基于改进交错网格差分结构的地震波场正演模拟

Seismic wavefield forward simulation based on improvedstaggered grid finite difference stencil

有限差分离散在地震波场数值模拟中广泛使用,相比于传统时间二阶差分,时间高阶差分具有更高的精度和稳定性,隐式差分比显式差分具有更高的精度。本文结合时间高阶方法和隐式差分的优势,提出了一种改进的交错网格差分结构求解三维一阶声波方程。在该方案中,时间高阶离散被用于补偿传统时间二阶差分的近似精度,同时采用隐式交错网格差分求解空间导数;给出了关于时间离散格式的泰勒展开差分系数,求取了空间隐式离散格式中的泰勒展开和最小二乘两种差分系数。与现有的几种交错网格差分方案相比,改进方案能够在空间不同方向上采用不同的网格间距和差分算子长度,因此在保证模拟精度的前提下灵活性更高。数值分析和模型算例表明,改进方案能够采用较短的算子长度获得高精度模拟结果。

Finite difference(FD)discretization schemes are widely used in seismic wave numerical simulation.Compared with the conventional temporal second-order FD,temporal high-order FDs are more accurate and stable.Implicit FD is more numerical than the explicit FD.Combining the advantages of temporal high-order method and implicit FD,this paper develops an improved staggered grid FD(SFD)stencil to solve the three-dimensional first-order acoustic wave equation.In this approach,temporal high-order discretization is applied for compensating the accuracy of the conventional temporal second-order FD,and the spatial derivatives are approximated by the implicit SFD.We further provide Taylor-expansion(TE)-based coefficients for temporal discretization scheme,and estimate implicit spatial coefficients using TE and least-square.Compared with the existing SFD methods,the improved method can adopt different grid intervals and diffrent operator lengths in different spatial directions.While ensuring simulation accuracy,it is more flexible.Numerical analyses and modeling examples have proven that the developed method can generate high-accuracy simulation results with shorter operator lengths.Therefore,it can be regeared as an effective tool for seismic wavefield simulation.