本章先分析说明伪谱法求解波动方程的算法原理，再给出弹性波场伪谱法数值模拟的改进算法；然后，通过直接引入P波波场变量和S波波场变量，给出可实现弹性波场的P波和S波分解的波动方程，并用伪谱法实现弹性波场的P波和S波分解的数值模拟；最后用伪谱法对井间地震的复杂波场作数值模拟，分析井间地震波场中各种波的传播规律。(In this chapter, the principle of pseudo-spectral method for solving wave equation is analyzed, and then an improved algorithm for numerical simulation of elastic wave field is given. Then, by directly introducing P-wave field variable and S-wave field variable, the wave equation which can realize P-wave and S-wave decomposition of elastic wave field is given, and the P-wave sum of elastic wave field is realized by pseudo-spectral method. Numerical simulation of S-wave decomposition; finally, pseudo-spectral method is used to simulate the complex cross-well seismic wave field and analyze the propagation law of various waves in cross-well seismic wave field.)