Retrieval of a Green's Function with Reflections from Partly Coherent Waves Generated by a Wave Packet Using Cross Correlations

• Autores: Maarten V. De Hoop, Josselin Garnier, Sean F. Holman, Knut Solna
• Localización: Siam journal on applied mathematics, ISSN 0036-1399, Vol. 73, Nº 1, 2013, págs. 493-522
• Idioma: inglés
• DOI: 10.1137/110836286
• Texto completo no disponible (Saber más ...)
• Resumen

  • We analyze the �field-field� cross correlation associated with partly coherent scattered waves generated by a wave packet. The configuration consists of a slab in which random medium fluctuations occur; the bottom of the slab is bounded by a deterministic discontinuity (a smooth reflector). Following the dyadic parabolic scaling of wave packets, and scaling the random fluctuations appropriately, we arrive at a description in terms of a system of linear Itô--Schrödinger diffusion models. Studying the Wigner distributions of the fields generated by these models leads to a �blurring� transformation, providing a complete characterization of the cross correlation. We obtain a description of the cross correlation in terms of this transformation applied to the effective transmission operator that arises as a solution of the Itô--Schrödinger model. Most of the analysis is focussed on the interaction of the deterministic reflector with the random fluctuations through the waves in the regime of fine scales