基于雷米兹交换法的时空域差分系数优化方法  

Finite-difference coefficients optimization method based on Remez exchange method in time-space domain

作　　者：娄璐烽 黄建平[1,2] 彭炜颋 LOU LuFeng;HUANG JianPing;PENG WeiTing(School of Geosciences,China University of Petroleum(East China),Qingdao 266580,China;Laboratory for Marine Mineral Resources,Qingdao National Laboratory for Marine Science and Technology,Qingdao 266071,China)

机构地区：[1]中国石油大学(华东)地球科学与技术学院,青岛266580 [2]青岛海洋科学与技术国家实验室海洋矿产资源评价与探测技术功能实验室,青岛266071

出　　处：《地球物理学报》2025年第4期1487-1510,共24页Chinese Journal of Geophysics

基　　金：山东省海洋科技基金青岛海洋科学与技术国家试点实验室(2021QNLM020001);山东能源集团深层高温地热重大科技项目(SNKJ2022A06-R23);创新研究群体项目(41821002);国家自然科学基金优秀青年项目(海外)(ZX20230152);中国石油重大科技专项(ZD2019-183-003)联合资助。

摘　　要：在有限差分正演模拟过程中,优化有限差分系数是压制数值频散的有效策略之一.在空间域内优化的差分系数空间频散小,但是无法处理时间频散问题,而在时空域中用泰勒展开法求取的差分系数时间频散小,但是空间频散严重.针对两种频散难以同时压制的现象,以时空域频散关系的相对误差为目标函数,构建了无穷范数形式的优化问题,采用改进的雷米兹交换法求解以提高复杂函数的计算效率,达到在时空域内优化差分系数的目的.通过频散曲线分析、稳定性分析、地震波场模拟对比发现:(1)相较在空间域求取的差分系数,新方法求取的优化差分系数时间频散误差小,在大CFL(Courant-Friedrichs-Lewy)数正演模拟时压制时间频散效果明显,相较用时空域泰勒展开法求取的差分系数,新方法求取的优化差分系数有效频带宽度更大,空间频散误差更小;(2)新方法的有限差分格式稳定性高于空间域差分系数求取方法,能在大CFL数正演模拟下保持波场稳定传播;(3)均匀模型正演模拟验证了新方法能在明显压制时间频散的同时降低空间频散,层状模型测试了新方法在高速地层中的频散压制效果,新方法能在高速模型中获得高精度波场,Marmousi模型证明新方法适用于复杂模型.Finite-Difference(FD)coefficients optimization is an effective strategy to suppress numerical dispersion in FD forward modeling.FD coefficients optimized in space domain have small spatial dispersion but cannot solve the problem of temporal dispersion.On the contrary,FD coefficients calculated by Taylor expansion in time-space domain have small temporal dispersion with serious spatial dispersion.In order to suppress the two types of dispersion simultaneously,we first derive the relative error from dispersion relationship in time-space domain.Based on the relative error,we construct the optimization problems in the form of infinite norm.Then we solve the problems by improved Remez exchange method,which can increase computational efficiency of complex problems.Finally,the new optimized FD coefficients in time-space domain can be obtained.Dispersion curves analysis,stability analysis and comparison of seismic wave field simulations show that:(1)Temporal dispersion error of FD coefficients calculated by new method is reduced compared to FD coefficients calculated in space domain,and the suppression of temporal dispersion is effective when performing forward modeling under large CFL(Courant-Friedrichs-Lewy)number.Compared with FD coefficients calculated by Taylor expansion in time-space domain,the effective bandwidth of FD coefficients calculated by new method is larger,which leads to smaller spatial dispersion error;(2)Stability of FD Scheme using new method is higher than that using space domain FD coefficients methods,which means new method can keep wave field stably propagation in forward modeling with large CFL number;(3)Forward modeling of homogeneous model verifies that new method can significantly suppress temporal dispersion while reducing spatial dispersion.Layered model tests the dispersion suppression effect of new method in high-speed formation.New method can obtain high-precision wave field in high-speed model.The result of Marmousi model also proves that new method is applicable to complex model.

关 键 词：正演模拟 数值频散 差分系数优化 时空域 雷米兹交换法 

分 类 号：P631[天文地球—地质矿产勘探]