起伏地表条件下基于无网格有限差分方法的频率域声波波动方程数值模拟  

A mesh-free fnite-difference scheme for frequency-domain acoustic wave simulation with topography

作　　者：蔡晓慧[1] 黄婵娟 陶然 范小平 刘恒 Cai Xiao-Hui;Huang Chan-Juan;Tao-Ran;Fan Xiao-Ping;Liu Heng(Institute of Geotechnical Engineering,Nanjing Tech University,Nanjing 210009,China)

机构地区：[1]南京工业大学岩土工程研究所,南京210009

出　　处：《Applied Geophysics》2023年第4期447-459,670,共14页应用地球物理（英文版）

基　　金：supported by National Natural Science Foundation of China project(No.41704122).

摘　　要：随着地震勘探对象日趋复杂,能精确描绘起伏地表、复杂地质构造的数值模拟方法显得十分重要。本文将基于无网格有限差分方法发展至起伏地表条件下频率域数值模拟中:无网格节点理论上能够适应任意地表和地质构造;有限差分方法具有计算效率高、内存占用小、模拟精度较高等优点。因此基于无网格的有限差分方法既保证了高效率又适用于不规则地表。此外,本文将完全匹配层(PML)吸收边界条件引入基于无网格有限差分频率域数值模拟中以压制边界反射,并对比了简化PML、经典PML以及复频移PML方法压制边界反射的效果;随后将起伏地表条件下压制边界反射效果较好的复频移PML方法应用到基于无网格与规则网格数值模拟的对比中,其中波场快照、地震记录以及地震子波波形对比结果都验证了基于无网格有限差分方法数值模拟的有效性。最后,将本文数值模拟方法应用到起伏地表的Marmousi模型与实际资料中,进一步验证了该方法的有效性与应用性。With the increasing complexity of seismic exploration objects,numerical simulation methods that can accurately describe topographical surfaces and complex geological structures are very important.In this study,we propose a mesh-free fnite-difference method for frequency-domain numerical simulation with topography.The mesh-free nodes method theoretically applies to any surface and geological structure,whereas the finite-difference scheme has the advantages of high calculation efficiency,small memory occupation,and high simulation accuracy.Therefore,the mesh-free finite-difference method ensures high efficiency and is suitable for irregular surfaces.In addition,we introduce the perfectly matched layer(PML)absorbing boundary condition into the mesh-free numerical simulation,and we compare the performance of the simplifed PML,the classical PML,and the complex frequency-shifted PML methods in suppressing boundary reflections.Then,the complex frequency-shift PML method,which is more accurate in suppressing boundary reflections under topographical surface conditions,is applied to the comparison of the mesh-free and regular grid numerical simulations.The comparisons reflected in snapshots,seismic records,and seismic wavelets demonstrate the effectiveness of the proposed mesh-free fnite-difference method.Finally,the proposed numerical simulation method is applied to the Marmousi model and feld data with topography to further demonstrate its effectiveness.

关 键 词：无网格 起伏地表 频率域 声波 数值模拟 

分 类 号：P631.4[天文地球—地质矿产勘探]