摘要
随着勘探深度和成像精度要求的不断提高,深层目标的反射时间越来越长,模型网格的剖分日趋细化,导致数值模拟的负担急剧加重.因此,迫切需要开发更精确且更高效的地震波数值模拟新方法.分裂龙格库塔格式是一种重要的时间离散方法,它能够采用较大的时间步长进行递推,具备显著的计算效率提升潜力;然而,其数值精度受到数值时间频散的制约,在长时程模拟中误差累积严重,尚无有效的解决策略.本文提出一种针对二阶分裂龙格库塔格式的参数选择策略,并给出对应的时间频散变换,旨在保持计算效率的同时提升数值精度.首先,我们基于龙格库塔格式的传递矩阵,推导了约束时间步长选择的优化问题,并给出参数组合策略,以获得尽可能大的稳定时间步长;随后,为多种参数组合推导对应的时间频散变换,以压制由大时间步长引入的数值时间频散;最后,通过系列数值实验验证本文方法的有效性.作为一种后处理方法,本文提出的时间频散变换可在很小的计算开销下显著降低长时程模拟中的数值时间频散,将数值精度提升了约三个量级.本文提出的参数组合与时间频散变换对分裂龙格库塔格式具有良好的通用性,为波动方程数值模拟提供了新思路,对实现自适应网格下的深层目标精细成像与高效长时程模拟具有重要意义,应用前景广阔.
As the demands for imaging depth and imaging precision in seismic exploration increase,the reflection time for reflectors lengthen and grid spacing becomes finer,significantly intensifying the computational burden of numerical simulation.Thus,it is crucial to develop more accurate and efficient numerical methods for simulating seismic wave propagation.The partitioned Runge-Kutta scheme,an important time discretization method,allows for the use of large time steps and holds significant potential to enhance computational efficiency.However,its numerical accuracy is constrained by numerical time dispersion,which leads to considerable error accumulation in long-term simulations.In this paper,we present a discrete parameter selection strategy for the second-order partitioned Runge-Kutta scheme and derive time-dispersion transforms to enhance its numerical accuracy while maintaining high computational efficiency.First,by analyzing the time-marching matrix of the partitioned Runge-Kutta scheme,we formulate a constrained optimization problem governing the selection of discrete parameter and derive a strategy for choosing parameters corresponding to the maximum stable time step.Second,we propose time-dispersion transforms to mitigate numerical time dispersion induced by large time steps.Finally,we conduct a series of numerical experiments to demonstrate the efficiency of the proposed method.As a post-processing technique,the proposed time-dispersion transforms significantly reduce numerical time dispersion in long-term simulations with minimal increases in computational cost,enhancing numerical accuracy by three orders of magnitude.The proposed discrete parameter selection strategy and time-dispersion transforms exhibit great adaptability for partitioned Runge-Kutta schemes and is significance for imaging deep targets with adaptive grids,offering broad application prospects.
作者
苗中正
张金海
MIAO ZhongZheng;ZHANG JinHai(Key Laboratory of Deep Petroleum Intelligent Exploration and Development,Institute of Geology and Geophysics,Chinese Academy of Sciences,Beijing 100029,China)
出处
《地球物理学报》
北大核心
2025年第9期3588-3599,共12页
Chinese Journal of Geophysics
基金
中国科学院重点研发计划(KGFZD-145-23-15,ZDBS-SSW-TLC001)
国家资助博士后研究人员计划(GZB20240736)
中国科学院地质与地球物理研究所重点部署项目(IGGCAS-202401)的联合资助.
关键词
数值模拟
分裂龙格库塔格式
大时间步长
大库朗数
数值时间频散
Numerical simulation
Partitioned Runge-Kutta scheme
Large time step
Large Courant number
Numerical time dispersion
