基于无网格的地震波场数值模拟方法综述  

Overview of mesh-free method of seismic forward numerical simulation

作　　者：刘立彬[1] 段沛然 张云银[1] 田坤[1] 谭明友[1] 李振春[2] 窦婧瑛 李青阳 LIU Li-bing;DUAN Pei-ran;ZHANG Yun-yin;TIAN Kun;TAN Ming-you;LI Zhen-chun;DOU Jing-ying;LI Qing-yang(Institute of Geophysical Exploration,Shengli Oilfield,Sinopec,Dongying 257022,China;School of Geosciences,China University of Petroleum(East China),Qingdao 266580,China)

机构地区：[1]中国石化胜利油田分公司物探研究院,东营257022 [2]中国石油大学(华东)地球科学与技术学院,青岛266580

出　　处：《地球物理学进展》2020年第5期1815-1825,共11页Progress in Geophysics

基　　金：国家自然科学基金(41774133);国家油气重大专项(2017ZX05072001,2016ZX05006-002-003)联合资助.

摘　　要：高精度地震波数值模拟方法是波动方程正演、偏移成像和全波形反演等问题的关键,为储层评价、岩性解释和油藏描述等提供重要的理论依据.传统波动理论的数值模拟方法基于固定采样步长进行网格剖分,难以适应复杂精细地质构造和起伏地表问题.与之相比,无网格法摆脱了网格的束缚,能够有效避免网格剖分产生的虚假反射;同时无网格节点半径随模型速度变化,在不同速度区域可灵活采取不同半径剖分策略,从根源上解决了速度差异较大区域的网格适配问题.但国内关于无网格的地震波场模拟研究并不多,未有融入最新进展的综述性文献.本文针对无网格地震波场数值模拟进行了回顾性分析,讨论了不同类型无网格方法的优劣.滑动最小二乘法计算成本和存储量远低于有限元法,但加载边界过程复杂;无单元Galerkin法求解精度高但计算量大,需要采用数值积分构造背景节点;广义有限差分法无需构建基函数且在导数逼近方面具有优势,但由节点构造的星存在病态性;径向基函数有限差分法形式简单、抗畸变能力强、灵活性好,为目前应用最为广泛的数值模拟算法,但不便于大型问题的求解.最后,详细阐述了无网格地震波数值模拟的发展现状与趋势,并给出相应的结论.As the key of wave equation forward modeling,migration imaging and full waveform inversion,high precision seismic wave numerical simulation plays an important role in reservoir evaluation,lithology interpretation and reservoir description.The traditional simulation method of wave theory is based on fixed sampling step for mesh generation,which is difficult to adapt to complex fine geological structure and surface undulation.The mesh-free method can get rid of the constraints of the mesh,effectively avoid the false reflection of the mesh generation,and the nodes can be flexibly divided with the change of the speed of the model.This method can naturally avoid spurious diffractions caused by the transition of different sampling areas with small additional computation,but most coordinate transformation may suffer from stability problem of surface boundary condition.As a powerful difference approximation-based method in recent years,meshfree method is proposed to simulating seismic wave propagation using constructing approximation functions based on a group of nodes.Without any relevant mesh partition or"element"links,nodes are adaptively and flexibly distributed with respect to irregular structures and velocity wavefield.A unit partition formed by meshfree approximation function has controllable continuity and integrity,and is independent of each other.Hence,meshfree method can effectively avoid spurious diffractions,and the partitioning points change flexibly with velocity of the model.Meshfree method could also save plenty of memory through distributing nodes suitably with respect to model parameters.However,there are few studies on Meshless seismic wave field simulation in China,and there is no comprehensive literature on the latest progress.In this paper,the numerical simulation of seismic wave field based on meshless method is retrospectively analyzed,and the advantages and disadvantages of the method are discussed.The computational cost and storage of sliding least squares method are much lower than that of fin

关 键 词：数值模拟 无网格 滑动最小二乘法 无单元Galerkin法 广义有限差分法 径向基函数有限差分法 

分 类 号：P631[天文地球—地质矿产勘探]