The problems of stretching and aliasing usually occur in prestack Kirchhoff migration. A multiwavelet-based approach is proposed to provide an alternative approach to resolve these problems. Two steps are involved in the multiwavelet-based algorithm: The first step is the decomposition of the seismic traces with a series of wavelets of different dominant frequencies. This step is based on the principle of basis pursuit and is enhanced for more accurate and sparse decomposition by adding an adaptive subdictionary that is associated with the minima and maxima of a seismic trace. The second step is wavelet migration based on the Kirchhoff formulation using a novel approach. The outer iteration is the wavelets of the input seismic traces, which ensures that an input wavelet is only used once in the entire migration process. This enables output of multiple migrated images of different wavelets of dominant frequency ranges, elimination of noisy images, and composition of images for specific interpretation and reservoir characterization purposes with very little extra computational cost. The stretching and aliasing problems are naturally resolved because interpolation on the seismic trace is not required in the migration. We tested the algorithm using a synthetic model with a dipping layer and a 2D real seismic section. We compared our results with results obtained by conventional Kirchhoff migration.

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