Three-dimensional seismic-while-drilling (SWD) migration in the angular frequency domain

Seismic depth migration back-propagates seismic data in the correct depth position using information about the velocity of the medium. Usually, Kirchhoff summation is the preferred migration procedure for seismic-while-drilling (SWD) data because it can handle virtually any configuration of sources and receivers and one can compensate for irregular spatial sampling of the array elements (receivers and sources). Under the assumption of a depth-varying velocity model, with receivers arranged along a horizontal circumference and sources placed along the central vertical axis, we reformulate the Kirchhoff summation in the angular frequency domain. In this way, the migration procedure becomes very efficient because the migrated volume is obtained by an inverse Fourier transform of the weighted data. The algorithm is suitable for 3D SWD acquisitions when the aforementioned hypothesis holds. We show migration tests onSWDsynthetic data, and we derive solutions to reduce the migration artifacts and to control aliasing. The procedure is also applied on a real 3D SWD data set. The result compares satisfactorily with the seismic stack section obtained from surface reflection data and with the results from traditional Kirchhoff migration.