曲网络伪谱法二维声波模拟

Pseudospectral method on curved grid for 2-D forward modeling

大连理工大学应用数学系,辽宁大连116023

Department of Applied Mathematics, Dailian University of Technology, 116023, China

为更精确地模拟地质界面和波的传播, 给出了一种曲界面波场模拟算法。提出了具体的计算方案, 并改进了快速傅氏变换的计算。为使用方便, 推导了稳定性条件。该方法利用多块映射和超限插值技术将直角坐标系下的曲界面变换成曲坐标系下的规则界面, 在曲坐标系下利用伪谱法模拟波场。它能有效地消除因离散化曲界面产生的人为阶梯状界面所带来的不必要的绕射。

For more accurately modeling geology interface and wave propagation, a pseudospectral Fourier method for solving 2-D acoustic wave equation on curved grids was developed. A computational scheme for the method was presented and the computation of fast Fourier transform was improved. For practice convenience the stability condition of the method was derived. Curved grids were generated using multiblock mapping and transfinite interpolation. This method can effectively eliminate the spurious diffraction caused by surface discretization. The comparison between synthetic seismograms generated with Cartesian grid and curved grid demonstrated clearly the effectiveness of the method.