Journal Article

Velocity continuation in the downward continuation approach to seismic imaging

Anton A. Duchkov and Maarten V. de Hoop

in Geophysical Journal International

Volume 176, issue 3, pages 909-924
Published in print March 2009 | ISSN: 0956-540X
Published online March 2009 | e-ISSN: 1365-246X | DOI: https://dx.doi.org/10.1111/j.1365-246X.2008.04023.x

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Summary

One way of developing a wave-equation approach to seismic imaging is based on the concept of downward continuation of observed surface reflection data. Seismic imaging is typically based on the single scattering approximation, and assumes the knowledge of a smooth background model in which the mentioned downward continuation is carried out using the double-square-root (DSR) equation. The downward continued data are subjected, at each depth, to an imaging condition generating an image or to an angle transform generating common-image gathers. Motivated by the problem of estimation of the background model we develop a framework for velocity continuation in the downward continuation approach to seismic imaging. Velocity continuation is a term used to describe the transformation of a common-image gather (or image) obtained in an ‘initial’ background velocity model into a gather (image) obtained in another ‘final’ model. We construct evolution equations for velocity continuation. We then introduce the concept of data-extended-image ‘volume’. In the data-extended-image ‘volume’ we consider so-called extended images, which are functions of subsurface source–receiver midpoint, subsurface source–receiver offset and depth. We introduce and analyse velocity continuation of the individual components that make up the process of migration, imaging and the transformation to angle common-image gathers.

Keywords: Controlled source seismology; Theoretical seismology; Wave propagation

Journal Article.  7945 words.  Illustrated.

Subjects: Geophysics