scholarly journals Absorbing boundary conditions for acoustic and elastic wave equations

1977 ◽  
Vol 67 (6) ◽  
pp. 1529-1540 ◽  
Author(s):  
Robert Clayton ◽  
Björn Engquist
Keyword(s):  
Boundary Conditions ◽  
Elastic Wave ◽  
Wave Equations ◽  
Absorbing Boundary Conditions ◽  
Limited Area ◽  
Absorbing Boundary ◽  
Physical Behavior ◽  
Wide Range ◽  
Elastic Wave Equations ◽  
Numerical Wave

abstract Boundary conditions are derived for numerical wave simulation that minimize artificial reflections from the edges of the domain of computation. In this way acoustic and elastic wave propagation in a limited area can be efficiently used to describe physical behavior in an unbounded domain. The boundary conditions are based on paraxial approximations of the scalar and elastic wave equations. They are computationally inexpensive and simple to apply, and they reduce reflections over a wide range of incident angles.

A transparent boundary technique for numerical modeling of elastic waves

Geophysics ◽  
1999 ◽  
Vol 64 (3) ◽  
pp. 963-966 ◽  
Author(s):  
Jianlin Zhu
Keyword(s):  
Numerical Modeling ◽  
Boundary Conditions ◽  
Elastic Waves ◽  
Wave Equations ◽  
Normal Incidence ◽  
Absorbing Boundary Conditions ◽  
S Wave ◽  
Absorbing Boundary ◽  
S Waves ◽  
Elastic Wave Equations

In numerical modeling of wave motions, strong reflections from artificial model boundaries may contaminate or mask true reflections from the interior model interfaces. Hence, developing a kind of exterior model boundary transparent to the outgoing waves is of critical importance. Among proposed solutions, e.g., Smith (1974), Kausel and Tassoulas (1981), and Higdon (1991), the most widely used may be the Clayton and Engquist (1977) method of absorbing boundary conditions, based on paraxial approximations for acoustic and elastic‐wave equations. However, absorbing boundary conditions make the reflection coefficients zero only for normal incidence, and suppression of reflected S-waves (Clayton and Engquist, 1977) becomes poorer as the ratio of P- to S-wave velocity ([Formula: see text]) becomes larger.

OPTIMISED ABSORBING BOUNDARY CONDITIONS FOR ELASTIC-WAVE PROPAGATION

2001 ◽  
Vol 09 (03) ◽  
pp. 1005-1014
Author(s):  
A. LANGE ◽  
J. ZHOU ◽  
N. SAFFARI
Keyword(s):  
Wave Propagation ◽  
Boundary Conditions ◽  
Elastic Wave ◽  
Normal Incidence ◽  
Absorbing Boundary Conditions ◽  
Elastic Wave Propagation ◽  
Reflection Coefficients ◽  
Absorbing Boundary ◽  
Wide Range ◽  
Complete Absorption

Second-order absorbing boundary conditions for numerical modeling of elastic-wave propagation are studied. The corresponding reflection coefficients are derived, from which a necessary and sufficient condition for complete absorption at normal incidence is deduced. We define a family of absorbing boundary conditions from symmetrically specified zero reflection incidences. Conditions to avoid singular reflection coefficients are given for this case, these ensure that the solutions of the elastic wave equation also satisfy the boundary conditions. These are then optimised over a wide range of materials, and absorbing boundary conditions that give an efficient absorption for the whole range are obtained. We also compare the results with absorbing boundary conditions developed from the least-squares solution of the system requiring complete absorption at all incidences. The best set of conditions are presented and compared with Clayton and Engquist6 (A2) condition.

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