A unified approach to 3-D seismic reflection imaging, Part I: Basic concepts

Abstract

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 reflection imaging is provided. This approach is composed of (1) a weighted Kirchhoff‐type diffraction‐stack integral to transform (migrate) seismic reflection data from the measurement time domain into the model depth domain, and of (2) a weighted Kirchhoff‐type isochrone‐stack integral to transform (demigrate) the migrated seismic image from the depth domain back into the time domain. Both the diffraction‐stack and isochrone‐stack integrals can be applied in sequence (i.e., they can be chained) for different measurement configurations or different velocity models to permit two principally different amplitude‐preserving image transformations. These are (1) the amplitude‐preserving transformation (directly in the time domain) of one 3-D seismic record section into another one pertaining to a different measurement configuration and (2) the transformation (directly in the depth domain) of a 3-D depth‐migrated image into another one for a different (improved) macro‐velocity model. The first transformation is referred to here as a “configuration transform” and the second as a “remigration.” Additional image transformations arise when other parameters, e.g., the ray code of the elementary wave to be imaged, are different in migration and demigration. The diffraction‐ and isochrone‐stack integrals incorporate a fundamental duality that involves the relationship between reflectors and the corresponding reflection‐time surfaces. By analytically chaining these integrals, each of the resulting image transformations can be achieved with only one single weighted stack. In this way, generalized‐Radon‐transform‐type stacking operators can be designed in a straightforward way for many useful image transformations. In this Part I, the common geometrical concepts of the proposed unified approach to seismic imaging are presented in simple pictorial, nonmathematical form. The more thorough, quantitative description is left to Part II.