非均匀弹性介质中旋转交错网格有限差分与任意高阶间断有限元地震波场模拟方法研究

Comparison of the rotated staggered grid finite difference method with DG finite element method in heterogeneous elastic media

复杂介质中的地震波数值模拟对于地震勘探非常重要.实际应用中经常遇到介质参数剧烈变化的情况,必须选择合适的数值方法进行正演,使波场模拟精度和计算效率满足要求.本文研究了旋转交错网格有限差分法与任意高阶间断有限元法在非均匀弹性介质中波场模拟的精度与计算效率,分析了界面两侧介质参数相对变化量以及界面倾角对上述两种方法数值模拟结果的影响.对于水平界面,界面两侧介质参数一定范围内的改变对旋转交错网格有限差分法的振幅精度和相位精度没有影响;在介质参数存在强反差的情况下,任意高阶间断有限元法需要使用高阶多项式基函数来达到较高的相位精度.有限元法的相位精度优于有限差分法,但需要更多的计算量.对于倾斜界面,当单位波长内含有14个网格点时,界面倾角的变化对旋转交错网格有限差分法的振幅精度及相位精度没有影响,且其精度与任意高阶间断有限元法的精度相接近.

Numerical modeling of seismic wavefield in complex media plays an important role in exploration geophysics. In some seismic numerical applications we have to simulate wave propagation with sharp medium discontinuities. The rotated staggered grid （RSG） finite difference （FD） method and the arbitrary high-order derivatives discontinuous Galerkin （ADER [）G） finite element （FE） method are both developed to solve the problem of strong material heterogeneities. In this paper we compared the RSG FD scheme with the ADER-DG FE scheme on their behaviors at high contrast discontinuities. We simulate wave propagation in two models, one is a two-layer model with flat interface, and the other with a dipping interface. In the first model, when we change the ratio of the material parameters in the first layer to the parameters in second layer, the envelop and phase misfits of the RSG FD scheme change little; the ADER-DG FE scheme needs to use a high-order polynomial basis functions to get small phase misfits with strong material heterogeneities. The FE scheme has advantage over the FD method on phase misfits, hut it needs a high CPU effort. In the second model, when we change the angle of the dipping interface, the envelop and phase misfits of the RSG FD scheme change little with 14 grid points per wavelength according to the dominant frequency.