Reconstruction of multiply-scattered arrivals from the cross-correlation of waves excited by random noise sources in a heterogeneous dissipative medium

Abstract

Imagining a medium composed of an arbitrary distribution of point-like heterogeneities, we study the reconstruction of scattered waves in Green's function derived from the cross-correlation function of waves excited by random noise sources of which the distribution is stationary and homogeneous. We show that the reconstruction process is intimately related to generalized forms of the optical theorem. The role of absorption in the formulation of the theorem is discussed. The reconstruction of multiply-scattered arrivals from the cross-correlation of two random wavefields is demonstrated to all orders of scattering for the simple case of two point scatterers, through application of the optical theorem for a single scatterer. In the case of N point scatterers, the cross-correlation of two Green's functions is expressed in the form of Feynman-like diagrams. The wavepaths that contribute to the reconstruction of an arbitrary multiply-scattered arrival of Green's function are identified. Repeated application of the generalized optical theorem, formulated as a diagrammatic rule, demonstrates the destructive interference between all spurious multiply-scattered arrivals.