Investigation of the effects of two Kirchhoff migration algorithms on reflection amplitudes

Zorondras Rodriguez and Gary F. Margrave

ABSTRACT

The effects of seismic migration on reflection amplitudes were tested with two Kirchhoff migration algorithms, one a simple diffraction stack algorithm and the other a full-featured, linear-interpolation Kirchhoff migration. A test acoustic velocity model was constructed and finite difference seismic forward modeling was done on the test velocity model to produce a zero offset section, which was then inverted by the two competing methods. Least-squares scale factors were determined and applied to each image in order to best fit the images to the model reflectivities. The least squares scalars for the two algorithms differed by almost five orders of magnitude, with neither being near unity. After scaling, the amplitudes of key reflectors in the scaled depth converted migrated sections were compared directly to the reflectivity that produced them. The L2 Norms of the residual of the scaled amplitudes and the reflectivity were compared for key reflection events. The diffraction stack method increases the contrast of the amplitudes between reflectors by 1.53-1.66 times, produces amplitudes that are erratic and uneven across reflectors as a function of position, and is highly sensitive to abrupt lateral changes in reflectivity. However the Kirchhoff migration algorithm decreases the contrast between amplitudes by 1.48-3.09 times, produces amplitudes which are fairly uniform and constant with respect to position along a reflector, and is also sensitive to abrupt lateral changes in reflectivity. Additionally comprehensive quantitative amplitude comparison and analysis test methodology was developed and described and is applicable to the testing of other varieties of migration algorithms. Finally two new CREWES MATLAB utilities vz2vt , and mig2depth , were developed to complete the testing, and are described.

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