A unified approach to 3-D seismic reflection imaging, Part II: Theory

Abstract

Diffraction‐stack and isochrone‐stack integrals are quantitatively described and employed. They constitute an asymptotic transform pair. Both integrals are the key tools of a unified approach to seismic reflection imaging that can be used to solve a multitude of amplitude‐preserving, target‐oriented seismic imaging (or image‐transformation) problems. These include, for instance, the generalizations of the kinematic map‐transformation examples discussed in Part I. All image‐transformation problems can be addressed by applying both stacking integrals in sequence, whereby the macro‐velocity model, the measurement configuration, or the ray‐code of the considered elementary reflections may change from step to step. This leads to weighted (Kirchhoff‐ or generalized‐Radon‐type) summations along certain stacking surfaces (or inplanats) for which true‐amplitude (TA) weights are provided. To demonstrate the value of the proposed imaging theory (which is based on analytically chaining the two stacking integrals and using certain inherent dualities), we examine in detail the amplitude‐preserving configuration transform and remigration for the case of a 3-D laterally inhomogeneous velocity medium.