复杂非均匀介质伪谱法波场数值模拟

Using the pseudo-spectral method for wave field numerical modeling of complex heterogeneous medium

（1.中国科学院地质与地球物理研究所，北京100029； 2.中国石油化工股份有限公司西南分公司物探研究院，四川德阳618000）

Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China

:在地震波场数值正演模拟方法的研究中，计算精度和计算效率是评价方法的有效性及优越性的2个关键问题。从一阶速度—应力弹性波动方程出发，利用伪谱法求解波动方程，对复杂非均匀介质模型中的波场进行了正演模拟，并利用经典的Marmousi速度模型验证了该方法所具有的优势及存在的问题。将伪谱法模拟结果与交错网格高阶有限差分法的模拟结果比较可知：对于较为简单的非均匀模型，伪谱法和交错网格高阶有限差分法生成了几乎相同的波场；而当模型非常复杂且存在变化较剧烈的速度间断面时，伪谱法的模拟结果比较差。尽管如此，伪谱法计算速度快，计算效率高，能够直观、高效地反映介质中波场的传播规律，因而仍不失为一种很好的地震波模拟方法。

Wave field numerical simulation is an important field in geophysics. For the forward modeling, the computational precision and efficiency are two key issues in evaluating the validity and the superiority of the method. Based on the first order velocity-stress elastic wave equation, the wave field forward modeling with the pseudo-spectral method was carried out for complex heterogeneous medium. Meanwhile, the classical Marmousi model was utilized to verify the advantages and the existing problems of the method. By comparing the results of the pseudo-spectral method with the staggered-grid high-order finite difference approach, we can see that the two methods generate nearly the same wave field for the simple heterogeneous model. For the complex model, however, the modeling result of the pseudo-spectral method is worse than that of the staggered-grid high-order finite difference approach. Nevertheness, the pseudo-spectral method has a high computation speed and computational efficiency and can reflect the propagation rules of the wave field in medium visually and effectively. As a result, the pseudo-spectral method is still an effective method to model the heterogeneous seismic wave field.