Replacing the reflection and transmission coefficients at a solid-solid interface by thin layered transition zone analogues is considered. These thin layered zones are often associated with hydrocarbon deposits in sedimentary strata. This is done within the context of zero order asymptotic ray theory (ART) using the stationary phase method, which essentially produces the same results. The frequency dependent reflectivities and transmittivities that replace the reflection and transmission coefficients are derived using propagator matrix methods, the basis for the classical reflectivity method and incorporated into the zero order ART solution for a plane layered structure composed of thick layers interspersed with thin layered transition zones. ART is used in the thick layers to introduce geometrical spreading.
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