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提出了以计算一个或两个空间坐标导数的谱方法与对剩余空间坐标和时间作一维有限差分近似相结合为基础的若干有效算法。讨论了几种依赖于弹性参数特性的算法。也提出了一种仅对空间坐标作有限差分近似而使问题简化的算法。对于这种情况,利用矩阵分解法,把获得的对时间的普通差分方程组简化成N个独立的柯西问题。对这些柯西问题可以使用解析方法求解。我们对不同模型给出了计算合成地震图的一些例子。
Several effective algorithms based on the spectral method of calculating one or two spatial coordinate derivatives and the one-dimensional finite difference approximation of the remaining space coordinates and time are proposed. Several algorithms that depend on the characteristics of elastic parameters are discussed. An algorithm is also proposed that simplifies the problem by approximating the finite difference of the space coordinates only. In this case, we use the matrix decomposition method to simplify the ordinary differential equations obtained over time into N independent Cauchy problems. The solution to these Cauchy problems can be solved analytically. We give some examples of calculating synthetic seismograms for different models.