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Book Chapter

Tutorial on seismic interferometry: Part 2 — Underlying theory and new advances

By
Kees Wapenaar
Kees Wapenaar
1Delft University of Technology, Department of Geotechnology, Delft, The Netherlands. E-mail: c.p.a.wapenaar@tudelft.nl; e.c.slob@tudelft.nl.
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Evert Slob
Evert Slob
1Delft University of Technology, Department of Geotechnology, Delft, The Netherlands. E-mail: c.p.a.wapenaar@tudelft.nl; e.c.slob@tudelft.nl.
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Roel Snieder
Roel Snieder
2Colorado School of Mines, Center for Wave Phenomena, Golden, Colorado, U.S.A. E-mail: rsnieder@mines.edu.
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Andrew Curtis
Andrew Curtis
3University of Edinburgh, School of GeoSciences, Edinburgh, U.K. E-mail: andrew.curtis@ed.ac.uk.
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Published:
January 01, 2010

Abstract

In the 1990s, the method of time-reversed acoustics was developed. This method exploits the fact that the acoustic wave equation for a lossless medium is invariant for time reversal. When ultrasonic responses recorded by piezoelectric transducers are reversed in time and fed simultaneously as source signals to the transducers, they focus at the position of the original source, even when the medium is very complex. In seismic interferometry the time-reversed responses are not physically sent into the earth, but they are convolved with other measured responses. The effect is essentially the same: The time-reversed signals focus and create a virtual source which radiates waves into the medium that are subsequently recorded by receivers. A mathematical derivation, based on reciprocity theory, formalizes this principle: The crosscorrelation of responses at two receivers, integrated over different sources, gives the Green’s function emitted by a virtual source at the position of one of the receivers and observed by the other receiver. This Green’s function representation for seismic interferometry is based on the assumption that the medium is lossless and nonmoving. Recent developments, circumventing these assumptions, include interferometric representations for attenuating and/or moving media, as well as unified representations for waves and diffusion phenomena, bending waves, quantum mechanical scattering, potential fields, elastodynamic, electromagnetic, poroelastic, and electroseismic waves. Significant improvements in the quality of the retrieved Green’s functions have been obtained with interferometry by deconvolution. A trace-by-trace deconvolution process compensates for complex source functions and the attenuation of the medium. Interferometry by multidimensional deconvolution also compensates for the effects of one-sided and/or irregular illumination.

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Contents

Geophysical References Series

Geophysics Today: A Survey of the Field as the Journal Celebrates its 75th Anniversary

Sergey Fomel
Sergey Fomel
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Society of Exploration Geophysicists
Volume
16
ISBN electronic:
9781560802273
Publication date:
January 01, 2010

GeoRef

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