ALBERT

Description: Field and laboratory observations show that seismicity has non-trivial period-dependent response to periodic stress perturbations. In Nepal, seismicity shows significant variations in response to annual monsoon-induced stress variations but not to semidiurnal tidal stresses of the same magnitude. Such period dependence cannot be explained by the Coulomb failure model and spring-slider rate-and-state model (SRM). Here, we study seismicity response to periodic stress perturbations in a 2-D continuum model of a rate-and-state fault (that is, a finite rate-and-state fault). We find that the resulting seismicity indeed exhibits nearly periodic variations. Their amplitude is maximum at a certain period, T a , and decreases with smaller and larger periods to the SRM predictions, remaining much larger than the SRM predictions for a wide range of periods around T a . We attribute the higher sensitivity of finite faults to their finite nucleation zones which vary in space and have a different slip-velocity evolution than that of the SRM. At periods T 〉〉 T a and T 〈〈 T a , the seismicity-rate variations are in phase with the stress-rate and stress variations, respectively, consistent with the SRM, although a gradual phase shift appears as T increases towards T a . Based on the similarities with the SRM and our simulations, we propose a semi-analytical expression for T a . Plausible sets of model parameters make T a equal to 1 yr, potentially explaining Nepal observations and constraining the fault properties. Our finite-fault findings indicate that a , where a is a rate-and-state parameter and is the effective normal stress, can be severely underestimated based on the SRM.

Description: A joint earthquake source inversion technique is presented that uses InSAR and long-period teleseismic data, and, for the first time, takes 3-D Earth structure into account when modelling seismic surface and body waves. Ten average source parameters (Moment, latitude, longitude, depth, strike, dip, rake, length, width and slip) are estimated; hence, the technique is potentially useful for rapid source inversions of moderate magnitude earthquakes using multiple data sets. Unwrapped interferograms and long-period seismic data are jointly inverted for the location, fault geometry and seismic moment, using a hybrid downhill Powell–Monte Carlo algorithm. While the InSAR data are modelled assuming a rectangular dislocation in a homogeneous half-space, seismic data are modelled using the spectral element method for a 3-D earth model. The effect of noise and lateral heterogeneity on the inversions is investigated by carrying out realistic synthetic tests for various earthquakes with different faulting mechanisms and magnitude ( M w 6.0–6.6). Synthetic tests highlight the improvement in the constraint of fault geometry (strike, dip and rake) and moment when InSAR and seismic data are combined. Tests comparing the effect of using a 1-D or 3-D earth model show that long-period surface waves are more sensitive than long-period body waves to the change in earth model. Incorrect source parameters, particularly incorrect fault dip angles, can compensate for systematic errors in the assumed Earth structure, leading to an acceptable data fit despite large discrepancies in source parameters. Three real earthquakes are also investigated: Eureka Valley, California (1993 May 17, M w 6.0), Aiquile, Bolivia (1998 February 22, M w 6.6) and Zarand, Iran (2005 May 22, M w 6.5). These events are located in different tectonic environments and show large discrepancies between InSAR and seismically determined source models. Despite the 40–50 km discrepancies in location between previous geodetic and seismic estimates for the Eureka Valley and Aiquile earthquakes, the seismic data are found to be compatible with the InSAR location. A 30° difference in strike between InSAR and seismic-derived source models is also resolved when taking 3-D Earth structure into account in the analysis of the Eureka Valley earthquake. The combination of both InSAR and seismic data further constrains the dip for the Zarand earthquake, and in all cases the seismic moment is more robustly constrained in the joint inversions than in the individual data set inversions. Unmodelled lateral heterogeneities in Earth and the models could partly explain some of the observed source parameter discrepancies related to the seismic data.

Description: On 2012 May 19, an m b  = 4 earthquake shook the town of Montes Claros, Brazil in the middle of the São Francisco Craton. Because of the scarce seismicity in the area, an event like this could provide valuable information to characterize the governing seismotectonics and stress field for the region. Here, we present the results of more than 1 yr of local seismic monitoring after the main shock. We found that the seismicity originated at approximately 1-km depth in an NNW-oriented blind reverse fault, dipping to the E. The magnitude of the main shock was 4 m b , with aftershocks reaching up to 3.6 m b . Focal mechanisms from first motion polarities and waveform moment tensor inversions indicate a reverse faulting in agreement with the orientation of the aftershock locations. In addition, we derived a new 1-D local velocity model using a simultaneous inversion of hypocentres and velocity layers. The results indicate P -wave velocities of 4.5 km s –1 for the upper layer of carbonate rocks and 5.23 and 5.69 km s –1 for the lower fractured and compact crystalline basement layers, respectively. Higher Vp / Vs ratios were obtained for the upper two layers compared to the lowermost layer, possibly indicating presence of rock fracturing and percolated water. The calculated stress drop for the main event is 0.33 MPa, which is a relatively low value for an intraplate earthquake but still within the observed range. The inversion of the main shock focal mechanism and previously published focal mechanisms suggests a compressional stress regime in the central part of the São Francisco Craton, which is different from the strike-slip regime in the southern part, although both have an EW-oriented 1. On the other hand, focal mechanisms of events located to the west of the craton indicate an NW–SE oriented 1 for central Brazil. This variability highlights the importance of local sources of stresses (e.g. flexural stresses) in mid-plate South America, unlike other mid-plate areas of the world, such as central and east North America, where a more uniform stress field is observed.

Description: The East Kunlun Fault zone, striking E–W to WNW–ESE, has been recognized as one of the largest and most active left-lateral strike-slip faults in the China continent. Presently, the Maqin-Maqu segment (MMS) is recognized as a seismic gap on the East Kunlun Fault. Since several highly populated counties are close to this region, understanding stress transfer and accumulation along this segment is important for hazard assessment along the MMS. In this study, we calculated the stress evolution along the MMS of the East Kunlun Fault zone during 1879–2008 by integrating coseismic effects, viscoelastic relaxation and tectonic loading. It is observed that the stress accumulation on the western part of the Maqin segment has been effected by the 1937 Tuosuo Lake earthquake, the stress on the eastern part of the Maqin segment. Also, the western part of the Maqu segment was relaxed by the 1947 Dari earthquake, and the stress loading on the eastern part of Maqu segment was increased by both the 1879 Wudu and 2008 Wenchuan earthquakes. It is observed that, compared to coseismic static stress changes, the post-seismic viscoelastic relaxation process has played a more important role on stress accumulation in the Maqu segment. The increased stress on the Maqin and Maqu segment is consistent with tectonic loading over 160 and 250 yr, respectively, which we expect will lead to future earthquakes and associated seismic hazard on these segments.

Description: The long and complex history of southern Africa makes it a geological nexus for understanding how crust forms, evolves and survives plate tectonic processes over billions of years. The goal of this study is to characterize the crustal thickness, composition, and Moho impedance contrasts across the Kaapvaal and Zimbabwe Cratons and surrounding mobile belts, which range in age from Archean to Palaeozoic. We use data gathered from the 1997–1999 Southern Africa Seismic Experiment, the Africa Array (2006–2007) and the Global Seismographic Network (1993–2009) to generate P -wave receiver function Gaussian-weighted common conversion point stacks across the region in order to provide a continuous 3-D image of crustal variations throughout southern Africa. We observe thickened crust associated with mobile belts and the intrusion of the Bushveld Complex relative to the less-deformed cratons. The southern Kaapvaal and eastern Zimbabwe Cratons have a well-defined Moho with an average depth of ~34 km and Vp / Vs of ~1.73, indicative of felsic average crustal composition. We explain the felsic composition observed in the Kaapvaal Craton in the context of significant crustal modification related to the deposition of the Ventersdorp lavas. We find that the Bushveld Province, the site of the world's largest layered mafic intrusion, has a thick (〉40 km) crust with a Vp / Vs 〉 1.8, indicative of a mafic average crustal composition. The magnitude of Moho conversions beneath the Bushveld Province is variable, with the lowest amplitude conversion appearing between the eastern and western limbs of the Bushveld Complex, indicative of mafic underplating beneath the region. In the Limpopo Belt and western Zimbabwe Craton, we observe low amplitude Moho conversions beneath the Okavango Dyke Swarm, and attribute this to the reworking of the crust by mafic underplating and intrusion during the Jurassic rifting of Gondwanaland. The Namaqua-Natal event thickened the crust and created a gradational transition from crust to mantle as seen by low amplitude Ps arrivals from receiver functions. Evidence for the presence of a mafic lower crust beneath the Namaqua-Natal Belt is observed in high Vp / Vs values (~1.8) and a high concentration of granulite xenoliths in kimberlite intrusions. In contrast to past interpretations for craton formation that suggest sharp Moho boundaries and low Vp / Vs ratios are characteristic of undisturbed cratons, we propose that these crustal properties are more controlled by tectonic events that later modify the existing cratonic crust. We cannot rule out secular crustal formation variations in the early Earth, but we propose that the southern African cratonic crust has been too heavily modified by later tectonic events to be used in arguments for secular variation, as may be the case for other cratons as well. Thus, it is important to consider the regional geological history of cratons to ensure that secular variation is not confused with the effects of later tectonic deformation and crustal modification.

Description: The numerical simulation of wave propagation in media with solid and fluid layers is essential for marine seismic exploration data analysis. The numerical methods for wave propagation that are applicable to this physical settings can be broadly classified as partitioned or monolithic: The partitioned methods use separate simulations in the fluid and solid regions and explicitly satisfy the interface conditions, whereas the monolithic methods use the same method in all the domain without any special treatment of the fluid-solid interface. Despite the accuracy of the partitioned methods, the monolithic methods are more common in practice because of their convenience. In this paper, we analyse the accuracy of several monolithic methods for wave propagation in the presence of a fluid-solid interface. The analysis is based on grid-dispersion criteria and numerical examples. The methods studied here include: the classical finite-difference method (FDM) based on the second-order displacement formulation of the elastic wave equation (DFDM), the staggered-grid finite difference method (SGFDM), the velocity-stress FDM with a standard grid (VSFDM) and the spectral-element method (SEM). We observe that among these, DFDM and the first-order SEM have a large amount of grid dispersion in the fluid region which renders them impractical for this application. On the other hand, SGFDM, VSFDM and SEM of order greater or equal to 2 yield accurate results for the body waves in the fluid and solid regions if a sufficient number of nodes per wavelength is used. All of the considered methods yield limited accuracy for the surface waves because the proper boundary conditions are not incorporated into the numerical scheme. Overall, we demonstrate both by analytic treatment and numerical experiments, that a first-order velocity-stress formulation can, in general, be used in dealing with fluid-solid interfaces without using staggered grids necessarily.

Description: Ground failures, caving processes and collapses of large natural or man-made underground cavities can produce significant socio-economic damages and represent a serious risk envisaged by the mine managements and municipalities. In order to improve our understanding of the mechanisms governing such a geohazard and to test the potential of geophysical methods to prevent them, the development and collapse of a salt solution mining cavity was monitored in the Lorraine basin in northeastern France. During the experiment, a huge microseismic data set (~50 000 event files) was recorded by a local microseismic network. 80 per cent of the data comprised unusual swarming sequences with complex clusters of superimposed microseismic events which could not be processed through standard automatic detection and location routines. Here, we present two probabilistic methods which provide a powerful tool to assess the spatio-temporal characteristics of these swarming sequences in an automatic manner. Both methods take advantage of strong attenuation effects and significantly polarized P -wave energies at higher frequencies (〉100 Hz). The first location approach uses simple signal amplitude estimates for different frequency bands, and an attenuation model to constrain the hypocentre locations. The second approach was designed to identify significantly polarized P -wave energies and the associated polarization angles which provide very valuable information on the hypocentre location. Both methods are applied to a microseismic data set recorded during an important step of the development of the cavity, that is, before its collapse. From our results, systematic spatio-temporal epicentre migration trends are observed in the order of seconds to minutes and several tens of meters which are partially associated with cyclic behaviours. In addition, from spatio-temporal distribution of epicentre clusters we observed similar epicentre migration in the order of hours and days. All together, we suggest that the recorded microseismicity mainly represents detachment and block breakage processes acting at the cavity's roof, indicating a zone of critical state of stress and where partial fractures cause chain reaction failures as a result of stress redistribution processes.

Description: The Paradox Valley Unit (PVU), a salinity control project in southwest Colorado, disposes of brine in a single deep injection well. Since the initiation of injection at the PVU in 1991, earthquakes have been repeatedly induced. PVU closely monitors all seismicity in the Paradox Valley region with a dense surface seismic network. A key factor for understanding the seismic hazard from PVU injection is the maximum magnitude earthquake that can be induced. The estimate of maximum magnitude of induced earthquakes is difficult to constrain as, unlike naturally occurring earthquakes, the maximum magnitude of induced earthquakes changes over time and is affected by injection parameters. We investigate temporal variations in maximum magnitudes of induced earthquakes at the PVU using two methods. First, we consider the relationship between the total cumulative injected volume and the history of observed largest earthquakes at the PVU. Second, we explore the relationship between maximum magnitude and the geometry of individual seismicity clusters. Under the assumptions that: (i) elevated pore pressures must be distributed over an entire fault surface to initiate rupture and (ii) the location of induced events delineates volumes of sufficiently high pore-pressure to induce rupture, we calculate the largest allowable vertical penny-shaped faults, and investigate the potential earthquake magnitudes represented by their rupture. Results from both the injection volume and geometrical methods suggest that the PVU has the potential to induce events up to roughly M W 5 in the region directly surrounding the well; however, the largest observed earthquake to date has been about a magnitude unit smaller than this predicted maximum. In the seismicity cluster surrounding the injection well, the maximum potential earthquake size estimated by these methods and the observed maximum magnitudes have remained steady since the mid-2000s. These observations suggest that either these methods overpredict maximum magnitude for this area or that long time delays are required for sufficient pore-pressure diffusion to occur to cause rupture along an entire fault segment. We note that earthquake clusters can initiate and grow rapidly over the course of 1 or 2 yr, thus making it difficult to predict maximum earthquake magnitudes far into the future. The abrupt onset of seismicity with injection indicates that pore-pressure increases near the well have been sufficient to trigger earthquakes under pre-existing tectonic stresses. However, we do not observe remote triggering from large teleseismic earthquakes, which suggests that the stress perturbations generated from those events are too small to trigger rupture, even with the increased pore pressures.

Description: The Bío Bío region of Chile experienced a vigorous aftershock sequence following the 2010 February 27 M w 8.8 Maule earthquake. The immediate aftershock sequence was captured by two temporary seismic deployments: the Quake Catcher Network Rapid Aftershock Mobilization Program (QCN RAMP) and the Incorporated Research Institutions for Seismology CHile Aftershock Mobilization Program (IRIS CHAMP). Here, we use moderate to large aftershocks ( M L ≥ 4.0) occurring between 2010 March 1 and June 30 recorded by QCN RAMP and IRIS CHAMP stations to determine the spectral decay parameter, kappa ( ). First, we compare waveforms and estimates from the lower-resolution QCN stations to the IRIS CHAMP stations to ensure the QCN data are of sufficient quality. We find that QCN stations provide reasonable estimates of in comparison to traditional seismic sensors and provide valuable additional observations of local ground motion variation. Using data from both deployments, we investigate the variation in for the region to determine if is influenced primarily by local geological structure, path attenuation, or source properties (e.g. magnitude, mechanism and depth). Estimates of for the Bío Bío region range from 0.0022 to 0.0704 s with a mean of 0.0295 s and are in good agreement with values previously reported for similar tectonic environments. correlates with epicentral distance and, to a lesser degree, with source magnitude. We find little to no correlation between the site kappa, 0 , and mapped geology, although we were only able to compare the data to a low-resolution map of surficial geology. These results support an increasing number of studies that suggest observations can be attributed to a combination of source, path and site properties; additionally, measured are often highly scattered making it difficult to separate the contribution from each of these factors. Thus, our results suggest that contributions from the site, path and source should be carefully considered when interpreting values.

Description: Earthquake rupture models inferred from inversions of geophysical and/or geodetic data exhibit remarkable variability due to uncertainties in modelling assumptions, the use of different inversion algorithms, or variations in data selection and data processing. A robust statistical comparison of different rupture models obtained for a single earthquake is needed to quantify the intra-event variability, both for benchmark exercises and for real earthquakes. The same approach may be useful to characterize (dis-)similarities in events that are typically grouped into a common class of events (e.g. moderate-size crustal strike-slip earthquakes or tsunamigenic large subduction earthquakes). For this purpose, we examine the performance of the spatial prediction comparison test (SPCT), a statistical test developed to compare spatial (random) fields by means of a chosen loss function that describes an error relation between a 2-D field (‘model’) and a reference model. We implement and calibrate the SPCT approach for a suite of synthetic 2-D slip distributions, generated as spatial random fields with various characteristics, and then apply the method to results of a benchmark inversion exercise with known solution. We find the SPCT to be sensitive to different spatial correlations lengths, and different heterogeneity levels of the slip distributions. The SPCT approach proves to be a simple and effective tool for ranking the slip models with respect to a reference model.

Description: For considering elastic seismic wave propagation in large domains, efficient absorbing boundary conditions are required with numerical modelling in finite domains. Since their introduction by Bérenger, the perfectly matched layers (PML) has become the state-of-the art method because of its efficiency and ease of implementation. However, for anisotropic media, theoretical analysis and numerical experiments show that the PML method is amplifying, that is it exhibits numerical instabilities. Numerical experiments can also exhibit numerical instabilities of the PML when dealing with long time simulations even for isotropic media, especially for finite element methods in unstructured grids. Recently, a new method, called SMART layers approach, has been proposed. This method is shown to be stable even for anisotropic media. The drawback is that the SMART layers are not perfectly matched. We have implemented this new approach in a discontinuous Galerkin method and we illustrate that this method does not exhibit numerical instabilities while PML do for an isotropic elastodynamic simulation. We show that this approach is also competitive with respect to the PML method in terms of efficiency and computational cost.

Description: This paper presents the mathematical derivation of an explicit relation for the apparent (or effective) phase velocity of Rayleigh waves in a vertically heterogeneous, isotropic elastic half-space for harmonic excitation. As a kinematical feature, the apparent phase velocity captures the superposition, in a spatial Fourier series, of the individual modes of propagation of Rayleigh waves and describes the speed of propagation of a composite waveform generated by a vertically oscillating point load. The relation, which is a function of the distance from the source, frequency and depth, depends explicitly on the modal phase and group velocities of Rayleigh waves, and their corresponding wavenumbers and eigenfunctions, which can be computed directly from the solution of the Rayleigh-wave eigenproblem. A practical scenario for the application of the notion of apparent Rayleigh-wave phase velocity is the modelling of the dispersion curve in the well-known surface wave measurement methods ‘spectral analysis of surface waves’ (SASW) and ‘multichannel analysis of surface waves’ (MASW). Apart from a theoretical motivation, the availability in surface wave testing of an explicit formula for the calculation of the apparent Rayleigh-wave phase velocity may lead to the development of a new class of inversion algorithms capable of taking into account the influence of all the modes of surface wave propagation. To demonstrate the exactness of the explicit relation, the predicted values of apparent phase velocity are compared to those computed synthetically from a numerical simulation of SASW and MASW testing for three case studies, which show both single as well as multiple mode dominance effects.

Description: The dramatic asymmetry in terms of surface elevation, Cenozoic volcanisms and earthquake activity across the Red Sea is an enigmatic issue in global tectonics, partially due to the unavailability of broad-band seismic data on the African Plate adjacent to the Red Sea. Here, we report the first comprehensive image of the mantle transition zone (MTZ) discontinuities using data from the Egyptian National Seismic Network, and compare the resulting depths of the 410 and 660-km discontinuities with those observed on the Arabian side. Our results show that when a standard earth model is used for time-to-depth conversion, the resulting depth of the discontinuities increases systematically towards the axis of the Afro-Arabian Dome (AAD) from both the west and east. Relative to the westernmost area, the maximum depression of the 410-km discontinuity is about 30 km, and that of the 660-km discontinuity is about 45 km. The observed systematic variations can best be explained by a model involving a hydrated MTZ and an upper-mantle low-velocity zone beneath the AAD. Models invoking one or more mantle plumes originated from the MTZ or the lower-mantle beneath the study area are not consistent with the observations.

Description: We have investigated the seismic anisotropy beneath the Central Andean southern Puna plateau by applying shear wave splitting analysis and shear wave splitting tomography to local S waves and teleseismic SKS, SKKS and PKS phases. Overall, a very complex pattern of fast directions throughout the southern Puna plateau region and a circular pattern of fast directions around the region of the giant Cerro Galan ignimbrite complex are observed. In general, teleseismic lag times are much greater than those for local events which are interpreted to reflect a significant amount of sub and inner slab anisotropy. The complex pattern observed from shear wave splitting analysis alone is the result of a complex 3-D anisotropic structure under the southern Puna plateau. Our application of shear wave splitting tomography provides a 3-D model of anisotropy in the southern Puna plateau that shows different patterns depending on the driving mechanism of upper-mantle flow and seismic anisotropy. The trench parallel a -axes in the continental lithosphere above the slab east of 68W may be related to deformation of the overriding continental lithosphere since it is under compressive stresses which are orthogonal to the trench. The more complex pattern below the Cerro Galan ignimbrite complex and above the slab is interpreted to reflect delamination of continental lithosphere and upwelling of hot asthenosphere. The a -axes beneath the Cerro Galan, Cerro Blanco and Carachi Pampa volcanic centres at 100 km depth show some weak evidence for vertically orientated fast directions, which could be due to vertical asthenospheric flow around a delaminated block. Additionally, our splitting tomographic model shows that there is a significant amount of seismic anisotropy beneath the slab. The subslab mantle west of 68W shows roughly trench parallel horizontal a -axes that are probably driven by slab roll back and the relatively small coupling between the Nazca slab and the underlying mantle. In contrast, the subslab region (i.e. depths greater than 200 km) east of 68W shows a circular pattern of a -axes centred on a region with small strength of anisotropy (Cerro Galan and its eastern edge) which suggest the dominant mechanism is a combination of slab roll back and flow driven by an overlying abnormally heated slab or possibly a slab gap. There seems to be some evidence for vertical flow below the slab at depths of 200–400 km driven by the abnormally heated slab or slab gap. This cannot be resolved by the tomographic inversion due to the lack of ray crossings in the subslab mantle.

Description: We analyse the role played by amplitude-variation-with-offset (AVO) information in the construction of full waveform inversion (FWI) updates from pre-critical seismic reflection data. A mixed continuous-discrete formulation of frequency-domain FWI is found to conveniently expose issues such as parameter cross-talk to quantitative interpretation. Two types of approximate inverse Hessian operator, differing in which off-diagonal elements are retained and which are neglected, are derivable within this formulation. The first, which emphasizes correlations between different parameters collocated in space, is referred to as an approximation of parameter-type . The second, which emphasizes correlations between spatially separated elements, is referred to as an approximation of space-type . The two approximations are such that, if they are both made simultaneously, the result is an update involving only the diagonal elements of the Hessian. The parameter-type inverse Hessian approximation appears to be capable of performing the kind of data manipulations through which linearized AVO-inversion and inverse scattering methods avoid cross-talk. This is confirmed with an analytic calculation of the first iteration in the reconstruction of a single acoustic boundary. The parameter-type FWI update, in this special case, reduces to linear admixtures of reflection coefficient versus angle which are consistent with those produced by direct AVO inversion. The parameter-type components in the full inverse Hessian represent, in this sense, the generalization of standard linearized AVO inversion within FWI.

Description: We present a methodology to model the spatio-temporal variations of microbarom detections at a global scale. Our model combines the source term resulting from the non-linear ocean-wave interaction and a simplified description of the long-range infrasound propagation through the stratospheric waveguide. We compare model predictions with observations at infrasound stations of the International Monitoring System between 2008 and 2009. Our results show a first-order consistency between the observed and modelled trends of microbarom backazimuth detections for most stations. Taking into account stratospheric wind effect on the infrasound propagation systematically improves the fit between the observations the model predictions. However, correctly predicting patterns of weekly variation of detections turns out to be more challenging and would require further improving the source and the propagation models. Short-term and regional quantitative comparisons could then be carried out based on the metrics developed in this study.

Description: This paper develops a probabilistic Bayesian approach to the problem of inferring the spatiotemporal evolution of earthquake rupture on a fault surface from seismic data with rigorous uncertainty estimation. To date, uncertainties of rupture parameters are poorly understood, and the effect of choices such as fault discretization on uncertainties has not been studied. We show that model choice is fundamentally linked to uncertainty estimation and can have profound effects on results. The approach developed here is based on a trans-dimensional self-parametrization of the fault, avoids regularization constraints and provides rigorous uncertainty estimation that accounts for model-selection ambiguity associated with the fault discretization. In particular, the fault is parametrized using self-adapting irregular grids which intrinsically match the local resolving power of the data and provide parsimonious solutions requiring few parameters to capture complex rupture characteristics. Rupture causality is ensured by parametrizing rupture-onset time by a rupture-velocity field and obtaining first rupture times from the eikonal equation. The Bayesian sampling of the parameter space is implemented on a computer cluster with a highly efficient parallel tempering algorithm. The inversion is applied to simulated and observed W-phase waveforms from the 2010 Maule (Chile) earthquake. Simulation results show that our approach avoids both over- and underparametrization to ensure unbiased inversion results with uncertainty estimates that are consistent with data information. The simulation results also show the ability of W-phase data to resolve the spatial variability of slip magnitude and rake angles. In addition, sensitivity to spatially dependent rupture velocities exists for kinematic slip models. Application to the observed data indicates that residual errors are highly correlated and likely dominated by theory error, necessitating the iterative estimation of a non-stationary data covariance matrix. The moment magnitude for the Maule earthquake is estimated to be ~8.9, with slip concentrated in two zones updip of and north and south of the hypocentre, respectively. While this aspect of the slip distribution is similar to previous studies, we show that the slip maximum in the southern zone is poorly resolved compared to the northern zone. Both slip maxima are higher than reported in previous studies, which we speculate may be due to the lack of bias caused by the regularization used in other studies.

Description: The conventional, phenomenological rate-and-state-dependent friction model of Dieterich–Ruina's type is discussed and slightly modified so that, after introducing an artificial internal variable (formally in a position like effective temperature) on the fault, it is driven by a free and a dissipative energies. In contrast to the original model, it thus allows for a formulation in the framework of rational thermodynamics, including the energy balance, and for rigorous numerical analysis. This also suggests an analogous rate-and-state-dependent plastic bulk model using damage/temperature as the state variable controlling the plastic yield stress.

Description: Groundwater level changes induced by the 2011 M w = 9.0 Tohoku earthquake were observed by the Chinese mainland hydrological network dedicated to earthquake prediction research at epicentral distances between 1300 and 5400 km. Out of 216 wells operating during the time of the event, 73 showed sustained changes that are evenly distributed between those experiencing water level rises and falls. Water level oscillations during the passage of the seismic waves were recorded at another 85 wells. At the remaining 58 wells, no response to the earthquake was observed. No spatial pattern in the different well response types is evident, neither in terms of distance nor in terms of azimuth with respect to the epicentre. About 80 per cent of the well-aquifer systems are sensitive to Earth tides. Statistical analysis revealed that those wells that showed a response to the Tohoku earthquake are characterized by admittance factors (with respect to the major tidal constituents M 2 and O 1 ) above 0.5 m of water level change per microstrain—corresponding to 5 kPa water pressure change per microstrain or 5 GPa, whereas the majority of the non-responding wells are characterized by lower tidal factors. However, no systematical difference in tidal admittance factors or phases can be seen between wells that displayed sustained changes and those showing coseismic oscillations/fluctuations. Postseismic phase shifts in the M 2 tide were observed at 31 sites, positive in 22 cases and negative in nine cases. Such phase shifts may indicate changes in the aquifer permeability. Thus, earthquake-induced temporal variations in the permeability might have occurred at about 43 per cent of those wells that displayed sustained water level changes, but less than 15 per cent of all observed wells. Statistical methods were used to analyse the relationships between the different types of groundwater level changes, tidal amplitude and phase, well-epicentre distance and azimuth, well depth and aquifer lithology. The statistical analysis did not indicate any obvious significant relationships between water level changes and any other parameter—except the tidal admittance—indicating that the processes behind groundwater level changes induced by a distant great earthquake are complex. Further detailed studies are required to understand these underlying mechanisms.

Description: This work presents a teleseismic P -wave receiver function study on 34 stations deployed across Ireland in order to determine the first-order crustal properties, thickness ( H ) and mean crustal V p / V s , over the entire island. We apply the H – V p / V s stacking method, which exploits the information contained in both the Ps and the multiple phases from the free-surface. In this way, we obtain the first Moho depth and V p / V s maps of Ireland based on a uniform distribution of measurements. The results are used to examine in detail the lateral variation of crustal thickness and V p / V s ratio across the major terrane boundaries in Ireland. Our results show a good agreement with the available previous estimates from onshore wide-angle/refraction experiments and add new information in poorly constrained areas such as Northern Ireland and the NW coast of Ireland. The mean V p / V s ratio is 1.73 ± 0.05 with a consistently low (1.70) value in the Leinster domain and in central Ireland. The mean crustal thickness is 30.9 ± 2.3 km. The southern portion of the island shows a nearly flat Moho at a depth of 32–33 km, while north of the Southern Uplands Fault, a relatively higher spatial frequency variation in Moho topography exists with values ranging from 28 to 32 km. This reflects the complex history of multiphase terranes accretion during the Caledonian orogeny, although locally, the superposition of more recent geological processes is not excluded. Crossing the Iapetus Suture Zone, our results support the presence of a ‘transitional’ Moho, that is, a 3–4 km smooth seismic transition between crust and mantle, while Moho depth remains constant. Anomalous values in Northern Ireland are interpreted as evidence of a 5- to 6-km-thick high S -wave velocity layer just above the Moho.

Description: We present a new approach to reduce a sparse, linear system of equations associated with tomographic inverse problems. We begin by making a modification to the commonly used compressed sparse-row format, whereby our format is tailored to the sparse structure of finite-frequency (volume) sensitivity kernels in seismic tomography. Next, we cluster the sparse matrix rows to divide a large matrix into smaller subsets representing ray paths that are geographically close. Singular value decomposition of each subset allows us to project the data onto a subspace associated with the largest eigenvalues of the subset. After projection we reject those data that have a signal-to-noise ratio (SNR) below a chosen threshold. Clustering in this way assures that the sparse nature of the system is minimally affected by the projection. Moreover, our approach allows for a precise estimation of the noise affecting the data while also giving us the ability to identify outliers. We illustrate the method by reducing large matrices computed for global tomographic systems with cross-correlation body wave delays, as well as with surface wave phase velocity anomalies. For a massive matrix computed for 3.7 million Rayleigh wave phase velocity measurements, imposing a threshold of 1 for the SNR, we condensed the matrix size from 1103 to 63 Gbyte. For a global data set of multiple-frequency P wave delays from 60 well-distributed deep earthquakes we obtain a reduction to 5.9 per cent. This type of reduction allows one to avoid loss of information due to underparametrizing models. Alternatively, if data have to be rejected to fit the system into computer memory, it assures that the most important data are preserved.

Description: We present a discontinuous Galerkin method for site effects assessment. The P – SV seismic wave propagation is studied in 2-D space heterogeneous media. The first-order velocity–stress system is obtained by assuming that the medium is linear, isotropic and viscoelastic, thus considering intrinsic attenuation. The associated stress–strain relation in the time domain being a convolution, which is numerically intractable, we consider the rheology of a generalized Maxwell body replacing the convolution by a set of differential equations. This results in a velocity–stress system which contains additional equations for the anelastic functions expressing the strain history of the material. Our numerical method, suitable for complex triangular unstructured meshes, is based on centred numerical fluxes and a leap-frog time-discretization. The method is validated through numerical simulations including comparisons with a finite-difference scheme. We study the influence of the geological structures of the Nice basin on the surface ground motion through the comparison of 1-D and 2-D soil response in homogeneous and heterogeneous soil. At last, we compare numerical results with real recordings data. The computed multiple-sediment basin response allows to reproduce the shape of the recorded amplification in the basin. This highlights the importance of knowing the lithological structures of a basin, layers properties and interface geometry.

Description: Non-linear elasticity has recently been considered as a source of scattering, therefore contributing to the coda of seismic waves, in particular for the case of explosive sources. This idea is analysed further here, theoretically solving the expression for the envelope of coda waves generated by a point moment tensor in order to compare with earthquake data. For weak non-linearities, one can consider each point of the non-linear medium as a source of scattering within a homogeneous and linear medium, for which Green's functions can be used to compute the total displacement of scattered waves. These sources of scattering have specific radiation patterns depending on the incident and scattered P or S waves, respectively. In this approach, the coda envelope depends on three scalar parameters related to the specific non-linearity of the medium; however these parameters only change the scale of the coda envelope. The shape of the coda envelope is sensitive to both the source time function and the intrinsic attenuation. We compare simulations using this model with data from earthquakes in Taiwan, with a good fit.

Description: Recent studies have inferred patterns of rheological weakness in the lithosphere from analyses of the coherence between gravity and topography data, and related these to tectonic evolution and lithospheric rheology. The methods employed all attempt to estimate the direction of weakest flexural rigidity and the magnitude of the mechanical anisotropy, and their spatial variations whether using the wavelet transform or moving-window multitaper Fourier transform. Here we apply the wavelet transform method to synthetic gravity and topography data derived from plates where the flexural rigidity is known a priori . When analysing plates that replicate the actual topography of North America and Australia, we find that, even when the synthetic plate is isotropic, spurious anisotropy is recovered in which the weak rigidity direction is aligned perpendicular to the strike of major topographic features and continental margins. It appears that strong anisotropy in the gravity and/or topography data is causing the spurious anisotropy in the observed coherence, and that very little artificial anisotropy arises during its inversion. We compare our model weak directions with those from real gravity and topography data over North America and Australia. From synthetic modelling, we also find spurious correlation of the weak rigidity direction with strong gradients in the flexural rigidity. These results suggest that many results of anisotropic spectral analyses of real data should, at best, be treated with caution, and at worst be discarded altogether.

Description: The lithospheric architecture of the Pyrenees is still uncertain and highly debated. Here, we provide new constraints from a high-resolution 3-D S -wave velocity model of the Pyrenees and the adjacent foreland basins. This model is obtained from ambient noise tomography on records of temporary and permanent seismic arrays installed in southwestern France and northern Spain. We first computed group velocity maps for Rayleigh waves in the 5 to 55 s period range using noise correlation stacks at 1500–8500 station pairs. As the crust is very heterogeneous, poor results were obtained using a single starting model in a linearized inversion of group velocity dispersion curves for the shear wave structure. We therefore built a starting model for each grid node by full exploration of the model space. The resulting 3-D shear wave velocity model is compared to data from previous geophysical studies as a validation test. Despite the poor sensitivity of surface waves to seismic discontinuities, the geometry of the top of the basement and the Moho depth are retrieved well, except along the Cantabrian coast. Major reflectors of the ECORS deep seismic sounding profiles in the central and western Pyrenees coincide with sharp velocity gradients in our velocity model. We retrieve the difference between the thicker Iberian crust and the thinner European crust, the presence of low-velocity material of the Iberian crust underthrust beneath the European crust in the central Pyrenees, and the structural dissymmetry between the South Pyrenean Zone and the North Pyrenean Zone at the shallow crustal level. In the Labourd–Mauléon–Arzacq region (western Pyrenees), there is a high S -wave velocity anomaly at 20–30 km in depth, which might explain the positive Bouguer anomaly of the Labourd Massif. This high-velocity lower crust, which is also detected beneath the Parentis area, might be an imprint of the Albian–Aptian rifting phase. The southeastern part of the Massif Central has an unusual velocity structure, with a very shallow Moho (21–25 km) above an uppermost mantle with anomalously low shear wave velocity.

Description: Seismic noise is generally considered as a reproducible and temporarily stationary natural source of energy. We present a study on the statistical features of the soil motion due to the seismic noise wavefield and the dependencies on the near-surface geology. We have investigated the variations of the 3-D average squared soil displacement over different timescales. The results clearly indicate ballistic behaviour for short timescales being indicative for the properties of the shallow material. Differences in the structural heterogeneity of the subsoil produce different scattering properties, changing the character of motion from nearly ballistic to diffusive on frequency-dependent timescales for all materials. Although in a strict sense the seismic noise wavefield is not completely isotropic, an ultimate pre-condition for a diffusive wavefield, the deviations compared to a uniform distribution are rather small. This means that the emergence of the Green's function is effective for all network sites after a sufficient self-averaging process that is provided by the scattering and the random spatial-temporal noise source distribution.

Description: The observation of seismic hum from 2 to 20 mHz, also known as Earth's background free oscillations, has been established. Recent observations by broad-band seismometers show simultaneous excitation of Love waves (fundamental toroidal modes) and Rayleigh waves (fundamental spheroidal modes). The excitation amplitudes above 10 mHz can be explained by random shear traction sources on Earth's surface. With estimated source distributions, the most likely excitation mechanism is a linear coupling between ocean infragravity waves and seismic surface waves through seafloor topography. Observed Love and Rayleigh wave amplitudes below 5 mHz suggest that surface pressure sources could also contribute to their excitations, although the amplitudes have large uncertainties due to the high noise levels of the horizontal components. To quantify the observation, we develop a new method for estimation of the source spectra of random tractions on Earth's surface by modelling cross-spectra between pairs of stations. The method is to calculate synthetic cross-spectra for spatially isotropic and homogeneous excitations by random shear traction and pressure sources, and invert them with the observed cross-spectra to obtain the source spectra. We applied this method to the IRIS, ORFEUS, and F-net records from 618 stations with three components of broad-band seismometers for 2004–2011. The results show the dominance of shear traction above 5 mHz, which is consistent with past studies. Below 5 mHz, however, the spectral amplitudes of the pressure sources are comparable to those of shear traction. Observed acoustic resonance between the atmosphere and the solid Earth at 3.7 and 4.4 mHz suggests that atmospheric disturbances are responsible for the surface pressure sources, although non-linear ocean wave processes are also candidates for the pressure sources. Excitation mechanisms of seismic hum should be considered as a superposition of the processes of the solid Earth, atmosphere and ocean as a coupled system.

Description: We develop a set of algorithms for automatic detection and picking of direct P and S waves, as well as fault zone head waves (FZHW), generated by earthquakes on faults that separate different lithologies and recorded by local seismic networks. The S -wave picks are performed using polarization analysis and related filters to remove P -wave energy from the seismograms, and utilize STA/LTA and kurtosis detectors in tandem to lock on the phase arrival. The early portions of P waveforms are processed with STA/LTA, kurtosis and skewness detectors for possible first-arriving FZHW. Identification and picking of direct P and FZHW is performed by a multistage algorithm that accounts for basic characteristics (motion polarities, time difference, sharpness and amplitudes) of the two phases. The algorithm is shown to perform well on synthetic seismograms produced by a model with a velocity contrast across the fault, and observed data generated by earthquakes along the Parkfield section of the San Andreas fault and the Hayward fault. The developed techniques can be used for systematic processing of large seismic waveform data sets recorded near major faults.

Description: We propose a level-set adjoint-state method for crosswell traveltime tomography using both first-arrival transmission and reflection traveltime data. Since our entire formulation is based on solving eikonal and advection equations on finite-difference meshes, our traveltime tomography strategy is carried out without computing rays explicitly. We incorporate reflection traveltime data into the formulation so that possible reflectors (slowness interfaces) in the targeted subsurface model can be recovered as well as the slowness distribution itself. Since a reflector may assume a variety of irregular geometries, we propose to use a level-set function to implicitly parametrize the shape of a reflector. Therefore, a mismatch functional is established to minimize the traveltime data misfit with respect to both the slowness distribution and the level-set function, and the minimization is achieved by using a gradient descent method with gradients computed by solving adjoint state equations. To assess uncertainty or reliability of reconstructed slowness models, we introduce a labelling function to characterize first-arrival ray coverage of the computational domain, and this labelling function satisfies an advection equation. We apply fast-sweeping type methods to solve eikonal, adjoint-state and advection equations arising in our formulation. Numerical examples demonstrate that the proposed algorithm is robust to noise in the measurements, and can recover complicated structure even with little information on the reflector.

Description: Since the emerging of ambient noise tomography (ANT) in 2005, it has become a routine method to image the structures of crust and uppermost mantle because of its exclusive capability to extract short-period surface waves. Most of previous ANT studies focus on surface waves at periods shorter than 40/50 s. There are only a few studies of long-period surface wave tomography from ambient noise (longer than 50 s) in global scale. No tomography studies have been performed using teleseismic long-period surface waves from ambient noise in a regional scale, probably due to the two reasons that (1) energy of long-period ambient noise is weaker and it is harder to retrieve good signal-to-noise ratio long-period surface waves from portable stations with several years of ambient noise data and (2) long-period dispersion measurements from ambient noise may have larger uncertainties than those at shorter periods (〈40/50 s). In this study, I investigate the feasibility of using teleseismic long-period surface waves from ambient noise in regional surface wave tomography and also evaluate the accuracy of long-period dispersion measurements at periods up to 150 s. About 300 USArray/Transportable Array (TA) stations located in the Colorado Plateau and surrounding areas and 400 teleseismic stations relative to the TA stations are selected. Clear, strong, and coherent long-period teleseismic surface waves at periods much longer than 50 s are observed in the teleseismic cross-correlations between the TA stations and the teleseismic stations. Using long-period dispersion curves from ambient noise, I generate phase velocity maps at 50–150 s periods and then compare them with phase velocity maps from teleseismic earthquake data. The results show that phase velocity maps from ambient noise data and earthquake data are similar at the 50–150 s period range, verifying the validity of using long-period surface wave from ambient noise in regional surface wave tomography.

Description: Seismic interferometry (SI) enables the retrieval of virtual sources at the location of receivers. In the case of passive SI, no active sources are used for the retrieval of the reflection response of the subsurface, but ambient-noise recordings only. The resulting retrieved response is determined by the illumination characteristics of the recorded ambient noise. Characteristics like geometrical distribution and signature of the noise sources, together with the complexity of the medium and the length of the noise records, determine the quality of the retrieved virtual-shot events. To retrieve body wave reflections, one needs to correlate body-wave noise. A source of such noise might be regional seismicity. In regions with notable human presence, the dominant noise sources are generally located at or close to the surface. In the latter case, the noise will be dominated by surface waves and consequently also the retrieved virtual common-source panels will contain dominant retrieved surface waves, drowning out possible retrieved reflections. In order to retrieve reflection events, suppression of the surface waves becomes the most important pre-processing goal. Because of the reasons mentioned above, we propose a fast method to evaluate the illumination characteristics of ambient noise using the correlation results from ambient-noise records. The method is based on the analysis of the so-called source function of the retrieved virtual-shot panel, and evaluates the apparent slowness of arrivals in the correlation results that pass through the position of the virtual source and at zero time. The results of the diagnosis are used to suppress the retrieval of surface waves and therefore to improve the quality of the retrieved reflection response. We explain the approach using modelled data from transient and continuous noise sources and an example from a passive field data set recorded at Annerveen, Northern Netherlands.

Description: 3-D full waveform inversion (FWI) of seismic wavefields is routinely implemented with explicit time-stepping simulators. A clear advantage of explicit time stepping is the avoidance of solving large-scale implicit linear systems that arise with frequency domain formulations. However, FWI using explicit time stepping may require a very fine time step and (as a consequence) significant computational resources and run times. If the computational challenges of wavefield simulation can be effectively handled, an FWI scheme implemented within the frequency domain utilizing only a few frequencies, offers a cost effective alternative to FWI in the time domain. We have therefore implemented a 3-D FWI scheme for elastic wave propagation in the Fourier domain. To overcome the computational bottleneck in wavefield simulation, we have exploited an efficient Krylov iterative solver for the elastic wave equations approximated with second and fourth order finite differences. The solver does not exploit multilevel preconditioning for wavefield simulation, but is coupled efficiently to the inversion iteration workflow to reduce computational cost. The workflow is best described as a series of sequential inversion experiments, where in the case of seismic reflection acquisition geometries, the data has been laddered such that we first image highly damped data, followed by data where damping is systemically reduced. The key to our modelling approach is its ability to take advantage of solver efficiency when the elastic wavefields are damped. As the inversion experiment progresses, damping is significantly reduced, effectively simulating non-damped wavefields in the Fourier domain. While the cost of the forward simulation increases as damping is reduced, this is counterbalanced by the cost of the outer inversion iteration, which is reduced because of a better starting model obtained from the larger damped wavefield used in the previous inversion experiment. For cross-well data, it is also possible to launch a successful inversion experiment without laddering the damping constants. With this type of acquisition geometry, the solver is still quite effective using a small fixed damping constant. To avoid cycle skipping, we also employ a multiscale imaging approach, in which frequency content of the data is also laddered (with the data now including both reflection and cross-well data acquisition geometries). Thus the inversion process is launched using low frequency data to first recover the long spatial wavelength of the image. With this image as a new starting model, adding higher frequency data refines and enhances the resolution of the image. FWI using laddered frequencies with an efficient damping schemed enables reconstructing elastic attributes of the subsurface at a resolution that approaches half the smallest wavelength utilized to image the subsurface. We show the possibility of effectively carrying out such reconstructions using two to six frequencies, depending upon the application. Using the proposed FWI scheme, massively parallel computing resources are essential for reasonable execution times.

Description: In this study we have investigated the directivity associated with the initial up-dip rupture propagation during the 2009 April 6 ( M w 6.1) L'Aquila normal-faulting earthquake. The objective is the understanding of how the peculiar initial behaviour of rupture history during the main shock has affected the near-source recorded ground motions in the L'Aquila town and surrounding areas. We have modelled the observed ground velocities at the closest near-source recording sites by computing synthetic seismograms using a discrete wavenumbers and finite difference approach in the low frequency bandwidth (0.02–0.4 Hz) to avoid site effects contaminations. We use both the rupture model retrieved by inverting ground motion waveforms and continuous high sampling-rate GPS time-series as well as uniform-slip constant-rupture speed models. Our results demonstrate that the initial up-dip rupture propagation, characterizing the first 3 s of the rupture history during the L'Aquila main shock and releasing only ~25 per cent of total seismic moment, controls the observed ground motions in the near-source. This initial stage of the rupture is characterized by the generation of ground velocity pulses, which we interpret as a forward directivity effect. Our modelling results confirm a heterogeneous distribution of rupture velocity during the initial up-dip rupture propagation, since uniform rupture speed models overestimate up-dip directivity effects in the footwall of the causative fault. The up-dip directivity observed in the near field during the 2009 L'Aquila main shock is that expected for a normal faulting earthquake, but it differs from that inferred from far-field observations that conversely provide evidence of along-strike directivity. This calls for a careful analysis as well as for the realistic inclusion of rupture directivity to predict ground motions in the near source.

Description: Wavefield extrapolation in orthorhombic anisotropic media incorporates complicated but realistic models to reproduce wave propagation phenomena in the Earth's subsurface. Compared with the representations used for simpler symmetries, such as transversely isotropic or isotropic, orthorhombic models require an extended and more elaborated formulation that also involves more expensive computational processes. The acoustic assumption yields more efficient description of the orthorhombic wave equation that also provides a simplified representation for the orthorhombic dispersion relation. However, such representation is hampered by the sixth-order nature of the acoustic wave equation, as it also encompasses the contribution of shear waves. To reduce the computational cost of wavefield extrapolation in such media, we generate effective isotropic inhomogeneous models that are capable of reproducing the first-arrival kinematic aspects of the orthorhombic wavefield. First, in order to compute traveltimes in vertical orthorhombic media, we develop a stable, efficient and accurate algorithm based on the fast marching method. The derived orthorhombic acoustic dispersion relation, unlike the isotropic or transversely isotropic ones, is represented by a sixth order polynomial equation with the fastest solution corresponding to outgoing P waves in acoustic media. The effective velocity models are then computed by evaluating the traveltime gradients of the orthorhombic traveltime solution, and using them to explicitly evaluate the corresponding inhomogeneous isotropic velocity field. The inverted effective velocity fields are source dependent and produce equivalent first-arrival kinematic descriptions of wave propagation in orthorhombic media. We extrapolate wavefields in these isotropic effective velocity models using the more efficient isotropic operator, and the results compare well, especially kinematically, with those obtained from the more expensive anisotropic extrapolator.

Description: The large regional earthquake (2008 February 21, M = 6.0) with epicentre near Wells, Nevada, occurred within a few hundred kilometres of the High Lava Plains (HLP) seismic experiment stations when the network was near its full deployment (〉100 stations with 10–30 km station spacing). The Wells earthquake provides an excellent opportunity to address two questions: What is the effect of small epicentral distances on surface-wave analyses at periods that are used in the analysis of teleseisms? Can one take advantage of a high-density seismic network to obtain improved phase-velocity maps? As small epicentral distances may introduce systematic errors in the surface-wave analysis for longer periods, we test for such effects by generating synthetic waveforms at locations for all regional-distance stations recording the Wells earthquake. Analysis of the synthetics suggests that our surface-waves analyses can be applied for the Wells earthquake up to periods of ~50 s. Applying the same method to data, we estimate two-station Rayleigh-wave fundamental-mode phase-velocities at selected periods and, for each acceptable path, assign the calculated phase velocity to the geographic location of the centre of the path. We contour the phase velocities for all path centres using a local gridding algorithm. The resulting maps for the Wells earthquake have well-constrained phase velocities up to 40–50 s period and allow us to see phase-velocity gradients not observed in earlier studies that used data from teleseisms or ambient noise tomography.

Description: Slip-rate function and the rupture velocity are two important parameters that are critical in understanding the physics of earthquakes. When conventional objective functions are used, the slip-rate function is not well resolved from seismic data. Here, we propose a new method to obtain the slip-rate function by utilizing the near-field phases recorded near the fault rupture. First we illustrate the sensitivity of near-field phases to the moment accumulation and modify the objective function in order to take advantage of this sensitivity. By utilizing near-field P waves along with S pulses on the near-source records and using a Bayesian approach, we show that we can constrain the average slip-rate function as well as the average rupture velocity for a strike-slip earthquake. As a case example, we apply this technique to the record of the 2003, M w 6.6 Bam Earthquake. Our results indicate an asymmetric slip-rate function, with acceleration duration of about 0.4 s, and deceleration duration of 1.4 s. The slip-rate function obtained from kinematic modelling of the 2003 Bam earthquake is consistent with those predicted by dynamic rupture simulations. The rupture velocity is about 82–90 per cent of the shear wave velocity, implying a sub-Rayleigh rupture velocity close to the Rayleigh wave speed. In future cases where abundant near-source strong-motion data exist and slip is well constrained, the method described in this study can be applied to obtain the variation of the slip-rate function along the fault which would improve our understanding of earthquake rupture physics.

Description: We use shear wave splitting (SWS) above microearthquakes to monitor stress variations before the 2010 March and April flank and summit eruptions of Eyjafjallajökull volcano in Iceland. SWS time delays before Eyjafjallajökull show characteristic variations similar to those seen before earthquakes. The time delays display a nearly linear increase before the eruption, an abrupt change of slope and a rapid nearly linear decrease until the flank eruption begins. Similar variations before earthquakes are interpreted as stress-accumulation increases, and stress-relaxation decreases as microcracks coalesce onto the eventual fault plane. The changes in SWS before Eyjafjallajökull are interpreted as a similar stress-accumulation increase, as magma penetrates the crust, and stress-relaxation decrease as microcracks coalesce onto the magma conduit prior to magma release. We suggest that the remarkable similarity between stress changes before eruption and earthquake is strong evidence for the New Geophysics of a critically microcracked crust.

Description: A new method is developed to measure Rayleigh- and Love-wave phase velocities globally using a cluster analysis technique. This method clusters similar waveforms recorded at different stations from a single event and allows users to make measurements on hundreds of waveforms, which are filtered at a series of frequency ranges, at the same time. It also requires minimal amount of user interaction and allows easy assessment of the data quality. This method produces a large amount of phase delay measurements in a manageable time frame. Because there is a strong trade-off between the isotropic part of the Rayleigh-wave phase velocity and azimuthal anisotropy, we include the effect of azimuthal anisotropy in our inversions in order to obtain reliable isotropic phase velocity. We use b-splines to combine these isotropic phase velocity maps with our previous group velocity maps to produce an internally consistent global surface wave dispersion model.

Description: We present a robust technique for the analysis of shear wave splitting in layered anisotropic media by using converted shear phases. In (weakly) anisotropic media, the P -to- S converted phases ( Ps ) exhibit a distinct variation in arrival time (cosine moveout) as function of backazimuth. This variation can be exploited by time-shifting and stacking radial receiver functions to constrain a range of possible splitting parameters (i.e. the fast-polarization direction and the delay time) for an anisotropic layer. Then, the minimization of the transverse-component energy is used to select the pair of splitting parameters that best describes the anisotropic properties of the layer. This two-step approach stabilizes the inversion process and significantly reduces the time for computing the best splitting parameters. In multilayered anisotropic media, the distinct cosine moveout of the radial component is also observed for Ps phases from deeper discontinuities. The direct application of the method leads to apparent (or effective) splitting parameters for all anisotropic layers above the converting interface. Explicit expressions for the apparent splitting parameters are derived. The splitting parameters for the individual layers can be inferred by a layer-stripping approach, where the splitting effect due to shallower layers on converted phases from deeper discontinuities is successively corrected. In comparison to the approach by Liu & Niu ( 2012 ), the method represents a computationally efficient extension to multiple anisotropic layers. We further investigate the influences of noise, gaps in the azimuthal distribution of events, and interface dip on the splitting analysis. As an example, we apply the method to data from two stations of the Iranian National Seismic Network. At station GHIR the observed azimuthal variations of the Ps phase yield splitting parameters t  = 0.26 s and f  = 48° for a 48-km-thick crust. At station SHGR anisotropic effects on the Ps phases can be accounted for by two anisotropic crustal layers with a total thickness of 44 km. For the upper 22-km-thick layer we obtain a delay time t 1  = 0.25 s and a fast axis 1  = 35°. Values for the lower layer are t 2  = 0.19 s and 2  = –88°. The delay times correspond to anisotropies of about 4 and 3 per cent in the upper and lower layer, respectively. The method also provides a robust tool to separate the anisotropic properties of the crust and mantle and, thus, to isolate the anisotropic signature of mantle-deformation processes.

Description: The lowermost few hundreds of kilometres of the Earth's mantle are elastically anisotropic; seismic velocities vary with direction of propagation and polarization. Observations of strong seismic anisotropy correlate with regions where subducted slab material is expected. In this study, we evaluate the hypothesis that crystal preferred orientation (CPO) in a slab, as it impinges on the core–mantle boundary, is the cause of the observed anisotropy. Next, we determine if fast polarization directions seen by shear waves can be mapped to directions of geodynamic flow. This approach is similar to our previous study performed for a 2-D geodynamic model. In this study, we employ a 3-D geodynamic model with temperature-dependent viscosity and kinematic velocity boundary conditions defined at the surface of the Earth to create a broad downwelling slab. Tracers track the deformation that we assume to be accommodated by dislocation creep. We evaluate the models for the presence of perovskite or post-perovskite and for different main slip systems along which dislocation creep may occur in post-perovskite [(100),(010) and (001)]—resulting in four different mineralogical models of CPO. Combining the crystal pole orientations with single crystal elastic constants results in seismically distinguishable models of seismic anisotropy. The models are evaluated against published seismic observations by analysing different anisotropic components: the radial anisotropy, the splitting for (sub-)vertical phases (i.e. azimuthal anisotropy), and the splitting for subhorizontal phases. The patterns in radial anisotropy confirm our earlier results in 2-D. Observations of radial anisotropy and splitting in subhorizontal phases are mostly consistent with our models of post-perovskite with (010)-slip and (001)-slip. Our model of (001)-slip predicts stronger splitting than for (010)-slip for horizontally propagating phases in all directions. The strongest seismic anisotropy in this model occurs where the slab impinges on the core–mantle boundary. The azimuthal anisotropy pattern for (001)-slip shows fast axis directions at the edges of the slab (sub-)parallel to flow directions, suggesting horizontal flows may be mapped out in the lowermost mantle using seismic observations.

Description: We present a new 3-D seismic model of the western United States crust derived from a joint inversion of Rayleigh-wave phase velocity and ellipticity measurements using periods from 8 to 100 s. Improved constraints on upper-crustal structure result from use of short-period Rayleigh-wave ellipticity, or Rayleigh-wave H/V (horizontal to vertical) amplitude ratios, measurements determined using multicomponent ambient noise cross-correlations. To retain the amplitude ratio information between vertical and horizontal components, for each station, we perform daily noise pre-processing (temporal normalization and spectrum whitening) simultaneously for all three components. For each station pair, amplitude measurements between cross-correlations of different components (radial–radial, radial–vertical, vertical–radial and vertical–vertical) are then used to determine the Rayleigh-wave H/V ratios at the two station locations. We use all EarthScope/USArray Tranportable Array data available between 2007 January and 2011 June to determine the Rayleigh-wave H/V ratios and their uncertainties at all station locations and construct new Rayleigh-wave H/V ratio maps in the western United States between periods of 8 and 24 s. Combined with previous longer period earthquake Rayleigh-wave H/V ratio measurements and Rayleigh-wave phase velocity measurements from both ambient noise and earthquakes, we invert for a new 3-D crustal and upper-mantle model in the western United States. Correlation between the inverted model and known geological features at all depths suggests good resolution in five crustal layers. Use of short-period Rayleigh-wave H/V ratio measurements based on noise cross-correlation enables resolution of distinct near surface features such as the Columbia River Basalt flows, which overlie a thick sedimentary basin.

Description: We present the first Rayleigh wave group speed maps of the British Isles constructed from ambient seismic noise. The maps also constitute the first surface wave tomography study of the crust under the British Isles at a relatively high resolution. We computed interferometric, interstation Rayleigh waves from vertical component records of ambient seismic noise recorded on 63 broad-band and short-period stations across the UK and Ireland. Group velocity measurements were made from the resulting surface wave dispersion curves between 5 and 25 s using a multiple phase-matched filter method. Uncertainties in the group velocities were computed by calculating the standard deviation of four dispersion curves constructed by stacking a random selection of daily cross-correlations. Where an uncertainty could not be obtained for a ray path using this method, we estimated it as a function of the interreceiver distance. Group velocity maps were computed for 5–25-s period using the Fast Marching forward solution of the eikonal equation and iterative, linearized inversion. At short and intermediate periods, the maps show remarkable agreement with the major geological features of the British Isles including: terrane boundaries in Scotland; regions of late Palaeozoic basement uplift; areas of exposed late Proterozoic/early Palaeozoic rocks in southwest Scotland, northern England and northwest Wales and, sedimentary basins formed during the Mesozoic such as the Irish Sea Basin, the Chester Basin, the Worcester Graben and the Wessex Basin. The maps also show a consistent low-velocity anomaly in the region of the Midlands Platform, a Proterozoic crustal block in the English Midlands. At longer periods, which are sensitive velocities in the lower crustal/upper mantle, the maps suggest that the depth of Moho beneath the British Isles decreases towards the north and west. Areas of fast velocity in the lower crust also coincide with areas thought to be associated with underplating of the lower crust such as Northern Ireland, the eastern Irish Sea and northwest Wales.

Description: With seismic interferometry, reflections can be retrieved between stations positioned on the Earth's surface. In the classical form, the reflections are retrieved by a crosscorrelation of observations and an integration over subsurface sources. For a specific data set, however, the actual source distribution might not be sufficient to approximate the source integral. Yet, there might be a dense distribution of receivers allowing an integration over the receiver domain. We rewrite the source integral to an integration over receiver pairs and call it receiver-pair seismic interferometry (RPSI). With this formulation, reflections can be retrieved even in the limiting case of only a single source. We illustrate the new relation both with synthetic data and data from the USArray, which is a large grid of stations covering the USA. The field observations are from an earthquake in Mexico. We show that RPSI can be applied both for a line and grid of receivers. When using isolated phases recorded over a line of stations inline with the earthquake, reflections are retrieved from the core-mantle boundary, which reflections can be ascribed to specific virtual source and receiver locations within the USArray. When using full responses as input to RPSI, the retrieved phases are an average over multiple virtual sources and receivers. Location is then only possible when the integrand is spatially windowed or when a clear leading term is identified. When using a grid of receivers, the location of the source does not need to be known, but spatially averaged instead of localized responses are obtained, also when isolated arrivals are used as input to RPSI.

Description: The frequency–wavenumber (fk) and Capon methods are widely used in seismic array studies of background or ambient noise to infer the backazimuth and slowness of microseismic sources. We present an implementation of these techniques for the analysis of microseisms (0.05–2 Hz) which draws on array signal processing literature from a range of disciplines. The presented techniques avoid frequency mixing in the cross-power spectral density and therefore yield an accurate slowness vector estimation of the incoming seismic waves. Using synthetic data, we show explicitly how the frequency averaged broad-band approach can result in a slowness-shifted spectrum. The presented implementation performs the slowness estimations individually for each frequency bin and sums the resulting slowness spectra over a specific frequency range. This may be termed an incoherently averaged signal, or IAS, approach. We further modify the method through diagonal loading to ensure a robust solution. The synthetic data show good agreement between the analytically derived and inferred error in slowness. Results for real (observed) data are compared between the approximate and IAS methods for two different seismic arrays. The IAS method results in the improved resolution of features, particularly for the Capon spectrum, and enables, for instance, Rg and Lg arrivals from similar backazimuths to be separated in the case of real data.

Description: Starting from the hypocentre, the point of initiation of seismic energy, we seek to estimate the subsequent trajectory of the points of emission of high-frequency energy in 3-D, which we term the ‘evocentres’. We track these evocentres as a function of time by energy stacking for putative points on a 3-D grid around the hypocentre that is expanded as time progresses, selecting the location of maximum energy release as a function of time. The spatial resolution in the neighbourhood of a target point can be simply estimated by spatial mapping using the properties of isochrons from the stations. The mapping of a seismogram segment to space is by inverse slowness, and thus more distant stations have a broader spatial contribution. As in hypocentral estimation, the inclusion of a wide azimuthal distribution of stations significantly enhances 3-D capability. We illustrate this approach to tracking source evolution in 3-D by considering two major earthquakes, the 2007 M w 8.1 Solomons islands event that ruptured across a plate boundary and the 2013 M w 8.3 event 610 km beneath the Sea of Okhotsk. In each case we are able to provide estimates of the evolution of high-frequency energy that tally well with alternative schemes, but also to provide information on the 3-D characteristics that is not available from backprojection from distant networks. We are able to demonstrate that the major characteristics of event rupture can be captured using just a few azimuthally distributed stations, which opens the opportunity for the approach to be used in a rapid mode immediately after a major event to provide guidance for, for example tsunami warning for megathrust events.

Description: Downtown L'Aquila suffered severe damage (VIII-IX EMS98 intensity) during the 2009 April 6 M w 6.3 earthquake. The city is settled on a top flat hill, with a shear-wave velocity profile characterized by a reversal of velocity at a depth of the order of 50–100 m, corresponding to the contact between calcareous breccia and lacustrine deposits. In the southern sector of downtown, a thin unit of superficial red soils causes a further shallow impedance contrast that may have influenced the damage distribution during the 2009 earthquake. In this paper, the main features of ambient seismic vibrations have been studied in the entire city centre by using array measurements. We deployed six 2-D arrays of seismic stations and 1-D array of vertical geophones. The 2-D arrays recorded ambient noise, whereas the 1-D array recorded signals produced by active sources. Surface-wave dispersion curves have been measured by array methods and have been inverted through a neighbourhood algorithm, jointly with the H/V ambient noise spectral ratios related to Rayleigh waves ellipticity. We obtained shear-wave velocity ( Vs ) profiles representative of the southern and northern sectors of downtown L'Aquila. The theoretical 1-D transfer functions for the estimated Vs profiles have been compared to the available empirical transfer functions computed from aftershock data analysis, revealing a general good agreement. Then, the Vs profiles have been used as input for a deconvolution analysis aimed at deriving the ground motion at bedrock level. The deconvolution has been performed by means of EERA and STRATA codes, two tools commonly employed in the geotechnical engineering community to perform equivalent-linear site response studies. The waveform at the bedrock level has been obtained deconvolving the 2009 main shock recorded at a strong motion station installed in downtown. Finally, this deconvolved waveform has been used as seismic input for evaluating synthetic time-histories in a strong-motion target site located in the middle Aterno river valley. As a target site, we selected the strong-motion station of AQV 5 km away from downtown L'Aquila. For this site, the record of the 2009 L'Aquila main shock is available and its surface stratigraphy is adequately known making possible to propagate the deconvolved bedrock motion back to the surface, and to compare recorded and synthetic waveforms.

Description: A spatially localized seismic sequence originated few tens of kilometres offshore the Mediterranean coast of Spain, close to the Ebro river delta, starting on 2013 September 5, and lasting at least until 2013 October. The sequence culminated in a maximal moment magnitude M w 4.3 earthquake, on 2013 October 1. The most relevant seismogenic feature in the area is the Fosa de Amposta fault system, which includes different strands mapped at different distances to the coast, with a general NE–SW orientation, roughly parallel to the coastline. However, no significant known historical seismicity has involved this fault system in the past. The epicentral region is also located near the offshore platform of the Castor project, where gas is conducted through a pipeline from mainland and where it was recently injected in a depleted oil reservoir, at about 2 km depth. We analyse the temporal evolution of the seismic sequence and use full waveform techniques to derive absolute and relative locations, estimate depths and focal mechanisms for the largest events in the sequence (with magnitude mbLg larger than 3), and compare them to a previous event (2012 April 8, mbLg 3.3) taking place in the same region prior to the gas injection. Moment tensor inversion results show that the overall seismicity in this sequence is characterized by oblique mechanisms with a normal fault component, with a 30° low-dip angle plane oriented NNE–SSW and a subvertical plane oriented NW–SE. The combined analysis of hypocentral location and focal mechanisms could indicate that the seismic sequence corresponds to rupture processes along shallow low-dip surfaces, which could have been triggered by the gas injection in the reservoir, and excludes the activation of the Amposta fault, as its known orientation is inconsistent with focal mechanism results. An alternative scenario includes the iterated triggering of a system of steep faults oriented NW–SE, which were identified by prior marine seismics investigations.

Description: We present a fully Bayesian inversion of kinematic rupture parameters for the 2011 M w 9 Tohoku-oki, Japan earthquake. Albeit computationally expensive, this approach to kinematic source modelling has the advantage of producing an ensemble of slip models that are consistent with physical a priori constraints, realistic data uncertainties, and realistic but simplistic uncertainties in the physics of the kinematic forward model, all without being biased by non-physical regularization constraints. Combining 1 Hz kinematic GPS, static GPS offsets, seafloor geodesy and near-field and far-field tsunami data into a massively parallel Monte Carlo simulation, we construct an ensemble of samples of the posterior probability density function describing the evolution of fault rupture. We find that most of the slip is concentrated in a depth range of 10–20 km from the trench, and that slip decreases towards the trench with significant displacements at the toe of wedge occurring in just a small region. Estimates of static stress drop and rupture velocity are ambiguous. Due to the spatial compactness of the fault rupture, the duration of the entire rupture was less than approximately 150 s.

Description: In order to study high-frequency seismic wave propagation, seismic wavefields generated by resonant-shaking experiments of the Millikan Library, on the campus of California Institute Technology (Pasadena, California, USA), were analysed. Because the resonant shaking frequencies are 1.12 Hz (the east–west direction) and 1.64 Hz (the north–south direction), this active-source experiment can provide opportunities for studying high-frequency seismic wave propagation in Southern California. Because they are very narrow frequency band data, the analyses must be quite different from ordinary time-domain analyses. We show, theoretically, that the signals must be dominated by surface waves. Adopting this surface wave assumption, we proceed to make two separate analyses, one on spectral amplitude and the other on phase. We present a new method to derive group velocity from phase based on the cross correlations between the station in the Millikan Library (MIK) and stations in the regional network. Our results support that an active-source experiment by resonant shaking of a building is a feasible approach for high-frequency seismic wave studies.

Description: We present tomographic images of crustal velocity structures in the complex Hot Springs and Trifurcation areas of the San Jacinto Fault Zone (SJFZ) based on double-difference inversions of earthquake arrival times. We invert for V P , V S and hypocentre location within 50 x 50 x 20 km 3 volumes, using 266 969 P and 148 249 S arrival times. We obtain high-fidelity images of seismic velocities with resolution on the order of a few kilometres from 2 to 12 km depth and validate the results using checkerboard tests. Due to the relatively large proportion of S -wave arrival times, we also obtain stable maps of V P / V S ratios in both regions. The velocity of the Trifurcation Area as a whole is lower than adjacent unfaulted material. We interpret a 4-km-wide low velocity zone with high V P / V S ratio in the trifurcation itself as related to fault zone damage. We also observe clear velocity contrasts across the Buck Ridge, Clark and Coyote Creek segments of the SJFZ. The Anza segment of the SJFZ, to the NW of the trifurcation area, displays a strong (up to 27 per cent) contrast of V S from 2 to 9 km depth. In the Hot Springs area, a low velocity zone between the Claremont and Casa Loma Strands narrows with depth, with clear velocity contrasts observed across both segments. A roughly 10-km-wide zone of low velocity and low V P / V S ratio at the NW tip of the Hot Springs fault is indicative of either unconsolidated sediments associated with the San Jacinto basin, or fluid-filled cracks within a broad deformation zone. High V P / V S ratios along the Anza segment could indicate a preferred nucleation location for future large earthquakes, while the across-fault velocity contrast suggests a preferred northwest rupture propagation direction for such events.

Description: We have redetermined focal depths of moderate and major earthquakes with reported lower-crust and upper-mantle depths that have occurred in Tien-Shan, since the availability of broad-band array data. Records of earthquakes at global arrays have been used for identification and modelling of depth phases in order to make accurate estimation of focal depths. Our results show that half of the purportedly deep earthquakes are indeed originating from depths attributable to middle-crust and lower-crust regions. Also one exceptional event in the northern foreland of Tien-Shan in Junggar Basin is located in the upper mantle at the depth of 64 km. Such unusually deep earthquakes for intraplate continental tectonic domain are all located at the margin of Tien-Shan with its adjacent stable blocks and at least some of them have occurred where the brittle behaviour of continental rocks is not highly expected. The reverse mechanisms of all these earthquakes and their proximity to formerly subducting and later colliding and underplating stable blocks and their interactions with overlying Tien-Shan are clues to explain this extremity.

Description: In recent years, the application of time-domain adjoint methods to improve large, complex underground tomographic models at the regional scale has led to new challenges for the numerical simulation of forward or adjoint elastic wave propagation problems. An important challenge is to design an efficient infinite-domain truncation method suitable for accurately truncating an infinite domain governed by the second-order elastic wave equation written in displacement and computed based on a finite-element (FE) method. In this paper, we make several steps towards this goal. First, we make the 2-D convolution formulation of the complex-frequency-shifted unsplit-field perfectly matched layer (CFS-UPML) derived in previous work more flexible by providing a new treatment to analytically remove singular parameters in the formulation. We also extend this new formulation to 3-D. Furthermore, we derive the auxiliary differential equation (ADE) form of CFS-UPML, which allows for extension to higher order time schemes and is easier to implement. Secondly, we rigorously derive the CFS-UPML formulation for time-domain adjoint elastic wave problems, which to our knowledge has never been done before. Thirdly, in the case of classical low-order FE methods, we show numerically that we achieve long-time stability for both forward and adjoint problems both for the convolution and the ADE formulations. In the case of higher order Legendre spectral-element methods, we show that weak numerical instabilities can appear in both formulations, in particular if very small mesh elements are present inside the absorbing layer, but we explain how these instabilities can be delayed as much as needed by using a stretching factor to reach numerical stability in practice for applications. Fourthly, in the case of adjoint problems with perfectly matched absorbing layers we introduce a computationally efficient boundary storage strategy by saving information along the interface between the CFS-UPML and the main domain only, thus avoiding the need to solve a backward wave propagation problem inside the CFS-UPML, which is known to be highly ill-posed. Finally, by providing several examples we show numerically that our formulation is efficient at absorbing acoustic waves for normal to near-grazing incident body waves as well as surface waves.

Description: We present a new method for the modelling of frequency-dependent and frequency-independent Q in time-domain seismic wave propagation. Unlike previous approaches, attenuation models are constructed such that Q as a function of position in the Earth appears explicitly as a parameter in the equations of motion. This feature facilitates the derivation of Fréchet kernels for Q using adjoint techniques. Being simple products of the forward strain field and the adjoint memory variables, these kernels can be computed with no additional cost, compared to Fréchet kernels for elastic properties. The same holds for Fréchet kernels for the power-law exponent of frequency-dependent Q , that we derive as well. To illustrate our developments, we present examples from regional- and global-scale time-domain wave propagation.

Description: Numerical modelling is a useful tool to understand the role of different parameters (site geometry, impedance contrast, material properties, constitutive model, input motion) governing site effects. We focus here on the 2-D P – SV seismic wave propagation in a simple-shaped asymmetric model. We consider two ways of describing the sedimentary infilling properties: the basin is either composed of distinct homogeneous geological layers or is described through properties progressively changing as a function of depth (smooth model). In order to study the wave propagation in the two basins with similar soil properties, P and S velocities of the layered basin are deduced from the smooth basin ones, making both models compatible in a kinematic point of view. P and S velocities globally increase with depth. Following EPRI, non-linear properties are considered as constant in layers for the two basins. We assess the influence of the model choice on the wave propagation while taking into account linear and non-linear constitutive models. We test the influence of the input motion by propagating two different input motions, the first being a simple impulsive one and the second a real complex accelerogram. We find that transfer functions computed in each basin are quite similar irrespective of the soil constitutive behaviour and the input motion. Moreover, we show that the maximum shear strain spatial distribution depends on the input motion frequency content and maximum values depend on the input motion strength and complexity. Maximum shear strains are generally higher for superficial layers than for deeper ones. We show that the highest shear strain values are located above discontinuities, where velocities are lower and the soil is more non-linear than in the underlying layer, regardless of the input motion. Indeed, in a layered basin, the shear strain is higher above interfaces for all the soil constitutive models that were used. In the smooth visco-elastoplastic model, a kind of layering appears, absent in a viscoelastic model, due to the different non-linear properties in each layer. Moreover, no matter what the model structure and the input motion used, maximum shear strain levels are higher in the visco-elastoplastic soil than in the viscoelastic one. Such a numerical study helps to understand the non-linearity location and therefore the consequences of a model choice when performing a site-specific study.

Description: We show how to ‘fingerprint’ individual diffractors inside an acoustic medium using interrogative wave energy from arrays of sources and receivers. For any recorded multiply diffracted wave observed between any source and any receiver, the set of such fingerprints is sufficient information to identify all diffractors involved in the corresponding diffraction path, and the sequential order in which diffractors are encountered. The method herein thus decomposes complex, multiply diffracted wavefields into constituent, single-diffraction interactions.

Description: We describe a 2.5-D, frequency domain, viscoelastic waveform tomography algorithm for imaging with seismograms of teleseismic body and surface waves recorded by quasi-linear arrays. The equations of motion are discretized with p -adaptive finite elements that allow for geometric flexibility and accurate solutions as a function of wavelength. Artificial forces are introduced into the media by specifying a known wavefield along the model edges and solving for the corresponding scattered field. Because of the relatively low frequency content of teleseismic data, regional scale tectonic settings can be parametrized with a modest number of variables and perturbations can be determined directly from a regularized Gauss–Newton system of equations. Waveforms generated by the forward problem compare well with analytic solutions for simple 1-D and 2-D media. Tests of different approaches to the inverse problem show that the use of an approximate Hessian serves to properly focus the scattered field. We also find that while full waveform inversion can provide significantly better resolution than standard techniques for both body and surface wave tomography modelled individually, joint inversion both enhances resolution and mitigates potential artefacts.

Description: Dispersive surface waves are routinely used to estimate the subsurface shear-wave velocity distribution, at all length scales. In the well-known Spatial Autocorrelation method, dispersion information is gained from the correlation of seismic noise signals recorded on the vertical (or radial) components. We demonstrate practical advantages of including the cross-correlation between radial and vertical components of the wavefield in a spatial cross-correlation method. The addition of cross-correlation information increases the resolution and robustness of the phase velocity dispersion information, as demonstrated in numerical simulations and a near-surface field study with active seismic sources, where our method confirms the presence of a fault-zone conduit in a geothermal field.

Description: Short-period seismograms of earthquakes are complex especially beneath volcanoes, where the S wave mean free path is short and low velocity bodies composed of melt or fluid are expected in addition to random velocity inhomogeneities as scattering sources. Resonant scattering inherent in a low velocity body shows trap and release of waves with a delay time. Focusing of the delay time phenomenon, we have to consider seriously multiple resonant scattering processes. Since wave phases are complex in such a scattering medium, the radiative transfer theory has been often used to synthesize the variation of mean square (MS) amplitude of waves; however, resonant scattering has not been well adopted in the conventional radiative transfer theory. Here, as a simple mathematical model, we study the sequence of isotropic resonant scattering of a scalar wavelet by low velocity spheres at low frequencies, where the inside velocity is supposed to be low enough. We first derive the total scattering cross-section per time for each order of scattering as the convolution kernel representing the decaying scattering response. Then, for a random and uniform distribution of such identical resonant isotropic scatterers, we build the propagator of the MS amplitude by using causality, a geometrical spreading factor and the scattering loss. Using those propagators and convolution kernels, we formulate the radiative transfer equation for a spherically impulsive radiation from a point source. The synthesized MS amplitude time trace shows a dip just after the direct arrival and a delayed swelling, and then a decaying tail at large lapse times. The delayed swelling is a prominent effect of resonant scattering. The space distribution of synthesized MS amplitude shows a swelling near the source region in space, and it becomes a bell shape like a diffusion solution at large lapse times.

Description: In view of significant discrepancy between the slip models of the 2009 April 6 L'Aquila, (Italy) earthquake based on seismic waveforms or geodetic data, a new inversion strategy is proposed to constrain the coseismic rupture model and early post-seismic afterslip model of this earthquake. Both models were jointly inverted simultaneously from the near-source strong ground motion recordings, teleseismic P waves, long-period Rayleigh waves, GPS displacement vectors and InSAR line-of-sight displacement image. The deformations are mapped onto the fault with strike 140° and dip 50° to the southwest. The coseismic period here represents the first 10 s after the rupture initiation, when over 99 per cent of our total seismic moment (3.07 10 18 Nm) is already released in our preferred coseismic model. Most coseismic slip occurs in a small rupture area of approximately 16 km along strike and in a depth range of 3–10 km. The average slip is 0.45 m; peak slip reaches about 0.90 m. Our result reveals that L'Aquila rupture has a lag of 0.6 s before it first propagates updip to break an asperity equivalent to an M w 5.7. And then the rupture propagates along strike to break a large patch located about 8.0 km along strike and 4.0 km updip from the hypocentre. The weighted average of the rise time and slip velocity are 0.71 s and 0.77 m s –1 , respectively. Our estimate of radiated seismic energy is 1.67 10 13 J, yielding an energy to seismic moment ratio of 0.55 10 –5 , considerably smaller than the global average for shallow earthquakes. The early post-seismic period here represents the time window from 10 s to about first day. During this period, our preferred post-seismic model has an accumulated seismic moment of 6.0 10 17 Nm, equivalent to an M w of 5.8. The afterslip distribution features two separated high slip fault patches, locating either near the hypocentre or the region with peak coseismic slip. Their locations only partially overlap with the fault patches with significant afterslip after the first day. In particular, the slip distribution of the shallower patch is quantitatively consistent with the Amoruso and Crescentini’ diffusive afterslip model. Therefore, the coseismic rupture of the 2009 L'Aquila earthquake was following by a slow-slip event with significant moment release in first hour.

Description: Stress inversions from focal mechanisms require knowledge of which nodal plane is the fault. If such information is missing, and faults and auxiliary nodal planes are interchanged, the stress inversions can produce inaccurate results. It is shown that the linear inversion method developed by Michael is reasonably accurate when retrieving the principal stress directions even when the selection of fault planes in focal mechanisms is incorrect. However, the shape ratio is more sensitive to the proper choice of the fault and substituting the faults by auxiliary nodal planes introduces significant errors. This difficulty is removed by modifying Michael's method and inverting jointly for stress and for fault orientations. The fault orientations are determined by applying the fault instability constraint and the stress is calculated in iterations. As a by-product, overall friction on faults is determined. Numerical tests show that the new iterative stress inversion is fast and accurate and performs much better than the standard linear inversion. The method is exemplified on real data from central Crete and from the West-Bohemia swarm area of the Czech Republic. The joint iterative inversion identified correctly 36 of 38 faults in the central Crete data. In the West Bohemia data, the faults identified by the inversion were close to the principal fault planes delineated by foci clustering. The overall friction on faults was estimated to be 0.75 and 0.85 for the central Crete and West Bohemia data, respectively.

Description: We analysed background surface waves in seismic ambient noise by cross-correlating continuous records of eight ocean bottom seismometers and nine differential pressure gauges deployed in the northwestern Pacific Ocean by the PLATE project. After estimating the clock delay and instrumental phase responses of differential pressure gauges by using cross-correlation functions, we measured average phase velocities in the area of the array for the fundamental-, first higher- and second higher-mode Rayleigh waves, and the fundamental-mode Love waves at a period range of 3–40 s by waveform fitting. We then measured phase-velocity anomalies of fundamental-mode and first higher-mode Rayleigh waves for each pair of stations at a period range of 5–25 s, and corrected the effect of variation in water-depths. The seismic anomalies imply the presence of strong azimuthal anisotropy beneath the eastern part of array. The direction of maximum velocity is approximately N35°E in the fossil seafloor spreading direction perpendicular to magnetic lineations from the ancient triple junction at this location. The peak-to-peak intensity of shear-wave velocity anisotropy in the mantle is ~7 per cent.

Description: Using analogies to gaming, we consider the problem of comparing multiple probabilistic seismicity forecasts. To measure relative model performance, we suggest a parimutuel gambling perspective which addresses shortcomings of other methods such as likelihood ratio, information gain and Molchan diagrams. We describe two variants of the parimutuel approach for a set of forecasts: head-to-head, in which forecasts are compared in pairs, and round table, in which all forecasts are compared simultaneously. For illustration, we compare the 5-yr forecasts of the Regional Earthquake Likelihood Models experiment for M 4.95+ seismicity in California.

Description: We investigated the sequence of 2-D resonance modes of the sediment fill of Rhône Valley, Southern Swiss Alps, a strongly overdeepened, glacially carved basin with a sediment fill reaching a thickness of up to 900 m. From synchronous array recordings of ambient vibrations at six locations between Martigny and Sion we were able to identify several resonance modes, in particular, previously unmeasured higher modes. Data processing was performed with frequency domain decomposition of the cross-spectral density matrices of the recordings and with time-frequency dependent polarization analysis. 2-D finite element modal analysis was performed to support the interpretation of processing results and to investigate mode shapes at depth. In addition, several models of realistic bedrock geometries and velocity structures could be used to qualitatively assess the sensitivity of mode shape and particle motion dip angle to subsurface properties. The variability of modal characteristics due to subsurface properties makes an interpretation of the modes purely from surface observations challenging. We conclude that while a wealth of information on subsurface structure is contained in the modal characteristics, a careful strategy for their interpretation is needed to retrieve this information.

Description: We present relatively relocated earthquake hypocentres for 〉1000 microearthquakes ( M L 〈 3) that occurred during the 2 weeks immediately prior to the 2010 March 20 fissure eruption at Fimmvörðuháls on the flank of Eyjafjallajökull volcano in Iceland. Our hypocentre locations lie predominantly in horizontally separated clusters spread over an area of 10 km 2 and approximately 4 km below sea level (5 km below the surface). Seismic activity in the final 4 d preceding the eruption extended to shallower levels 〈2 km below sea level and propagated to the surface at the Fimmvörðuháls eruption site on the day the eruption started. We demonstrate using synthetic data that the observed apparent ~1 km vertical elongation of seismic clusters is predominantly an artefact caused by only small errors (0.01–0.02 s) in arrival time data. Where the signal-to-noise ratio was sufficiently good to make subsample arrival time picks by cross-correlation of both P - and S -wave arrivals, the mean depth of 103 events in an individual cluster were constrained to 3.84 ± 0.06 km. Epicentral locations are significantly less vulnerable to arrival time errors than are depths for the seismic monitoring network we used. Within clusters of typically 100 recorded earthquakes, most of the arrivals exhibit similar waveforms and identical patterns of P -wave first-motion polarities across the entire monitoring network. The clusters of similar events comprise repetitive sources in the same location with the same orientations of failure, probably on the same rupture plane. The epicentral clustering and similarity of source mechanisms suggest that much of the seismicity was generated at approximately static constrictions to magma flow in an inflating sill complex. These constrictions may act as a form of valve in the country rock, which ruptures when the melt pressure exceeds a critical level, then reseals after a pulse of melt has passed through. This would generate recurring similar source mechanisms on the same weak fault plane as the connection between segments of the sill system is repeatedly refractured in the same location. We infer that the magmatic intrusion causing most of the seismicity was likely to be a laterally inflating complex of sills at about 4 km depth, with seismogenic pinch-points occurring between aseismic compartments of the sills, or between adjacent magma lobes as they inflated. During the final 4 d preceding the eruption onset between 22:30 and 23:30 UTC on 2010 March 20, the seismicity suggests that melt progressed upwards to a depth of ~2 km. This seismicity was probably caused by fracturing of the country rock at the margins of the propagating dyke. Subsequently, on the morning of the eruption a dyke propagated eastward from the region of precursory seismic activity to the Fimmvörðuháls eruption site.

Description: Source–receiver interferometric imaging can be used to synthesize a subsurface acoustic or elastic image, consisting of a zero-time, zero-offset response (or Green's function) between a colocated pseudo-source and pseudo-receiver placed at each point in the subsurface image. However, if the imaging process does not properly account for multiple reflections, and enclosing boundaries of sources and receivers are not available, the image shows artefacts, poorly illuminated areas and distorted image amplitudes. Here we demonstrate with numerical examples that two-sided non-linear imaging provides the best elastic pure-mode ( PP and SS ) and converted-mode ( PS ) images, having higher resolution and more uniform illumination than those obtained from both one-sided linear imaging and from other intermediate steps of imaging (e.g. non-linear one-sided, linear two-sided). We also propose practical approaches to construct the additional fields required by two-sided non-linear imaging without the need for a detailed velocity model and receivers (and/or sources) in the subsurface. Moreover, when conversions are used for imaging, ‘true-amplitude’ images (here true-amplitude means properly retrieving amplitudes that represent the zero-time, zero-offset elastic response) should theoretically vanish because neither P -to- S or S -to- P conversions arise at zero-time and zero-offset. Applying a correction procedure that accounts for the polarity reversal in PS (or SP ) single-shot images helps with their structural interpretation but results in an unphysical estimate of the subsurface response and uninterpretable amplitudes. This suggests that there are advantages in exploiting pure-mode SS reflections/transmissions, in addition to converted waves only, because they require no polarity correction and the resulting image contains meaningful amplitudes that are proportional to the local shear-wave properties of the medium.

Description: We present a time-independent gridded earthquake rate forecast for the European region including Turkey. The spatial component of our model is based on kernel density estimation techniques, which we applied to both past earthquake locations and fault moment release on mapped crustal faults and subduction zone interfaces with assigned slip rates. Our forecast relies on the assumption that the locations of past seismicity is a good guide to future seismicity, and that future large-magnitude events occur more likely in the vicinity of known faults. We show that the optimal weighted sum of the corresponding two spatial densities depends on the magnitude range considered. The kernel bandwidths and density weighting function are optimized using retrospective likelihood-based forecast experiments. We computed earthquake activity rates ( a - and b -value) of the truncated Gutenberg–Richter distribution separately for crustal and subduction seismicity based on a maximum likelihood approach that considers the spatial and temporal completeness history of the catalogue. The final annual rate of our forecast is purely driven by the maximum likelihood fit of activity rates to the catalogue data, whereas its spatial component incorporates contributions from both earthquake and fault moment-rate densities. Our model constitutes one branch of the earthquake source model logic tree of the 2013 European seismic hazard model released by the EU-FP7 project ‘Seismic HAzard haRmonization in Europe’ (SHARE) and contributes to the assessment of epistemic uncertainties in earthquake activity rates. We performed retrospective and pseudo-prospective likelihood consistency tests to underline the reliability of our model and SHARE's area source model (ASM) using the testing algorithms applied in the collaboratory for the study of earthquake predictability (CSEP). We comparatively tested our model's forecasting skill against the ASM and find a statistically significant better performance for testing periods of 10–20 yr. The testing results suggest that our model is a viable candidate model to serve for long-term forecasting on timescales of years to decades for the European region.

Description: Microseismic monitoring is an essential tool for the characterization of hydraulic fractures. Fast estimation of the parameters that define a microseismic event is relevant to understand and control fracture development. The amount of data contained in the microseismic records however, poses a challenge for fast continuous detection and evaluation of the microseismic source parameters. Work inspired by the emerging field of Compressive Sensing has showed that it is possible to evaluate source parameters in a compressed domain, thereby reducing processing time. This technique performs well in scenarios where the amplitudes of the signal are above the noise level, as is often the case in microseismic monitoring using downhole tools. This paper extends the idea of the compressed domain processing to scenarios of microseismic monitoring using surface arrays, where the signal amplitudes are commonly at the same level as, or below, the noise amplitudes. To achieve this, we resort to the use of an imaging operator, which has previously been found to produce better results in detection and location of microseismic events from surface arrays. The operator in our method is formed by full-waveform elastodynamic Green's functions that are band-limited by a source time function and represented in the frequency domain. Where full-waveform Green's functions are not available, ray tracing can also be used to compute the required Green's functions. Additionally, we introduce the concept of the compressed inverse, which derives directly from the compression of the migration operator using a random matrix. The described methodology reduces processing time at a cost of introducing distortions into the results. However, the amount of distortion can be managed by controlling the level of compression applied to the operator. Numerical experiments using synthetic and real data demonstrate the reductions in processing time that can be achieved and exemplify the process of selecting the compression rate that produces a tolerable amount of distortion into the results.

Description: We propose a method for the design of seismic observables with maximum sensitivity to a target model parameter class, and minimum sensitivity to all remaining parameter classes. The resulting optimal observables thereby minimize interparameter trade-offs in multiparameter inverse problems. Our method is based on the linear combination of fundamental observables that can be any scalar measurement extracted from seismic waveforms. Optimal weights of the fundamental observables are determined with an efficient global search algorithm. While most optimal design methods assume variable source and/or receiver positions, our method has the flexibility to operate with a fixed source–receiver geometry, making it particularly attractive in studies where the mobility of sources and receivers is limited. In a series of examples we illustrate the construction of optimal observables, and assess the potentials and limitations of the method. The combination of Rayleigh-wave traveltimes in four frequency bands yields an observable with strongly enhanced sensitivity to 3-D density structure. Simultaneously, sensitivity to S velocity is reduced, and sensitivity to P velocity is eliminated. The original three-parameter problem thereby collapses into a simpler two-parameter problem with one dominant parameter. By defining parameter classes to equal earth model properties within specific regions, our approach mimics the Backus–Gilbert method where data are combined to focus sensitivity in a target region. This concept is illustrated using rotational ground motion measurements as fundamental observables. Forcing dominant sensitivity in the near-receiver region produces an observable that is insensitive to the Earth structure at more than a few wavelengths’ distance from the receiver. This observable may be used for local tomography with teleseismic data. While our test examples use a small number of well-understood fundamental observables, few parameter classes and a radially symmetric earth model, the method itself does not impose such restrictions. It can easily be applied to large numbers of fundamental observables and parameters classes, as well as to 3-D heterogeneous earth models.

Description: To estimate the slowness vector of infrasound waves propagating across an infrasound array, it is often considered that the sensors are located in a perfectly horizontal plane (2-D approximation). However, the arrays are not planar and differences between sensor altitudes cannot be neglected without introducing biases when estimating the parameters of interest (backazimuth and incidence). A closed-formula of this error depending on the geometry of the array and the wave incidence is presented. Since the unbiased 3-D estimation of the slowness parameters results in a significant alteration of the variance, a metric based on the mean square error is proposed. We found it useful to compare the 3-D to the 2-D processed results. We show the 3-D estimator does not always give the best estimates. We propose also a formulation of the boundary that allow us to choose between these two estimators depending on the situation (arrays, incidence and signal-to-noise ratios). Finally, we compare these two approaches (2-D/3-D) to all International Monitoring System arrays with synthetic data, and perform a comparative estimation of backazimuth for real data.

Description: An important goal of computational seismology is to simulate dynamic earthquake rupture and strong ground motion in realistic models that include crustal heterogeneities and complex fault geometries. To accomplish this, we incorporate dynamic rupture modelling capabilities in a spectral element solver on unstructured meshes, the 3-D open source code SPECFEM3D, and employ state-of-the-art software for the generation of unstructured meshes of hexahedral elements. These tools provide high flexibility in representing fault systems with complex geometries, including faults with branches and non-planar faults. The domain size is extended with progressive mesh coarsening to maintain an accurate resolution of the static field. Our implementation of dynamic rupture does not affect the parallel scalability of the code. We verify our implementation by comparing our results to those of two finite element codes on benchmark problems including branched faults. Finally, we present a preliminary dynamic rupture model of the 2011 M w 9.0 Tohoku earthquake including a non-planar plate interface with heterogeneous frictional properties and initial stresses. Our simulation reproduces qualitatively the depth-dependent frequency content of the source and the large slip close to the trench observed for this earthquake.

Description: Full-waveform inversion (FWI) of shallow-seismic surface waves is able to reconstruct lateral variations of subsurface elastic properties. Line-source simulation for point-source data is required when applying algorithms of 2-D adjoint FWI to recorded shallow-seismic field data. The equivalent line-source response for point-source data can be obtained by convolving the waveforms with $\sqrt{t^{-1}}$ ( t : traveltime), which produces a phase shift of /4. Subsequently an amplitude correction must be applied. In this work we recommend to scale the seismograms with $\sqrt{2 r v_{\rm ph}}$ at small receiver offsets r , where v ph is the phase velocity, and gradually shift to applying a $\sqrt{t^{-1}}$ time-domain taper and scaling the waveforms with $r\sqrt{2}$ for larger receiver offsets r . We call this the hybrid transformation which is adapted for direct body and Rayleigh waves and demonstrate its outstanding performance on a 2-D heterogeneous structure. The fit of the phases as well as the amplitudes for all shot locations and components (vertical and radial) is excellent with respect to the reference line-source data. An approach for 1-D media based on Fourier–Bessel integral transformation generates strong artefacts for waves produced by 2-D structures. The theoretical background for both approaches is presented in a companion contribution. In the current contribution we study their performance when applied to waves propagating in a significantly 2-D-heterogeneous structure. We calculate synthetic seismograms for 2-D structure for line sources as well as point sources. Line-source simulations obtained from the point-source seismograms through different approaches are then compared to the corresponding line-source reference waveforms. Although being derived by approximation the hybrid transformation performs excellently except for explicitly back-scattered waves. In reconstruction tests we further invert point-source synthetic seismograms by a 2-D FWI to subsurface structure and evaluate its ability to reproduce the original structural model in comparison to the inversion of line-source synthetic data. Even when applying no explicit correction to the point-source waveforms prior to inversion only moderate artefacts appear in the results. However, the overall performance is best in terms of model reproduction and ability to reproduce the original data in a 3-D simulation if inverted waveforms are obtained by the hybrid transformation.

Description: Locating earthquakes from the beginning of the modern instrumental period is complicated by the fact that there are few good-quality seismograms and what traveltimes do exist may be corrupted by both large phase-pick errors and clock errors. Here, we outline a Bayesian approach to simultaneous inference of not only the hypocentre location but also the clock errors at each station and the origin time of the earthquake. This methodology improves the solution for the source location and also provides an uncertainty analysis on all of the parameters included in the inversion. As an example, we applied this Bayesian approach to the well-studied 1909 M w 7 Taipei earthquake. While our epicentre location and origin time for the 1909 Taipei earthquake are consistent with earlier studies, our focal depth is significantly shallower suggesting a higher seismic hazard to the populous Taipei metropolitan area than previously supposed.

Description: During the Cenozoic, the geodynamics of the western Mediterranean domain has been characterized by a complex history of subduction of Mesozoic oceanic lithosphere. The final stage of these processes is proposed to have led to the development of the Calabria and Gibraltar arcs, whose formation is still under debate. In this study, we take advantage of the dense broad-band station networks now available in the Alborán Sea region, to develop a high-resolution 3-D tomographic P velocity model of the upper mantle beneath the African/Iberian collision zone that will better constraint the past dynamics of this zone. The model is based on 13200 teleseismic arrival times recorded between 2008 and 2012 at 279 stations for which cross-correlation delays are measured with a new technique in different frequency bands centred between 0.03 and 1.0 Hz, and for the first time interpreted using multiple frequency tomography. Our model shows, beneath the Alborán Sea, a strong (4 per cent) fast vertically dipping anomaly observed to at least 650 km depth. The arched shape of this anomaly, and its extent at depth, are coherent with a lithospheric slab, thus favouring the hypothesis of a westward consumption of the Ligurian ocean slab by roll-back during Cenozoic. In addition to this fast anomaly in the deep upper mantle, high intensity slow anomalies are widespread in the lithosphere and asthenosphere beneath Morocco and southern Spain. These anomalies are correlated at the surface with the position of the Rif and Atlas orogens and with Cenozoic volcanic fields. We thus confirm the presence, beneath Morocco, of an anomalous (hot?) upper mantle, but without clear indication for a lateral spreading of the Canary plume to the east.

Description: The High Atlas and the Anti Atlas are fold-belts linked to former and still ongoing continent–continent collisions. Despite their high elevation, studies indicate a lack of a deep crustal root (〈40 km) while the lithosphere underneath is thinned (〈100 km). Previous explanations for this thinning include asthenospheric upwelling due to small-scale convection or a small plume. We use data recorded at stations in SW Morocco to analyse teleseismic P - and S -wave receiver functions. Our study yields a crustal thickness ranging from 24 km near the Atlantic coast to 44 km beneath the High Atlas with an average crustal V p / V s ratio of 1.77 in the entire region. A crustal thickness of 40 km cannot entirely support the topography in this region. Furthermore, we find the lithosphere–asthenosphere boundary at ~80 km depth. The lithosphere beneath SW Morocco is thinner than beneath northern Morocco (〉150 km). This lithospheric thinning supports the theory of thermal compensation of the mountain ranges. The mantle transition zone thickness amounts to 240 ± 10 km. The transition zone seems to be slightly thinned which might indicate a higher mantle temperature in this region.

Description: Amplitude versus offset of P to P reflection is commonly used by the exploration seismology community for hydrocarbon exploration. In this paper, we investigate the feasibility to estimate crustal velocity structure from transmitted P- to S -wave amplitude variation with ray-parameter. First the transmission coefficient for the plane P wave converting to S wave ( P - to - S ) is approximated and expressed as a function of slowness. The resulting linear relation involves two coefficients (intercept, X and gradient, Y), which are functions of velocities and densities. Due to the stable nature of X and the fact that P - to - S amplitudes are weakly dependent on the density contrast, we use this parameter next to estimate the shear wave velocity contrast across an interface using the forward scattered P - to - S amplitude versus slowness data. We report on the effectiveness of the approach using various synthetics data sets. The present methodology is also tested on real data sets from two broad-band seismic stations from HYB and COR.

Description: Real-time applications such as earthquake early warning (EEW) typically use empirical ground-motion prediction equations (GMPEs) along with event magnitude and source-to-site distances to estimate expected shaking levels. In this simplified approach, effects due to finite-fault geometry, directivity and site and basin response are often generalized, which may lead to a significant under- or overestimation of shaking from large earthquakes ( M  〉 6.5) in some locations. For enhanced site-specific ground-motion predictions considering 3-D wave-propagation effects, we develop support vector regression (SVR) models from the SCEC CyberShake low-frequency (〈0.5 Hz) and broad-band (0–10 Hz) data sets. CyberShake encompasses 3-D wave-propagation simulations of 〉415 000 finite-fault rupture scenarios (6.5 ≤ M ≤ 8.5) for southern California defined in UCERF 2.0. We use CyberShake to demonstrate the application of synthetic waveform data to EEW as a ‘proof of concept’, being aware that these simulations are not yet fully validated and might not appropriately sample the range of rupture uncertainty. Our regression models predict the maximum and the temporal evolution of instrumental intensity (MMI) at 71 selected test sites using only the hypocentre, magnitude and rupture ratio, which characterizes uni- and bilateral rupture propagation. Our regression approach is completely data-driven (where here the CyberShake simulations are considered data) and does not enforce pre-defined functional forms or dependencies among input parameters. The models were established from a subset (~20 per cent) of CyberShake simulations, but can explain MMI values of all 〉400 k rupture scenarios with a standard deviation of about 0.4 intensity units. We apply our models to determine threshold magnitudes (and warning times) for various active faults in southern California that earthquakes need to exceed to cause at least ‘moderate’, ‘strong’ or ‘very strong’ shaking in the Los Angeles (LA) basin. These thresholds are used to construct a simple and robust EEW algorithm: to declare a warning, the algorithm only needs to locate the earthquake and to verify that the corresponding magnitude threshold is exceeded. The models predict that a relatively moderate M 6.5–7 earthquake along the Palos Verdes, Newport-Inglewood/Rose Canyon, Elsinore or San Jacinto faults with a rupture propagating towards LA could cause ‘very strong’ to ‘severe’ shaking in the LA basin; however, warning times for these events could exceed 30 s.

Description: Equivalent line-source seismograms can be obtained from shallow seismic field recordings by (1) convolving the waveforms with $\sqrt{t^{-1}}$ , (2) applying a $\sqrt{t^{-1}}$ time-domain taper, where t is traveltime and (3) scaling the waveform with $r_{{\rm offset}}\sqrt{2}$ , where r offset is source-to-receiver offset. We require such a procedure when applying algorithms of 2-D adjoint full-waveform inversion (FWI) to shallow-seismic data. Although derived from solutions for acoustic waves in homogeneous full space this simple procedure performs surprisingly well when applied to vertical and radial components of shallow-seismic recordings from hammer blows or explosions. This is the case even in the near field of the force, although the procedure is derived from a far-field approximation. Similar approximative procedures recommended in literature are optimized for reflected waves and do not convert the amplitudes of all shallow seismic wavefield constituents equally well. We demonstrate the suitability of the proposed method for the viscoelastic case by numerical examples as well as analytical considerations. In contrast to the proposed single-trace procedure, integral-transform approaches are exact for all viscoelastic wavefield constituents of the near- and far-field in unknown 1-D-heterogeneous structure. Unfortunately, integral-transform approaches suffer from artefacts in applications to data sampled on 2-D structures. Here, we use the Fourier–Bessel integral transformation as a reference in 1-D heterogeneous structures. We unroll the wave-theoretical background of both approaches in order to demonstrate, why the simplistic single-trace simulation approach derived from the asymptotic acoustic case can perform so well when applied to the shallow elastic wavefield. Further we give recommendations for practical implementation and application to field data of the proposed simulation method and compare to the results of alternative conversion rules. The performance of the conversion procedure to data recorded on 2-D heterogeneous structures is presented in a companion study by FWI reconstruction tests.

Description: Numerical simulations of dynamic earthquake rupture require an artificial initiation procedure, if they are not integrated in long-term earthquake cycle simulations. A widely applied procedure involves an ‘overstressed asperity’, a localized region stressed beyond the static frictional strength. The physical properties of the asperity (size, shape and overstress) may significantly impact rupture propagation. In particular, to induce a sustained rupture the asperity size needs to exceed a critical value. Although criteria for estimating the critical nucleation size under linear slip-weakening friction have been proposed for 2-D and 3-D problems based on simplifying assumptions, they do not provide general rules for designing 3-D numerical simulations. We conduct a parametric study to estimate parameters of the asperity that minimize numerical artefacts (e.g. changes of rupture shape and speed, artificial supershear transition, higher slip-rate amplitudes). We examine the critical size of square, circular and elliptical asperities as a function of asperity overstress and background (off-asperity) stress. For a given overstress, we find that asperity area controls rupture initiation while asperity shape is of lesser importance. The critical area obtained from our numerical results contrasts with published theoretical estimates when background stress is low. Therefore, we derive two new theoretical estimates of the critical size under low background stress while also accounting for overstress. Our numerical results suggest that setting the asperity overstress and area close to their critical values eliminates strong numerical artefacts even when the overstress is large. We also find that properly chosen asperity size or overstress may significantly shorten the duration of the initiation. Overall, our results provide guidelines for determining the size of the asperity and overstress to minimize the effects of the forced initiation on the subsequent spontaneous rupture propagation.

Description: We raise attention to the issue of consistency between the reference frame with respect to which the seismological model calculations of displacement are made on one hand, and that to which the geodetic measurements of crustal deformation refer (e.g. the ITRF) on the other. This issue is critical in principle if the seismologically calculated displacement (or gravity change) is to be compared or used in joint inversion with geodetic measurements. A necessary set of conditions to be satisfied by inertial frames is the conservations of linear and angular momentums: no net change in them can be induced by a seismic source indigenous to the Earth. We show that the momentums are embodied in the degree-1 terms of the vector spherical-harmonic expansion of the displacement field. Using three largest recent earthquakes as case examples we find that the algorithms of seismological dislocation modelling in the literature do not conserve the momentums. However, quantitatively this inconsistency amounts to two orders of magnitude smaller than the current precision in the definition of the ITRF, hence insignificant in practice. Some caveats are raised.

Description: In the past decades, risk management in the financial community has been dominated by data-intensive statistical methods which rely on short historical time series to estimate future risk. Many observers consider this approach as a contributor to the current financial crisis, as a long period of low volatility gave rise to an illusion of control from the perspectives of both regulators and the regulated. The crucial question is whether there is an alternative. There are voices which claim that there is no reliable way to detect bubbles, and that crashes can be modeled as exogenous "black swans". Others claim that "dragon kings", or crashes which result from endogenous dynamics, can be understood and therefore be predicted, at least in principle. The authors suggest that the concept of "Bayesian risk management" may efficiently mobilize the knowledge, comprehension, and experience of experts in order to understand what happens in financial markets.

Description: ine andere Kultur des Umgangs mit Ressourcen ist notwendig, um nachhaltiges Wirtschaften zu ermöglichen. Der Sammelband "RessourcenKultur" befasst sich mit der Frage: Was zeichnet kleine und mittlere Unternehmen (KMU) aus, die erfolgreich ressourceneffizient wirtschaften und Innovationen hervorbringen? Antworten auf diese Frage erforscht derzeit das Verbundprojekt "RessourcenKultur" (Projektlaufzeit 2009-2013, gefördert vom Bundesministerium für Bildung und Forschung). In diesem Band werden anhand verschiedener Fragestellungen die neuesten Forschungserkenntnisse zu betrieblichen Vertrauenskulturen und Innovationen für Ressourceneffizienz in KMU diskutiert sowie die fördernden und hemmenden Bedingungen zur Umsetzung einer RessourcenKultur dargestellt und Handlungsempfehlungen aufgezeigt. Behandelt werden die Themenfelder Bedeutung von Vertrauen und Kultur im Unternehmen, Innovations- und Veränderungsprozesse als Belastung von Vertrauen, Ressourceneffizienzstrategie als Förderung von Vertrauenskulturellen Elementen, Kompetenzentwicklung für Ressourceneffizienzberatung, Betriebliche Umsetzung Ressourceneffizienz und Implikationen für RessourcenKultur.

Description: Ida et al. (2005) document significant changes in the multi-fractal parameters of the ULF geomagnetic field H component starting about one month before the 1993 Guam earthquake. According to the authors, these multi-fractal signatures can be considered as precursory signals of the Guam earthquake. As a consequence, they conclude that the multifractal analysis may have an important role in the development of short-term earthquake prediction capabilities. Since this and other similar reports have motivated the idea that earthquake prediction based on electromagnetic precursory signals may one day become a routine technique, the presumed precursors need to be validated through independent datasets. In this review the seismogenic origin of the multifractal magnetic signatures documented by Ida et al. (2005) before the 8 August 1993 Guam earthquake is seriously put into question. By means of the geomagnetic ΣKp index, it is demonstrated that these multi-fractal parameter changes are normal signals induced by the variation of the global geomagnetic activity level.

Description: Published

Description: 187-191

Description: 2.6. TTC - Laboratorio di gravimetria, magnetismo ed elettromagnetismo in aree attive

Description: JCR Journal

Description: open

Description: Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2013

Description: In this thesis we present results from inversion of data using dense arrays of collocated seismic and magnetotelluric stations located in the Cascadia subduction zone region of central Washington. In the migrated seismic section, we clearly image the top of the slab and oceanic Moho, as well as a velocity increase corresponding to the eclogitization of the hydrated upper crust. A deeper velocity increase is interpreted as the eclogitization of metastable gabbros, assisted by fluids released from the dehydration of upper mantle chlorite. A low velocity feature interpreted as a fluid/melt phase is present above this transition. The serpentinized wedge and continental Moho are also imaged. The magnetotelluric image further constrains the fluid/melt features, showing a rising conductive feature that forms a column up to a conductor indicative of a magma chamber feeding Mt. Rainier. This feature also explains the disruption of the continental Moho found in the migrated image. Exploration of the assumption of smoothness implicit in the standard MT inversion provides tools that enable us to generate a more accurate MT model. This final MT model clearly demonstrates the link between slab derived fluids/melting and the Mt. Rainier magma chamber.

Description: Funding for this work was made possible by the American Society for Engineering education through a National Defense Science and Engineering Fellowship, and by the National Science Foundation through two grants for the CAFE and CAFE MT projects.