Geophysical noise interferometry: Repairing the broken mirror

Under conditional circumstances, the correlation of noise at two receivers is approximately proportional to the Green’s function between these receivers. Hence, the correlation process turns one of the receivers into a virtual source, of which the response is observed by the other receiver. This principle, also known as ambient-noise interferometry, is used by researchers in geophysics, ultrasonics and underwater acoustics to infer information about an unknown object from passive noise measurements. In geophysics, ambient-noise interferometry is used for tomographic velocity inversion when surface waves are dominant, or for high-resolution reflection imaging when a significant amount of body waves is present in the noise field. The virtual-source response obtained with geophysical noise interferometry is accurate when the medium is lossless and the noise field is equipartitioned. In practice these assumptions are often violated: the medium of interest is often illuminated from one side only, the sources may be irregularly distributed and losses may be significant. For those cases, it is as if the virtual source is viewed in a broken (time-reversal) mirror, which causes blurring of the source. This blurring is quantified by the so-called point-spread function, which, like the correlation function, can be derived from the observed data (that is, without the need to know the actual sources and the medium). The broken mirror can be repaired by deconvolving the correlation function for the point-spread function. As a result, the virtual source is refocused and hence the virtual-source response becomes more reliable