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A Fundamental View on Implementation of the Material Interface in the Finite-Difference Modeling

Description: 

Capability of a numerical modeling of seismic wave propagation and earthquake ground motion to faithfully represent material interfaces in realistic models of the Earth’s interior is of key importance. A sharp sediment-bedrock interface can be a key factor causing an anomalous earthquake ground motion and strong site effects. A sharp interface, e.g., a seabed, is an important structural feature in seismic exploration.

We address fundamental implications of presence of the material interface and spatial discretization for the finite-difference modeling by analyzing the equations of motion and constitutive relations in the wavenumber domain.

We present heterogeneous formulations of the equations of motion and constitutive relations for several basic configurations of a wavefield in an elastic isotropic medium. We Fourier-transform the entire equations to the wavenumber domain. Subsequently, we apply the band-limited inverse Fourier transform back to the space domain.

The heterogeneity of the medium, spatial discretization and the Nyquist-wavenumber band limitation of the entire equations have important implications for a FD modeling. The grid representation of the heterogeneous medium must be limited by the Nyquist wavenumber. The wavenumber band limitation replaces spatial derivatives both in the homogeneous medium and across a material interface by continuous spatial convolutions. The latter means that the wavenumber band limitation removes discontinuities of the spatial derivatives of the particle velocity and stress at the material interface. This allows to apply proper FD operators across material interfaces. A wavenumber band-limited heterogeneous formulation of the equations of motion and constitutive relations is the general condition for a heterogeneous FD scheme.

Session: Numerical Modeling in Seismology: Developments and Applications

Type: Oral

Date: 4/20/2023

Presentation Time: 02:15 PM (local time)

Presenting Author: Peter Moczo

Student Presenter: No

Invited Presentation: 

Authors