Numerous producing and actively subsiding gas fields worldwide have salt top seals, but surface subsidence records exist for very few. This paper summarizes both reservoir pore pressure data and subsidence measurements obtained for a salt-sealed gas field in northern Europe. The data indicate a time dependence in subsidence evolution, with subsidence rates remaining relatively constant, while pore pressure depletion rates decrease. The creep of the thick, overlying salt may play a part in causing this timedependence. The present work assesses salt creep flow’s role in controlling the evolution of subsidence through finite element models. Salt creep effects are investigated in isolation, and independently of other factors, incorporating uncertainty in salt flow mechanisms and rheology. Comparing model results with field subsidence measurements suggests that salt flow can account for part of the timedependent subsidence observed but cannot fully explain the field data, a finding that is also potentially important for other salt-sealed reservoirs around the world. Another important conclusion of the current study is that additional mechanisms that can lead to timedependent subsidence must be active in the field studied.

Earthquakes involve mass redistribution within the solid Earth and the ocean, and as a result, perturb the Earth's gravitational field. For most of the shallow (<60 km) earthquakes with M_w > 8.0, the GRACE satellite gravity measurements suggest considerable volumetric disturbance of rocks. At a spatial scale of hundreds of km, the effect of volumetric change exceeds gravity change by vertical deformation; for example, negative gravity anomalies associated with volumetric expansion are characteristic patterns after shallow thrust events. In this study, however, we report contrasting observations of gravity change from two intermediate-depth (100–150 km) earthquakes of 2016 & 2017 Mw 8.0 (two combined) Papua New Guinea thrust faulting events and 2019 Mw 8.0 Peru normal faulting and highlight the importance of compressibility in earthquake deformation. The combined 2016/17 thrust events resulted in a positive gravity anomaly of 5–6 microGal around the epicenter, while the 2019 normal faulting produced a negative gravity anomaly of 3–4 microGal. Our modeling found that these gravity changes are manifestation of vertical deformation with limited volumetric change, distinct from gravity changes after the shallow earthquakes. The stronger resistance of rocks to volume change at intermediate-depth results in largely incompressible deformation and thus in a gravity change dominated by vertical deformation. In addition, malleable rocks under high pressure and temperature at depth facilitated substantial afterslip and/or fast viscoelastic relaxation causing additional vertical deformation and gravity change equivalent to the coseismic change. For the Papua New Guinea events, this means that postseismic relaxation enhanced coseismic uplift and relative sea level decrease.

In this study, we examine the effect of transient mantle creep on the prediction of glacial isostatic adjustment (GIA) signals. Specifically, we compare predictions of relative sea level (RSL) change from GIA from a set of Earth models in which transient creep parameters are varied in a simple Burgers model to a reference case with a Maxwell viscoelastic rheology. The model predictions are evaluated in two ways: first, relative to each other to quantify the effect of parameter variation, and second, for their ability to reproduce well-constrained sea level records from selected locations. Both the resolution and geographic location of the RSL observations determine whether the data can distinguish between model cases. Model predictions are most sensitive to the inclusion of transient mantle deformation in regions that are near-field and peripheral relative to former ice sheets. This sensitivity appears particularly true along the North American west coast in the region of the former Cordilleran Ice Sheet, which experienced rapid sea-level fall following deglaciation between 14 and 12 kyr BP. Relative to the Maxwell case, Burgers models better reproduce this rapid phase of regional postglacial sea-level fall. As well, computed goodness-of-fit values in this region show a clear preference for models where transient deformation is present in the whole or lower mantle, and for models where the rigidity of the Kelvin element is weakened relative to the rigidity of the Maxwell element. In contrast, model predictions of relative sea-level change in the far-field show weak sensitivity to the inclusion of transient deformation.

A devastating tsunami struck Palu Bay in the wake of the 28 September 2018 M_w = 7.5 Palu earthquake (Sulawesi, Indonesia). With a predominantly strike-slip mechanism, the question remains whether this unexpected tsunami was generated by the earthquake itself, or rather by earthquake-induced landslides. In this study we examine the tsunami potential of the co-seismic deformation. To this end, we present a novel geodetic data set of Global Positioning System and multiple Synthetic Aperture Radar-derived displacement fields to estimate a 3D co-seismic surface deformation field. The data reveal a number of fault bends, conforming to our interpretation of the tectonic setting as a transtensional basin. Using a Bayesian framework, we provide robust finite fault solutions of the co-seismic slip distribution, incorporating several scenarios of tectonically feasible fault orientations below the bay. These finite fault scenarios involve large co-seismic uplift (>2 m) below the bay due to thrusting on a restraining fault bend that connects the offshore continuation of two parallel onshore fault segments. With the co-seismic displacement estimates as input we simulate a number of tsunami cases. For most locations for which video-derived tsunami waveforms are available our models provide a qualitative fit to leading wave arrival times and polarity. The modeled tsunamis explain most of the observed runup. We conclude that co-seismic deformation was the main driver behind the tsunami that followed the Palu earthquake. Our unique geodetic data set constrains vertical motions of the sea floor, and sheds new light on the tsunamigenesis of strike-slip faults in transtensional basins.

Satellite gravimetry and altimetry measurements record gravity and elevation changes, respectively, which are useful for determining mass and volume change of the Antarctic Ice Sheet. Common methods employ products from regional climate modeling and firn modeling to aid interpretation and to link volume changes to mass changes. Estimating deterministic parameters over defined time periods is a conventional way to evaluate those changes. To overcome limitations of deterministic analyses with respect to time-variable signals, we have developed a state-space model framework. Therein, we jointly evaluate four mass and volume data sets by coupling of temporal signal variations. We identify long-term signals of ice drainage basins that are observed by the satellite gravimetry mission GRACE and several satellite altimetry missions from April 2002 until August 2016. The degree to which we can separate long-term and short-term variations strongly depends on the similarity of the mass and volume change time series. For the drainage system of the Pine Island Glacier (West Antarctica), our results show noticeable variations of the long-term trend with an acceleration of the contribution of ice dynamics to the mass balance from −11 ± 8 to −58 ± 8 Gt a⁻¹. Our results in Dronning Maud Land (East Antarctica) show a positive long-term contribution to the mass balance at almost a constant rate. The presented approach can fit time-variable changes without artificial selection of periods of interest. Furthermore, because we only enforce common long-term time variations between mass and volume data, differences in mean trend rates help to uncover model discrepancies.

Particle image velocimetry (PIV), a method based on image cross-correlation, is widely used for obtaining velocity fields from time-series of images of deforming objects. Rather than instantaneous velocities, we are interested in reconstructing cumulative deformation, and use PIV-derived incremental displacements for this purpose. Our focus is on analogue models of tectonic processes, which can accumulate large deformation. Importantly, PIV provides incremental displacements during analogue model evolution in a spatial reference (Eulerian) frame, without the need for explicit markers in a model. We integrate the displacements in a material reference (Lagrangian) frame, such that displacements can be integrated to track the spatial accumulative deformation field as a function of time. To describe cumulative, finite deformation, various strain tensors have been developed, and we discuss what strain measure best describes large shape changes, as standard infinitesimal strain tensors no longer apply for large deformation. PIV or comparable techniques have become a common method to determine strain in analogue models. However, the qualitative interpretation of observed strain has remained problematic for complex settings. Hence, PIV-derived displacements have not been fully exploited before, as methods to qualitatively characterize cumulative, large strain have been lacking. Notably, in tectonic settings, different types of deformation-extension, shortening, strike-slip-can be superimposed. We demonstrate that when shape changes are described in terms of Hencky strains, a logarithmic strain measure, finite deformation can be qualitatively described based on the relative magnitude of the two principal Hencky strains. Thereby, our method introduces a physically meaningful classification of large 2-D strains. We show that our strain type classification method allows for accurate mapping of tectonic structures in analogue models of lithospheric deformation, and complements visual inspection of fault geometries. Our method can easily discern complex strike-slip shear zones, thrust faults and extensional structures and its evolution in time. Our newly developed software to compute deformation is freely available and can be used to post-process incremental displacements from PIV or similar autocorrelation methods.

Stress-dependent nonlinear upper mantle rheology has a firm base in rock mechanical tests, where this nonlinearity results from dislocation creep of minerals. In the last few decades there has been some attention to nonlinear, power-law, materials for application in scaled analogue experiments for tectonic processes. However, studies describing the rheology of analogue materials with the same nonlinear dependency on stress as observed for lithospheric mantle materials at relevant stress levels, are still lacking. In this study we have developed and rheologically tested materials based on combinations of silicone polymers and plasticine, with the aim of obtaining a material that can serve as a laboratory analogue to the power-law rheology of olivine aggregates at lithospheric mantle conditions. From our steady-state creep tests we find that it is possible to obtain such a power-law material, with effective viscosities over relevant model stress ranges [5–4000 Pa] that allow for nonlinear deformation at laboratory time scales. We apply the developed material to a process where localized deformation of the lithosphere can be expected: slab break-off. We study this process using analogue models, where we apply the new nonlinear material to the lithospheric mantle domains, while we use Newtonian glucose to represent the low viscous asthenosphere. Now that we properly manage power-law behavior in our analogue lithosphere materials, we are able to model localized lithospheric tearing.

In regions undergoing glacial isostatic adjustment present-day horizontal surface motion is observed to point mostly, but not always, away from the former ice load. To interpret these observations, we investigate the direction of horizontal velocities using glacial isostatic adjustment models. The direction is controlled by the opposing actions of inward mantle flow and outward lithosphere motion. In contrast with the prevailing idea that glacial isostatic adjustment-induced horizontal velocities point outward, we show that velocities can be either outward or inward. Immediately after deglaciation velocities point inward but change direction to outward after a time that is controlled by mantle viscosity. Present-day horizontal velocities point outward for a uniform mantle viscosity below 10²⁰ Pa s and inward for above 10²² Pa s, with a combination of outward and inward in between. Our results help to interpret GPS-observed horizontal velocities in areas with varying mantle viscosity.

One of the primary observational data sets of sea level is represented by the tide gauge record. We propose a new method to estimate variability on decadal time scales from tide gauge data by using a state space formulation, which couples the direct observations to a predefined state space model by using a Kalman filter. The model consists of a time-varying trend and seasonal cycle, and variability induced by several physical processes, such as wind, atmospheric pressure changes and teleconnection patterns. This model has two advantages over the classical least-squares method that uses regression to explain variations due to known processes: a seasonal cycle with time-varying phase and amplitude can be estimated, and the trend is allowed to vary over time. This time-varying trend consists of a secular trend and low-frequency variability that is not explained by any other term in the model. As a test case, we have used tide gauge data from stations around the North Sea over the period 1980-2013. We compare a model that only estimates a trend with two models that also remove intra-annual variability: one by means of time series of wind stress and sea level pressure, and one by using a two-dimensional hydrodynamic model. The last two models explain a large part of the variability, which significantly improves the accuracy of the estimated time-varying trend. The best results are obtained with the hydrodynamic model. We find a consistent low-frequency sea level signal in the North Sea, which can be linked to a steric signal over the northeastern part of the Atlantic.

The Gravity Recovery and Climate Experiment (GRACE) mission (launched 2002) and the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) mission (March 2009 to November 2013) collected spaceborne gravity data for the preseismic and postseismic periods of the 2011 Tohoku-Oki earthquake. In addition, the dense Japan GeoNet Global Navigation Satellite Systems (GNSS) network measured with approximately 1050 stations the coseismic and postseismic surface displacements. We use a novel combination of GNSS, GRACE, and GOCE observations for a distributed fault slip model addressing the issues with gravimetric and geometric change over consistent time windows. Our model integrates the coseismic and postseismic effects as we include GOCE observations averaged over a 2 year interval, but their inclusion reveals the gravity change with unprecedented spatial accuracy. The gravity gradient grid, evaluated at GOCE orbit height of 265 km, has an estimated formal error of 0.20 mE which provides sensitivity to the mainly coseismic and integrated postseismic-induced gravity gradient signal of -1.03 mE. We show that an increased resolution of the gravity change provides valuable information, with GOCE gravity gradient observations sensitive to a more focused slip distribution in contrast to the filtered GRACE equivalent. The 2 year averaging window of the observations makes it important to incorporate estimates of the variance/covariance of unmodeled processes in the inversion. The GNSS and GRACE/GOCE combined model shows a slip pattern with 20 m peak slip at the trench. The total gravity change (≈200 μGal) and the spatial mapping accuracy would have been considerably lower by omitting the GOCE-derived fine-scale gravity field information.

The 2011 Tohoku-Oki earthquake with 9.0 Mw led to an enormous mass redistribution originated from large deformation due to faulting and had a massive impact on the coastal area of eastern Japan. While the satellite gravity mission GRACE (Gravity Recovery and Climate Experiment) can detect the gravitational change caused by this tremendous event, slip distributions are usually derived from GPS, seismic and (in the more particular case) tsunami data. We evaluate the differences between measured and modeled coseismic gravity changes for three fault slip models derived from either GPS and tsunami data, GRACE data, or a combination of all three data types. The data are weighted according to their measurement accuracy in a Bayesian joint inversion approach. We perform a long term average of GRACE data, which increases sensitivity and reduces artefacts, and find that the postseismic gravity change leaks into the derived mean gravity field. We try to reduce this problem by averaging only 6 months of postseismic GRACE data, where the postseismic gravity signal, which superimposes onto the coseismic signal of ≈ 6μGal (for a geometric based model) peaks approximately 3 months after earthquake occurrence. Consequently fault slip models merely derived from GPS (10 days avg.) and tsunami data (<5h time span) show deviations of ≈ 2 μGal to a GRACE 6 monthly averaged combined solution which indicates the difference accumulated from the geometric and gravimetric modeling and the postseismic gravity signal in the GRACE data.