Effect of spatial discretization order in fault slip inversions

Brad T. Aagaard, Matthew G. Knepley, & Charles A. Williams

Published September 8, 2024, SCEC Contribution #13704, 2024 SCEC Annual Meeting Poster #070

We illustrate the effects of different spatial discretization orders (uniform slip over a fault patch, linear variation in slip over a fault patch, and quadratic variation in slip over a fault patch) in static fault slip inversions. We show that higher-order spatial discretization of the fault slip (for example, quadratic variations over a fault patch) generally results in greater accuracy with fewer unknowns in the inversion compared with using uniform slip patches. Observations of fault slip along earthquake surface ruptures exhibit substantial variations along strike, and kinematic source inversions indicate the slip distribution over the entire rupture exhibits similar spatial variations. Nevertheless, it is common to assume uniform slip on fault patches in seismic and geodetic fault slip inversions. This assumption often comes from the numerical technique used to generate Green’s functions, such as rectangular or triangular patches of uniform slip, based on Okada’s analytical solution. We leverage the flexible spatial discretization available in the PyLith open-source finite-element code to demonstrate the effects of discretizing fault slip with a basis order of 0 (uniform slip over a fault patch), 1 (linear variation in slip over a fault patch), and 2 (quadratic variation in slip over a fault patch). Our test case is a hypothetical strike-slip fault in a 2D domain with fault slip prescribed as a piecewise cubic polynomial and displacement observations (such as those from geodetic instruments) at randomly distributed locations. We quantify the misfit in fault slip as a function of the basis order in the fault slip discretization, the number of observations, and the number of unknowns. Although we perform the inversion using a simple linear least squares algorithm, the methodology generalizes to any technique using Green’s functions, including Bayesian methods. Future work may include two- and three-dimensional benchmarks using Bayesian inversion methods with noise added to the fake observations. PyLith is developed and distributed through the Computational Infrastructure for Geodynamics (https://geodynamics.org/resources/pylith) and includes source code, binary packages, online documentation (https://pylith.readthedocs.io), video tutorials, and a Docker container for software development.

Key Words
crustal deformation, software, fault slip, inversion

Citation
Aagaard, B. T., Knepley, M. G., & Williams, C. A. (2024, 09). Effect of spatial discretization order in fault slip inversions. Poster Presentation at 2024 SCEC Annual Meeting.

Related Projects & Working Groups
Stress and Deformation Over Time (SDOT)