二维频率域全波场有限差分数值模拟方法

2Dfull-wavefield modeling in frequency domain using finite-difference.

由于面波和体波不同的物理特性,包含面波的频率域全波形反演仍然是一个挑战,而忽略自由边界的影响会降低反演结果的分辨率以及产生虚假信息,故考虑自由边界的频率域全波场数值模拟是解决这一问题的基础。本文从弹性波波动方程出发,采用最佳匹配层吸收边界条件消除边界反射,并尝试将时间域数值模拟中的隐式自由边界条件引入频率域数值模拟中,利用最优化25点差分法实现频率域全波场数值模拟。通过与均匀介质中面波解析解以及层状介质中理论相速度频散曲线的对比,验证了全波场模拟的正确性,并设计两个层状模型分析了地震波在频率域和时间域中的传播特性。

Full-waveform inversion(FWI)including surface wave and body wave in frequency domain is still a challenge because of their different physical behavior and nature.But it would lose of resolution and show artifacts if we neglect the free surface in inversion.Therefore,full-wavefield modeling considering free surface condition in the frequency domain is a fundamental work to solve this problem.Based on frequency domain elastic wave equations,we use perfectly matched layer to attenuate the refection of the artificial boundary,and try to introduce implicit boundary conditions to frequency domain modeling in order to simulate Rayleigh waves,which is usually used as free surface condition in time domain seismic modeling.By using 25-point finite difference method,we perform full-wavefield modeling in the frequency domain.Then,we validate our results by comparing them with elastic wave analytic solutions in homo-geneous medium and theoretic phase velocities of Rayleigh wave in layered medium.Finally,we analyze wave propagation in both the frequency domain and the time domain in two layered medium.