A reflecting interface with irregular shape is overlain by a material of constant velocity VT. Multifold reflection data are collected on a plane above the reflector and the reflector is imaged by first stacking then migrating the reflection data. There are three velocity functions encountered in this process: the measured stacking velocity Vnmo; the true overburden velocity VT; and a profile migration velocity Vm, which is required by present point-imaging migration programs. Methods of determining Vnmo and, subsequently, VT are well-known. The determination of VM from VT, on the other hand, has not been previously discussed. By considering a line-imaging migration process we find that VM, depends not only on the true section velocity but also on certain geometrical factors which relate the profile direction to the structure. The relation between VM and VT is similar to, but should not be confused with, the known relation between Vnmo and VT. The correct profile migration velocity is always equal to or greater than the true overburden velocity but may be less than, equal to, or greater than the best stacking velocity. When a profile is taken at an angle of (90 - 0) degrees to the trend of a two-dimensional structure, then the appropriate migration velocity is VjJcos 0 and is independent of the magnitude of any dips present. If, in addition, the two-dimensional structure plunges along the trend at an angle y, then the correct migration velocity is given by VjJ(l - sin2 0 cos2 y)1/2. The time axis of the migrated profile for the plunging two-dimensional case must be rescaled by a factor of [(l - sin2 0 cos2 y)/cos2 0 cos2 y]1/2, and structures on the rescaled profile must be projected to the surface along diagonal lines to find their true positions. When three-dimensional data are collected and automatic three-dimensional migration is performed, the geometrical factors are inherently incorporated. In that case, the migration velocity is always equal to the true velocity regardless of whether the structure is two-dimensional, plunging two-dimensional, or three-dimensonal. Processed model data support these conclusions.
The equations given above are intended for use in conventional migration-after-stack. Recently developed schemes combining migration-before-stack with velocity analysis give VM directly. In that case, the above equations provide a method of determining VT from VM.
Figures & Tables
The use of diffraction imaging to complement the seismic reflection method is rapidly gaining momentum in the oil and gas industry. As the industry moves toward exploiting smaller and more complex conventional reservoirs and extensive new unconventional resource plays, the application of the seismic diffraction method to image sub-wavelength features such as small-scale faults, fractures and stratigraphic pinchouts is expected to increase dramatically over the next few years. “Seismic Diffraction” covers seismic diffraction theory, modeling, observation, and imaging. Papers and discussion include an overview of seismic diffractions, including classic papers which introduced the potential of diffraction phenomena in seismic processing; papers on the forward modeling of seismic diffractions, with an emphasis on the theoretical principles; papers which describe techniques for diffraction mathematical modeling as well as laboratory experiments for the physical modeling of diffractions; key papers dealing with the observation of seismic diffractions, in near-surface-, reservoir-, as well as crustal studies; and key papers on diffraction imaging.