地震工程学报2016，Vol.38Issue(5)：815-821,7.DOI:10.3969/j.issn.1000-0844.2016.05.0815
适于声波方程数值模拟的时间-空间域有限差分算子改进线性算法
Acoustic Wave Equation Modeling with a New Time-Space Domain Finite Difference Stencil and an Improved Linear Algorithm
摘要
Abstract
Numerical methods prove useful in exploration seismology.The most commonly used numerical methods are the finite difference,finite volume,and finite element methods.These methods constitute the basis for reverse time migration and full-waveform inversion.Finite differ-ence methods are widely used in wave field extrapolation because of their higher computation effi-ciency,lower memory requirements,and easier implementation.During discretization of the time and the spatial derivatives in the wave equation,grid dispersion often occurs.Grid dispersion can result in artificial waves and inaccurate wave fields.Therefore,finding suitable finite difference operator coefficients to preserve the dispersion relationship of the wave equation,thus reducing grid dispersion,is one of the most important issues when using finite difference methods.To reduce grid dispersion,the traditional method uses high-order finite difference schemes in the spatial domain.However,waves are simultaneously propagated in time and space.Therefore, some researchers propose finite difference schemes based on the time-space domain dispersion relationship.Most commonly used are the high-order Taylor expansion method and the optimized method.However,the time step is relative small even in the optimized time-space domain meth-od.Recently,a new finite difference stencil has been proposed to increase the time step while pre-serving the accuracy with the least-squares method.The time-space domain dispersion relation-ship of this new finite difference stencil is linear.Therefore,in this paper,we propose using this improved linear method,with the new finite difference stencil,to obtain the finite difference coef-ficients for the acoustic wave equation.We demonstrate,by dispersion analysis and numerical simulation,that with this new FD stencil and its improved linear solution,the wave equation simulation speed can be doubled compared with the previous linear method.关键词
声波正演/时间-空间域/有限差分格式/线性方法Key words
acoustic wave-equation modeling/time-space domain/finite difference scheme/linear method分类
天文与地球科学引用本文复制引用
梁文全,赖永明,姜琳,吴超凡..适于声波方程数值模拟的时间-空间域有限差分算子改进线性算法[J].地震工程学报,2016,38(5):815-821,7.基金项目
福建省科技厅青年基金(2016J05104) （2016J05104）
福建省教育厅项目(JK2014050) （JK2014050）
龙岩学院博士启动基金(LB2014010) （LB2014010）
