![]() ![]() The theoretical basis for acoustic wavefield extrapolation is developed from first principles. Quantitative validation is achieved by testing the weighting functions using synthetic seismic data. A framework for qualitative validation of prestack time migration is described in terms of accuracy of focusing, accuracy of relative positioning, and accuracy of absolute positioning. As is typical in geophysical inverse problems, a quantitative solution is provided for the estimation problem, and the appraisal problem is replaced by a validation process. The imaging problem is treated as an inverse problem consisting of an estimation problem and an appraisal problem. In this dissertation, I determine the exact optimum weighting function that produces an image as a stack of angle-dependent reflectivities, and suggest practical alternatives that are appropriate for imaging using prestack time migrations. EOM is implemented as a nonrecursive diffraction stack, where samples in the data space are weighted, filtered, and summed to produce samples in the image space. The kinematics of prestack time migration by the equivalent offset method (EOM) are well established as a simple reformulation of the double-square-root equation of seismic imaging. ![]()
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