Incomplete boundaries and partial equations in source-receiver interferometry (SRI)

Source-receiver interferometry (SRI) refers to a technique to construct the Green's function between a source and a receiver using only energy that has travelled from and to surrounding boundaries of sources and receivers. When the full boundary requirements for seismic interferometry are violated, spurious or non-physical energy is introduced into Green's function estimates. Using an acoustic model of a homogeneous medium embedding a single scatterer, we analyse the properties of the interferometric estimate for the case of a partial boundary located on one side of our model, as is commonly the case in practical experiments. We find, that it can be favourable, rather than a shortcoming, to use incomplete boundaries in order to preserve the information from non-physical arrivals that help to constrain the location of a scattering perturbation. Moreover, we show that one term of the SRI equation for scattering media is associated with standard imaging (migration) methods, and that for this term using a partial boundary is an advantage since this suppresses non-physical energy that might otherwise distort the image.