地震波数值模拟中差分近似的各向异性分析

Anisotropic analysis of difference approximation in seismic wave numerical modeling

(大庆油田有限责任公司勘探开发研究院,黑龙江大庆163712)

Exploration and Development Research Institute,Daqing Oilfield Company Limited,CNPC,Daqing 163371,China

有限差分算法存在固有的数值频散问题,在正演过程中会严重干扰有效波场,降低地震波场的分辨率。针对此,从最简单的平面波数值理论分析出发,推导了任意高阶有限差分近似条件下相对相速度和相对群速度的计算公式,给出了求解最佳Courant数的计算方法,分析了差分近似造成的各向异性效应。理论分析和数值实例研究表明,正演数值模拟的精度与最小波长节点数、Courant数、有限差分近似阶数这3个因素密切相关,通过合理调节这3个量可以提高有效波场区域的数值模拟精度,拓宽正演波场的频带宽度,提高数值模拟的计算效率。

The finite difference algorithm has its inherent numerical dispersion problem,which seriously disturb the effective wavefield during forward simulation and therefore decrease the resolution of seismic wavefield.In order to solve the problem,starting from the analysis of the simplest plane wave numerical theory,we derived the formula of relative phase velocity and group velocity under the condition of arbitrary high-order finite-difference approximation,and gave the computational method for acquiring the optimum Courant number,and then analyzed the anisotropic effects due to finite difference approximation.The theory analysis and numerical examples show that the precision of seismic wave forward numerical modeling has close relationship with the least wavelength nodes,the Courant number and the finite-difference approximating order.Rationally adjusting the three factors can improve the numerical modeling precision in the effective wavefield region,extend the frequency bandwidth of the forward modeling wavefield and improve the computational efficiency of the numerical simulation.