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A support-operator method for 3D rupture dynamics

Geoffrey P. Ely, Steven M. Day, & Jean B. Minster

Published 2009, SCEC Contribution #1163

We present a numerical method to simulate spontaneous shear crack propagation within a heterogeneous, three-dimensional, viscoelastic medium. Wave motions are computed on a logically rectangular hexahedral mesh, using the generalized finite difference method of Support Operators (SOM). This approach enables modeling of non-planar surfaces and non-planar ruptures. Our implementation, the Support Operator Rupture Dynamics code (SORD), is highly scalable, enabling large scale, multi-processors calculations. The fault surface is modeled by coupled double nodes, where rupture occurs as dictated by the local stress conditions and a frictional failure law. The method successfully performs test problems developed for the Southern California Earthquake Center (SCEC) rupture dynamics code comparison exercise, showing good agreement with semi-analytical boundary integral method results. We undertake further dynamic rupture tests to quantify numerical errors introduced by shear deformations to the hexahedral mesh. We generate a family of meshes distorted by simple shearing, in the along-strike direction, up to a maximum of 73-degrees. For SCEC Validation Problem 3, grid-induced errors increase with mesh shear angle, with the logarithm of error approximately proportional to angle over the range tested. At 73-degrees, RMS misfits are about 10\% for peak slip rate, and 0.5\% for both rupture time and total slip, indicating that the method (which up to now we have applied mainly to near-vertical strike-slip faulting) is also capable of handling geometries appropriate to low-angle surface-rupturing thrust earthquakes. Additionally, we demonstrate non-planar rupture effects, by modifying the test geometry to include, respectively, cylindrical curvature and sharp kinks.

Key Words
perfectly matched layer, electromagnetic waves, nonplanar fault, 3D simulations, shear crack, finite, propogation, bends, absorption, mechanics

Ely, G. P., Day, S. M., & Minster, J. B. (2009). A support-operator method for 3D rupture dynamics. Geophysical Journal International, 177(3), 1140-1150. doi: 10.1111/j.1365-246X.2009.04117.x.