Three-dimensional pre-stack shot-record depth migration of seismic reflection data accurately imaged the salt body and part of a complex sub-salt structure of the SEG/EAGE physical model. The data with 3-D geological effects are in 3-D common-receiver gathers collected from the simulation of vertical cable data acquisition over the model. Two methods of forward propagation of the receiver wave-field in the pre-stack depth migration (PSDM) algorithm are compared. They are denoted as PSDM-1 for the one which uses the eikonal equation and PSDM-2 for the one which uses 3-D phase shift plus interpolation. The results show that PSDM-2 correctly focuses the 3-D salt body without the artifacts created by using PSDM-1. PSDM-2 also better images the sub-salt layer. The comparison of the results of imaging the up-coming and down-going wave-fields from vertical cable data shows that the up-coming field has a better focus on steep dips, while the down-going field has a better focus on the shallow horizons and on the sub-salt layer. Separation of these two fields prior to migration shows slight improvement in imaging the shallow layers.; In order to prepare the vertical cable data acquired for PSDM, an unconventional processing procedure is carried out: first, setting up the 3-D geometry; second, deconvolution to improve the temporal resolution; and third, sorting the data into common-receiver gathers. The vertical cable facilitates various receiver levels in the water layer, and some of the levels are in the far-field of the seismic source. The best region to measure the source wavelet for the deterministic deconvolution is between the source far-field depth and the depth where the up-coming field does not interfere with the wavelet. Thus, multi-azimuth signatures can be measured directly from the direct wave.; I developed the formulas for computing 3-D ray paths and travel times in both T-X and tau-p domains for the media consisting of a series of constant-velocity layers separated by planes. These formulas are useful for investigating the subsurface coverage of vertical cable data acquisition and for developing travel-time inversion equations in the tau- p domain to obtain velocities, depths and dips at the vertical cable position.
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