On the undesired behaviour of higher-order correlations

Seismic interferometry yields a correlation wavefield that is closely related to the Green’s function of the medium under the condition of homogeneously distributed sources. In cases where this condition is not met, iteratively computing the correlations of correlation wavefields (“higher-order correlations”) has been argued to improve Green’s function retrieval and thus be a useful processing step for imaging applications. Higher-order correlations can also retrieve correlation wavefields between stations that were not installed simultaneously, which can help to homogenize the imaging conditions for asychronous deployments.

We show that higher-order correlations do not improve correlation wavefields when isolated noise sources are present, which is common for seismic field data. Instead, higher-order correlations enhance the travel time bias introduced by such source distributions. This impacts both far-field investigations, such as tomographic studies, and near-field investigations, such as spatial autocorrelations and focal spots. We simulate several source scenarios numerically to showcase this behaviour. Field data observations from a large-N nodal deployment in Eastern Austria confirm these considerations. This work exposes the need for a reliable strategy to assess the correlation wavefield properties before applying advanced processing, such as higher-order correlations.