The signature of depth‐dependent viscosity structure in post‐seismic deformation

SUMMARY Geodetic observations of post‐seismic ground motion reflect the integrated effects of several relaxation mechanisms. To evaluate the viscous relaxation component accurately the crustal viscosity structure beneath a region must be estimated. In this study, using a 3‐D finite element model, we describe the viscoelastic relaxation that follows an instantaneous strike‐slip faulting event in a crustal layer whose viscosity decreases exponentially with depth. At any surface observation point the depth‐dependent viscosity (DDV) model displacement history closely fits the history predicted for a uniform viscosity (UNV) model. The difference can be minimized to obtain the UNV viscosity ( η u ) that best fits the DDV model displacement at that location. The differences in displacement histories between DDV and best‐fit UNV models are minor but depend on distance from fault, the viscosity gradient and the fault configuration. In the near field, the DDV model prediction can be well approximated by the UNV model, regardless of the viscosity gradient and fault configuration. On the other hand, in the far field, small differences between DDV model and best‐fit UNV model become apparent: the displacements are controlled by greater viscosities in later phases, and the differences are greater for DDV models with greater viscosity gradient. The more important result we obtain is that: apparent viscosity η u decreases with distance from the fault, and its rate of decrease is directly diagnostic of the vertical viscosity gradient. This result points to a practical method of analysing post‐seismic ground‐displacement data for the variation of viscosity in the ductile crust; the apparent crustal viscosity should be determined at a series of points at increasing distance from the fault. The variation of apparent viscosity with distance can then be used to directly infer the vertical gradient of viscosity in the crust.