Kalman filter based estimation of lithospheric viscosity and fault slip from postseismic deformation: application to the 2010 El Mayor-Cucapah earthquake

Geodetic measurements of postseismic deformation are commonly attributed to aseismic slip after an earthquake and/or viscous relaxation of coseismic stresses within the lithosphere. Differentiating between these two mechanisms is crucial for a complete understanding of lithospheric rheology, and may also have implication for model-based seismic hazard assessments. Most attempts to model postseismic deformation with both afterslip and viscous relaxation are hindered by a computationally expensive forward problem, requiring a reduction in the number of model parameters that can be feasibly explored. Consequently, idealized representations of lithospheric viscosity are often assumed, which may be too simplistic to robustly describe the viscosity structure. We present a Kalman filter based method to directly invert postseismic deformation for both fault slip throughout the postseismic period and an arbitrarily discretized lithospheric viscosity structure. Our method is made computationally tractable by approximating viscoelastic postseismic deformation with an easily evaluated truncated series expansion. We apply our method to postseismic deformation following the 2010 El Mayor-Cucapah earthquake, which is ongoing five years later. Even when we account for viscoelastic relaxation, we find that a large amount of afterslip, comparable in magnitude to the mainshock, is needed to describe most of the postseismic data.