用于声波方程数值模拟的时间-空间域有限差分系数确定新方法

Acoustic wave equation modeling with new time-space domain finite difference operators

声波方程数值模拟已广泛应用于理论地震计算,同时构成了地震逆时偏移成像技术的基础.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.如何有效地缓解或压制数值频散是有限差分方法研究的关键所在.为精确求解空间偏导数,相继发展了高阶差分格式优化方法和伪谱方法.近期,为更好地缓解数值频散,提出了时间-空间域有限差分方法,该方法采用了泰勒展开近似方法来确定有限差分格式系数,因而只能保证在一定的小范围内很好的拟合波场传播规律.为进一步压制数值频散效应,本文引入了时间-空间域特定波数点满足频散关系的方法,根据震源、波速和网格间距确定波数范围,同时考虑了多个传播角度,然后建立方程确定了相应的有限差分格式系数,使得差分系数能在更大范围符合波场传播规律.通过频散分析和正演模拟,验证了本文方法的有效性.

Numerical simulation of acoustic wave equation is widely used to synthesize seismograms theoretically, and is also the basis of the reverse time migration. 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. Time-space domain methods using plane-wave theory and Taylor series expansion are proposed to suppress grid dispersion recently. However, these methods can only preserve the real wavefield in a small range of frequencies and angles of propagation. To suppress the grid dispersion further, we propose to satisfy the grid dispersion relationship in arange of frequencies and angles of propagation. Dispersion analysis and seismic numerical simulation demonstrate the effectiveness of the proposed method.