In this paper, we present a new method of seismogram synthesis for multi-layered media with irregular interfaces due to an arbitrary source. This method can be viewed as either an extension of the T matrix method for an inclusion to multi-layered media by introducing the global generalized R/T matrices, or an extension of the generalized R/T coefficients method for horizontally layered media to irregular layered ones by incorporating the T matrix method. The formulation obtained in this paper is expressed in terms of the global generalized R/T matrices. These global generalized R/T matrices can be determined from integrals along each interface and integral over source area via a recursive relation. This formulation provides an efficient scheme of computation, especially when the number of layers increases. Also, this formulation can be applied to any finite frequency, although for higher frequency it needs more computation time than for lower frequency. As examples, we give solutions of three specific problems, namely, horizontally layered media, irregular topography, and an irregular layer over a half-space.

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