Conference Paper

Graded boundary simulation of air/Earth interfaces in finite‐difference elastic wave modeling

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Abstract

The air/earth interface is accurately represented in a 3D finite-difference elastic wave propagation algorithm merely by assigning material properties of air to the spatial grid nodes above the earth's surface. Computational stability is maintained by making the boundary gradational. Synthetic seismic traces calculated by this approach compare favorably with those computed by imposing an explicit stress-free condition on the surface.

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... In this paper, I use the simplest example of a heterogeneous model — that of two half-spaces. I embark on this investigation bearing in mind the documented occurrences of numerical instabilities at interfaces with strong material contrasts Crase, 1990; Seron et al., 1996; Bartel et al., 2000; Saenger et al., 2000 . These instabilities arise even though the stability criterion derived using conventional von Neumann analysis may be satisfied for each gridpoint in the numerical model. ...
... For a pure velocity contrast, as the velocity in medium 2 becomes smaller, the stability value never exceeds unity and actually decreases. In contrast, the pure density contrast goes unstable for small values of density in medium 2. This agrees with the observation that instabilities arise at strong density contrasts when using the standard staggered grid Bartel et al., 2000; Saenger et al., 2000. ...
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... The simplest is the inclusion of a density contrast to mimic an air layer, at the expense of numerical accuracy. For elastic wave propagation, Bartel et al. (2000) find that some smoothing of the extreme density contrast is required for numerical stability. Boore (1972), Robertsson (1996), Mittet (2002), Bohlen and Saenger (2006), and Zeng et al. (2012) consider variants of the vacuum approach. ...
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... This can be amended by using very fine grids at the expense of computational time. A similar limitation is encountered when considering a heterogeneous medium that includes topography such as hills and mountains (Hestholm and Ruud, 1994;Bartel et al., 2000;Bohlen and Saenger, 2006). In contrast, finite-element methods (FEMs) easily handle unstructured meshes and spatial local refinement. ...
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