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

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 absorbing boundary condition for acoustic-wave propagation using a mesh-free method

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. T145-T154 ◽  
Author(s):  
Junichi Takekawa ◽  
Hitoshi Mikada
Keyword(s):  
Boundary Condition ◽  
Wave Propagation ◽  
Acoustic Wave ◽  
Boundary Conditions ◽  
Absorbing Boundary Conditions ◽  
Absorbing Boundary Condition ◽  
Acoustic Wave Propagation ◽  
Absorbing Boundary ◽  
Mesh Free ◽  
Mesh Free Method

We have developed an absorbing boundary condition for acoustic-wave propagation using a mesh-free method without sacrificing the flexibility of the mesh-free framework. When we simulate acoustic-wave propagation using a numerical method, artificial reflections from model edges induced by a truncated computational domain should be avoided. Although many absorbing boundary conditions have been developed, most of them have been based on a regular latticed alignment of grids or nodes, and the efficiency of such absorbing boundary conditions for irregular arrangement of grids or nodes has not been examined yet. We have studied the artificial reflections generated at the boundaries of a model for a mesh-free method, and we have proposed a novel approach for suppressing the artifacts. The method uses a hybrid approach with a transition zone, in which the wavefield is estimated by a weighted average of solutions from the one- and two-way wave equations. Numerical experiments indicate that the proposed method can provide good performance in suppression of the artificial edge reflections even for irregular distributions of calculation points in the vicinity of model edges.

Relationship between Liao and Clayton-Engquist absorbing boundary conditions: Acoustic case

1995 ◽  
Vol 85 (3) ◽  
pp. 954-956
Author(s):  
Ningya Cheng ◽  
Chuen Hon Cheng
Keyword(s):  
Boundary Condition ◽  
Reflection Coefficient ◽  
Boundary Conditions ◽  
Closed Form ◽  
Differential Form ◽  
Short Note ◽  
Absorbing Boundary Conditions ◽  
Absorbing Boundary Condition ◽  
Absorbing Boundary ◽  
Close Relationship

Abstract In this short note, we derive the differential form of Liao's multi-transmitting formula. The reflection coefficient of the multi-transmitting formula in the acoustic case is obtained in closed form. These formulas are compared with Clayton-Engquist absorbing boundary condition and are shown to have a very close relationship.

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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