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Higher-order Finite-difference Spatial Operators Across a Material Interface

Description: 

Recently, we have analyzed consequences of the heterogeneity of the medium, spatial discretization and the Nyquist-wavenumber band limitation for a finite-difference (FD) modeling of seismic wave propagation and earthquake ground motion. We have found that: 1) The grid representation of the material interface must be limited by the Nyquist wavenumber. 2) The wavenumber band limitation replaces spatial derivatives both in the homogeneous medium and across a material interface by continuous spatial convolutions. 3) The convolution of an infinite spatial extent must be replaced by a finite-extent discrete convolution, that is, by a proper FD spatial operator.

It is obvious that higher-order FD schemes significantly reduce grid dispersion in smoothly and weakly heterogeneous medium. Higher-order schemes involve relatively spatially-long FD operators. Can a long FD operator be applied across a material interface? Are the higher-order FD operators more accurate in evaluating spatial derivatives across a material interface?

We compare errors of spatial derivatives obtained using the spatial FD operators of the 4^th, 6^th, 8^th, 10^th and 12^th orders across the material interface for two interface representations. In the first one, a sharp material discontinuity is represented using an exact Heaviside step function. In the second one, the same material discontinuity is represented using a wavenumber band-limited Heaviside step function.

Based on the numerical investigations, we formulate implications for the FD modeling of seismic waves and earthquake ground motion in media with material interfaces.

Session: Numerical Modeling in Seismology: Developments and Applications [Poster]

Type: Poster

Date: 4/20/2023

Presentation Time: 08:00 AM (local time)

Presenting Author: Peter Moczo

Student Presenter: No

Invited Presentation: 

Authors