中文摘要：

传统的高阶有限差分波动方程数值模拟方法采用高阶差分算子近似空间偏导数,能有效抑制空间频散.然而,传统的有限差分法仅采用二阶差分算子近似时间偏导数,这使得地震波场沿时间外推的精度较低.当采用较大的时间采样间隔,传统的有限差分法模拟波场会出现明显的时间频散,甚至不稳定.本文基于新的差分结构和中心网格剖分,发展了一种空间任意偶数阶精度、时间四阶和六阶精度的时空域有限差分方法.基于对离散后的频散关系进行泰勒展开,本文推导了时空域高阶有限差分算子的差分系数.相速度分析表明时间四阶、六阶精度的差分方法能显著地减小传统时间二阶精度差分方法的时间频散.在相同的精度下与传统差分法比较,本文发展的时间四阶、六阶有限差分方法的计算效率比传统方法高.均匀和非匀均介质中的波场数值模拟实验进一步证实本文研究的时空高阶有限差分方法的优越性.

英文摘要：

The traditional finite-difference（FD）seismic wave simulation scheme adopts highorder FD operators to discretize the spatial derivatives,and the second-order FD operator to discretize the temporal derivative.Therefore,the traditional high-order FD method only achieves high-order accuracy in space,but exhibits low-order accuracy in time.When a relatively large time step is applied,the traditional FD method suffers from visible temporal dispersion and even instability.This paper develops new time-space domain high-order FD methods that attainarbitrary even-order accuracy in space,fourth-and sixth-order accuracy in time.The new FD methods are developed based on new FD stencils and a centered-grid.The FD coefficients are determined from the discrete dispersion relation using the Taylor-series expansion（TE）approach.Dispersion analysis indicates that our temporal fourth-and sixth-order FD methods improve the accuracy of the traditional temporal second-order FD method significantly. Computational cost analysis demonstrates that our temporal high-order FD methods are more efficient than the traditional temporal second-order method.Numerical simulation of seismic waves in homogeneous and heterogeneous media further validates the effectiveness of our high-order FD methods.