旋转网格和常规网格混合的时空域声波有限差分正演  

Scalar wave equation modeling using the mixed-grid finite-difference method in the time-space domain

作　　者：胡自多[1,2] 贺振华[1] 刘威[2] 王宇超[2] 韩令贺[2] 王述江[2] 杨哲[2] 

机构地区：[1]成都理工大学油气藏地质及开发工程国家重点实验室,成都610059 [2]中国石油勘探开发研究院西北分院,兰州730020

出　　处：《地球物理学报》2016年第10期3829-3846,共18页Chinese Journal of Geophysics

基　　金：国家油气专项"天然气地球物理烃类检测;评价技术及应用"(2016ZX05007-006)资助

摘　　要：压制数值频散,提高正演模拟精度,一直是有限差分正演模拟研究的重要内容.基于时空域频散关系的有限差分法,比基于空间域频散关系的传统有限差分法,模拟精度更高.时空域声波方程数值模拟,普遍采用常规十字交叉型高阶有限差分格式.而在频率-空间域,普遍采用旋转网格和常规网格混合的有限差分格式,有效提高了模拟精度和计算效率.本文将频率-空间域混合网格有限差分的思想引入到时空域,提出了时空域混合网格2 M+N型声波方程有限差分方法.首先推导出基于时空域频散关系的混合网格差分系数计算方法,然后进行频散分析、稳定性分析,并和传统高阶、时空域高阶有限差分法对比,结果表明:计算量相同时,新方法能有效压制数值频散,显著提高模拟精度;新方法相比传统2 M阶有限差分法,稳定性增强,与时空域2 M阶有限差分法稳定性基本相当.最后利用新方法进行均匀介质、层状介质、盐丘模型的数值模拟和盐丘模型的逆时偏移,模拟效果和成像质量进一步证实了该方法的有效性和普遍适用性.The finite-difference method has been widely used in seismic forward modeling,RTM（Reverse Time Migration） and FWI（Full Waveform Inversion） because of its easy implementation,small memory and low computational cost.Numerical dispersion,due to discretization of time and space derivatives,seriously affects the forward modeling accuracy of the finite-difference method.So suppressing the numerical dispersion to improve the forward modeling accuracy is the key problem for the finite-difference method.In the frequency-space domain,the mixed-grid finite-difference method is often used,which can effectively improve the forward modeling accuracy.In the time-space domain,the traditional2 Mth-order finite-difference method is commonly used,which essentially has only 2nd-order accuracy.The time-space domain 2 Mth-order finite-difference method,in which the differencecoefficients are determined by satisfying time-space dispersion relation,has relatively high modeling accuracy,but its dispersion curves are still divergent.Although the rhombus-grid finite-difference method has indeed high modeling accuracy,it requires high computational cost.In this article,by introducing the mixed-grid strategy from the frequency-space domain to the time-space domain,we propose a new kind of mixed-grid 2 M ＋ N style finite-difference method,and derive the approach for calculating the finite-difference coefficients by satisfying time-space domain dispersion relation.In addition,we conduct dispersion analysis,stability analysis,and numerical simulation.The results demonstrate that（1）with almost the same computational cost,the traditional 2 Mth-order finite-difference method has seriously numerical dispersion mainly in the time dispersion,and has the lowest modeling accuracy.The time-space domain 2 Mth-order finite-difference method has some time dispersion and space dispersion,and has relatively high modeling accuracy.The mixed-grid 2 M＋Nstyle finite-difference method has no obvious numerical dispersion,and so has the highest mode

关 键 词：混合网格 时空域 有限差分 频散分析 正演模拟 

分 类 号：P631[天文地球—地质矿产勘探]