Essential noise sources for Green's function recovery in passively‐monitored diffusion systems

Abstract

The principle of extracting Green's function in geophysically cluttered environments makes it possible to retrieve the impulse response of a system without using controlled point sources. Urban areas, oilfield and industrial facilities are the sites that may provide a rich spectrum of noise from which to draw upon for Green's function estimation. Green's function can be extracted by correlation of diffusive wavefields at two separate locations where sources are available everywhere throughout a volume. However, in the real world the number of noise sources in an area is limited, and furthermore, unevenly distributed in time, space and spectral content. Hence, quantification of the requisite noise sources that enable us to calculate Green's function acceptably well remains an open research question. In this study, the area of noise with more contribution to the cross‐correlation results is investigated in homogeneous and inhomogeneous media. The results confirmed previous findings that the sources located between two receiver positions are the most important ones for the purpose of Green's function recovery. For the 2D case, a suite of double halfspace models was examined in with one receiver located on either side of the contact. Varying the angle between the contact and the line connecting the receivers revealed that in general, the region between receivers remains that which contributes most to Green's function estimation. However, the difference in diffusion rates across the interface skews the geometry of this region, ‐ in some cases leading to significant off‐axis contributions to the recovered Green's function.