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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. 

Abstract Geologic and geodetic observations provide constraints on tectonic and earthquake cycle kinematics. Block models offer one approach to integrating the effects of plate rotations, elastic strain accumulation, applied basal displacements, internal block strain, and idealized pressure sources. Here, we describe the construction of block models where spatially variable slip rates are parameterized by distance‐weighted eigenmodes operating over meshes of triangular dislocation elements. This dimensionally reduced model is recast as a quadratic programming problem with upper and lower bounds on both geologic fault slip rates and spatially variable slip deficit rates. We propose iterating over successive quadratic programming estimates with evolving slip rate bounds to find a solution consistent with specified coupling at all points on geometrically complex fault surfaces.