Kinematic Representations of Linear and Power-Law Viscoelastic Deformation Through the Earthquake Cycle

Viscoelastic deformation below the Earth's elastic crust is modulated by stresses generated by both plate tectonic and earthquake cycle processes. Rapid near-fault deformation following large earthquakes has been interpreted as the signature of viscoelastic stress diffusion in the upper mantle and earthquake cycle models have been developed that integrated this effect throughout the duration of the earthquake cycle. Here we develop a surrogate method to approximate the upper crustal kinematics associated with time-dependent viscoelastic deformation that does not require knowledge of nor provide constraints on subcrustal rheology. To do this we show how the effects of deformation in the viscoelastic upper mantle can be emulated by introducing a set of effective dislocations at crust-mantle interface. The approach is shown to approximate both linear and power-law viscoelastic rheologies and offers a way to accurately represent viscoelastic kinematics even in the case where upper mantle rheology is poorly constrained.