A Stable Optimal Absorbing Boundary Condition for Finite-Difference Modelling

1999 ◽  
Author(s):  
M. G. Imhof
Keyword(s):  
Boundary Condition ◽  
Finite Difference ◽  
Absorbing Boundary Condition ◽  
Absorbing Boundary

Absorbing boundary condition for the elastic wave equation

Geophysics ◽  
1988 ◽  
Vol 53 (5) ◽  
pp. 611-624 ◽  
Author(s):  
C. J. Randall
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Finite Difference ◽  
Elastic Wave ◽  
Grazing Incidence ◽  
Scalar Fields ◽  
Absorbing Boundary Conditions ◽  
Absorbing Boundary Condition ◽  
Elastic Wave Equation ◽  
Absorbing Boundary

Extant absorbing boundary conditions for the elastic wave equation are generally effective only for waves nearly normally incident upon the boundary. High reflectivity is exhibited for waves traveling obliquely to the boundary. In this paper, a new and efficient absorbing boundary condition for two‐dimensional and three‐dimensional finite‐difference calculations of elastic wave propagation is presented. Compressional and shear components of the incident vector displacement fields are separated by calculating intermediary scalar potentials, allowing the use of Lindman’s boundary condition for scalar fields, which is highly absorbing for waves incident at any angle. The elastic medium is assumed to be homogeneous in the region immediately adjacent to the boundary. The reflectivity matrix of the resulting absorbing boundary for elastic waves is calculated, including the effects of finite‐difference truncation error. For effectively all angles of incidence, reflectivities are much smaller than those of the commonly employed paraxial absorbing boundaries, and the boundary condition is stable for any physical Poisson’s ratio. The nearly complete absorption predicted by the reflectivity matrix calculations, even at near grazing incidence, is demonstrated in a finite‐difference application.

An optimal absorbing boundary condition for elastic wave modeling

Geophysics ◽  
1995 ◽  
Vol 60 (1) ◽  
pp. 296-301 ◽  
Author(s):  
Chengbin Peng ◽  
M. Nafi Toksöz
Keyword(s):  
Boundary Condition ◽  
Wave Propagation ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Elastic Wave ◽  
Short Note ◽  
Absorbing Boundary Conditions ◽  
Parallel Computer ◽  
Absorbing Boundary Condition ◽  
Absorbing Boundary

Absorbing boundary conditions are widely used in numerical modeling of wave propagation in unbounded media to reduce reflections from artificial boundaries (Lindman, 1975; Clayton and Engquist, 1977; Reynolds, 1978; Liao et al., 1984; Cerjan et al., 1985; Randall, 1988; Higdon, 1991). We are interested in a particular absorbing boundary condition that has maximum absorbing ability with a minimum amount of computation and storage. This is practical for 3-D simulation of elastic wave propagation by a finite‐difference method. Peng and Toksöz (1994) developed a method to design a class of optimal absorbing boundary conditions for a given operator length. In this short note, we give a brief introduction to this technique, and we compare the optimal absorbing boundary conditions against those by Reynolds (1978) and Higdon (1991) using examples of 3-D elastic finite‐difference modeling on an nCUBE-2 parallel computer. In the Appendix, we also give explicit formulas for computing coefficients of the optimal absorbing boundary conditions.

Absorbing boundary condition for the elastic wave equation: Velocity‐stress formulation

Geophysics ◽  
1989 ◽  
Vol 54 (9) ◽  
pp. 1141-1152 ◽  
Author(s):  
C. J. Randall
Keyword(s):  
Boundary Condition ◽  
Finite Difference ◽  
Elastic Wave ◽  
Three Dimensions ◽  
Absorbing Boundary Condition ◽  
Elastic Wave Equation ◽  
Absorbing Boundary ◽  
Absorbing Boundaries ◽  
Locally Homogeneous ◽  
Incident Waves

This paper describes an absorbing boundary condition for finite‐difference modeling of elastic wave propagation in two and three dimensions. The boundary condition is particularly effective for obliquely incident waves, typically quite troublesome for absorbing boundaries. Analytical predictions of the boundary reflection coefficients of a few percent or less for angles of incidence up to 89° are verified in example finite‐difference applications. The algorithm is appropriate for use in a velocity‐stress finite‐difference (vs‐fd) formulation. It is computationally simpler than a similar absorbing boundary given previously for the standard displacement formulation. A second algorithm is presented which may be advantageous when the boundary of interest is exposed to strong evanescent waves. Both algorithms require that the adjacent elastic medium be locally homogeneous.

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