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The reciprocity theorem for the scattered field is the progenitor of the generalized optical theorem
J. Acoust. Soc. Am. Volume 129, Issue 5, pp. 2765-2771 (2011); (7 pages)
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Add to FacebookBy analyzing correlation-type reciprocity theorems for wavefields in perturbed media, it is shown that the correlation-type reciprocity theorem for the scattered field is the progenitor of the generalized optical theorem. This reciprocity theorem, in contrast to the generalized optical theorem, allows for inhomogeneous background properties and does not make use of a far-field condition. This theorem specializes to the generalized optical theorem when considering a finite-size scatterer embedded in a homogeneous background medium and when utilizing the far-field condition. Moreover, it is shown that the reciprocity theorem for the scattered field is responsible for the cancellation of non-physical (spurious) arrivals in seismic interferometry, and as such provides the mathematical description of such arrivals. Even though here only acoustic waves are treated, the presented treatment is not limited to such wavefields and can be generalized to general wavefields. Therefore, this work provides the framework for deriving equivalents of the generalized optical theorem for general wavefields.
© 2011 Acoustical Society of America
ACKNOWLEDGMENTS
H.D. and I.V. thank ION Geophysical/GXT Imaging solutions for permission to publish this work.The careful comments and suggestions from Kees Wapenaar are much appreciated and helped to improve the manuscript.
Article Outline
- INTRODUCTION
- RECIPROCITY THEOREM OF THE CORRELATION-TYPE FOR ACOUSTIC WAVEFIELDS IN PERTURBED MEDIA
- SEISMIC INTERFEROMETRY
- RECIPROCITY THEOREM FOR THE SCATTERED FIELD
- GENERALIZED OPTICAL THEOREM
- ENERGY CONSIDERATIONS
- VOLUME INTEGRAL REPRESENTATIONS FOR THE SCATTERED, ABSORBED, AND EXTINGUISHED POWER
- GENERALIZATION TO GENERAL LINEAR SYSTEMS
- CONCLUSIONS
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History
Received 02 Dec 2010
Accepted 28 Feb 2011
Revised 23 Feb 2011
Accepted 28 Feb 2011
Revised 23 Feb 2011
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