Green's function retrieval from the CCF of coda waves in a scattering medium

Abstract

The cross-correlation function (CCF) of noises has been widely used to measure Green's function in the Earth medium. Most of theoretical works for Green's function retrieval are based on the equipartition state of random waves or the illumination by distributed stationary noise sources; however, there have been few appropriate frameworks how to retrieve Green's function from the CCF of coda waves in a scattering medium. By using the first-order Born approximation for scalar waves, we show Green's function retrieval from the CCF of coda for an impulsive spherical radiation from a point source, where the scattering medium is a random distribution of delta-function velocity anomalies in 3-D space. The CCF of single scattering coda waves at two receivers located at the opposite sides of the source is written by using Green's function in the homogenous medium. The lapse time and the time window length define the spherical shell, which is the responsible distribution of single scatterers that illuminate the receivers. The coda CCF amplitude is proportional to the inverse square of the lapse time measured from the origin time. Single scattering waves are omni-directional and equal amplitude near the source and receivers, that is, the equipartition state in the wavenumber space.