Finite difference elastic wave modeling with an irregular free surface using ADER scheme

In numerical modeling of seismic wave propagation in the earth, we encounter two important issues: the free surface and the topography of the surface (i.e. irregularities). In this study, we develop a 2D finite difference solver for the elastic wave equation that combines a 4th- order ADER scheme (A...

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Bibliographic Details
Published in:Journal of geophysics and engineering 2015-06, Vol.12 (3), p.435-447
Main Authors: Almuhaidib, Abdulaziz M, Toksöz, M Nafi
Format: Article
Language:English
Subjects:
ADER
Boundaries
boundary condition
Computational efficiency
elastic
Elastic waves
finite difference
free surface
Irregularities
Mathematical analysis
Mathematical models
modeling
Solvers
Topography
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Summary:In numerical modeling of seismic wave propagation in the earth, we encounter two important issues: the free surface and the topography of the surface (i.e. irregularities). In this study, we develop a 2D finite difference solver for the elastic wave equation that combines a 4th- order ADER scheme (Arbitrary high-order accuracy using DERivatives), which is widely used in aeroacoustics, with the characteristic variable method at the free surface boundary. The idea is to treat the free surface boundary explicitly by using ghost values of the solution for points beyond the free surface to impose the physical boundary condition. The method is based on the velocity-stress formulation. The ultimate goal is to develop a numerical solver for the elastic wave equation that is stable, accurate and computationally efficient. The solver treats smooth arbitrary-shaped boundaries as simple plane boundaries. The computational cost added by treating the topography is negligible compared to flat free surface because only a small number of grid points near the boundary need to be computed. In the presence of topography, using 10 grid points per shortest shear-wavelength, the solver yields accurate results. Benchmark numerical tests using several complex models that are solved by our method and other independent accurate methods show an excellent agreement, confirming the validity of the method for modeling elastic waves with an irregular free surface.
ISSN:1742-2132
1742-2140
DOI:10.1088/1742-2132/12/3/435