Tutorial on seismic interferometry: Part 2 — Underlying theory and new advances
Kees Wapenaar, Evert Slob, Roel Snieder, Andrew Curtis, 2010. "Tutorial on seismic interferometry: Part 2 — Underlying theory and new advances", Geophysics Today: A Survey of the Field as the Journal Celebrates its 75th Anniversary, Sergey Fomel
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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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“In celebration of the 75th year of publication, the Geophysics editorial team invited a collection of papers written by well-recognized experts in various areas of exploration geophysics. These invited papers not only form part of the present book, but they also appear in the September-October 2010 special section of the journal. Geophysics Today: A Survey of the Field as the Journal Celebrates its 75th Anniversary complements this special section with an additional group of papers, drawn from Geophysics during the recent past, that addresses areas the invited articles did not. The result is a snapshot of the state-ofthe- art in the field as Geophysics passes its three-quarter-century mark. This book is Geophysical References Series No. 16.”