Analysis of the resolution function in seismic prestack depth imaging |
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Authors: | L-J Gelius I Lecomte H Tabti |
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Institution: | Department of Geology, University of Oslo, PO Box 1047 Blindern, 0316 Oslo,;NORSAR, PO Box 51, 2027 Kjeller, and;PGS Geophysical AS, PO Box 290, 1326 Lysaker, Norway |
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Abstract: | We consider the problem of estimating subsurface quantities such as velocity or reflectivity from seismic measurements. Because of a limited aperture and band-limited signals, the output from a seismic prestack reconstruction method is a distorted or blurred image. This distortion can be computed using the concept of resolution function, which is a quantity readily accessible in the Fourier space of the model. The key parameter is the scattering wavenumber, which at a particular image point is defined by the incident and scattered ray directions in a given background model. Any location in any background model can be considered. In general, the resolution function will depend on the following four quantities: the background velocity model, the frequency bandwidth, the wavefield type and the acquisition geometry. We first establish the resolution function for a general scattering model assuming local reaction. We then adapt this result for two well-known scattering models: Born and Kirchhoff. For each of these approximations the corresponding resolution function is derived and discussed. Finally, by employing a simple synthetic data example we demonstrate the ability of the resolution function to predict the image distortions. |
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