Numerical Resolution of Seismic Wavefield Simulations in Southern California

Abstract:

Seismic wavefield simulations can provide accurate solutions to the wave equation, even for three-dimensional seismic velocity models with topography, basin structures, anisotropy, attenuation, and other complexities. But how accurate are these numerical solutions? In many cases the effect of numerical dispersion on the synthetic seismograms looks quite similar to the effects of structural complexities. Therefore it is important to know the numerical resolution of the synthetic seismograms, that is, the minimum period that provides a quantifiably numerically accurate solution to the wave equation. Numerical resolution can be discussed in terms of a combined mesh and velocity model, or in terms of an individual source-station path within the same mesh and velocity model. Here we discuss two approaches for quantifying the numerical resolution. In the first approach we estimate the minimum resolvable period of each element within the finite element mesh. This calculation, performed within SPECFEM3D, requires no wavefield simulations and is based only on the size of each element and the minimum velocity within each element. The calculation produces a volumetric field that shows the estimated minimum resolvable period within each element of the (generally unstructured) mesh. In the second approach we choose a set of earthquakes to be used within a tomographic inversion. For each earthquake we compute one simulation using a fine discretization of gridpoints on the finite-element mesh and another simulation using a coarse discretization. We filter both sets of seismograms over a range of periods and then quantify the waveform differences. The minimum resolvable period (or numerical resolution) is identified by the minimum period for which the synthetic seismogram from the coarse-mesh and fine-mesh simulations is quantifiably the same. This calculation provides a path-specific minimum resolvable period that can be used to guide the choice of measurement filtering for a tomographic inversion. The seismogram-based assessment of numerical resolution requires a significant computational cost, but it provides a comprehensive view of the numerical resolution for the parts of the mesh that are directly relevant for the seismological investigation.