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1. Kinematic Representations of Viscoelastic Postseismic Deformation

   https://doi.org/10.1029/2025EA004460  

   Loveless, John P; Meade, Brendan J (August 2025, Earth and Space Science)

   Abstract Following large earthquakes, viscoelastic stress relaxation may contribute to postseismic deformation observed at Earth's surface. Mechanical representations of viscoelastic deformation require a constitutive relationship for the lower crust/upper mantle material where stresses are diffused and, for non‐linear rheologies, knowledge of absolute stress level. Here, we describe a kinematic approach to representing geodetically observed postseismic motions that does not require an assumed viscoelastic rheology. The core idea is to use observed surface motions to constrain time‐dependent displacement boundary conditions applied at the base of the elastic upper crust by viscoelastic motions in the lower crust/upper mantle, approximating these displacements as slip on a set of dislocation elements. Using three‐dimensional forward models of viscoelastically modulated postseismic deformation in a thrust fault setting, we show how this approach can accurately represent surface motions and recover predicted displacements at the base of the elastic layer. Applied to the 1999 Chi‐Chi (Taiwan) earthquake, this kinematic approach can reproduce geodetically observed displacements and estimates of the partitioning between correlated postseismic deformation mechanisms. Specifically, we simultaneously estimate afterslip on the earthquake source fault that is similar to previous estimates, along with slip on dislocations at the base of the elastic layer that mimic predictions from viscous stress dissipation models in which viscosity is inferred to vary three‐dimensionally. A use case for the dislocation approach to modeling viscoelastic deformation is the estimation of spatiotemporally variable fault slip processes, including across sequential interseismic phases of the earthquake cycle, without assuming a lower crust/upper mantle rheology. 

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2. An adjoint-based optimization method for jointly inverting heterogeneous material properties and fault slip from earthquake surface deformation data

   https://doi.org/10.1093/gji/ggad442  

   Puel, S.; Becker, T. W.; Villa, U.; Ghattas, O.; Liu, D. (November 2023, Geophysical Journal International)

   SUMMARY Analysis of tectonic and earthquake-cycle associated deformation of the crust can provide valuable insights into the underlying deformation processes including fault slip. How those processes are expressed at the surface depends on the lateral and depth variations of rock properties. The effect of such variations is often tested by forward models based on a priori geological or geophysical information. Here, we first develop a novel technique based on an open-source finite-element computational framework to invert geodetic constraints directly for heterogeneous media properties. We focus on the elastic, coseismic problem and seek to constrain variations in shear modulus and Poisson’s ratio, proxies for the effects of lithology and/or temperature and porous flow, respectively. The corresponding nonlinear inversion is implemented using adjoint-based optimization that efficiently reduces the cost function that includes the misfit between the calculated and observed displacements and a penalty term. We then extend our theoretical and numerical framework to simultaneously infer both heterogeneous Earth’s structure and fault slip from surface deformation. Based on a range of 2-D synthetic cases, we find that both model parameters can be satisfactorily estimated for the megathrust setting-inspired test problems considered. Within limits, this is the case even in the presence of noise and if the fault geometry is not perfectly known. Our method lays the foundation for a future reassessment of the information contained in increasingly data-rich settings, for example, geodetic GNSS constraints for large earthquakes such as the 2011 Tohoku-oki M9 event, or distributed deformation along plate boundaries as constrained from InSAR. 

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3. A Dense Block Model Representing Western Continental United States Deformation for the 2023 Update to the National Seismic Hazard Model

   https://doi.org/10.1785/0220220141  

   Evans, Eileen L. (August 2022, Seismological Research Letters)

   Abstract Seismic hazard assessment, such as the U.S. Geological Survey (USGS) National Seismic Hazard Model (NSHM), relies on estimates of fault slip rate based on geology and/or geodetic observations such as the Global Navigation Satellite System (GNSS), including the Global Positioning System. Geodetic fault slip rates may be estimated within a 3D spherical block model, in which the crust is divided into microplates bounded by mapped faults; fault slip rates are determined by the relative rotations of adjacent microplates. Uncertainty in selecting appropriate block-bounding faults and in forming closed microplates has limited the interpretability of block models for seismic hazard modeling. By introducing an automated block closure algorithm and regularizing the resulting densely spaced block model with total variation regularization, I develop the densest and most complete block model of the western continental United States to date. The model includes 853 blocks bounded by 1017 geologically identified fault sections from the USGS NSHM Fault Sections database. Microplate rotations and fault slip rates are constrained by 4979 GNSS velocities and 1243 geologic slip rates. I identify a regularized solution that fits the GNSS velocity field with a root mean square misfit of 1.9 mm/yr and reproduces 57% of geologic slip rates within reported geologic uncertainty and model sensitivity, consistent with other geodetic-based models in this Focus Section. This block model includes slip on faults that are not included in the USGS NSHM Fault sections database (but are required to form closed blocks) for an estimate of “off-fault” deformation of 3.62×1019  N·m/yr, 56% of the total calculated moment accumulation rate in the model. 

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4. Detection of dislocations in a 2D anisotropic elastic medium

   Aspri, Andrea; Beretta, Elena; de Hoop, Maarten; Mazzucato, Anna L. (February 2021, Rendiconti di matematica e delle sue applicazioni)

   Mascia, Corrado; Terracina, Andrea; Tesei, Alberto (Ed.)

   We study a model of dislocations in two-dimensional elastic media. In this model, the displacement satisfies the system of linear elasticity with mixed displacement-traction homogeneous boundary conditions in the complement of an open curve in a bounded planar domain, and has a specified jump, the slip, across the curve, while the traction is continuous there. The stiffness tensor is allowed to be anisotropic and inhomogeneous. We prove well-posedness of the direct problem in a variational setting, assuming the coefficients are Lipschitz continuous. Using unique continuation arguments, we then establish uniqueness in the inverse problem of determining the dislocation curve and the slip from a single measurement of the displacement on an open patch of the traction-free part of the boundary. Uniqueness holds when the elasticity operators admits a suitable decomposition and the curve satisfies additional geometric assumptions. This work complements the results in Arch. Ration. Mech. Anal., 236(1):71-111, (2020), and in Preprint arXiv:2004.00321, which concern three-dimensional isotropic elastic media. 

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5. Structural Controls Over the 2019 Ridgecrest Earthquake Sequence Investigated by High‐Fidelity Elastic Models of 3D Velocity Structures

   https://doi.org/10.1029/2020JB021124  

   Tung, Sui; Shirzaei, Manoochehr; Ojha, Chandrakanta; Pepe, Antonio; Liu, Zhen (July 2021, Journal of Geophysical Research: Solid Earth)

   Abstract We develop finite element models of the coseismic displacement field accounting for the 3D elastic structures surrounding the epicentral area of the 2019 Ridgecrest earthquake sequence containing two major events of M_w7.1 and M_w6.4. The coseismic slip distribution is inferred from the surface displacement field recorded by interferometric synthetic aperture radar. The rupture dip geometry is further optimized using a novel nonlinear‐crossover‐linear inversion approach. It is found that accounting for elastic heterogeneity and fault along‐strike curvilinearity improves the fit to the observed displacement field and yields a more accurate estimate of geodetic moment and Coulomb stress changes. We observe spatial correlations among the locations of aftershocks and patches of high slip, and rock anomalous elastic properties, suggesting that the shallow crust's elastic structures possibly controlled the Ridgecrest earthquake sequence. Most of the coseismic slip with a peak slip of 7.4 m at 3.6 km depth occurred above a zone of reducedS‐wave velocity and significant post‐M_w7.1 afterslip. This implies that viscous materials or fluid presence might have contributed to the low rupture velocity of the mainshock. Moreover, the zone of high slip on the northwest‐trending fault segment is laterally bounded by two aftershock clusters, whose location is characterized by intermediate rock rigidity. Notably, some minor orthogonal faults consistently end above a subsurface rigid body. Overall, these observations of structural controls improve our understandings of the seismogenesis within incipient fault systems. 

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