Noise interferometry in an inhomogeneous environment in the geometric limit

Abstract

An approximation to the transient Green’s function G(xa|xb,t) between points xa and xb can be estimated by taking the time derivative of the correlation function Cab(t) of records of ambient noise measured at locations xa and xb. From the general relationship between Cab(t) and G(xa|xb,t) it is shown, using a stationary-phase-like argument, that in an inhomogeneous environment in the geometric limit Cab(t) consists of a superposition of signed step functions and two-sided logarithmic singularities that are delayed in time by the travel times of the rays connecting xa and xb.