Beasley 1994 pointed to the fact that focusing solely on algorithmic accuracy ignores an issue often even more detrimental to amplitude preservation: the effect of sparse and irregular geometry. Gardner and canning 1994 demonstrated some effects of irregular sampling on 3-D prestack migration through synthetic examples using true 3-D land aquisition geometry. Given this effect, the design of any processing sequence has to address both issues of irregular sampling and algorithmic accuracy.
Amplitude-preserved processing aims at providing reliable amplitudes for AVO studies. In 3-D, AVO analysis is routinely performed on partial stacks or angle stacks on which amplitudes are smeared over a range of offsets (or angles). Unfortunately, during this process azimuthal information is completely destroyed by the addition of traces from different source receiver orientation. The stacked trace, therefore, loses some information present in the prestack domain that may be related to lithology, fluid saturation, fracture density and orientation, and anisotropy. Some of the recent work at SEP has focused on the use of azimuth-- a parameter inherently recorded in seismic data-- in the processing of 3-D surveys. Biondi and Palacharla developed an economical and efficient algorithm for 3-D prestack depth migration of common-azimuth data. In the context of 3-D velocity estimation, Clapp and Biondi 1995 showed that inverting for interval velocity is better constrained when data collected along multiple offset-azimuth are jointly inverted. Biondi and Chemingui introduced a new partial prestack migration operator named AMO that has a wide variety of applications, such as regularization of data geometry for uneven and sparse coverage, reduction of the size of 3-D surveys by coherent partial stacking Biondi et al. (1996) and synthesis of common offset and common azimuth data sets. In subsequent SEP reports, Fomel and Biondi developed a practical and accurate implementation for the time and space formulation of AMO which properly handles the limited aperture of the operator and avoids aliasing of the operator along its steep traveltime slopes. In order that amplitude variations as function of offset and azimuth are not distorted by the AMO transformation, Chemingui and Biondi 1995 developed an amplitude-preserving function for an accurate AMO algorithm that adapts to our needs for true amplitude processing.
Recently, the issue of whether azimuthal anisotropy, and, more precisely, fracture-induced anisotropy is detectable and measurable on 3-D P-wave data has been posed for research and investigation, i.e, Lefeuvre (1994); Lynn et al. (1995a,b). It is evident that this effect can be observed only on data with wide azimuth coverage, a type of surveying that is often considered problematic. The challenge is not the wide azimuth range itself, but the way in which wide azimuth surveys are acquired, where, most often, each azimuth is not sufficiently sampled in midpoints and offsets Canning and Gardner (1995). These sampling irregularities may introduce noise, cause amplitude distortions, and even structural distortions, when 3-D prestack migration is applied to the data Canning and Gardner (1995); Gardner and Canning (1994). All these issues related to irregular geometry, undersampling along azimuths, and the need for accurate algorithms, have led some exploration geophysicists to favor narrow azimuth surveys on wide azimuth acquisitions.
Correct analysis of amplitude information requires prestack migration to determine the location and extent of AVO anomalies. The migration algorithm should be derived so that amplitude variations as a function of offset are not distorted by the procedure. In the SEP80 report, Francois Audebert and the migration group at SEP presented an extensive comparative summary about why one should use Kirchhoff migration for 3-D prestack imaging. The group based their conclusions on the capacity for data manipulation and cost comparison of Kirchhoff migration to other competitive algorithms, namely, poststack finite difference, phase shift, and SG migration. They concluded that a simple kinematic Kirchhoff migration is unbeatable in manipulating input data and is cheaper than other methods. Kirchhoff methods evade the question of total cost by being target oriented and are the foremost and nearly the only choice. The analysis did not intend to compare the efficiency of the algorithms and their ability to preserve amplitudes. In regard to the effects of irregular geometry, the group's perception was that Kirchhoff migration does not care if the data is regular or not. They concluded that Kirchhoff methods are the solution to adapting the operator to fit the data and process it in its real time-space coordinates.
In this work, we explore the issue of true amplitude processing in constant offset migration and we argue that Kirchhoff methods are not quite the solution for handling the irregular geometry. We present a method that synthesizes wide 3-D surveys as a collection of lower fold single-azimuth surveys. Therefore, when discrete azimuths are processed independently, each azimuth simulates a marine 3-D survey. After AMO transformation, each common azimuth subset is regularly sampled in midpoint-offsets. Common-azimuth common-offset cubes are then migrated using an amplitude-preserving Kirchhoff migration algorithm. We apply this true amplitude sequence to a synthetic model that simulates a real 3-D survey over a fractured reservoir in the Powder River Basin in Wyoming. The survey was designed in a Button-Patch geometry that aims at providing a wide range of azimuthal coverage that would allow study of the azimuthal variations in the AVO gradient. With the limitation of weak anisotropy, the azimuthal difference in AVO gradient is closely related to crack density, a very important parameter in tight-reservoir characterization.