Seismic data mapping and reconstruction

Seismic data mapping uses data at source and receiver locations one actually has to create or simulate data at the locations one desires to have. The process is similar to seismic migration, though less demanding in that only data relatively near to the desired output point need be employed. Basic data mapping adjusts phase and amplitude of the data to conform to the geometry at the output location under the assumption that reflectivity does not change with angle of incidence. Full seismic data reconstruction goes beyond basic data mapping by also allowing reflection coefficients to change with incident angle. In the straight-raypath approximation, both data mapping and full data reconstruction are Kirchhoff-like operations of small integration aperture, with data mapping the simpler of the two. Operating on moveout-corrected data, they are (up to a point) velocity independent. The operators can map or continue data from one offset to another [dip moveout (DMO) being a special case of data mapping] or from one source or receiver location to another. Both 2-D and 3-D versions of the operators can be constructed. The 2-D mapping and reconstruction operators apply when input and output offset azimuths are aligned. The 3-D operators are equivalent, at least in principle, to two passes of the corresponding 2-D operators: the first pass a DMO to zero offset, the second an inverse DMO to the desired location. Potential uses for data mapping and reconstruction include filling in missing data, regularizing a data set, consolidating to a smaller data set, removing acquisition footprints, and so on.