Abstract AStacked cross-correlation functions have become ubiquitous in the ambient seismic imaging and monitoring community as approximations to the Green’s function between receivers. Although the quantification of this approximation to ballistic arrivals (transmission waves) is well established, the equivalent analysis for non-ballistic arrivals (scattered waves) is inadequate. To provide a clearer understanding of the signal and noise components of the non-ballistic arrivals, we derive analytical stationary phase solutions for ambient noise cross-correlations with a focus on the scattered waves. We establish the mathematical and corresponding physical conditions for accurate scattered wave reconstructions in the stacked cross-correlation function (XCF) and quantify the crosstalk artifacts that could severely degrade the signal-to-noise ratio (SNR). In ambient environments where seismic sources are random and continuous, cross-talk artifacts due to overlapping random noise sources may not be distinguishable from the coda waves resulting from random medium scatterings of an impulsive source. This general ambiguity underscores the importance of additional constraints when interpreting large-lag-time arrivals in the XCFs as coda waves for deterministic information about the propagation medium. When the source effect is sufficiently suppressed, the stationary phase solutions for scattered waves provide a solid basis for extracting reliable scattering information from stacked XCFs, enabling future development of high-resolution passive imaging and monitoring.
Li et al. (Sun,) studied this question.