We introduce a new partial prestack-migration operator called "azimuth moveout" (AMO) that rotates the azimuth and modifies the offset of 3-D prestack data. Followed by partial stacking, AMO can reduce the computational cost of 3-D prestack imaging. We have successfully applied AMO to the partial stacking of a 3-D marine data set over a range of offsets and azimuths. When AMO is included in the partial-stacking procedure, highfrequency steeply dipping energy is better preserved than when conventional partial-stacking methodologies are used. Because the test data set requires 3-D prestack depth migration to handle strong lateral variations in velocity, the results of our tests support the applicability of AMO to prestack depth-imaging problems. AMO is a partial prestack-migration operator defined by chaining a 3-D prestack imaging operator with a 3-D prestack modeling operator. The analytical expression for the AMO impulse response is derived by chaining constant-velocity DMO with its inverse. Equivalently, it can be derived by chaining constant-velocity prestack migration and modeling. Because 3-D prestack data are typically irregularly sampled in the surface coordinates, AMO is naturally applied as an integral operator in the time-space domain. The AMO impulse response is a skewed saddle surface in the time-midpoint space. Its shape depends on the amount of azimuth rotation and offset continuation to be applied to the data. The shape of the AMO saddle is velocity independent, whereas its spatial aperture is dependent on the minimum velocity. When the azimuth rotation is small (≤20 •), the AMO impulse response is compact, and its application as an integral operator is inexpensive. Implementing AMO as an integral operator is not straightforward because the AMO saddle may have a strong curvature when it is expressed in the midpoint coordinates. An appropriate transformation of the midpoint axes to regularize the AMO saddle leads to an effective implementation.

We introduce a new partial-migration operator, named Azimuth Moveout (AMO), that rotates the azimuth and modifies the offset of 3-D prestack data. AMO can be effectively applied to improve the accuracy and to reduce the computational cost of 3-D prestack imaging. For example, a 3-D prestack dataset can be drastically reduced in size by coherent partial-stacking after AMO. The reduced dataset can be then imaged by prestack depth migration, a process that would have been too expensive to apply to the original dataset. AMO can also be effectively used for regularizing data geometries (e.g. correct for cable feather) and for interpolating unevenly sampled data. AMO is defined as the cascade of DMO and inverse DMO at different offsets and azimuths. We derive the time-space domain formulation of the AMO operator by first deriving its Fourier domain representation, and then analytically evaluating the stationaryphase approximation. The impulse response of AMO is a surface in the time-midpoint space; the shape of the surface is a skewed saddle, and its spatial extent is determined by the amount of azimuth rotation and offset continuation to be applied to the data. When the azimuth rotation is small (≤ 20 •), the AMO operator is compact and inexpensive to apply in the time-space domain. We successfully tested AMO by coherently stacking traces with similar offsets and azimuths from a synthetic land survey.

Imaging with separated wavefields (SWIM) is an innovative depth-imaging technology that uses upgoing and downgoing wavefields at the surface to deliver high-resolution images of the subsurface. It takes advantage of the extended illumination provided by surface-multiple energy, and thus, it exploits data that the seismic industry historically has treated as unwanted noise. The fundamental concept behind SWIM is based on using each receiver as a “virtual” source, effectively expanding the surface coverage of the seismic experiment and enhancing the subsurface illumination, particularly for shallow reflectors. By effectively turning the streamer spread into a source (and receiver) array, the resulting equivalent survey has spatial sampling that is much improved and a richer distribution of offsets and azimuths. The improved spatial sampling enhances the angular illumination greatly at every image point. Therefore, SWIM produces densely sampled angle gathers that provide greater opportunities for velocity-model building and for improved interpretation of complex structures. Several issues need to be considered for proper imaging with SWIM: migration-imaging conditions, attenuation of cross talk, and acquisition design. The latter must be addressed to support proper sampling of both upgoing and downgoing wavefields used for imaging. A broad overview and examples of these subjects are presented. Applications to a deepwater wide-azimuth (WAZ) survey from the Gulf of Mexico and a shallow-water narrow-azimuth (NAZ) data set from offshore Malaysia demonstrate the enhanced areal illumination and improved imaging resolution from imaging using multiple-reflection energy.

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