Abstract: Powerful techniques have been developed for calculating the plane wave response of horizontally layered models.This method is quite general and is widely used in synthetic wave algorithms.The generalized reflection and transmission method takes an important role in this formalism,it can determine the complicate response of a series layers.Expansion in series of the reflection and transmission matrix can help us to deep understand the contributions of the multiple reflections and transmissions.

Key words: wave function, generalized reflection and transmission coefficients