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Comparison of Fault Representation Methods in Finite Difference Simulations of Dynamic Rupture

Luis A. Dalguer, & Steven M. Day

Published October 2006, SCEC Contribution #956

Assessing accuracy of numerical methods for spontaneous rupture simulation is challenging because we lack analytical solutions for reference. Previous comparison of a boundary integral method (BI) and finite-difference method (called DFM) that explicitly incorporates the fault discontinuity at velocity nodes (traction- at-split-node scheme) shows that both converge to a common, grid-independent solution and exhibit nearly identical power-law convergence rates with respect to grid spacing {Delta}x. We use this solution as a reference for assessing two other proposed finite-difference methods, the thick fault (TF) and stress glut (SG) methods, both of which approximate the fault-jump conditions through inelastic increments to the stress components (inelastic-zone schemes). The TF solution fails to match the qualitative rupture behavior of the reference solution and has quantitative misfits in root- mean-square rupture time of ~30% for the smallest computationally feasible {Delta}x (with ~9 grid-point resolution of cohesive zone, denoted Nc = 9). For sufficiently small values of {Delta}x, the SG method reproduces the qualitative features of the reference solution, but rupture velocity remains systematically low for SG relative to the reference solution, and SG lacks the well-defined power-law convergence seen for BI and DFM. The rupture-time error for SG, with Nc ~ 9, remains well above uncertainty in the reference solution, and the split-node method attains comparable accuracy with Nc 1/4 as large (and computation timescales as (Nc)4). Thus, accuracy is highly sensitive to the formulation of the fault-jump conditions: The split-node method attains power-law convergence. The SG inelastic-zone method achieves solutions that are qualitatively meaningful and quantitatively reliable to within a few percent, but convergence is uncertain, and SG is computationally inefficient relative to the split-node approach. The TF inelastic-zone method does not achieve qualitatively meaningful solutions to the 3D test problem and is sufficiently computationally inefficient that it is not feasible to explore convergence quantitatively.

Dalguer, L. A., & Day, S. M. (2006). Comparison of Fault Representation Methods in Finite Difference Simulations of Dynamic Rupture. Bulletin of the Seismological Society of America, 96(5), 1764-1778. doi: 10.1785/0120060024.