Event‐oriented velocity estimation based on prestack data in time or depth domain¹

A 2D reflection tomographic method is described, for the purpose of estimating an improved macrovelocity field for prestack depth migration. An event‐oriented local approach of the ‘layer‐stripping’ type has been developed, where each input event is defined by its traveltime and a traveltime derivative, taken with respect to one of four coordinates in the source/receiver and midpoint half‐offset systems.

Recent work has shown that the results of reflection tomography may be improved by performing event picking in a prestack depth domain. We adopt this approach and allow events to be picked either before or after prestack depth migration. Hence, if events have been picked in a depth domain, such as the common‐shot depth domain or the common‐offset depth domain, then a depth‐time transformation is required before velocity estimation. The event transformation may, for example, be done by conventional kinematic ray tracingr and with respect to the original depth‐migration velocity field. By this means, we expect the input events for velocity updating to become less sensitive to migration velocity errors.

For the purpose of velocity estimation, events are subdivided into two categories; reference horizon events and individual events. The reference horizon events correspond to a fixed offset in order to provide basic information about reflector geometry, whereas individual events, corresponding to any offset, are supposed to provide the additional information needed for velocity estimation. An iterative updating approach is used, based on calculation of derivatives of event reflection points with respect to velocity. The event reflection points are obtained by ray‐theoretical depth conversion, and reflection‐point derivatives are calculated accurately and efficiently from information pertaining to single rays. A number of reference horizon events and a single individual event constitute the minimum information required to update the velocity locally, and the iterations proceed until the individual event reflection point is consistent with those of the reference horizon events. Normally, three to four iterations are sufficient to attain convergence. As a by‐product of the process, we obtain so‐called uncertainty amplification factors, which relate a picking error to the corresponding error in the estimated velocity or depth horizon position.

The vector formulation of the updating relationship makes it applicable to smooth horizons having arbitrary dips and by applying velocity updating in combination with a flexible model‐builder, very general macro‐model structures can be obtained. As a first step in the evaluation of the new method, error‐free traveltime events were generated by applying forward ray tracing within given macrovelocity models. When using such ‘perfect’ observations, the velocity estimation algorithm gave consistent reconstructions of macro‐models containing interfaces with differential dip and curvature, a low‐velocity layer and a layer with a laterally varying velocity function.