A UNIFIED APPROACH TO 3-D SEISMIC-REFLECTION IMAGING .1. BASIC CONCEPTS

Given a 3-D seismic record for an arbitrary measurement configuration and assuming a laterally and vertically inhomogeneous, isotropic macro -velocity model, a unified approach to amplitude-preserving seismic re flection imaging is provided. This approach is composed of (1) a weigh ted Kirchhoff-type diffraction-stack integral to transform (migrate) s eismic reflection data from the measurement time domain into the model depth domain, and of (2) a weighted Kirchhoff-type isochronestack int egral to transform (demigrate) the migrated seismic image from the dep th domain back into the time domain. Both the diffraction-stack and is ochrone-stack integrals can be applied in sequence (i.e., they can be chained) for different measurement configurations or different velocit y models to permit two principally different amplitude-preserving imag e transformations. These are (1) the amplitude-preserving transformati on (directly in the time domain) of one 3-D seismic record section int o another one pertaining to a different measurement configuration and (2) the transformation (directly in the depth domain) of a 3-D depth-m igrated image into another one for a different (improved) macro-veloci ty model. The first transformation is referred to here as a ''configur ation transform'' and the second as a ''remigration.'' Additional imag e transformations arise when other parameters, e.g., the ray code of t he elementary wave to be imaged, are different in migration and demigr ation. The diffraction- and isochrone-stack integrals incorporate a fu ndamental duality that involves the relationship between reflectors an d the corresponding reflection-time surfaces. By analytically chaining these integrals, each of the resulting image transformations can be a chieved with only one single weighted stack. In this way, generalized- Radon-transform-type stacking operators can be designed in a straightf orward way for many useful image transformations. In this Part I, the common geometrical concepts of the proposed unified approach to seismi c imaging are presented in simple pictorial, nonmathematical form. The more thorough, quantitative description is left to Part II.