resolution as inversion with a denser distribution of gravity data points, but with the advantage of using fewer measurement stations.

Description: This paper compares GRACE (Gravity Recovery and Climate Experiment) and ICESat (Ice, Cloud and land Elevation Satellite) observations to confirm whether the observed gravity increase in the Tibetan Plateau (TP) was primarily caused by lake storage gain, and comprehensively analyses the changing pattern of lake level over 2003–2009. An improved automated method was used to obtain lake-level changes and the underestimation of lake water storage was considered due to lake area expansion and lake density. The result demonstrates that GRACE recorded a mass gain (16.43 ± 1.65/11.79 ± 1.25 gt a –1 ) in the total/inner TP, of which lake storage increase accounts for (8.78 ± 0.75/7.53 ± 0.56 gt a –1 ) based on ICESat. The northwestern residual may be stored in new lakes and soil moisture as a result of net precipitation gain. According to the character of the lake-level changes, we divide the TP into four subregions. Generally, the changing pattern of lake level concurs with the distribution of precipitation, which is increasing in the inner TP and decreasing in the upstream area of the Indus and Brahmaputra Rivers. An excess of rainfall in the northeastern TP in the summer of 2005 and 2009 caused a simultaneous large increase in water level in many lakes. The correlation of lake changes with precipitation demonstrates that precipitation rather than glacial melt is the main cause of lake-level change in most places. Nonetheless, the meltwater is a considerable supplement for lakes near glaciers such as Selin Co and Nam Co, which partly explains why GRACE indicates a much weaker signal in this region.

Description: Traditional processing of Global Navigation Satellite System (GNSS) data using dedicated scientific software has provided the highest levels of positional accuracy, and has been used extensively in geophysical deformation studies. To achieve these accuracies a significant level of understanding and training is required, limiting their availability to the general scientific community. Various online GNSS processing services, now freely available, address some of these difficulties and allow users to easily process their own GNSS data and potentially obtain high quality results. Previous research into these services has focused on Continually Operating Reference Station (CORS) GNSS data. Less research exists on the results achievable with these services using large campaign GNSS data sets, which are inherently noisier than CORS data. Even less research exists on the quality of velocity fields derived from campaign GNSS data processed through online precise point positioning services. Particularly, whether they are suitable for geodynamic and deformation studies where precise and reliable velocities are needed. In this research, we process a very large campaign GPS data set (spanning 10 yr) with the online Jet Propulsion Laboratory Automated Precise Positioning Service. This data set is taken from a GNSS network specifically designed and surveyed to measure deformation through the central North Island of New Zealand. This includes regional CORS stations. We then use these coordinates to derive a horizontal and vertical velocity field. This is the first time that a large campaign GPS data set has been processed solely using an online service and the solutions used to determine a horizontal and vertical velocity field. We compared this velocity field to that of another well utilized GNSS scientific software package. The results show a good agreement between the CORS positions and campaign station velocities obtained from the two approaches. We discuss the implications of these results for how future GNSS campaign field surveys might be conducted and how their data might be processed.

Description: We have developed a method to estimate the geometry, location and densities of anomalies coming from 2-D gravity data based on compact gravity inversion technique. Compact gravity inversion is simple, fast and user friendly but severely depends on the number of model parameters, that is, by increasing the model parameters, the anomalies tend to concentrate near the surface. To overcome this ambiguity new weighting functions based on density contrast, depth, and compactness models have been introduced. Variable compactness factors have been defined here to get either a sharp or a smooth model based on the depth of the source or existence of prior information. Depth weighting derived from one station of gravity data whereas the effect of gravity data is 2-D and 3-D. To compensate this limitation an innovating weighting function namely kernel function has been introduced which multiplies with weight and compactness matrixes to yield a general model weighting function. The method is tested using three different sets of synthetic examples: a body at various depths (20, 40, 80 and 140 m), two bodies at the same depth but various distances to estimate lateral resolution and three bodies with negative and positive density contrast in different depths. The method is also applied to three real gravity data of Woodlawn massive sulphide body, sulphides mineralization of British Colombia and iron ore body of Missouri. The method produces solutions consistent with the known geologic attributes of the gravity sources, illustrating its potential practicality.

Description: We present numerical models of mantle dynamics forced by plate velocities history in the last 450 Ma. The lower-mantle rheology and the thickness of a dense basal layer are systematically varied and several initial procedures are considered for each case. For some cases, the dependence on the mantle convection vigour is also examined. The resulting evolution of the CMB heat flux is analysed in terms of criteria to promote or inhibit reversals inferred from numerical dynamos. Most models present a rather dynamic lower mantle with the emergence of two thermochemical piles towards present-day. Only a small minority of models present two stationary piles over the last 450 Myr. At present-day, the composition field obtained in our models is found to correlate better with tomography than the temperature field. In addition, the temperature field immediately at the CMB (and thus the heat flux pattern) slightly differs from the average temperature field over the 100-km thick mantle layer above it. The evolution of the mean CMB heat flux or of the amplitude of heterogeneity seldom presents the expected correlation with the evolution of the palaeomagnetic reversal frequency suggesting these effects cannot explain the observations. In contrast, our analysis favours ‘inertial control’ on the geodynamo associated with polar cooling and in some cases break of Taylor columns in the outer core as sources of increased reversal frequency. Overall, the most likely candidates among our mantle dynamics models involve a viscosity increase in the mantle equal or smaller than 30: models with a discontinuous viscosity increase at the transition zone tend to agree better at present-day with observations of seismic tomography, but models with a gradual viscosity increase agree better with some of the criteria proposed to affect reversal frequency.

Description: Lateral viscosity variations (LVVs) in the mantle influence geodynamic processes and their surface expressions. With the observed long-wavelength geoid, free-air anomaly, gravity gradient in three directions and discrete, high-accuracy residual topography, we invert for depth- and temperature-dependent and tectonically regionalized mantle viscosity with a mantle flow model. The inversions suggest that long-wavelength gravitational and topographic signals are mainly controlled by the radial viscosity profile; the pre-Cambrian lithosphere viscosity is slightly (~ one order of magnitude) higher than that of oceanic and Phanerozoic lithosphere; plate margins are substantially weaker than plate interiors; and viscosity has only a weak apparent, dependence on temperature, suggesting either a balancing between factors or a smoothing of actual higher amplitude, but short wavelength, LVVs. The predicted large-scale lithospheric stress regime (compression or extension) is consistent with the world stress map (thrust or normal faulting). Both recent compiled high-accuracy residual topography and the predicted dynamic topography yield ~1 km amplitude long-wavelength dynamic topography, inconsistent with recent studies suggesting amplitudes of ~100 to ~500 m. Such studies use a constant, positive admittance (transfer function between topography and gravity), in contrast to the evidence which shows that the earth has a spatially and wavelength-dependent admittance, with large, negative admittances between ~4000 and ~10 4 km wavelengths.

Description: This paper resurrects a version of Poisson's Partial Differential Equation (PDE) associated with the gravitational field at the Earth's surface and illustrates how the PDE possesses a capability to extract the mass density of Earth's topography from land-based gravity data. Herein, first we propound a theorem which mathematically introduces this version of Poisson's PDE adapted for the Earth's surface and then we use this PDE to develop a method of approximating the terrain mass density. Also, we carry out a real case study showing how the proposed approach is able to be applied to a set of land-based gravity data. In the case study, the method is summarized by an algorithm and applied to a set of gravity stations located along a part of the north coast of the Persian Gulf in the south of Iran. The results were numerically validated via rock-samplings as well as a geological map. Also, the method was compared with two conventional methods of mass density reduction. The numerical experiments indicate that the Poisson PDE at the Earth's surface has the capability to extract the mass density from land-based gravity data and is able to provide an alternative and somewhat more precise method of estimating the terrain mass density.

Description: We present a new, computationally efficient numerical method to simulate global seismic wave propagation in realistic 3-D Earth models. We characterize the azimuthal dependence of 3-D wavefields in terms of Fourier series, such that the 3-D equations of motion reduce to an algebraic system of coupled 2-D meridian equations, which is then solved by a 2-D spectral element method (SEM). Computational efficiency of such a hybrid method stems from lateral smoothness of 3-D Earth models and axial singularity of seismic point sources, which jointly confine the Fourier modes of wavefields to a few lower orders. We show novel benchmarks for global wave solutions in 3-D structures between our method and an independent, fully discretized 3-D SEM with remarkable agreement. Performance comparisons are carried out on three state-of-the-art tomography models, with seismic period ranging from 34 s down to 11 s. It turns out that our method has run up to two orders of magnitude faster than the 3-D SEM, featured by a computational advantage expanding with seismic frequency.

Description: We report on a study to explore the deep electrical conductivity structure of the Dead Sea Basin (DSB) using magnetotelluric (MT) data collected along a transect across the DSB where the left lateral strike-slip Dead Sea transform (DST) fault splits into two fault strands forming one of the largest pull-apart basins of the world. A very pronounced feature of our 2-D inversion model is a deep, subvertical conductive zone beneath the DSB. The conductor extends through the entire crust and is sandwiched between highly resistive structures associated with Precambrian rocks of the basin flanks. The high electrical conductivity could be attributed to fluids released by dehydration of the uppermost mantle beneath the DSB, possibly in combination with fluids released by mid- to low-grade metamorphism in the lower crust and generation of hydrous minerals in the middle crust through retrograde metamorphism. Similar high conductivity zones associated with fluids have been reported from other large fault systems. The presence of fluids and hydrous minerals in the middle and lower crust could explain the required low friction coefficient of the DST along the eastern boundary of the DSB and the high subsidence rate of basin sediments. 3-D inversion models confirm the existence of a subvertical high conductivity structure underneath the DSB but its expression is far less pronounced. Instead, the 3-D inversion model suggests a deepening of the conductive DSB sediments off-profile towards the south, reaching a maximum depth of approximately 12 km, which is consistent with other geophysical observations. At shallower levels, the 3-D inversion model reveals salt diapirism as an upwelling of highly resistive structures, localized underneath the Al-Lisan Peninsula. The 3-D model furthermore contains an E–W elongated conductive structure to the northeast of the DSB. More MT data with better spatial coverage are required, however, to fully constrain the robustness of the above-mentioned off-profile features.

Description: Estimating how topography is maintained provides insights into the different factors responsible for surface deformations and their relative roles. Here, we develop a new and simple approach to assess the degree of isostatic compensation of continental topography at regional scale from GOCE gravity gradients. We calculate the ratio between the radial gradient observed by GOCE and that calculated from topography only. From analytical and statistical formulations, simple relationships between this ratio and the degree of compensation are obtained under the Airy–Heiskanen isostasy hypothesis. Then, a value of degree of compensation at each point of study area can be easily deduced. We apply our method to the Alaska-Canada Cordillera and validate our results by comparison with a standard isostatic gravity anomaly model and additional geophysical information for this area. Both our GOCE-based results and the isostatic anomaly show that Airy–Heiskanen isostasy prevails for the Yukon Plateau whereas additional mechanisms are required to support topography below the Northwest Territories Craton and the Yakutat collision zone.

Description: Bayesian sampling based inversions require many thousands or even millions of forward models, depending on how nonlinear or non-unique the inverse problem is, and how many unknowns are involved. The result of such a probabilistic inversion is not a single ‘best-fit’ model, but rather a probability distribution that is represented by the entire model ensemble. Often, a geophysical inverse problem is non-unique, and the corresponding posterior distribution is multimodal, meaning that the distribution consists of clusters with similar models that represent the observations equally well. In these cases, we would like to visualize the characteristic model properties within each of these clusters of models. However, even for a moderate number of inversion parameters, a manual appraisal for a large number of models is not feasible. This poses the question whether it is possible to extract end-member models that represent each of the best-fit regions including their uncertainties. Here, I show how a machine learning tool can be used to characterize end-member models, including their uncertainties, from a complete model ensemble that represents a posterior probability distribution. The model ensemble used here results from a nonlinear geodynamic inverse problem, where rheological properties of the lithosphere are constrained from multiple geophysical observations. It is demonstrated that by taking vertical cross-sections through the effective viscosity structure of each of the models, the entire model ensemble can be classified into four end-member model categories that have a similar effective viscosity structure. These classification results are helpful to explore the non-uniqueness of the inverse problem and can be used to compute representative data fits for each of the end-member models. Conversely, these insights also reveal how new observational constraints could reduce the non-uniqueness. The method is not limited to geodynamic applications and a generalized MATLAB code is provided to perform the appraisal analysis.

Description: Inference of the mantle viscosity from observations for glacial isostatic adjustment (GIA) process has usually been conducted through the analyses based on the simple three-layer viscosity model characterized by lithospheric thickness, upper- and lower-mantle viscosities. Here, we examine the viscosity structures for the simple three-layer viscosity model and also for the two-layer lower-mantle viscosity model defined by viscosities of 670, D (670- D km depth) and D ,2891 ( D -2891 km depth) with D -values of 1191, 1691 and 2191 km. The upper-mantle rheological parameters for the two-layer lower-mantle viscosity model are the same as those for the simple three-layer one. For the simple three-layer viscosity model, rate of change of degree-two zonal harmonics of geopotential due to GIA process (GIA-induced 2 ) of –(6.0–6.5)  x  10 –11 yr –1 provides two permissible viscosity solutions for the lower mantle, (7–20)  x  10 21 and (5–9)  x  10 22  Pa s, and the analyses with observational constraints of the 2 and Last Glacial Maximum (LGM) sea levels at Barbados and Bonaparte Gulf indicate (5–9)  x  10 22  Pa s for the lower mantle. However, the analyses for the 2 based on the two-layer lower-mantle viscosity model only require a viscosity layer higher than (5–10)  x  10 21  Pa s for a depth above the core–mantle boundary (CMB), in which the value of (5–10)  x  10 21  Pa s corresponds to the solution of (7–20)  x  10 21  Pa s for the simple three-layer one. Moreover, the analyses with the 2 and LGM sea level constraints for the two-layer lower-mantle viscosity model indicate two viscosity solutions: 670,1191  〉 3  x  10 21 and 1191,2891  ~ (5–10)  x  10 22  Pa s, and 670,1691  〉 10 22 and 1691,2891  ~ (5–10)  x  10 22  Pa s. The inferred upper-mantle viscosity for such solutions is (1–4)  x  10 20  Pa s similar to the estimate for the simple three-layer viscosity model. That is, these analyses require a high viscosity layer of (5–10)  x  10 22  Pa s at least in the deep mantle, and suggest that the GIA-based lower-mantle viscosity structure should be treated carefully in discussing the mantle dynamics related to the viscosity jump at ~670 km depth. We also preliminarily put additional constraints on these viscosity solutions by examining typical relative sea level (RSL) changes used to infer the lower-mantle viscosity. The viscosity solution inferred from the far-field RSL changes in the Australian region is consistent with those for the 2 and LGM sea levels, and the analyses for RSL changes at Southport and Bermuda in the intermediate region for the North American ice sheets suggest the solution of 670, D  〉 10 22 , D ,2891  ~ (5–10)  x  10 22  Pa s ( D  = 1191 or 1691 km) and upper-mantle viscosity higher than 6  x  10 20  Pa s.

Description: Mid-crustal conductors are a common phenomenon in magnetotelluric studies. In the Andean Cordillera of southern Chile, they appear to concentrate along major fault zones. A high-resolution, broad-band magnetotelluric survey including 31 stations has been carried out along two profiles perpendicular to (1) the Liquiñe-Ofqui Fault Systems (LOFS) and (2) the Villarrica-Quetrupillán-Lanín volcanic lineament running parallel to the Mocha-Villarrica Fault Zone (MVFZ). The survey aimed at tracing one of the known conductors from mid-crustal depth to near-surface along these faults. Directionality and dimensionality were analysed using tensor decomposition. Phase tensors and induction arrows reveal two major geoelectric strike directions following the strike of LOFS and MVFZ. 2-D inversion shows low resistivity zones along both fault systems down to a depth of 〉10 km, where the brittle-ductile transition is expected. Along the LOFS, the two anomalies are linked to (1) Lake Caburgua, where the LOFS broadens to about 2 km of lateral extension and seems to represent a pull-apart structure, and (2) the intersection with the Villarrica-Quetrupillán-Lanín volcanic lineament, where seismic activity was observed during the latest eruption in March 2015. A connection of the mid-crustal conductor to the ESE-WNW-striking fault zones is indicated from the presented data.

Description: The Moho surface can be determined according to isostatic theories, and among them, the recent Vening Meinesz-Moritz (VMM) theory of isostasy has been successfully applied for this purpose. In this paper, this method is studied from a theoretical prospective and its connection to the Airy–Heiskanen (AH) and Vening Meinesz original theories are presented. Jeffrey's inverse solution to isostasy is developed according to the recent developments of the VMM method and both are compared in similar situations. It is shown that they are generalizations of the AH model in a global and continuous domain. In the VMM spherical harmonic solution for Moho depth, the mean Moho depth contributes only to the zero-degree term of the series, while in Jeffrey's solution it contributes to all frequencies. In addition, the VMM spherical harmonic series is improved further so that the mean Moho can contribute to all frequencies of the solution. This modification makes the VMM global solution superior to the Jeffrey one, but in a global scale, the difference between both solutions is less than 3 km. Both solutions are asymptotically convergent and we present two methods to obtain smooth solutions for Moho from them.

Description: We present new rotations that describe the relative positions and velocities of the Pacific and North America plates at 22 times during the past 19.7 Myr, offering 1-Myr temporal resolution for studies of the geotectonic evolution of western North America and other plate boundary locations. Derived from 18 000 magnetic reversal, fracture zone and transform fault identifications from the Pacific–Antarctic–Nubia–North America plate circuit and the velocities of 935 GPS sites on the Pacific and North America plates, the new rotations and GPS-derived angular velocity indicate that the rate of motion between the two plates increased by 70 per cent from 19.7 to 9±1 Ma, but changed by less than 2 per cent since 8 Ma and even less since 4.2 Ma. The rotations further suggest that the relative plate direction has rotated clockwise for most of the past 20 Myr, with a possible hiatus from 9 to 5 Ma. This conflicts with previously reported evidence for a significant clockwise change in the plate direction at 8–6 Ma. Our new rotations indicate that Pacific plate motion became obliquely convergent with respect to the San Andreas Fault of central California at 5.2–4.2 Ma, in agreement with geological evidence for a Pliocene onset of folding and faulting in central California. Our reconstruction of the northern Gulf of California at 6.3 Ma differs by only 15–30 km from structurally derived reconstructions after including 3–4 km Myr –1 of geodetically measured slip between the Baja California Peninsula and Pacific plate. This implies an approximate 15–30 km upper bound for plate non-rigidity integrated around the global circuit at 6.3 Ma. A much larger 200±54 km discrepancy between our reconstruction of the northern Gulf of California at 12 Ma and that estimated from structural and marine geophysical observations suggests that faults in northwestern Mexico or possibly west of the Baja California Peninsula accommodated large amounts of obliquely divergent dextral shear from 12–6.3 Ma. Pacific–North America plate motion since 16 Myr estimated with our new rotations agrees well with structurally summed deformation along two transects of western North America between the Colorado Plateau and western California, with a difference as small as 40 km out of 760 km of margin-parallel motion. A strong resemblance between a 20-Myr-to-present flow line reconstructed with our new rotations and the traces of the 700-km-long Queen Charlotte Fault and continental slope west of Canada suggests that the plate margin geometry was influenced by the passage of the Pacific plate and Yakutat block. The new rotations also suggest that (1) oblique convergence west of Canada initiated at 12–11 Ma, 5–8 Myr earlier than previously estimated, (2) no significant margin-normal shortening has occurred in areas of Canada located east of the Haida Gwaii archipelago since 20 Ma and (3) Pacific plate underthrusting of Haida Gwaii has accommodated the margin-normal component of plate motion since 12–11 Ma. Our rotations suggest an 70 per cent increase in the rate that the Pacific plate has been consumed by subduction beneath the Aleutian arc since 19.7 Ma, with still-unknown consequences for the rate of arc magmatism.

Description: In a pioneering study, Wahr & Bergen developed the widely adopted, pseudo-normal mode framework for predicting the impact of anelastic effects on the Earth's body tides. Lau et al. have recently derived an extended normal mode treatment of the problem (as well as a minor variant of the theory known as the direct solution method) that makes full use of theoretical developments in free oscillation seismology spanning the last quarter century and that avoids a series of assumptions and approximations adopted in the traditional theory for predicting anelastic effects. There are two noteworthy differences between these two theories: (1) the traditional theory only considers perturbations to the eigenmodes of an elastic Earth, whereas the new theory augments this set of modes to include the relaxation modes that arise in anelastic behaviour; and (2) the traditional theory approximates the complex perturbation to the tidal Love number as a scaled version of the complex perturbation to the elastic moduli, whereas the new theory computes the full complex perturbation to each eigenmode. In this study, we highlight the above differences using a series of synthetic calculations, and demonstrate that the traditional theory can introduce significant error in predictions of the complex perturbation to the Love numbers due to anelasticity and the related predictions of tidal lag angles. For the simplified Earth models we adopt, the computed lag angles differ by ~20 per cent. The assumptions in the traditional theory have important implications for previous studies that use model predictions to correct observables for body tide signals or that analyse observations of body tide deformation to infer mantle anelastic structure. Finally, we also highlight the fundamental difference between apparent attenuation (i.e. attenuation inferred from observations or predicted using the above theories) and intrinsic attenuation (i.e. the material property investigated through experiments), where both are often expressed in terms of lag angles or Q –1 . In particular, we demonstrate the potentially significant (factor of two or more) bias introduced in estimates of Q –1 and its frequency dependence in studies that have treated Q –1 determined from tidal phase lags or measured experimentally as being equal. The observed or theoretically predicted lag angle (or apparent Q –1 ) differs from the intrinsic, material property due to inertia, self-gravity and effects associated with the energy budget. By accounting for these differences we derive, for a special case, an expression that accurately maps apparent attenuation predicted using the extended normal mode formalism of Lau et al. into intrinsic attenuation. The theory allows for more generalized mappings which may be used to robustly connect observations and predictions of tidal lag angles to results from laboratory experiments of mantle materials.

Description: Described are results of laboratory experiments which revealed regularities of gradual transition from stick-slip mode to aseismic creep. The behaviour of model gouge-filled fault was investigated with experimental setup of the spring-bock model. It was experimentally proven that small variations of a percentage of materials with velocity strengthening and velocity weakening properties in the fault principal slip zone may result in significant variation of the portion of seismic energy radiated during a fault slip event. The tests simulated different modes of interblock sliding whose characteristic values of scaled kinetic energy varied by several orders of magnitude, while differences in contact strength and shear stress drop remained relatively small. The obtained results led to the conclusion that the earthquake radiation efficiency and the fault slip mode are governed by the ratio of two parameters—maximum fault slip-weakening rate and shear stiffness of the enclosing massif. The ratio can be essentially changed by small variations of the material composition of the fault principal slip zone.

Description: Among the outstanding tectonic questions regarding the convergence between the Tien Shan and Tarim basin in northwestern China are the manner in which deformation is accommodated within their lithospheres, and the extent that the Tarim lithosphere underthrusts the Tien Shan. In particular, the amount and type of deformation within the Tarim basin is poorly understood. It is also uncertain if the convergence between the Tarim and the Tien Shan takes place mainly along a discrete boundary, or if the Tarim lithosphere simply indents into the Kazach shield, forming the Tien Shan through crustal thickening accommodated by a distributed series of thrust faults. In this study we use hypocentres from published earthquake catalogues and waveforms recorded by regional seismic networks to determine earthquake source parameters through regional centroid moment tensor inversion. The entire dataset consists of 160 earthquakes that occurred between 1969 and 2009 and with moment magnitudes between 3.5 and 7 distributed throughout the central Tien Shan and northwestern Tarim Basin. The estimated focal depths of these earthquakes range from the near-surface to about 44 km. Focal mechanisms throughout much of the Tien Shan indicate active deformation accommodated by thrust faults from at least the upper crust to 30 km depth. South of the Tien Shan, the Jia-shi earthquake sequence within the Tarim basin suggests that both crustal shortening and localized flexure are part of a complicated process involving rotational convergence. Inside the Tarim basin, two earthquakes with thrust faulting mechanisms near the crust–mantle boundary beneath the Bachu uplift imply a brittle rheology of the lower crust. High-angle thrust events occur broadly across the Tien Shan, suggesting that the Tarim lithosphere as a whole is strong and indents into the Kazach shield to create the mountain range.

Description: The subduction of lithospheric plates is partitioned between subducting plate motion and lateral slab migration (i.e. trench retreat and advance). We use 3-D, dynamic models of subduction to address the role of a power-law mantle viscosity on subduction dynamics and, in particular, rates of trench retreat. For all numerical models tested, we find that a power-law rheology results in reduced rates of trench retreat, and elevated slab dip angles, relative to the equivalent isoviscous mantle model. We analyse the asthenospheric pressure distribution and the style of mantle flow, which exhibits only limited variability as a function of mantle rheology, in order to compute estimates of the mantle forces associated with subduction. The inclusion of a power-law rheology reduces the mantle shear force (which resists subducting plate motion) to a greater degree than it reduces the dynamic pressure gradient across the slab (which resists trench retreat). Therefore, the inclusion of a power-law mantle rheology favours a shift towards a subduction mode with a reduced trench retreat component, typically a relative reduction of order 25 per cent in our 3-D models. We suggest that this mechanism may be of importance for reducing the high trench retreat rates observed in many previous models to levels more in line with the average subduction partitioning observed on Earth at present (i.e. trench velocity ≤ plate velocity), for most absolute plate motion reference frames.

Description: Pulverized rocks (PR) are extremely incohesive and highly fractured rocks found within the damage zones of several large strike-slip faults around the world. They maintain their crystal structure, show little evidence of shearing or chemical alteration, and are believed to be produced by strong tensile forces. Several mechanisms for pulverization have been proposed based on simple qualitative analyses or laboratory experiments under simplified loading conditions. Numerical modelling, however, can offer new insights into what is needed to produce PR and likely conditions of formation. We perform dynamic rupture simulations of different earthquakes, varying the magnitude, the slip distribution, and the rupture speed (supershear and subshear), while measuring the stresses produced away from the fault. To contextualize our results, a basic threshold of 10 MPa is set as the tensile strength of the rock mass and recordings are made of where, when, and by how much this threshold is exceeded for each earthquake type. Guided by field observations, we discern that a large (〉 M w 7.1) subshear earthquake along a bimaterial fault produces a pulverized rock distribution most consistent with observations. The damage is asymmetric with the majority on the stiffer side of the fault extending out for several hundred metres. Within this zone there is a large and sudden volumetric expansion in all directions as the rupture passes. We propose that such an extreme tensile stress state, repeated for every earthquake, eventually produces the PR seen in the field.

Description: We consider a new approach to both the forward and inverse problems in post-seismic deformation. We present a method for forward modelling post-seismic deformation in a self-gravitating, heterogeneous and compressible earth with a variety of linear and nonlinear rheologies. We further demonstrate how the adjoint method can be applied to the inverse problem both to invert for rheological structure and to calculate the sensitivity of a given surface measurement to changes in rheology or time-dependence of the source. Both the forward and inverse aspects are illustrated with several numerical examples implemented in a spherically symmetric earth model.

Description: Kinematics of divergent boundaries and Rift-Rift-Rift junctions are classically studied using long-term geodetic observations. Since significant magma-related displacements are expected, short-term deformation provides important constraints on the crustal mechanisms involved both in active rifting and in transfer of extensional deformation between spreading axes. Using InSAR and GPS data, we analyse the surface deformation in the whole Central Afar region in detail, focusing on both the extensional deformation across the Quaternary magmato-tectonic rift segments, and on the zones of deformation transfer between active segments and spreading axes. The largest deformation occurs across the two recently activated Asal-Ghoubbet (AG) and Manda Hararo-Dabbahu (MH-D) magmato-tectonic segments with very high strain rates, whereas the other Quaternary active segments do not concentrate any large strain, suggesting that these rifts are either sealed during interdyking periods or not mature enough to remain a plate boundary. Outside of these segments, the GPS horizontal velocity field shows a regular gradient following a clockwise rotation of the displacements from the Southeast to the East of Afar, with respect to Nubia. Very few shallow creeping structures can be identified as well in the InSAR data. However, using these data together with the strain rate tensor and the rotations rates deduced from GPS baselines, the present-day strain field over Central Afar is consistent with the main tectonic structures, and therefore with the long-term deformation. We investigate the current kinematics of the triple junction included in our GPS data set by building simple block models. The deformation in Central Afar can be described by adding a central microblock evolving separately from the three surrounding plates. In this model, the northern block boundary corresponds to a deep EW-trending trans-tensional dislocation, locked from the surface to 10–13 km and joining at depth the active spreading axes of the Red Sea and the Aden Ridge, from AG to MH-D rift segments. Over the long-term, this plate configuration could explain the presence of the en-échelon magmatic basins and subrifts. However, the transient behaviour of the spreading axes implies that the deformation in Central Afar evolves depending on the availability of magma supply within the well-established segments.

Description: Volcanic crises are often preceded and accompanied by volcano deformation caused by magmatic and hydrothermal processes. Fast and efficient model identification and parameter estimation techniques for various sources of deformation are crucial for process understanding, volcano hazard assessment and early warning purposes. As a simple model that can be a basis for rapid inversion techniques, we present a compound dislocation model (CDM) that is composed of three mutually orthogonal rectangular dislocations (RDs). We present new RD solutions, which are free of artefact singularities and that also possess full rotational degrees of freedom. The CDM can represent both planar intrusions in the near field and volumetric sources of inflation and deflation in the far field. Therefore, this source model can be applied to shallow dikes and sills, as well as to deep planar and equidimensional sources of any geometry, including oblate, prolate and other triaxial ellipsoidal shapes. In either case the sources may possess any arbitrary orientation in space. After systematically evaluating the CDM, we apply it to the co-eruptive displacements of the 2015 Calbuco eruption observed by the Sentinel-1A satellite in both ascending and descending orbits. The results show that the deformation source is a deflating vertical lens-shaped source at an approximate depth of 8 km centred beneath Calbuco volcano. The parameters of the optimal source model clearly show that it is significantly different from an isotropic point source or a single dislocation model. The Calbuco example reflects the convenience of using the CDM for a rapid interpretation of deformation data.

Description: The Seiland Igneous Province (SIP) is the largest complex of mafic and ultramafic intrusions in northern Fennoscandia intruded at ca . 580–560 Ma. The depth extent and the deep structure of the SIP are mainly unknown apart from three profiles modelled by gravity and refraction seismic data. Utilizing 3-D gravity modelling, a complex model of the deep subsurface structure of the SIP has been developed. The structure is presented in a multiprofile model ranging from the surface to the Moho. The mafic/ultramafic rocks of the SIP are modelled with densities of 3100 and 3300 kg m –3 , the surrounding rocks by densities of 2700 and 2900 kg m –3 for upper and lower crust, respectively. This density model explains the pronounced positive Bouguer gravity anomaly of up to 100 mGal above background. Its minimum volume is estimated from the subsurface model to 17 000 km 3 and as such we revise downwards the earlier estimations of 25 000 km 3 . The new subsurface model suggests that most of the SIP has a thickness between 2 and 4 km. An area with roots in an annular pattern is found and two deep-reaching roots have been identified located below the islands of Seiland and Sørøy. The depth of these roots is estimated to approximatively 9 km. The SIP is presently interpreted to be in the Caledonian Kalak Nappe Complex and the roots depth constrains its minimum thickness which is larger than earlier estimated. Furthermore, the rather undisturbed shape of the annular root pattern indicates that the SIP has not been subjected to strong tectonic reworking during the Caledonian orogeny.

Description: Tehran, the capital city of Iran with a population of over 12 million, is one of the largest urban centres within the seismically active Alpine–Himalayan orogenic belt. Although several historic earthquakes have affected Tehran, their relation to individual faults is ambiguous for most. This ambiguity is partly due to a lack of knowledge about the locations, geometries and seismic potential of structures that have been obscured by dramatic urban growth over the past three decades, and which have covered most of the young geomorphic markers and natural exposures. Here we use aerial photographs from 1956, combined with an ~1 m DEM derived from stereo Pleiades satellite imagery to investigate the geomorphology of a growing anticline above a thrust fault—the Pardisan thrust—within central Tehran. The topography across the ridge is consistent with a steep ramp extending from close to the surface to a depth of ~2 km, where it presumably connects with a shallow-dipping detachment. No primary fault is visible at the surface, and it is possible that the faulting dissipates in the near surface as distributed shearing. We use optically stimulated luminescence to date remnants of uplifted and warped alluvial deposits that are offset vertically across the Pardisan fault, providing minimum uplift and slip-rates of at least 1 mm yr –1 . Our study shows that the faults within the Tehran urban region have relatively rapid rates of slip, are important in the regional tectonics, and have a great impact on earthquake hazard assessment of the city and surrounding region.