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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