地震波传播数值模拟中的频散问题

DISPERSIVE PROBLEM IN SEISMIC WAVE PROPAGATION NUMERICAL MODELING

数值频散程度直接决定了地震波数值模拟效果。在高频情况下 ,有限元法以及低阶差分法地震波数值模拟效果不好的主要原因 ,就是这些方法引起的数值频散比较严重。对高阶差分法声波模拟和交错网格弹性波模拟而言 ,影响数值频散的三个因素是地震波传播方向、差分精度和一个波长内离散点数 ,对交错网格弹性波模拟而言还包括介质的泊松比。Marmousi模型以及弹性波模型的模拟及成像结果表明 ,高阶差分方法 (包括交错网格 )可以显著地降低数值频散 ,有效提高地震波正演计算的精度 ,拓宽模拟波场的频带。两种方法的频散理论分析证明 ,和规则网格以及低阶差分方法相比 ,高阶差分方法 (包括交错网格 )在不降低模拟精度前提下 ,空间网格可以增大数倍 ,从而大幅度提高正演效率。因此 ,高阶差分以及交错网格高阶差分是提高声波和弹性波传播数值模拟精度和效率的有效方法 ,为复杂地区地震波传播规律研究、野外地震观测系统优化设计、地震资料解释结果的验证、地震波形反演提供了有效的地震波正演工具。

The seismic wave numerical modeling effect is directly dependent upon the degree of numerical dispersion. Under high-frequency circumstances, the principal reason of producing little effect to the seismic wave numerical modeling by use of finite element method and low-order difference method is the serious numerical dispersion caused by these methods. In regard to high-order difference acoustic modeling and staggered-grid elastic wave modeling, three factors affecting the numerical dispersion include the direction of seismic wave propagation, the difference accuracy and the number of grids in a wavelength, the Poisson ratio of media being yet attached to the elastic wave modeling. The modeling and imaging results of the Marmousi model and elastic wave model indicated that the high-order difference method (including the staggered-grid) may obviously decrease the numerical dispersion, effectively raise the accuracy of seismic wave forward calculation and widen the frequency band of modeling wave field. Through dispersion theoretical analysis of the two methods, it was proved that as compared with the regular grids and low-order difference method, the spacial grids may increase by several times by use of the high-order difference method (including the staggered-grid) under the premise of not decreasing modeling accuracy, thus raising greatly forward efficiency. Therefore the high-order difference and staggered-grid high-order difference are the effective methods of raising the accuracies and efficiencies of the acoustic and elastic wave propagation numerical modelings, thus providing an effective seismic wave forward tool for the research on seismis wave propogation law at the complicated areas, the design of field seismic observation system,the verification of seismic data interpretation results and the seismic waveform inversion.