Experiments with Higdon's absorbing boundary conditions for a number of wave equations |
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Authors: | W A Mulder |
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Institution: | (1) Shell International Exploration and Production B.V., Research and Technology Services, P.O. Box 60, 2280 AB Rijswijk, The Netherlands E-mail: w.a.mulder@siep.shell.com |
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Abstract: | Simulation of wave propagation for seismic purposes is usually restricted to a small portion of the earth. Artificial boundary
conditions are required where the subsurface model is truncated. Absorbing boundaries should ensure that waves hitting the
artificial boundaries are not reflected. The vast amount of literature on the subject suggests that “good” conditions have
not been found, and only “reasonable” solutions exist. A cursory overview of existing and a few new ideas is presented that
may guide the construction of suitable boundary conditions. Because the intended application of the boundary conditions was
a high-order finite-difference code that runs on a parallel computer, we have restricted our attention to local boundary conditions.
A fundamental problem in the design of accurate local boundary conditions is pointed out: accuracy is required to keep the
amount of reflected energy small, but at the same time allows for growing low-frequency modes. We have settled for Higdon’s
boundary conditions. Higdon proposes to include some damping to suppress the growing low-frequency modes. We show that third-order
conditions provide acceptable results for the simple scalar wave equation and the acoustic equation. In the elastic case,
an additional low-frequency growing mode may occur. This mode can be suppressed by using a dissipative boundary scheme and
by increasing the amount of damping. The increase in damping results in an increase in the amount of reflected energy, which
is larger than in the scalar case. Numerical experiments exhibit a reasonable performance, although some improvement would
be useful, particularly in the anisotropic elastic case.
This revised version was published online in July 2006 with corrections to the Cover Date. |
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Keywords: | wave equation finite differences absorbing boundary conditions anisotropy 65M06 73B40 86A15 |
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