Gamra: Simple Meshes for Complex Earthquakes

TL;DR

Gamra introduces a novel immersed interface method for elastostatic earthquake modeling, enabling accurate and efficient simulations of fault discontinuities on parallel finite difference grids, improving over traditional mesh-aligned finite element approaches.

Contribution

The paper presents a new numerical method and implementation in Gamra for modeling earthquake-induced discontinuities without complex mesh alignment, enhancing accuracy and computational efficiency.

Findings

Method achieves high-precision solutions for realistic earthquake models.

Demonstrates correctness through analytic tests.

Efficiently runs on parallel computing architectures.

Abstract

The static offsets caused by earthquakes are well described by elastostatic models with a discontinuity in the displacement along the fault. A traditional approach to model this discontinuity is to align the numerical mesh with the fault and solve the equations using finite elements. However, this distorted mesh can be difficult to generate and update. We present a new numerical method, inspired by the Immersed Interface Method, for solving the elastostatic equations with embedded discontinuities. This method has been carefully designed so that it can be used on parallel machines on an adapted finite difference grid. We have implemented this method in Gamra, a new code for earth modelling. We demonstrate the correctness of the method with analytic tests, and we demonstrate its practical performance by solving a realistic earthquake model to extremely high precision.