Equivalent Medium Parameters for Numerical Modeling in Media with Near-Surface Low Velocities

Abstract

We have developed a methodology to discretize an isotropic velocity model with low velocities near the free surface for full waveform numerical modeling. The method modifies the near-surface minimum velocity in a given (original) model by replacing parts of the model with equivalent medium parameters (EMP). The discretized model (with EMP) has a higher minimum velocity and minimizes the difference between the seismograms evaluated for the original model and the model with EMP. The method is suitable for studies requiring full waveform numerical modeling with a limited frequency range (such as a finite-difference full waveform modeling in a sedimentary basin). The discretized model with EMP is set to match locally surface-wave velocities evaluated in the original model over the frequency range of interest. The difference in group velocity calculated for the original vertical profile and the vertical profile with EMP provides an estimate of the error due to the modification of the original model.Online material: source code for the discussed algorithm.

Simulating strong ground motion from complex sources by reciprocal Green functions

“…We have used the equivalent medium parameters method of Eisner and Clayton (2002b) to resample the top low velocity layers to avoid artifacts due to an arbitrary velocity clamping (establishing a floor on velocity values in the model). This finite difference model representation ensures that the original Southern California Velocity Model is properly represented for the wave propagation at long periods (greater than three seconds in this study).…”

“…This finite difference model representation ensures that the original Southern California Velocity Model is properly represented for the wave propagation at long periods (greater than three seconds in this study). The sampling shown in Eisner and Clayton (2002b) accounts for both the site effects and propagation effects. The minimum velocity in the resampled model used for the numerical simulations was 0.5 km/s for modeling of a signal with periods of 3 seconds and longer.…”

Three‐dimensional finite difference method and hybrid modeling of earthquake ground motion

“…Irregular grid approaches for 2‐D media are, for example, from Jastram and Tessmer [1994] (various nonuniform rectangular grids in one model) and Falk et al [1996] ( P ‐ SV , staggered, vertically and horizontally irregular), Hestholm and Ruud [1994] (mapping topography to a flat surface, rectangular grid). Three‐dimensional FD simulations on irregular grids were used, for example, by McLaughlin and Day [1994] or recently by Pitarka [1999] and Eisner and Clayton [2001].…”

A Full Waveform Test of the Southern California Velocity Model by the Reciprocity Method

“…For the SCVM, Version 1, only the S-wave velocities were clamped with the value of 0.5 km/sec in the top 600 meters. The simple velocity clamping is not the best method to preserve the surface-wave velocities for a velocity model (see EISNER and CLAYTON, 2001b for a detailed analysis); however, if the velocity clamping value (0.5 km/sec in this case) is sufficiently lower than the group velocities of the original model, it approximately maintains the same group velocities as in the original model. Figure 2 shows the Love wave group velocities in the SCVM, Version 1.…”