虚谱法求解波动方程的算法改进

THE IMPROVEMENT ON THE ALGORITHM OF PSEUDO-SPECTRUM METHOD IN SOLVING WAVE EQUATION

虚谱法利用付里叶变换和有限差分求解波动方程 ,是地震波场正演模拟的重要方法之一 ,但其常规算法运算量大 ,运算时间长。为此 ,我们在常规算法的基础上作了些改进 ,主要是提出了反付里叶变换的快速算法 ,并运用正反付里叶变换的快速算法和避免重复运算等手段 ,使运算量大大减少 。

The pseudospectrum method uses Fourier transform and finite difference to solve wave equation It is one of the important methods used to simulate the seismic wave field But its routine algorithm needs large quantity of computation and spends long computing time It will be improven the routine algorithm in this paper. At first, it is presented that the formulas of fast reverse Fourier tranform ( 1- D , 2- D ) And then, by using the fast Fourier transform and the fast reverse Fourier transform as well as other techniques in the algorithm, it makes the quantity of computation compressed greatly,and makes the computing time reduced to 1/4 of the routine computing time