To advance the mathematical and computational treatments of direct problems of the AVO involving multilayered media, a new derivation of the RT matrix method (reflection-transmission matrix method) is presented. This method allows calculate the complete dynamic response including both the displacement and stress fields in a layered half-space. The stability and accuracy of the direct problem’s solution are studied by numerical experiments on the model data. The synthetic seismogram building is realized. Based on actual data performance capabilities of the AVO inverse problems’ solution are investigated using iterative selections of models of the medium. It is shown that selection of models of the medium using a realized algorithm allows tracing the alterations of the medium parameters (bed thicknesses) between key wells.


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