Dynamic propagation of shear ruptures on a frictional interface in an elastic solid is a useful idealization of natural earthquakes. The conditions relating discontinuities in particle velocities across fault zones and tractions acting on the fault are often expressed as nonlinear friction laws. The corresponding initial boundary value problems are both numerically and computationally challenging. In addition, seismic waves generated by earthquake ruptures must be propagated for many wavelengths away from the fault. Therefore, reliable and efficient numerical simulations require both provably stable and high order accurate numerical methods.We present a high order accurate finite difference method for: a) enforcing nonlinear friction laws, in a consistent and provably stable manner, suitable for efficient explicit time integration; b) dynamic propagation of earthquake ruptures along nonplanar faults; and c) accurate propagation of seismic waves in heterogeneous media with free surface topography.We solve the first order form of the 3D elastic wave equation on a boundary-conforming curvilinear mesh, in terms of particle velocities and stresses that are collocated in space and time, using summation-by-parts (SBP) finite difference operators in space. Boundary and interface conditions are imposed weakly using penalties. By deriving semi-discrete energy estimates analogous to the continuous energy estimates we prove numerical stability. The finite difference stencils used in this paper are sixth order accurate in the interior and third order accurate close to the boundaries. However, the method is applicable to any spatial operator with a diagonal norm satisfying the SBP property. Time stepping is performed with a 4th order accurate explicit low storage Runge-Kutta scheme, thus yielding a globally fourth order accurate method in both space and time. We show numerical simulations on band limited self-similar fractal faults revealing the complexity of rupture dynamics on rough faults.
|Original language||English (US)|
|Number of pages||23|
|Journal||Journal of Computational Physics|
|State||Published - Jan 2016|
Bibliographical noteKAUST Repository Item: Exported on 2021-04-02
Acknowledged KAUST grant number(s): KAUST Academic Excellence Alliance (AEA)
Acknowledgements: This work was supported by the National Science Foundation (ACI-1148493), King Abdullah University of Science and Technology (KAUST) through a joint KAUST Academic Excellence Alliance (AEA) grant with Stanford, and the Southern California Earthquake Center. SCEC is funded by NSF Cooperative Agreement EAR-1033462 and USGS Cooperative Agreement G12AC20038. The SCEC contribution number for this paper is 2062. The numerical simulations were conducted at the Stanford Center for Computational Earth and Environmental Science with computational support by Dennis Michael. The assistance of Samuel Bydlon in making Fig. 1, Fig. 2 is gratefully acknowledged.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)
- Computer Science Applications