Prestack migration by equivalent offsets and CSP gathers

A method of prestack time migration is presented that is simpler, faster, and provides better velocity information than conventional methods. It is based on prestack Kirchhoff time migration and can be applied to both 2-D and 3-D data. The method is divided into two steps, a gathering process that forms common scatterpoint (CSP) gathers, and an imaging process using a Kirchhoff migration performed independently on each CSP gather. The CSP gathering process sums input traces into equivalent offset bins in each CSP gather with no time shifting. The equivalent offset is defined by an exact algebraic transformation of the double square root (DSR) equation of prestack time migration into a hyperbolic form. A CSP gather is similar to a CMP gather as both contain offset traces, and both represent a vertical array of scatterpoints. CSP gathers can be formed at any arbitrary location, have higher fold in their offset bins, and have a much larger offset range due to the gathering of all input traces within the migration aperture. The imaging process collapses each CSP gather into a single migrated output trace. It is performed as a Kirchhoff process which consists of scaling, filtering, normal moveout (NMO) correction, and stacking. The migration velocities are determined by conventional velocity analysis of the CSP gathers. Significant computational savings result from delaying arithmetic operations on the input samples until after the CSP gather has been formed. The high fold and large offsets of the CSP gather provide better focusing and improved velocity analysis. This space-time domain method is suitable for uneven geometries, enables velocity analysis at random locations, and permits prestack migration of a 3-D volume into an arbitrary 2-D line. It may also be adapted to migrate from topography, and to migrate converted wave (P-SV) data. Results from conventional processing of real 2-D and 3-D data are compared with the new method, demonstrating improved velocity analysis and superior migrated

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