对计算水平分层介质响应正交归一化法的改进

汪荣江提出一个简单的正交归一化技术来克服经典的Thomson-Haskell传播矩阵方法中存在的数值不稳定问题.为了进一步提高计算效率,给出该方法的2种改进.一种改进方法是将传播矩阵中与频率无关的部分分离出来,对于某一固定的水平慢度,这些矩阵只需计算一次;另一个改进是利用Langer块对角化的技术,将传播矩阵分解为几个稀疏矩阵的乘积.我们将改进之后的算法应用于计算水平分层模型中的广义反射系数.较之原有方案,提出的改进能节省一半计算时间.

An improvement to the orthonormalization method for efficient computation of plane-wave response in multi-layered media

Wang proposed a simple orthonormalization technique to overcome the numerical instability in the original Thomson-Haskell propagator algorithm. In this paper, two kinds of improvements to the method for computational efficiency are presented. One is to separate the frequency independent matrices from the propagator, these terms can be computed once for a fixed slowness; the other is to decompose the propagator by the Langer block-diagonalization into a product of several sparse matrices. The new developments are applied to calculate the generalized reflection coefficients for a multi-layered model. It leads nearly half reduction in computation time compared with the original scheme.