Simulation Method

The simulation method that we use is a 4th order accurate staggered-grid finite- difference code, e3d, developed at Lawrence Livermore National Laboratory (LLNL) (Larsen an d Schultz, 1995). An advantage of this code is that it has been tested, and calibrated in a PEER/SCEC funded effort to validate numerical methods for ground motion simulation.

In addition, e3d simulates complete seismic waveforms in terms of near- intermediate- and far-field terms of the solution to the elasto-dynamic equation of motion. At such a close distance the fault all of these terms are important in strong ground motion generation.

We use a very fine model discretization of 20m. Motions at the closest stations to the fault (15m) are obtained by interpolation, and have been verified analytically for the strike-slip case. This high spatial resolution has the advantage that the kinematic source model also has high resolution producing a smooth evolution of the rupture front and the slip time function. The drawback of course is that it is computationally very expensive.

We simulate motions for a Mw6.5 earthquake using Wells and Coppersmith (1994) to estimate the fault length and width. From the scalar seismic moment and the fault area the average slip is specified. We use Somerville et al., (1999) to specify the slip rise time from the moment. Simulations have been performed for models ranging from a pure vertical strike-slip event to a 20-degree dipping thrust fault. We have tested rupture velocities of 70% and 140% (super-shear) of the shear wave velocity, although most of the simulations are for 80% of the shear wave velocity as is commonly reported in the literature for moderate earthquakes. We are in the process of setting up a distributed slip and variable rise time simulation to assess the effect of such source complexity on very near-fault strong ground motion.

The initial models are simplified greatly and using the finite-difference approach is "over-kill", but in the future we may consider more complex source functions and 3D fault structures such as velocity discontinuities across the fault or low-velocity fault gouge. It is desireable that the ground motion computation and the source resolution are at the same resolution, and in the future when comparisions are made with more complex models all of the ground motions will have been computed with the same theory and numerical algorithm.

The total model dimension is 50x20x15 $km^3$ and with the grid spacing of 20m this translates to 2.3 billion grid points, requiring 121.8 Gbytes of memory. The simulations were performed on a LLNL super computer.

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