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.%有限差分法广泛应用于地震波场的数值延拓,确定合适的有限差分算子以减小数值频散是有限差分法的一个重要研究内容.近年来为了进一步抑制数值频散和增加时间步长,新的有限差分模板得到了应用,对于此,前人使用泰勒展开方法和最小二乘方法确定有限差分算子系数.本文在以前工作的基础上,使用改进的线性方法确定新模板的有限差分系数,并与传统模板线性方法进行对比;通过频散分析和正演模拟验证出新模板线性方法能够更好地保持频散关系,在相同的精度下效率提高了一倍,从而说明了改进的线性方法的有效性.
展开▼
