Study of seismic wave excitation and propagation in laterally heterogeneous media was an active and important subject in seismology in the past two decades, numerous analytical and numerical efforts have been made in this research field. In this article, I have, first, made a brief review on those developments and then introduced and summarized a unified and efficient method, global generalized reflection-transmission (abbreviated to R/T thereafter) matrices method, for synthetic seismograms in multi-layered media with irregular interfaces developed by the author [24~26]. As demonstrated in this article, this method could be regarded as an extension of the generalized R/T coefficients method for the horizontally layered case [2,5] to the layered media with irregularly shaped interfaces by incorporating the T matrices technique [27,28]. Because of the use of a recursive scheme in computing the global generalized R/T matrices, this method is efficient, particularly for the case with a large number of
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