双相介质P波波动方程小波域多尺度模拟

相比于单相介质理论而言,双相介质理论更接近实际地层的真实情况,因此在地球物理勘探、地震工程和岩土动力学等领域有着广泛的应用。传统的波动方程数值解法由于本身固有的不足不利于求解诸如双相介质波动方程等复杂的非线性和不规则性问题;而小波方法则由于自身良好的特性可以用来构建解决此类问题的自适应性算法。本文详细推导了双相介质P波波动方程的有限差分矩阵表示形式,利用小波变换将其转移到小波域,设置阈值形成更为稀疏的迭代矩阵以构建自适应算法,从而达到减少计算量,增加地震波场数值模拟灵活性和准确性的目的。地球物理勘探的数值模拟实例验证了方法的有效性。

The wavelet multi-scale simulation of P-wave wave equation in the two-phase media

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.