基于优化方法的时间-空间域隐格式有限差分算子确定方法

声波方程数值模拟构成了地震逆时偏移成像技术和全波形反演的基础。对于有限差分法而言,在满足一定的稳定性条件时,普遍存在着因网格化而形成的数值频散效应。如何有效地压制数值频散是有限差分方法研究的关键所在。为了进一步抑制数值频散,利用隐式有限差分比显式有限差分更能压制数值频散的特点,采用前人提出的新的有限差分模板(在保持相同精度的情况下增大了时间步长),应用信赖域优化方法在时间-空间域确定隐格式有限差分系数。频散分析和数值模拟试算的结果表明,这种新模板隐格式有限差分优化方法既提高了声波数值模拟精度又提高了计算效率。

Numerical simulation of acoustic wave equation is the basis of the reverse time migration and full waveform inversion. With some stability conditions,grid dispersion often exists because of the discretization of the time and the spatial derivatives in the wave equation. How to suppress the grid dispersion is therefore a key problem for finite difference approaches. Finite-difference scheme of partial differential equations are either explicit or implicit. Implicit finite difference scheme can suppress the grid dispersion further. Meanwhile,a new finite difference stencil was proposed to increase the time step while preserving the accuracy by previous researchers. Therefore,we propose to determine the optimal implicit finite difference operators in time-space domain with a new finite difference stencil. Dispersion analysis and seismic numerical simulation demonstrate that the accuracy of acoustic wave numerical simulation and the computation efficiency can be improved by the method.

国家自然科学基金(41325016,11271349)、国家重大科研装备研制项目(ZDYZ2012-1-02-04)、龙岩学院博士科研启动基金(LB2014010)和福建省教育厅JK项目(2014050)联合资助。