Interferometry examines the general interference phenomena between pairs of signals in order to gain useful information about the subsurface. Seismic interferometry (SI) utilizes the crosscorrelation of signal pairs to reconstruct the impulse response of a given media. Papers by Keiiti Aki (1957), Géza Kunetz, and Jon Claerbout (1968) helped develop the technique for seismic applications and provided the framework upon which modern theory is based.
A signal at a location A can be crosscorrelated with a signal at a location B to reproduce a virtual source-receiver pair using seismic interferometry. Crosscorrelation is often considered the key mathematical operation in this approach, but it is also possible to use convolution to come up with a similar result. The crosscorrelation of passive noise measured at a free surface reproduces the subsurface response as if it was induced by an impulsive point source, which is, by definition, equal to Green's function. As such, it is possible to obtain information about the subsurface with no need for an active seismic source. This method, however, is not limited to passive sources, and can be extended for use with active sources and computer–generated waveforms.
As of 2006 the field of seismic interferometry was beginning to change the way geophysicists view seismic noise. Seismic interferometry uses this previously–ignored background wavefield to provide new information that can be used to construct models of the subsurface as an inverse problem. Potential applications range from the continent scale to much smaller-scale natural hazards, industrial, and environmental applications.
History and development
Claerbout (1968) developed a workflow to apply existing interferometry techniques to investigating the shallow subsurface, although it was not proven until later that seismic interferometry could be applied to real world media. The long term average of random ultrasound waves can reconstruct the impulse response between two points on an aluminum block. However, they had assumed random diffuse noise, limiting interferometry in real world conditions. In a similar case, it was shown that the expressions for uncorrelated noise sources reduce to a single crosscorrelation of observations at two receivers. The interferometric impulse response of the subsurface can be reconstructed using only an extended record of background noise, initially only for the surface and direct wave arrivals.
Crosscorrelations of seismic signals from both active and passive sources at the surface or in the subsurface can be used to reconstruct a valid model of the subsurface. Seismic interferometry can produce a result similar to traditional methods without limitations on the diffusivity of the wavefield or ambient sources. In a drilling application, it is possible to utilize a virtual source to image the subsurface adjacent to a downhole location. This application is increasingly utilized particularly for exploration in subsalt settings.
Mathematical and Physical Explanation
Seismic interferometry provides for the possibility of reconstructing the subsurface reflection response using the crosscorrelations of two seismic traces. Recent work has mathematically demonstrated applications of crosscorrelation for reconstructing Green's function using wave field reciprocity theorem in a lossless, 3D heterogeneous medium. Traces are most often extended records of passive background noise, but it is also possible to utilize active sources depending on the objective. Seismic interferometry essentially exploits the phase difference between adjacent receiver locations to image the subsurface.
The conditions for the method to be valid, meaning to retrieve the Green's function from correlated signals, are given as follows:
sources are uncorrelated in time, sources are located all around the receivers to reconstruct surface waves, the wavefield is equipartitioned, meaning it comprises both compressional and shear waves.
The last two conditions are hard to meet directly in nature. However, thanks to the wave scattering, the waves are converted, which satisfies the equipartition condition. The equal distribution of sources is met thanks to the fact, that the waves are scattered in every direction.
Seismic interferometry consists of simple crosscorrelation and stacking of actual receiver responses to approximate the impulse response as if a virtual source was placed at the location of the applicable receiver. Crosscorrelation of continuous functions in the time domain is presented as Equation 1.