AN OPERATOR APPROACH TO FORWARD MODELING, DATA PROCESSING AND MIGRATION*

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Abstract
The response of a seismic model to excitation by a source can be represented in terms of the action of reflection and transmission operators for portions of the structure. This approach provides a flexible framework for both modeling and processing problems.The operator development provides a physical description of the wave propagation process and, via the expansion of reverberation operators, gives a mechanism for assessing the accuracy of approximate developments. The representation suggests new ways of developing modeling algorithms by balancing the computational effort expended on minor and major features of the model.For processing problems, the operator representation shows the relation of processing stages to the seismic wave field and thereby indicates effective sequences of operations. For migration it is possible to specify an ideal pre‐stack migration procedure in terms of the inverse of the propagation operators and to examine the problems which need to be overcome by practical algorithms.