Dynamic earthquake rupture simulation on nonplanar faults embedded in 3D geometrically complex, heterogeneous Earth models

Monday, 15 December 2014
Kenneth Duru, Eric M Dunham, Sam A. Bydlon and Hari Radhakrishnan, Stanford University, Stanford, CA, United States
Dynamic propagation of shear ruptures on a frictional interface is a useful idealization of a natural earthquake.
The conditions relating slip rate and fault shear strength 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, far away from fault zones, to seismic stations and remote areas.
Therefore, reliable and efficient numerical simulations require both provably stable and high order accurate numerical methods.

We present a numerical 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 rough faults;
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 finite differences in space. 
The finite difference stencils are 6th order accurate in the interior and 3rd order accurate close to the boundaries. 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. Time stepping is performed with a 4th order accurate explicit low storage Runge-Kutta scheme.

 We have performed extensive numerical experiments using a slip-weakening friction law on non-planar faults, including recent SCEC benchmark problems. We also show simulations on fractal faults revealing the complexity of rupture dynamics on rough faults. We are presently extending our method to rate-and-state friction laws and off-fault plasticity.