Directional balancing for seismic and general wavefield interferometry

In passive seismic interferometry using naturally occurring, heterogeneous noise sources and in active-source seismic interferometry where sources can usually only be distributed densely on the exterior of solid bodies, bias can be introduced in Green's function estimates when amplitudes of energy have directional variations. We have developed an algorithm to remove bias in Green's function estimates constructed using seismic interferometry when amplitudes of energy used have uncontrollable directional variations. The new algorithm consists of two parts: (1) a method to measure and adjust the amplitudes of physical, incoming energy using an array of receivers and (2) a method to predict and remove nonphysical energy that remains (and can be accentuated) in interferometrically derived Green's functions after applying the method in step 1. To accomplish step 2, we have created two data-driven methods to predict the nonphysical energy using direct computation or move-out-based methods, and a way to suppress such energy using (in this case) helical least-squares filters. Two-dimensional acoustic scattering examples confirm the algorithm's effectiveness.