Efficient Numerical Modeling of 3D, Half-Space, Slow-Slip and Quasi-Dynamic Earthquake Ruptures
Abstract
Motivated by the hypothesis that dilatancy plays a critical role in faulting in subduction zones, we are developing FDRA2 (Fault Dynamics with the Radiation-damping Approximation), a software package to simulate three-dimensional quasi-dynamic faulting that includes rate-state friction, thermal pressurization, and dilatancy (following Segall and Rice [1995]) in a finite-width shear zone. This work builds on the two-dimensional simulations performed by FDRA1 (Bradley and Segall [AGU 2010], Segall and Bradley [submitted]). These simulations show that at lower background effective normal stress (\bar σ), slow slip events occur spontaneously, whereas at higher \bar σ , slip is inertially limited. At intermediate \bar σ , dynamic events are followed by quiescent periods and then long durations of repeating slow slip events. Models with depth-dependent properties produce sequences similar to those observed in Cascadia. Like FDRA1, FDRA2 solves partial differential equations in pressure and temperature on profiles normal to the fault. The diffusion equations are discretized in space using finite differences on a nonuniform mesh having greater density near the fault. The full system of equations is a semiexplicit index-1 differential algebraic equation (DAE) in slip, slip rate, state, fault zone porosity, pressure, and temperature. We integrate state, porosity, and slip explicitly; solve the momentum balance equation on the fault for slip rate; and integrate pressure and temperature implicitly. Adaptive time steps are limited by accuracy and the stability criterion governing explicit integration of hyperbolic, but not the more stringent one governing parabolic, PDE. To compute elasticity in a 3D half-space, FDRA2 compresses the large, dense matrix arising from the boundary element method using an H-matrix. The work to perform a matrix-vector product scales almost linearly, rather than quadratically, in the number of fault cells. A new technique to relate the error tolerance on the approximation to parameters of the compression algorithms (Bradley [submitted]) improves the compression efficiency for the third-order 1/r3 singularity with elastic Green's functions, relative to the standard method, by factors of two to five---importantly, while still providing the same straightforward error bound on the approximation. The compression (and so, roughly, the speedup) factor for a problem in which the fault is discretized by 156 ± 402 rectangles and the tolerance on the relative error is 10-5 is just over 75. We will describe our numerical methods and present preliminary simulation results.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2011
- Bibcode:
- 2011AGUFM.S23B2242B
- Keywords:
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- 0560 COMPUTATIONAL GEOPHYSICS / Numerical solutions;
- 7209 SEISMOLOGY / Earthquake dynamics;
- 8118 TECTONOPHYSICS / Dynamics and mechanics of faulting;
- 8170 TECTONOPHYSICS / Subduction zone processes