Fast, accurate solutions for 3D strain volumes in a heterogeneous half space

Abstract

Deformation in the Earth displays many degrees of localization. The mechanics of faulting can be well represented by slip on a 2D surface discretized in piecewise linear boundary elements. Distributed anelastic deformation associated with fluid flow, magma transfer, or viscoelastic relaxation can be approximated by anelastic strain discretized in 3D volume elements. The stress, traction, and displacement kernels for these elements form the basis of forward and inverse modeling of Earth's deformation during the seismic cycle, volcanic unrest or hydrologic change. While there are a number of techniques for computing these kernels for 2D fault surfaces, the techniques for 3D strain volumes are less developed. To improve the models of Earth's deformation, we extend previous work to numerically calculate these kernels for 3D strain volumes in a heterogeneous half space. The model provides high-precision displacement and stress for all these cases in a self-consistent manner. We exploit the adaptive multi-grid elastic solver implemented in the software Gamra (Landry and Barbot, 2016) to compute the deformation induced by boundary and volume elements with high numerical efficency. We demonstrate the correctness of the method with analytic tests. We illustrate the performance by computing a large-scale model of postseismic deformation for the 2015 Mw 7.8 Gorkha, Nepal earthquake with heterogeneous material properties. The open-source, freely available software can be useful for the calculation of elasto-static Green's functions for localized and distributed deformation in a heterogeneous Earth.