Direct Inversion of Postseismic Deformation for 3D Lithosphere Viscosity Structure and Fault Slip

Abstract:

Geodetic measurements of postseismic deformation are rich signals with which the mechanical behavior of the lithosphere can be inferred, predominantly localized fault creep and distributed viscoelastic deformation. Numerous studies have used postseismic deformation to estimate the lithosphere’s rheology but they are hindered by potentially computationally intensive forward problems with nonlinear relationships between surface deformation and the rheologic properties. As a result, most studies oversimplify the rheologic structure of the lithosphere and rely on forward estimation methods, such as grid or monte carlo searches. We present a novel method to simultaneously estimate patterns of fault slip and heterogeneous distribution of effective Maxwell viscoelasticity from postseismic deformation. Our method utilizes an approximation which linearizes the viscoelastic contribution to postseismic deformation with respect to the inverse relaxation time of discrete regions in the lithosphere, allowing the use of least squares techniques, akin to seismic tomographic methods. The validity of this approximation is inversely proportional to the time since the main rupture and holds for roughly as long as the lowest relaxation time in the lithosphere proximal to the coseismic rupture. Our estimation of both the slip history on a fault and the effective Maxwell relaxation times of the lithosphere takes a matter of minutes. We apply our method to postseismic deformation following the 2010 El Mayor earthquake, as well as the 1999 İzmit-Düzce earthquake sequence. We discuss the significance of both fault creep and three dimensional viscosity structure in describing postseismic deformation.