A new finite-difference stress modeling method governed by elastic wave equations

Abstract

Numerical stress or strain modeling has been a focused subject in many fields, especially in assessing the stability of key engineering structures and better understanding in local or tectonic stress patters and seismicity. Here we proposed a new stress modeling method governed by elastic wave equations using finite-difference scheme. Based on the modeling scheme of wave propagation, the proposed method is able to solve both the dynamic stress evolution and the static stress state of equilibrium by introducing an artificial damping factor to the particle velocity. We validate the proposed method in three geophysical benchmarks: (a) a layered earth model under gravitational load, (b) a rock mass model under nonuniform loads on its exterior boundaries and (c) a fault zone with strain localization driven by regional tectonic loading that measured by GPS velocity field.  Because the governing equations of the proposed method are wave equations instead of equilibrium equations, we are able to use the perfectly matched layer as the artificial boundary conditions for models in unbounded domain, which will substantially improve the accuracy of them. Also, the proposed scheme maps the physical model on simple computational grids and therefore is more memory efficient for grid points’ positions not been stored. Besides, the efficient parallel computing of the finite-different method guarantees the proposed method’s advantage in computational speed. As a minor modification to wave modeling scheme, the proposed stress modeling method is not only accurate for geological models through different scales, but also physically reasonable and easy to implement for geophysicists.