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Applications to Data Regularization

To illustrate the applications of the PS-AMO operator, I will use two problems that are present in 3-D OBS dataset: First, the irregular acquisition geometry problem. Irregularly sampled data degrades the final image with amplitude artifacts and phase distortions; therefore, I need to map the data to a regular grid. Second, the high cost of 3-D wave-equation migration; the size of the 3-D prestack data cube is proportional to the cost of wave-equation migration. To reduce this cost I just need to reduce the dimensionality of the data space. To accomplish these two problems, I combine an interpolation operator with the f-k log-stretch PS-AMO operator in a lest-squares objective function.