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| The wavelet multi-scale simulation of P-wave wave equation in the two-phase media |
| Revised:May 11, 2004 |
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| DOI：10.7511/jslx20063048 |
| KeyWord:two-phase media,finite difference method,wavelet transform,multi-scale simulation |
| LIU Ke-an ZHANG Xin-ming LIU Jia-qi |
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| Abstract: |
| Compared with the single media theory,the two-phase media theory considers the porous elastic solid filled with compressible viscous fluid such as water,oil and etc.So,it describes the actual earth stratum more precisely and can be used widely in many fields,such as geophysical prospecting,earthquake engineering and rock & soil dynamics.The traditional numerical methods have some trouble in solving the nonlinear problem because of its inherent shortcoming.However,based on many good properties,wavelet method could solve the problem better.In this paper,combining the wavelet analysis method with the finite difference method,the multi-scale wavelet finite difference method is introduced to the numerical simulation of P-wave wave equation in the two-phase media.The finite difference matrix form of the P-wave wave equation in the two-phase media is deduced and then is transferred to the wavelet field using the wavelet transformation.The sparser iterative matrix can be obtained and the adaptive algorithm is formed by using the wavelet thresholding.The wavelet field multiscale simulation of seismic wave can reduce the cost of computation and increase the flexibility and the accusacy of the seismic wave numerical simulation,especially for the large scale problem.Two numerical simulation results prove the validity of the method. |
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