高精度频率域弹性波方程有限差分方法及波场模拟

The method of finite difference of high precision elastic wave equations in the frequency domain and wave-field simulation

有限差分方法是波场数值模拟的一个重要方法,但常规的有限差分法本身存在着数值频散问题,会降低波场模拟的精度与分辨率,为了克服常规差分算子的数值频散,本文采用25点优化差分算子,再根据最优化理论求取的优化系数,建立了频率空间域中弹性波波动方程的差分格式;为了消除边界反射,引入最佳匹配层,构造了各向同性介质中弹性波方程在不同边界和角点处的边界条件.最后由弹性波波动方程和边界条件,通过频率域有限差分法,分别利用不同震源对弹性波在均匀各向同性介质、层状介质及凹陷模型中的传播过程进行了数值正演模拟,得到了单频波波场、时间切片和共炮点道集,为下一步的研究工作(如成像、反演)提供了研究基础.

The finite difference which is widely applied in seismic wave forward modeling, excursion and imaging, is an important method of wave-field numerical simulation. However, the routine finite difference has the problem of numerical dispersion which reduces precision and resolution of wave-field simulation. In order to overcome the numerical dispersion of routine finite-difference operators, 25-point optimized finite-difference operators are applied, and get the optimized coefl3cient on the basis of the optimization theory and establish a finite-difference format of elastic wave equations in the frequency-space domain. We introduce perfectly matched layer to attenuate the refection of the artificial boundary, and construct boundary and corner point conditions of elastic wave equations in isotropy media. Finally, according to elastic wave equations and boundary conditions, we respectively use different sources to implement simulation of elastic wave propagation in a homogenous isotropy medium, layered medium and a depression model with the frequency-domain finite-difference method. And a monochromatic wave field, time snapshot and common-shot point gathers are obtained, making the foundation for seismic imaging and inversion study.