峰谷平均法及其在计算浅源合成地震图中的应用

为了计算在震源和接收点深度相同或相近情况下分层半空间介质中的合成地震图,在重复平均法的基础上加以改进,提出一种有效的数值积分方法--峰谷平均法.根据被积函数的变化特点,将波峰和波谷值抽取出来组成慢收敛序列,利用重复平均法快速而准确地求出其极限值.与半解析方法相比,本文方法不仅数学处理上非常简单,而且易于数值实现.数值试验表明,本文方法是准确和高效的.

PEAK-TROUGH AVERAGING METHOD AND ITS APPLICATION TO CALCULATION OF SYNTHETIC SEISMOGRAMS WITH SHALLOW FOCUSES

In order to calculate synthetic seismograms in a layered half space with the sources and the receivers at close or same depths, an efficient numerical integration method the Peak Trough Averaging Method (PTAM) is proposed, based on the repeated averaging method. According to the variation, features of the integrand, the values of peaks and troughs are taken out and formed a slowly convergent series, and the repeated averaging scheme is performed to calculate the limit rapidly and accurately. Compared with the semi analytic method, PTAM is not only much simpler mathematically, but also easier to implement practically. Numerical tests indicate that PTAM is accurate and efficient.