Seismic interferometry

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. • 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 is fundamentally similar to the optical interferogram produced by the interference of a direct and reflected wave passing through a glass lens where intensity is primarily dependent upon the phase component. Equation 2 I = 1 +2R^{2} \cos [\omega ( \lambda_{Ar} + \lambda_{rB}) ] +R^{4} Where: Intensity ( I) is related to the magnitude of the reflection coefficient ( R) and the phase component \omega ( \lambda_{Ar} + \lambda_{rB}) . An estimate of the reflectivity distributions can be obtained through the crosscorrelation of the direct wave at a location A with the reflection recorded at a location B where A represents the reference trace. A similar model demonstrated the reconstruction of a simulated subsurface geometry. In this case, the reconstructed subsurface response correctly modeled the relative positions of primaries and multiples. Additional equations can be derived to reconstruct signal geometries in a wide variety of cases. ==Applications==

Seismic interferometry is currently utilized primarily in research and academic settings. In one example, passive listening and the crosscorrelation of long noise traces was used to approximate the impulse response for shallow subsurface velocity analysis in Southern California. Seismic interferometry provided a result comparable to that indicated using elaborate inversion techniques. Seismic interferometry is most often used for the examination of the near surface and is often utilized to reconstruct surface and direct waves only. As such, seismic interferometry is commonly used to estimate ground roll to aid in its removal. Seismic interferometry has been applied to image the seismic scattering and velocity structure of volcanoes. Exploration and production Increasingly, seismic interferometry is finding a place in exploration and production. SI can image dipping sediments adjacent to salt domes. Complex salt geometries are poorly resolved using traditional seismic reflection techniques. An alternative method calls for the use of downhole sources and receivers adjacent to subsurface salt features. It is often difficult to generate an ideal seismic signal in a downhole location. Seismic interferometry can virtually move a source into a downhole location to better illuminate and capture steeply dipping sediments on the flank of a salt dome. In this case, the SI result was very similar to that obtained using an actual downhole source. Seismic interferometry can locate the position of an unknown source and is often utilized in hydrofrac applications to map the extent of induced fractures. It is possible that interferometric techniques can be applied to timelapse seismic monitoring of subtle changes in reservoir properties in the subsurface. ==Limitations==

Seismic interferometry applications are currently limited by a number of factors. Real world media and noise represent limitations for current theoretical development. For example, for interferometry to work noise sources must be uncorrelated and completely surround the region of interest. In addition, attenuation and geometrical spreading are largely neglected and need to be incorporated into more robust models. Other challenges are inherent to seismic interferometry. For example, the source term only drops out in the case of the crosscorrelation of a direct wave at a location A with a ghost reflection at a location B. The correlation of other waveforms can introduce multiples to the resulting interferogram. Velocity analysis and filtering can reduce but not eliminate the occurrence of multiples in a given dataset. Although there have been many advancements in seismic interferometry challenges still remain. One of the biggest remaining challenges is extending the theory to account for real world media and noise distributions in the subsurface. Natural sources typically do not comply with mathematical generalizations and may in fact display some degree of correlation. Additional problems must be addressed before applications of seismic interferometry can become more widespread. ==Notes==