Finite‐difference modeling of scalar‐wave propagation in cracked media

Geophysics ◽  
2001 ◽  
Vol 66 (1) ◽  
pp. 267-276 ◽  
Author(s):  
Gerben B. van Baren ◽  
Wim A. Mulder ◽  
Gérard C. Herman
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Neumann Boundary Condition ◽  
Neumann Boundary ◽  
Point Sources ◽  
Small Scale ◽  
Scalar Wave ◽  
Equation Solution ◽  
Finite Difference Technique ◽  
Embedding Medium

We discuss a finite‐difference modeling technique for the simplified case of scalar, two‐dimensional wave propagation in a medium containing a large number of small‐scale cracks. The cracks are characterized by an explicit (Neumann) boundary condition whereas the embedding medium can be heterogeneous. The boundaries of the cracks are not represented in the finite‐difference mesh, but the cracks are incorporated as distributed point sources. This enables the use of grid cells that are considerably larger than the crack sizes. We compare our method to an accurate integral‐equation solution for the case of a homogeneous embedding and conclude that the finite‐difference technique is accurate and computationally fast.

FINITE-DIFFERENCE MODELING IN MEDIA WITH MANY SMALL-SCALE CRACKS

2001 ◽  
Vol 09 (03) ◽  
pp. 815-831
Author(s):  
GERBEN B. VAN BAREN ◽  
GERARD C. HERMAN ◽  
WIM A. MULDER
Keyword(s):  
Integral Equation ◽  
Wave Propagation ◽  
Finite Difference ◽  
Point Sources ◽  
Small Scale ◽  
Two Dimensional ◽  
Equation Solution ◽  
Finite Difference Technique ◽  
Embedding Medium ◽  
Dimensional Wave

We discuss a finite-difference modeling technique for scalar, two-dimensional wave propagation in a medium containing a large number of small-scale cracks. The embedding medium can be heterogeneous. The boundaries of the cracks are not represented in the finite-difference mesh but the cracks are incorporated as distributed point sources. This enables the use of grid cells that are considerably larger than the crack sizes. We compare our method to an accurate integral-equation solution for the case of a homogeneous embedding and conclude that the finite-difference technique is accurate and computationally fast.

Boundary conditions for the numerical solution of wave propagation problems

Geophysics ◽  
1978 ◽  
Vol 43 (6) ◽  
pp. 1099-1110 ◽  
Author(s):  
Albert C. Reynolds
Keyword(s):  
Wave Propagation ◽  
Reflection Coefficient ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Neumann Boundary ◽  
Synthetic Seismograms ◽  
Neumann Boundary Conditions ◽  
Numerical Calculations ◽  
Reflection Coefficients

Many finite difference models in use for generating synthetic seismograms produce unwanted reflections from the edges of the model due to the use of Dirichlet or Neumann boundary conditions. In this paper we develop boundary conditions which greatly reduce this edge reflection. A reflection coefficient analysis is given which indicates that, for the specified boundary conditions, smaller reflection coefficients than those obtained for Dirichlet or Neumann boundary conditions are obtained. Numerical calculations support this conclusion.

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