ALBERT

Description: Previous formalisms for determining the static perturbation of spherically symmetric self-gravitating elastic Earth models due to displacement dislocations deal with each infinitesimal element of the fault system in its epicentral reference frame. In this work, we overcome this restriction and present novel and compact formulas for obtaining the perturbation due to the whole fault system in an arbitrary and common reference frame. Furthermore, we show that, even in an arbitrary reference frame, it is still possible to discriminate the contributions associated with the polar, bipolar and quadrupolar patterns of the seismic source response, as well as their relation with the along strike, along dip and tensile components of the displacement dislocation. These results allow a better understanding of the relation between the static perturbation and the whole fault system, and find direct applications in geodetic problems, like the modelling of long-wavelength geoid or gravity data from GRACE and GOCE space missions and of the perturbation of the deviatoric inertia tensor of the Earth.

Description: Sensitive instruments like strainmeters and tiltmeters are necessary for measuring slowly varying low amplitude Earth deformations. Nonetheless, laser and fibre interferometers are particularly suitable for interrogating such instruments due to their extreme precision and accuracy. In this paper, a practical design of a simple pendulum borehole tiltmeter based on laser fibre interferometric displacement sensors is presented. A prototype instrument has been constructed using welded borosilicate with a pendulum length of 0.85 m resulting in a main resonance frequency of 0.6 Hz. By implementing three coplanar extrinsic fibre Fabry-Perot interferometric probes and appropriate signal filtering, our instrument provides tilt measurements that are insensitive to parasitic deformations caused by temperature and pressure variations. This prototype has been installed in an underground facility (Rustrel, France) where results show accurate measurements of Earth strains derived from Earth and ocean tides, local hydrologic effects, as well as local and remote earthquakes. The large dynamic range and the high sensitivity of this tiltmeter render it an invaluable tool for numerous geophysical applications such as transient fault motion, volcanic strain and reservoir monitoring.

Description: Pursuit of multiple avenues can speed incorporating the value of natural capital and ecosystem services into operations of individuals and institutions, such as businesses, government, development banks, nongovernmental institutions, and households. As Phelps et al. (1) rightly point out, the PNAS Special Feature (2) and much of the existing literature...

Description: Jacobson et al. (1) aim to demonstrate that an all-renewable energy system is technically feasible. Not only are the study’s conclusions based on strong assumptions and key methodological oversights, but its framing also omits the essential notion of trade-offs. A far more relevant question is how renewable energy technologies relate...

Description: Bistline and Blanford’s (1) (hereinafter BB16) comments about Jacobson et al. (2) (hereinafter J15) are incorrect or unsubstantiated, and thus affect no conclusion in J15. However, their remarks highlight the failure of previous decarbonization studies to treat many existing storage options, load reduction upon electrification, accurate wind power, and true...

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

Description: We thank Ronit Levine-Schnur for the interest she took in our paper and for taking the time to suggest improvements to the methods (1). Finding ways to accurately measure enforcement is an important challenge for sustainability research, and especially so for research conducted in data-poor environments such as the Gran...

Description: le Polain de Waroux et al. (1) argue for a correlation between lower deforestation regulation enforcement and agricultural companies’ land investments decisions. Two methods are used: a statistical model, where index schemes for level of regulation and enforcement are introduced; and interviews with agricultural companies. The authors fail to address...

Description: Fishery reform in North America and Europe has substantially improved the prospects for recovery of ecosystems affected by overfishing. Costello et al. (1) draw from lessons learnt and suggest, in their view, commonsense approaches for improved resource management, including fishing to maximize long-term catch and rights-based fishery management approaches that...

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

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

Description: Data from the Gravity Recovery and Climate Experiment (GRACE) satellite mission can be used to estimate the mass change rate for separate drainage systems (DSs) of the Greenland Ice Sheet (GrIS). One approach to do so is by inversion of the level-2 spherical harmonic data to surface mass changes in predefined regions, or mascons. However, the inversion can be numerically unstable for some individual DSs. This occurs mainly for DSs with a small mass change signal that are located in the interior region of Greenland. In this study, we present a modified mascon inversion approach with an improved implementation of the constraint equations to obtain better estimates for individual DSs. We use separate constraints for mass change variability in the coastal zone, where run-off takes place, and for the ice sheet interior above 2000 m, where mass changes are smaller. A multi-objective optimization approach is used to find optimal prior variances for these two areas based on a simulation model. Correlations between adjacent DSs are suppressed when our optimized prior variances are used, while the mass balance estimates for the combination of the DSs that make up the GrIS above 2000 m are not affected significantly. The resulting mass balance estimates for some DSs in the interior are significantly improved compared to an inversion with a single constraint, as determined by a comparison with mass balance estimates from surface mass balance modelling and discharge measurements. The rate of mass change of the GrIS for the period of January 2003 to December 2012 is found to be –266.1 ± 17.2 Gt yr –1 in the coastal zone and areas below 2000 m, and +8.2 ± 8.6 Gt yr –1 in the interior region.

Description: Climate change impact assessment on agricultural crop productivity is becoming an important research arena given the increasing yield losses due to the high frequency of droughts in recent years and the anticipated prevalence of extreme events in future climate scenarios (1–3). It is said that by the middle of the...

Description: Measurements of ground deformation can be used to identify and interpret geophysical processes occurring at volcanoes. Most studies rely on a single geodetic technique, or fit a geophysical model to the results of multiple geodetic techniques. Here we present a methodology that combines GPS, Total Station measurements and InSAR into a single reference frame to produce an integrated 3-D geodetic velocity surface without any prior geophysical assumptions. The methodology consists of five steps: design of the network, acquisition and processing of the data, spatial integration of the measurements, time series computation and finally the integration of spatial and temporal measurements. The most significant improvements of this method are (1) the reduction of the required field time, (2) the unambiguous detection of outliers, (3) an increased measurement accuracy and (4) the construction of a 3-D geodetic velocity field. We apply this methodology to ongoing motion on Arenal's western flank. Integration of multiple measurement techniques at Arenal volcano revealed a deformation field that is more complex than that described by individual geodetic techniques, yet remains consistent with previous studies. This approach can be applied to volcano monitoring worldwide and has the potential to be extended to incorporate other geodetic techniques and to study transient deformation.

Description: In autumn 2012, the new release 05 (RL05) of monthly geopotencial spherical harmonics Stokes coefficients (SC) from Gravity Recovery and Climate Experiment (GRACE) mission was published. This release reduces the noise in high degree and order SC, but they still need to be filtered. One of the most common filtering processing is the combination of decorrelation and Gaussian filters. Both of them are parameters dependent and must be tuned by the users. Previous studies have analyzed the parameters choice for the RL05 GRACE data for oceanic applications, and for RL04 data for global application. This study updates the latter for RL05 data extending the statistics analysis. The choice of the parameters of the decorrelation filter has been optimized to: (1) balance the noise reduction and the geophysical signal attenuation produced by the filtering process; (2) minimize the differences between GRACE and model-based data and (3) maximize the ratio of variability between continents and oceans. The Gaussian filter has been optimized following the latter criteria. Besides, an anisotropic filter, the fan filter, has been analyzed as an alternative to the Gauss filter, producing better statistics.

Description: The static and transient deformations produced by earthquakes cause density perturbations which, in turn, generate immediate, long-range perturbations of the Earth's gravity field. Here, an analytical solution is derived for gravity perturbations produced by a point double-couple source in homogeneous, infinite, non-self-gravitating elastic media. The solution features transient gravity perturbations that occur at any distance from the source between the rupture onset time and the arrival time of seismic P waves, which are of potential interest for real-time earthquake source studies and early warning. An analytical solution for such prompt gravity perturbations is presented in compact form. We show that it approximates adequately the prompt gravity perturbations generated by strike-slip and dip-slip finite fault ruptures in a half-space obtained by numerical simulations based on the spectral element method. Based on the analytical solution, we estimate that the observability of prompt gravity perturbations within 10 s after rupture onset by current instruments is severely challenged by the background microseism noise but may be achieved by high-precision gravity strainmeters currently under development. Our analytical results facilitate parametric studies of the expected prompt gravity signals that could be recorded by gravity strainmeters.

Description: Driscoll et al. (1) have recently drawn attention to the risk of new pasture plants becoming invasive, because the same biological traits that promote pasture productivity may also facilitate the invasion of natural areas. The authors indicate some aspects that could mitigate the risk of invasion: namely, the use of...

Description: Proença et al. (1) highlight that sown biodiverse pastures (SBP) can provide local solutions that increase production while limiting the risk of new pasture taxa invading natural areas. We agree that in Portugal SBP is an innovative approach for reducing the weed risk. However, SBP does not offer a universal...

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

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

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

Description: The relative gravimeter is the primary terrestrial instrument for measuring spatially and temporally varying gravitational fields. The background noise of the instrument—that is, non-linear drift and random tares—typically requires some form of least-squares network adjustment to integrate data collected during a campaign that may take several days to weeks. Here, we present an approach to remove the change in the observed relative-gravity differences caused by hydrologic or other transient processes during a single campaign, so that the adjusted gravity values can be referenced to a single epoch. The conceptual approach is an example of coupled hydrogeophysical inversion, by which a hydrologic model is used to inform and constrain the geophysical forward model. The hydrologic model simulates the spatial variation of the rate of change of gravity as either a linear function of distance from an infiltration source, or using a 3-D numerical groundwater model. The linear function can be included in and solved for as part of the network adjustment. Alternatively, the groundwater model is used to predict the change of gravity at each station through time, from which the accumulated gravity change is calculated and removed from the data prior to the network adjustment. Data from a field experiment conducted at an artificial-recharge facility are used to verify our approach. Maximum gravity change due to hydrology (observed using a superconducting gravimeter) during the relative-gravity field campaigns was up to 2.6 μGal d –1 , each campaign was between 4 and 6 d and one month elapsed between campaigns. The maximum absolute difference in the estimated gravity change between two campaigns, two months apart, using the standard network adjustment method and the new approach, was 5.5 μGal. The maximum gravity change between the same two campaigns was 148 μGal, and spatial variation in gravity change revealed zones of preferential infiltration and areas of relatively high groundwater storage. The accommodation for spatially varying gravity change would be most important for long-duration campaigns, campaigns with very rapid changes in gravity and (or) campaigns where especially precise observed relative-gravity differences are used in the network adjustment.

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

Description: The interagency consultation provisions of the Endangered Species Act are critical to its implementation and have been at the center of the most high-profile controversies triggered by its implementation, including the battles over the Tellico Dam, the Northwest forests, the Klamath River, and, more recently, management of the San Francisco...

Description: In the present work we illustrate a new local inversion algorithm to retrieve the Moho depth from GOCE (Gravity field and steady-state Ocean Circulation Explorer) gravity field. In details the proposed procedure can be divided into two main steps: the first one consists in recognizing and isolating the different geological provinces in the study area by exploiting information coming from the GOCE global gravity field model. Once the main geological provinces are defined, a function relating the crust density of each province with depth is built and used to reduce the data. The gravitational effects of sediments, topography, bathymetry and upper mantle are also removed. In the second step the residual gravitational field is inverted to retrieve the Moho depth and some information on the crustal density. In particular, the clustering of geological province is performed by means of an automatic Bayesian classification algorithm while the inversion of GOCE residual field is performed by adapting the global algorithm developed in the framework of the GEMMA project to the local scale. The procedure, based on an iterative Wiener filter, allows to compute the Moho depth considering lateral as well as radial variations of crustal density. The algorithm has been applied to the fifth release of GOCE time-wise global gravity field model to infer information on the crustal structure in the Western Balkan area, that is, the region laying between Bulgaria and the Adriatic Sea. This region is one of the most complex and active, from the tectonic point of view, in the whole Europe and it is characterized by the presence of the Alpine-Himalayan orogenic belt, formed by the collision between the African and Eurasian plates, and by the opening of the Pannonian Basin. Results show a good agreement between the obtained geological provinces with the actual knowledge on the region. The resulting Moho depth ranges between about 20 km beneath the Adriatic Sea and 45 km in the Dinarides. Comparisons with available seismic data show differences smaller than 1 km (standard deviation).

Description: Gravity variations associated with Earth's oblateness ( J 2 ) have been observed by satellite laser ranging (SLR) since 1976. The J 2 time-series has been used to measure and help understand many geophysical processes within the Earth system ranging from the mantle to the atmosphere. While post glacial rebound and the Earth climate system are believed to be the primary driving forces of long-term and seasonal J 2 variations, the physical cause of decadal and longer timescale J 2 variations has remained uncertain, although recent evidence indicates that polar ice mass changes are important. In this study, we estimate a variety of climate contributions to J 2 over the period 1979–2010, and find that ice mass variations in Greenland and Antarctica are the dominant cause of observed decadal and longer J 2 variations. Residual variations at periods near 10–11 years may reflect limitations of numerical climate models in estimating mass change variability at long periods, but are also suggestive of potential contribution related to variable solar activity.

Description: Interferometric synthetic aperture radar (InSAR) technology provides a valuable tool for obtaining Earth surface deformation and topography at high spatial resolution for crustal deformation studies. Similar to global positioning system (GPS), InSAR measurements are affected by the Earth's ionospheric and tropospheric layers as the electromagnetic signals significantly refract while propagating through the different layers. While GPS signals propagating through the neutral atmosphere are affected primarily by the distribution, pressure and temperature of atmospheric gases, including water vapour, the propagation through the ionosphere is mainly affected by the number of free electrons along the signal path. Here, we present the use of dense regional GPS networks for extracting tropospheric zenith delays and ionospheric total electron content (TEC) maps in order to reduce the noise levels in InSAR images. The results show significant reduction in the root mean square (RMS) values when simultaneously combining the two corrections, both at short time periods where no surface deformation is expected, and at longer periods, where imaging of localized subsidence and fault creep is enhanced.

Description: The main objective of the Gravity Recovery and Climate Experiment (GRACE) Atmospheric and Oceanic De-Aliasing Level-1B product (AOD1B) is the removal of high-frequency non-tidal mass variations due to sub-monthly mass transport in the atmosphere and oceans. Application of AOD1B shall avoid aliasing of these high-frequency signals into monthly gravity models derived from modern gravity missions and shall help to derive consistent orbit solutions for altimetry and Satellite Laser Ranging missions. The AOD1B 6-h series of spherical harmonic coefficients up to degree and order 100 are routinely generated at the German Research Centre for Geoscience and distributed to the GRACE Science Data System and the user community. Inputs for this product are acquired from numerical weather prediction models which are regularly revised and consequently not stable in time. The latest AOD1B release 5 (RL05) is based, as all other releases, on input from ECMWF and does not resolve this problem of discontinuities present in the surface pressure and surface geopotential input data. This might contaminate the gravity field variations derived from atmospheric mass variations. In this paper we present a method to overcome this problem during future AOD1B product generation, as well as two new Level-2 products (GAE and GAF) that, over land, fix a posteriori the two jumps present in the already distributed Level-2 RL05 monthly gravity models which were based on AOD1B RL05. The impact of the proposed correction on the variations and long-term trend of the total mass of the atmosphere and on the ice mass balance over Antarctica and over Greenland is also illustrated. We found that the GAE/GAF-corrected trend of the global atmospheric mass over the GRACE mission lifetime significantly decreased from –0.05 to –0.02 mm yr –1 in terms of geoid height. A considerable effect (33 per cent) was also found in the quadratic term of ice mass loss over Antarctica which results in an acceleration of 3.2 Gt yr –1  yr –1 smaller than without applying this correction.

Description: A diverse diet is more likely to meet nutrient requirements (1), and so diverse farm production has been encouraged as a means to increase dietary diversity (2). However, Sibhatu et al. (3) argue that the impact of market access and the buying and selling of food swamps and eliminates the...

Description: In his letter (1), Berti argues that our failure to find a relationship between farm production diversity (PD) and household dietary diversity (DD) may be due to the fact that PD and DD were measured using different scales. First, we would like to clarify that the main result of our...

Description: Previous studies of Earth rotation perturbations due to ice-age loading have predicted a slow secular drift of the rotation axis relative to the surface geography (i.e. true polar wander, TPW) of order of several degrees over the Plio-Pleistocene. It has been argued that this drift and the change in the geographic distribution of solar insolation that it implies may have been responsible for important transitions in ice-age climate, including the termination of ice-age cycles.We use a revised rotational stability theory that incorporates a more accurate treatment of the Earth's background ellipticity to reconsider this issue, and demonstrate that the net displacement of the pole predicted in earlier studies disappears. This more muted polar motion is due to two factors: first, the revised theory no longer predicts the permanent shift in the rotation axis, or the so-called ‘unidirectional TPW’, that appears in the traditional stability theory; and, second, the increased background ellipticity incorporated in the revised predictions acts to reduce the normal mode amplitudes governing the motion of the pole. We conclude that ice-age-induced TPW was not responsible for the termination of the ice age. This does not preclude the possibility that TPW induced by mantle convective flow may have played a role in major Plio-Pleistocene climate transitions, including the onset of Northern Hemisphere glaciation.

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

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

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

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

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

Description: A new approach based on energy conservation principle for satellite gravimetry mission has been developed and yields more accurate estimation of in situ geopotential difference observables using K-band ranging (KBR) measurements from the Gravity Recovery and Climate Experiment (GRACE) twin-satellite mission. This new approach preserves more gravity information sensed by KBR range-rate measurements and reduces orbit error as compared to previous energy balance methods. Results from analysis of 11 yr of GRACE data indicated that the resulting geopotential difference estimates agree well with predicted values from official Level 2 solutions: with much higher correlation at 0.9, as compared to 0.5–0.8 reported by previous published energy balance studies. We demonstrate that our approach produced a comparable time-variable gravity solution with the Level 2 solutions. The regional GRACE temporal gravity solutions over Greenland reveals that a substantially higher temporal resolution is achievable at 10-d sampling as compared to the official monthly solutions, but without the compromise of spatial resolution, nor the need to use regularization or post-processing.

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

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

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

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

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

Description: Romero and Agrawal (1) question the usefulness of our framework to link functional diversity with social actor strategies (2), arguing that it oversimplifies the complexity of the social dimensions of socioecological systems. We agree on the crucial importance of such dimensions, and we repeatedly highlighted this in our article, as is obvious from figure 1, the text, and the examples. While focusing on functional diversity, ecosystem services, and their role in different social actor strategies, we situated these in a broader setting that can be analyzed with the tools and concepts of social sciences, including institutional analyses.Rather than replacing major...

Description: Essl et al. (1) tested whether historical socioeconomic conditions have created an invasion debt in Europe (i.e., a suite of nonnative species that have not yet been discovered but whose establishment has been determined by previous socioeconomic conditions). Essl et al. (1) tested this theory by asking whether the cumulative numbers of nonnative species presently established in 28 European countries were more closely correlated to socioeconomic conditions in the year 1900 or 2000. In this letter, we describe a flaw in their logic that biases the analysis to concluding that an invasion debt does occur.Essl et al. (1) modeled the...

Description: Success of the emerging Low Emissions Development paradigm in Southeast Asia depends on mitigating impacts of oil palm (OP) expansion on carbon-dense ecosystems, especially tropical peatlands. To this end, Koh et al. (1) mapped OP planted before 2002 across Peninsular Malaysia, Sumatra, and Borneo to estimate emissions and biodiversity losses from peatland conversion (≈880,000 ha). Unfortunately, emissions scenarios are oversimplified, remote-sensing (RS) methods are unsuitable for OP monitoring, and recommendations for peatland restoration are overstated.The article risks misinforming national and international climate change policies under development.Koh et al. overestimated emissions from aboveground biomass (AGB) conversion to OP (136 million MgC)...

Description: Díaz et al. (1) proposed an “interdisciplinary framework for the analysis of relationships between functional diversity, ecosystem services, and human actions.” Their framework addresses the linkages between land uses and ecosystem service (ES) provision to inform decisions by relevant parties. We welcome the development and practical application of tools for analyzing the complexity of social-ecological systems (SESs), but there are fundamental gaps in the oversimplified framework of Díaz et al. (1). These flaws obscure critical aspects of the functioning of SESs, preclude their improved understanding, and thereby undermine the goal of fruitful scientific analysis.In particular, the proposed local-level framework does...

Description: Paoli et al. (1) raise some interesting criticisms of our article (2), but we think that they misinterpret important elements of our study, ignore our consideration of model uncertainties, and fail to recognize the wider significance of our work.We presented a framework for quantifying the impacts of oil-palm expansion on biodiversity and carbon stocks. We did so by combining a unique remote-sensing methodology with a unique species-area model and recently published carbon flux estimates. We also explicitly accounted for and presented uncertainties in all model projections. We estimated that the conversion of peatswamp forests to large-scale, closed canopy oil-palm plantations...

Description: We recently showed (1) that, for a wide range of taxa, the current numbers of established alien species in 28 European countries were generally more closely related to socioeconomic indicators from the year 1900 than 2000. Thus, the establishment of alien species seemed to lag considerably behind one of the main drivers of alien species introductions (2). We concluded that current high socioeconomic activity could result in considerable additional accumulation of alien species in the future, a phenomenon that we have called invasion debt.Keller and Springborn (3) suggest that cumulative numbers of established alien species would be better explained by...

Description: We interpreted the TRIDENT satellite derived gravity field to provide detailed insights into the spatial distribution of the crustal density structures in the area of the Yellow Sea. We used 3-D forward density modelling for the interpretation that incorporated constraints from existing geological and geophysical information. A gravity stripping method is used to separate out the gravity effects of different geological crustal structures. From this analysis we see that (1) the Gunsan sedimentary basin is isostatically compensated. (2) The satellite-derived Bouguer anomalies ranging from 15 to –30 x 10 –5 m s –2 are linked to basin thicknesses in the Yellow Sea. (3) The calculated Moho depth in the Yellow Sea varies from 27 km beneath the deep sedimentary basin to 34 km in the uplifted zones. (4) Moho depth calculations show two distinct areas, characterized by the deepest Moho depths and the largest crustal thicknesses in the Yellow Sea. The one region extends along the Qianliyan Uplift Zone from Jiaodong to Hongsung while the other area extends from southeastern China to Hongsung in the Korean peninsula. Compared to previous works we suggest that they are the part of the collisions zone between North and South China Blocks extending from China to the Korean peninsula via the Yellow Sea.

Description: Regional refinement of the gravity field models from satellite data using spherical radial base functions (SRBF) is an ill-posed problem. This is mainly due to the regional confinement of the data and the base functions, which leads to severe instabilities in the solutions. Here, this ill-posedness as well as the related regularization process are investigated. We compare three methods for the choice of the regularization parameter, which have been frequently used in gravity modelling. These methods are (1) the variance component estimation (VCE), (2) the generalized cross validation (GCV) and (3) the L-curve criterion. A particular emphasis is put on the impact of the SRBF type on the regularization parameter. To do this, we include two types of SRBF which are often used for regional gravity field modelling. These are the Shannon SRBF or the reproducing kernel and the Spline SRBF. The investigations are performed on two months of the real GOCE ultrasensitive gravity gradients over Central Africa and Amazon. The solutions are validated against a state-of-the-art global gravity solution. We conclude that if a proper regularization method is applied, both SRBF deliver more or less the same accuracy. We show that when the Shannon wavelet is used, the L-curve method gives the best results, while with the Spline kernel, the GCV outperforms the other two methods. Moreover, we observe that the estimated coefficients for the Spline kernel cannot be spatially interpreted. In contrast, the coefficients obtained for the Shannon wavelet reflect the energy of the recovered gravity field with a correlation factor of above 95 per cent. Therefore, when combined with the L-curve method, the Shannon SRBF is advantageous for regional gravity field estimation, since it is one of the simplest band-limited SRBF. In addition, it delivers promising solutions and the estimated coefficients represent the characteristics of the gravity field within the target region.

Description: This paper describes an alternative acceleration approach for determining GRACE monthly gravity field models. The main differences compared to the traditional acceleration approach can be summarized as: (1) The position errors of GRACE orbits in the functional model are taken into account; (2) The range ambiguity is eliminated via the difference of the range measurements and (3) The mean acceleration equation is formed based on Cowell integration. Using this developed approach, a new time-series of GRACE monthly solution spanning the period January 2003 to December 2010, called Tongji_Acc RL01, has been derived. The annual signals from the Tongji_Acc RL01 time-series agree well with those from the GLDAS model. The performance of Tongji_Acc RL01 shows that this new model is comparable with the RL05 models released by CSR and JPL as well as with the RL05a model released by GFZ.

Description: In this paper, we present a method for incorporating prior geological information into potential field data inversion problem. As opposed to the traditional inverse algorithm, our proposed method takes full advantage of prior geological information as a constraint and thus obtains a new objective function for inversion by adding Lagrangian multipliers and slack variables to the traditional inversion method. These additional parameters can be easily solved during iterations. We used both synthetic and observed data sets to test the stability and validity of the proposed method. Our results using synthetic gravity data show that our new method predicts depth and density anomalies more efficiently and accurately than the traditional inversion method that does not include prior geological constraints. Then using observed gravity data in the Three Gorges area and geological constraint information, we obtained the density distribution of the upper and middle crust in this area thus revealing its geological structure. These results confirm the proposed method's validity and indicate its potential application for magnetism data inversion and exploration of geological structures.

Description: It remains enigmatic how slow slip events (SSEs) interact with other slow seismic events and large distant earthquakes at many subduction zones. Here we model the spatiotemporal slip evolution of the most recent long-term SSE in 2009–2011 in the Bungo Channel region, southwest Japan using GEONET GPS position time-series and a Kalman filter-based, time-dependent slip inversion method. We examine the space-time relationship between the geodetically determined slow slip transient and seismically observed low frequency earthquakes (LFEs) and very-low frequency earthquakes (V-LFEs) near the Nankai trough. We find a strong but distinct temporal correlation between transient slip and LFEs and V-LFEs, suggesting a different relationship to the SSE. We also find the great Tohoku-Oki earthquake appears to disrupt the normal source process of the SSE, probably reflecting large-scale stress redistribution caused by the earthquake. Comparison of the 2009–2011 SSE with others in the same region shows much similarity in slip and moment release, confirming its recurrent nature. Comparison of transient slip with plate coupling shows that slip transients mainly concentrate on the transition zone from strong coupling region to downdip LFEs with transient slip relieving elastic strain accumulation at transitional depth. The less consistent spatial correlation between the long-term SSE and seismic slow earthquakes, and susceptibility of these slow earthquakes to various triggering sources including long-term slow slip, suggests caution in using the seismically determined slow earthquakes as a proxy for slow slip.

Description: Normal mode treatments of the Earth's body tide response were developed in the 1980s to account for the effects of Earth rotation, ellipticity, anelasticity and resonant excitation within the diurnal band. Recent space-geodetic measurements of the Earth's crustal displacement in response to luni-solar tidal forcings have revealed geographical variations that are indicative of aspherical deep mantle structure, thus providing a novel data set for constraining deep mantle elastic and density structure. In light of this, we make use of advances in seismic free oscillation literature to develop a new, generalized normal mode theory for the tidal response within the semi-diurnal and long-period tidal band. Our theory involves a perturbation method that permits an efficient calculation of the impact of aspherical structure on the tidal response. In addition, we introduce a normal mode treatment of anelasticity that is distinct from both earlier work in body tides and the approach adopted in free oscillation seismology. We present several simple numerical applications of the new theory. First, we compute the tidal response of a spherically symmetric, non-rotating, elastic and isotropic Earth model and demonstrate that our predictions match those based on standard Love number theory. Second, we compute perturbations to this response associated with mantle anelasticity and demonstrate that the usual set of seismic modes adopted for this purpose must be augmented by a family of relaxation modes to accurately capture the full effect of anelasticity on the body tide response. Finally, we explore aspherical effects including rotation and we benchmark results from several illustrative case studies of aspherical Earth structure against independent finite-volume numerical calculations of the semi-diurnal body tide response. These tests confirm the accuracy of the normal mode methodology to at least the level of numerical error in the finite-volume predictions. They also demonstrate that full coupling of normal modes, rather than group coupling, is necessary for accurate predictions of the body tide response.

Description: Reconstructions and observations of relative sea level (RSL) must be corrected for vertical land movements from glacial isostatic adjustment (GIA) to facilitate comparisons among regions and identify deviations from background rates. Late Holocene (past 2 ka) GIA rates are estimated from geological data and permanent global positioning system (GPS) stations or predicted from GIA models. We used a linear trend fitted to the regional, compaction-free, RSL reconstructions compiled by Engelhart et al. (1) for the past 2 ka (excluding data since AD 1900) as a GIA estimate. Similarly, GIA models also attribute all RSL changes during the past 2 ka...

Description: Kemp et al. (1) presented a new salt-marsh proxy record of relative sea level (RSL) from North Carolina (NCRSL). The salt marsh is slowly subsiding as a result of glacial isostatic adjustment (GIA), and the NCRSL record needs to be adjusted to remove this vertical land movement from the sea level record. Kemp et al. (1) corrected for a constant subsidence rate of approximately 1 mm/y. This is a “geologic” estimate based on sea level index points, which are determined from linear fits to data from other North American RSL proxy records. Thus, the geologic method implicitly assumes that the...

Description: We are grateful to Auffhammer and Vincent (1) for having pointed out that Eqs. 1 and 2 in Feng et al. (2) do not represent the model actually used to produce the estimates presented in Tables 1 and 2 of the latter paper (2). What we actually estimated was a...

Description: The PNAS 100th Anniversary Special Feature on natural capital and ecosystem services highlights a range of opportunities and challenges to operationalize these concepts to strengthen environmental governance (1). However, the issue’s focus is largely on the role these concepts play in ex ante decision-making, and overlooks their role in informing...

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

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

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

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

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

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

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

Description: In their recent article, Karp et al. (1) address a serious problem inherent in nature conservation: the necessity for prioritization when faced with competing conservation objectives (cf. ref. 2). In principle, the authors (1) provide a very useful approach toward tackling this problem. However, a closer look reveals at least...

Description: Kirchhoff (1) highlights inherent difficulties in organizing the rationales that motivate conservation. The author provides two critiques: first, that our conservation objective typology aggregates conflicting subgoals, and second that the objectives are not mutually exclusive (2). We contend that homogenous and mutually exclusive typologies are neither feasible nor desirable for...

Description: Crustal vertical deformation (CVD) observed by continuous GPS height time-series can be explained largely by surface loading effects recovered from both Gravity Recover and Climate Experiment (GRACE) and General Circulation Models (GCMs) data. We first show that lower degree CVD spatial spectrum due to the Earth's elastic response to a uniform surface loading plays more important roles than that of high-degree case. We then demonstrate that GRACE data with 300–400 km spatial resolution have the ability to detect 99 per cent power of global and regional CVD in spatial spectrum domain using a global frequency–wavenumber spectrum method. We can just use either GRACE or GCMs 36 degree/order (d/o) spherical harmonic coefficients (SHCs) which correspond to 500 km spatial resolution to acquire more than 90 per cent variance of total CVD modeled by up to 180 d/o SHCs at 98 per cent global gridpoints. Globally, CVD modeled by GRACE loading can explain 72 per cent annual amplitude and 69 per cent variance of GPS observed height time-series, which is better than the GCMs results of 64 per cent for annual amplitude and 41 per cent for variance. Using a three cornered hat method, we also show that the noise level of monthly averaged CVD is about 3 mm for both GPS height time-series and GRACE loading result, while that of GCMs result is only 1.3 mm.

Description: Sea cucumber fisheries exemplify resource systems under intense exploitation pressure from lucrative Asian markets. Plagányi et al. (1) model the performance of rotational harvests of sea cucumbers on the Great Barrier Reef (GBR) and advocate it globally. We support their aim to evaluate management models but believe the tenets of...

Description: Plagányi et al. (1) show that a rotational zone strategy (RZS) applied to sea cucumbers in a multispecies fishery on Australia’s Great Barrier Reef significantly reduces the risk of overall and localized species depletion in the fishery. In addition to implementing limits on catch and minimum size, Plagányi et al....

Description: We present a new method to derive 3-D surface deformation from an integration of interferometric synthetic aperture radar (InSAR) images and Global Navigation Satellite System (GNSS) observations based on Akaike's Bayesian Information Criterion (ABIC), considering relationship between deformations of neighbouring locations. This method avoids interpolated errors by excluding the interpolation of GNSS into the same spatial resolution as InSAR images and harnesses the data sets and the prior smooth constraints of surface deformation objectively and simultaneously by using ABIC, which were inherently unresolved in previous studies. In particular, we define surface roughness measuring smoothing degree to evaluate the performance of the prior constraints and deduce the formula of the covariance for the estimation errors to estimate the uncertainty of modelled solution. We validate this method using synthetic tests and the 2008 M w 7.9 Wenchuan earthquake. We find that the optimal weights associated with ABIC minimum are generally at trade-off locations that balance contributions from InSAR, GNSS data sets and the prior constraints. We use this method to evaluate the influence of the interpolated errors from the Ordinary Kriging algorithm on the derivation of surface deformation. Tests show that the interpolated errors may contribute to biasing very large weights imposed on Kriged GNSS data, suggesting that fixing the relative weights is required in this case. We also make a comparison with SISTEM method, indicating that our method allows obtaining better estimations even with sparse GNSS observations. In addition, this method can be generalized to provide a solution for situations where some types of data sets are lacking and can be exploited further to account for data sets such as the integration of displacements along radar lines and offsets along satellite tracks.

Description: While it has been known for some time that offsets in the time-series of Global Navigation Satellite System (GNSS) position estimates degrade station velocity determinations, the magnitude of the effect has not been clear. Using products of the International GNSS Service (IGS), we assess the impact empirically by injecting progressively larger numbers of artificial offsets and solving for a series of long-term secular GNSS frames. Our results show that the stability of the IGS global frame datum is fairly robust, with significant effects at the formal error level only for the R x (and Y-pole) and R z rotational orientations. On the other hand, station velocity estimates are more seriously affected, especially the vertical component. For the typical IGS station, the mean vertical rate uncertainty is already limited to 0.34 mm yr –1 for the current set of position discontinuities. If the number of breaks doubles, which might occur using newer detection schemes, then that uncertainty will worsen by ~40 per cent to 0.48 mm yr –1 . This error source is generally a more important component of realistic velocity uncertainties than any other, including accounting for temporal correlations in the GNSS data. The only way to improve future GNSS velocity estimates is to severely limit manmade displacements at the tracking stations.

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

Description: We welcome the interest Dunkel and Weber (1) show in our work (2). We intended this paper to stimulate other researchers to think about scientific issues in using tools from portfolio theory to help decision makers choose conservation investment portfolios across space that efficiently reduce climate change-related uncertainty in future...

Description: Preservation of biodiversity is a major ecological challenge to present and future generations (1). Success will largely depend on the optimal allocation of limited funding resources to the most relevant conservation projects. In a recent issue of PNAS, Ando and Mallory (2) proposed to tackle the problem with Modern Portfolio...

Description: The ideas of Pearson and Pearson (1) are pertinent to better analysis of historical change, as well as to test how past experiences may relate to current sustainability questions. Important issues would include the limitations of resilience theory, the interplay of transformation and collapse, and the importance of open societal networks for transformability. Research groupings may share ultimate goals, but, by following divergent legacies, use different assumptions and methods to address coupled systems. Successful societal transformation probably does involve centrifugal processes, yet what is logical in contemporary perspective may be unpredictable in the light of good field, archival, or other...

Description: The recent article by Butzer (1) illustrated, through historical analysis, that resilience is not enough: many societies have collapsed irrespective of their resilience capacity. We argue that it might be because of their preoccupation with resilience. What they needed, and what Butzer also writes, is transformability: “…after overcoming initial, ideological dissonance, people can indeed come together to support change” (1). This is truly a message for our times as governments struggle with transforming to low-carbon societies.So, how might we frame future studies that Butzer advocates? Butzer avoids the resilience-vs.-transformation issue by recommending research into information diffusion and socioeconomic integration across...

Description: In the article entitled “Economic and energetic analysis of capturing CO2 from ambient air,” House et al. (1) drew an analogy between air capture and other gas separation processes. It concludes that (i) “unless air capture significantly outperforms these systems, it is likely to require more than 400 kJ of work per mole of CO2” and (ii) “costs of air capture systems will be on the order of $1,000 per tonne of CO2” (1).The underlying logic in this conclusion is clearly circular because the key phrase is “unless” and is flawed in making a connection between energy used and cost....

Description: Caldeira and Myhrvold (1) argue that the temperature change metric proposed in their recent paper (2) would be more useful to policymakers than the cumulative radiative forcing metric used by Alvarez et al. (3). We believe both metrics are useful, although the simplicity, transparency, and relatively low uncertainty of the cumulative radiative forcing metric makes it particularly useful in policy formulation.Emissions of greenhouse gases lead to an increase in their atmospheric concentrations and radiative forcing, which in turn perturbs many aspects of climate including global atmospheric and oceanic temperatures, precipitation, and sea level. The changing climate affects a diverse array...

Description: Alvarez et al. (1) proposed assessing the relative climate benefits of alternative energy technologies for policy purposes by comparing a time-integrated approximation to the radiative forcing produced by each alternative. In contrast, Myhrvold and Caldeira (2) propose comparing the change in global mean temperature that each alternative technology would produce under various schedules of deployment.Myhrvold and Caldeira (2) propose that temperature at some time t after deployment of the system can be approximated by a one-dimensional diffusive column,where T(t, z) is the temperature perturbation to the ocean at depth z at time t (cf. ref. 3). The upper boundary condition...

Description: We strongly disagree with the statement made by Realff and Eisenberger (1) that the approach we used in our analysis of the energy requirements and of “air capture” systems is circular (2). On the contrary, our analysis is linear:i) We calculated the minimum work based on fundamental thermodynamics.ii) We then estimated second-law efficiencies using a large amount of empirical data from real processes.iii) We estimated the energy costs based on market prices.The statement by Realff and Eisenberger (1) that “the notion of minimum work does not apply” is wrong. By definition, all air capture processes start with ambient air and...

Description: According to Ridoutt and Huang (1), “environmental relevance must be taken into consideration if water footprints are to inform wise decision making and policy development.” Indeed, reduction targets regarding water footprints (WFs) within catchments should be formulated on the basis of relative water scarcity per catchment, because local environmental impact of water use is generally larger when scarcity is higher. In many river basins, the blue WF exceeds blue freshwater availability, causing substantial environmental impact (2). However, local environmental impact is only one of a range of factors to be considered when prioritizing options for WF reduction (3). Other relevant...

Description: Schuiling's letter (1) concerning my commentary on geoengineering (2) makes two major claims: (i) decarbonization of the global industrial metabolism is not driven by climate protection but by the exhaustion dynamics of fossil fuels, and (ii) there is an attractive option for artificial CO2 removal from the atmosphere, namely, milling of olivine-rich rocks.However, Schuiling (1) is too pessimistic regarding the first point and too optimistic regarding the second one. To begin with, the aphorism that “the stone age was not terminated by the depletion of stones” (Ahmed Yamani) also applies to the contemporary climate–energy challenge: An incumbent technical culture is...

Description: Schellnhuber (1) proposed some well-known solutions to the climate problem:i) Phasing out of CO2 in the next decadesii) Energy efficiencyiii) Emission reductioniv) Systematic decarbonationv) Efficiency and renewablesThese suggestions are commendable, but their suggested time scheme lacks realism. The emerging economies (China, India, and Brazil) want to develop their economies and raise the standard of living. A prerequisite is access to abundant and cheap energy. They want to realize their objectives by using their large coal reserves.The climate problem can be solved by removing CO2 from the atmosphere. House et al. (2) state that capturing CO2 from the air costs around...

Description: West et al.’s recent paper (1) compared tradeoffs of carbon and crop production in temperate and tropical zones. We welcome the empirical evidence in support of agricultural intensification rather than extensification. We strongly caution against the implicit conclusion that food production might need to be concentrated in the temperate zone, however. First, this has implications for food security. People vulnerable to food insecurity live largely in low-income tropical countries and depend predominantly on local agriculture both for food supplies and to provide the livelihoods that underpin food security (2). Second, as the maps of West et al. (1) show, there...

Description: Vermeulen and Wollenberg (1) caution against interpreting our recent paper (2) as a call to concentrate food production in temperate areas. We did not intend our research to be interpreted as such. As Vermeulen and Wollenberg state, even very low yields can play an extremely important role in providing food security, particularly in low-income tropical countries. We agree that it is important to make the distinction between yields and food security.As noted in our paper, the tradeoff between carbon and crop yields that results from expanding croplands is particularly strong in the tropics, where natural ecosystems generally store a lot...

Description: Both our study (1) and the follow-up described by Frederick et al. (2) indicate that people know relatively little about how much energy is used by different devices and appliances. In our view, the additional data strengthen rather than weaken our original conclusions.It is well known that numerical judgments are subject to anchoring effects, with initial values having substantial influence on final answers (3). In our article, we noted that the compressed range of respondents’ energy estimates “almost certainly resulted from an anchoring bias in which the reference point provided in the task served as an anchor for participants’ estimates,...

Description: The adoption of energy-saving technologies is presumably deterred by underestimates of energy use and by corresponding underestimates of the difference between more- and less-efficient appliances. Thus, it is easy to grasp the potential policy significance of a recent study (1) concluding that Americans underestimate energy use by a factor of 2.8.However, the apparent precision of that statistic belies its arbitrary origins. By manipulating just two experimental details (the provided numeric referent and the units in which judgments were rendered), we show that one can readily reach qualitatively different conclusions.For the study in question (1), respondents were first told that a...

Description: Enhanced weathering of olivine as a means of sequestering carbon is investigated by Köhler et al. (1). Specifically, the study discusses the potential distribution of fine olivine powder, obtained from dunite mines, in the humid tropic regions of the Amazon and Congo River catchments. Olivine (forsterite) dissolution (Eq. 1) implies the sequestration of 4 moles of CO2 for each mole of olivine (2).Köhler et al. (1) suggested that the saturation of silicic acid (H4SiO4) in river runoff would crucially limit olivine dissolution. As an example of the weathering of pulverized ultramafic rock, Wilson et al. (3) present evidence that the...

Description: Schuiling et al. (1) question our conclusion (2) that the annual dissolution rate of olivine is limited by the saturation of waters with silicic acid (H4SiO4), which is one product of the dissolution reaction of olivine. In support of this point they discuss findings of CO2 sequestration in a mine in Yukon, Canada, claiming that a minimum of 1,700 g C m−2 y−1 was sequestered between 1978 and 2004 by silicate weathering and precipitation of (mainly) magnesium carbonates (3). This value is approximately 20 times larger than the 85 g C m−2 y−1 calculated in our study for the Amazon...

Description: Do short-term climatic changes increase civil war risk? This question has been subject to much scientific debate, prompted by a pair of PNAS studies that reached different conclusions (1, 2). Now, another paper (3), authored by colleagues of the first study, seeks to reconcile this debate by claiming that the...

Description: The paper in question by Van Camp and co-authors [MVC] challenges previous work showing that ground gravity data arising from hydrology can provide a consistent signal for the comparison with satellite gravity data. The data sets used are similar to those used previously, that is, the gravity field as measured by the GRACE satellites versus ground-based data from superconducting gravimeters (SGs) over the same continental area, in this case Central Europe. One of the main impediments in this paper is the presentation that is frequently confusing and misleading as to what the data analysis really shows, for example, the irregular treatment of annual components that are first subtracted then reappear in the analysis. More importantly, we disagree on specific points. Two calculations are included in our comment to illustrate where we believe that the processing in [MVC] paper is deficient. The first deals with their erroneous treatment of the global hydrology using a truncated spherical harmonic approach which explains almost a factor 2 error in their computation of the loading. The second shows the effect of making the wrong assumption in the GRACE/hydrology/surface gravity comparison by inverting the whole of the hydrology loading for underground stations. We also challenge their claims that empirical orthogonal function techniques cannot be done in the presence of periodic components, and that SG data cannot be corrected for comparisons with GRACE data. The main conclusion of their paper, that there is little coherence between ground gravity stations and this invalidates GRACE comparisons, is therefore questionable. There is nothing in [MVC] that contradicts any of the previous papers that have shown clearly a strong relation between seasonal signals obtained from both ground gravity and GRACE satellite data.

Description: The influence of changes in surface ice-mass redistribution and associated viscoelastic response of the Earth, known as glacial isostatic adjustment (GIA), on the Earth's rotational dynamics has long been known. Equally important is the effect of the changes in the rotational dynamics on the viscoelastic deformation of the Earth. This signal, known as the rotational feedback, or more precisely, the rotational feedback on the sea level equation, has been mathematically described by the sea level equation extended for the term that is proportional to perturbation in the centrifugal potential and the second-degree tidal Love number. The perturbation in the centrifugal force due to changes in the Earth's rotational dynamics enters not only into the sea level equation, but also into the conservation law of linear momentum such that the internal viscoelastic force, the perturbation in the gravitational force and the perturbation in the centrifugal force are in balance. Adding the centrifugal-force perturbation to the linear-momentum balance creates an additional rotational feedback on the viscoelastic deformations of the Earth. We term this feedback mechanism, which is studied in this paper, as the rotational feedback on the linear-momentum balance. We extend both the time-domain method for modelling the GIA response of laterally heterogeneous earth models developed by Martinec and the traditional Laplace-domain method for modelling the GIA-induced rotational response to surface loading by considering the rotational feedback on linear-momentum balance. The correctness of the mathematical extensions of the methods is validated numerically by comparing the polar-motion response to the GIA process and the rotationally induced degree 2 and order 1 spherical harmonic component of the surface vertical displacement and gravity field. We present the difference between the case where the rotational feedback on linear-momentum balance is considered against that where it is not. Numerical simulations show that the resulting difference in radial displacement and sea level change between these situations since the Last Glacial Maximum reaches values of ±25 and ±1.8 m, respectively. Furthermore, the surface deformation pattern is modified by up to 10 per cent in areas of former or ongoing glaciation, but by up to 50 per cent at the bottom of the southern Indian ocean. This also results in the movement of coastlines during the last deglaciation to differ between the two cases due to the difference in the ocean loading, which is seen for instance in the area around Hudson Bay, Canada and along the Chinese, Australian or Argentinian coastlines.

Description: During megathrust earthquakes, great ruptures are accompanied by large scale mass redistribution inside the solid Earth and by ocean mass redistribution due to bathymetry changes. These large scale mass displacements can be detected using the monthly gravity maps of the GRACE satellite mission. In recent years it has become increasingly common to use the long wavelength changes in the Earth's gravity field observed by GRACE to infer seismic source properties for large megathrust earthquakes. An important advantage of space gravimetry is that it is independent from the availability of land for its measurements. This is relevant for observation of megathrust earthquakes, which occur mostly offshore, such as the $M_{\text{w}} \sim 9$ 2004 Sumatra–Andaman, 2010 Maule (Chile) and 2011 Tohoku-Oki (Japan) events. In Broerse et al. , we examined the effect of the presence of an ocean above the rupture on long wavelength gravity changes and showed it to be of the first order. Here we revisit the implementation of an ocean layer through the sea level equation and compare the results with approximated methods that have been used in the literature. One of the simplifications usually lies in the assumption of a globally uniform ocean layer. We show that especially in the case of the 2010 Maule earthquake, due to the closeness of the South American continent, the uniform ocean assumption is not valid and causes errors up to 57 per cent for modelled peak geoid height changes (expressed at a spherical harmonic truncation degree of 40). In addition, we show that when a large amount of slip occurs close to the trench, horizontal motions of the ocean floor play a mayor role in the ocean contribution to gravity changes. Using a slip model of the 2011 Tohoku-Oki earthquake that places the majority of slip close to the surface, the peak value in geoid height change increases by 50 per cent due to horizontal ocean floor motion. Furthermore, we test the influence of the maximum spherical harmonic degree at which the sea level equation is performed for sea level changes occurring along coastlines, which shows to be important for relative sea level changes occurring along the shore. Finally, we demonstrate that ocean floor loading, self-gravitation of water and conservation of water mass are of second order importance for coseismic gravity changes. When GRACE observations are used to determine earthquake parameters such as seismic moment or source depth, the uniform ocean layer method introduces large biases, depending on the location of the rupture with respect to the continent. The same holds for interpreting shallow slip when horizontal motions are not properly accounted for in the ocean contribution. In both cases the depth at which slip occurs will be underestimated.

Description: Long-term volcanic subsidence provides insight into intereruptive processes, which comprise the longest portion of the eruptive cycle. Ground-based geodetic surveys of Medicine Lake Volcano (MLV), northern CA, document subsidence at rates of ~–10 mm yr –1 between 1954 and 2004. The long observation period plus the duration and stable magnitude of this signal presents an ideal opportunity to study long-term volcanic deformation, but this first requires accurate knowledge of the geometry and magnitude of the source. Best-fitting analytical source models to past levelling and GPS data sets show conflicting source parameters—primarily the model depth. To overcome this, we combine multiple tracks of InSAR data, each with a different look angle, to improve upon the spatial resolution of ground-based measurements. We compare the results from InSAR to those of past geodetic studies, extending the geodetic record to 2011 and demonstrating that subsidence at MLV continues at ~–10 mm yr –1 . Using geophysical inversions, we obtain the best-fitting analytical source model—a sill located at 9–10 km depth beneath the caldera. This model geometry is similar to those of past studies, providing a good fit to the high spatial density of InSAR measurements, while accounting for the high ratio of vertical to horizontal deformation derived from InSAR and recorded by existing levelling and GPS data sets. We discuss possible causes of subsidence and show that this model supports the hypothesis that deformation at MLV is driven by tectonic extension, gravitational loading, plus a component of volume loss at depth, most likely due to cooling and crystallization within the intrusive complex that underlies the edifice. Past InSAR surveys at MLV, and throughout the Cascades, are of variable success due to dense vegetation, snow cover and atmospheric artefacts. In this study, we demonstrate how InSAR may be successfully used in this setting by applying a suite of multitemporal analysis methods that account for atmospheric and orbital noise sources. These methods include: a stacking strategy based upon the noise characteristics of each data set; pixelwise rate-map formation (-RATE) and persistent scatterer InSAR (StaMPS).

Description: In the literature, the inverted coseismic slip models from seismological and geodetic data for the 2011 Tohoku-Oki earthquake portray significant discrepancies, in particular regarding the intensity and the distribution of the rupture near the trench. For a megathrust earthquake, it is difficult to discern the slip along the shallow part of the fault from the geodetic data, which are often acquired on land. In this paper, we discuss the uncertainties in the slip distribution inversion using the geodetic data for the 2011 Tohoku earthquake and the Fully Bayesian Inversion method. These uncertainties are due to the prior information regarding the boundary conditions at the edges of the fault, the dip subduction angle and the smoothing operator. Using continuous GPS data from the Japan Island, the results for the rigid and free boundary conditions show that they produce remarkably different slip distributions at shallow depths, with the latter producing a large slip exceeding 30 m near the surface. These results indicate that the smoothing operator (gradient or Laplacian schemes) does not severely affect the slip pattern. To better invert the coseismic slip, we then introduce the ocean bottom GPS (OB-GPS) data, which improve the resolution of the shallow part of the fault. We obtain a near-trench slip greater than 40 m that reaches the Earth's surface, regardless of which boundary condition is used. Additionally, we show that using a mean dip angle for the fault as derived from subduction models is adequate if the goal is to invert for the general features of the slip pattern of this megathrust event.

Description: In general, observations are normally considered to refer to an epoch in time, however, observations take time. During this time span temporal variations of the observable alias the measurement. Similar phenomenon can be defined in the space domain as well: data treated to refer to a geographical location often contains integrated information of the surroundings. In each case the appropriate signal content can partially be recovered by desmoothing the averaged data. The present study delivers the theoretical foundation of a desmoothing method, and suggests its use on different applications in geodesy. The theoretical formulation of the desmoothing has been derived for 1-D and 2-D signals, the latter is interpreted on a plain and also on a sphere. The presented case studies are less elaborated, but intended to demonstrate the need and usefulness of the desmoothing tool.

Description: We have recently developed a method that allows the quantification of spare capacity in urban taxi systems through trip sharing (1), hence making it more efficient and less resource intensive—all other things being equal—in particular fares, which can be modified by public policy. In their comment on our study, Lopez...

Description: Extracting geophysical signals from Global Positioning System (GPS) coordinate time-series is a well-established practice that has led to great insights into how the Earth deforms. Often small discontinuities are found in such time-series and are traceable to either broad-scale deformation (i.e. earthquakes) or discontinuities due to equipment changes and/or failures. Estimating these offsets accurately enables the identification of coseismic deformation estimates in the former case, and the removal of unwanted signals in the latter case which then allows tectonic rates to be estimated more accurately. We develop a method to estimate accurately discontinuities in time series of GPS positions at specified epochs, based on a so-called ‘offset series’. The offset series are obtained by varying the amount of GPS data before and after an event while estimating the offset. Two methods, a mean and a weighted mean method, are then investigated to produce the estimated discontinuity from the offset series. The mean method estimates coseismic offsets without making assumptions about geophysical processes that may be present in the data (i.e. tectonic rate, seasonal variations), whereas the weighted mean method includes estimating coseismic offsets with a model of these processes. We investigate which approach is the most appropriate given certain lengths of available data and noise within the time-series themselves. For the Sumatra–Andaman event, with 4.5 yr of pre-event data, we show that between 2 and 3 yr of post-event data are required to produce accurate offset estimates with the weighted mean method. With less data, the mean method should be used, but the uncertainties of the estimated discontinuity are larger.

Description: Complications arise in the interpretation of gravity fields because of interference from systematic degradations, such as boundary blurring and distortion. The major sources of these degradations are the various systematic errors that inevitably occur during gravity field data acquisition, discretization and geophysical forward modelling. To address this problem, we evaluate deconvolution method that aim to detect the clear horizontal boundaries of anomalous sources by the suppression of systematic errors. A convolution-based multilayer projection model, based on the classical 3-D gravity field forward model, is innovatively derived to model the systematic error degradation. Our deconvolution algorithm is specifically designed based on this multilayer projection model, in which three types of systematic error are defined. The degradations of the different systematic errors are considered in the deconvolution algorithm. As the primary source of degradation, the convolution-based systematic error is the main object of the multilayer projection model. Both the random systematic error and the projection systematic error are shown to form an integral part of the multilayer projection model, and the mixed norm regularization method and the primal-dual optimization method are therefore employed to control these errors and stabilize the deconvolution solution. We herein analyse the parameter identification and convergence of the proposed algorithms, and synthetic and field data sets are both used to illustrate their effectiveness. Additional synthetic examples are specifically designed to analyse the effects of the projection systematic error, which is caused by the uncertainty associated with the estimation of the impulse response function.