STACKING OF NARROW APERTURE COMMON SHOT INVERSIONS

A typical inversion experiment consists of a source and an array of receivers. Data from a single shot usually will not suffice to produce an image of the subsurface, thus, the need for some kind of post inversion summing (stacking, in the geophysical literature) of the data. Here the question of how to carry out that stacking of data is examined. This paper was motivated, in part, by a post stack parameter estimation technique proposed by G. Beylkin and R. Burridge to aperture limited, band limited data. It is shown by classical methods that their procedure is an integration over the angle between rays from the source and receiver to the output point. It is crucial in their analysis that the range of integration in this opening angle be known. Drawing on earlier results, it is explained why, in general, that angular range is unknown for high frequency band limited data. Under the assumption that those problems can be resolved, the system of equations is presented that arise for the determination of earth parameter variations at a reflector in the case of acoustic reflection, PP, SHSH, and SVSV reflection with a constant background. It is proposed, as an alternative, that the simple sum of all of the separate inversions produce an image of the subsurface, and it is recommended that the separate common shot inversions be used for parameter estimation.