摘要
有限差分方法(Finite-difference Method, FD)广泛用于地震波场数值模拟,但其存在固有的数值频散问题,影响模拟的计算效率和数值精度.本文主要研究了有限差分方法的空间数值频散误差和网格划分精度以及差分算子的关系,基于计算量最小准则,提出了最优化有限差分参数选取流程,为有限差分数值模拟参数选取提供理论指导.本文主要工作包括:(1)提出了空间数值频散正变换过程(Forward Space Dispersion Transform, FSDT)方法,该方法可以高效模拟出不同网格划分精度(波长采样点数)的带有空间数值频散的波场;(2)提出了波场空间数值频散误差衡量准则,可以定量地判断出数值模拟导致的波形频散程度,选取合适的频散误差阈值;(3)研究了给定空间数值频散误差阈值下,差分算子系数、差分算子阶数、网格划分精度与计算量之间的关系.文中基于雷米兹交换方法(Remez Exchange Method, RE)和泰勒级数展开方法(Taylor-series Expansion Method, TE)的差分系数,在空间数值频散误差阈值0.01时,数值模拟了不同差分算子阶数、网格划分精度与计算量的关系,并给出了有限差分参数选取的参考值.
The finite-difference(FD)method is widely used for simulating complex wavefield propagation because of its high accuracy and efficiency.However,it suffers from numerical dispersions caused by spatial discretization with coarse grid sizes.The dispersions affect the computational efficiency and modeling accuracy.This study investigates the relationship among numerical dispersion error,FD operators,and the number of samples per shortest wavelength.Based on the criterion of minimum computational cost,we propose a scheme to estimate the optimal FD parameters,i.e.,the number of samples per shortest wavelength and the spatial order of FD operators.Firstly,we introduce a method called Forward Space Dispersion Transform(FSDT)to add spatial dispersion to the reference wavefield for various scenarios of grid spacing and FD orders;Secondly,we measure the normalized L2norm of the error between the reference wavefield and dispersed wavefield,so we can estimate the dispersion error directly to set a proper error threshold;Finally,we study the relationship among FD coefficients,FD operator length,grid spacing,and computational cost to find out the optimal grid spacing and FD order for giving the minimum computational cost under a preset error threshold.We also show some numerical tests of the relationship among the FD operator length,grid points per shortest wavelength,and computational cost under an error threshold of 0.01with the finite-difference coefficients generated using the Remez Exchange(RE)method and Taylor-series Expansion(TE)method.Based on the tests,some FD parameters are recommended.
作者
方修政
姚刚
钮凤林
吴迪
FANG XiuZheng;YAO Gang;NIU FengLin;WU Di(State Key Laboratory of Petroleum Resources and Prospecting,China University of Petroleum(Beijing),Beijing102249,China;Changjiang Geotechnical Engineering CO.,LTD,Wuhan 430010,China;Unconventional Petroleum Research Institute,China University of Petroleum(Beijing),Beijing102249,China;College of Geophysics,China University of Petroleum(Beijing),Beijing102249,China)
出处
《地球物理学报》
SCIE
EI
CAS
CSCD
北大核心
2023年第6期2520-2533,共14页
Chinese Journal of Geophysics
基金
中石油集团前瞻性基础性项目“物探岩石物理与前沿储备技术研究”(2022DQ0604-02)
国家自然科学基金项目(41974142,42074129)
中国石油大学(北京)油气资源与探测国家重点实验室项目(PRP/indep-4-2012)联合资助。
关键词
高阶有限差分
数值频散
空间数值频散正变换
优化参数选取
High-order finite-difference
Numerical dispersion
Forward space dispersion transform
Optimal parameter estimation
