TY - JOUR T1 - Analyses and Applications of the Second-Order Cross Correlation in the Passive Imaging JO - Communications in Computational Physics VL - 5 SP - 1191 EP - 1220 PY - 2018 DA - 2018/04 SN - 19 DO - http://doi.org/10.4208/cicp.scpde14.26s UR - https://global-sci.org/intro/article_detail/cicp/11125.html KW - AB -

The first-order cross correlation and corresponding applications in the passive imaging are deeply studied by Garnier and Papanicolaou in their pioneer works. In this paper, the results of the first-order cross correlation are generalized to the second-order cross correlation. The second-order cross correlation is proven to be a statistically stable quantity, with respective to the random ambient noise sources. Specially, with proper time scales, the stochastic fluctuation for the second-order cross correlation converges much faster than the first-order one. Indeed, the convergent rate is of order $\mathcal{O}$($T^{−1+α}$), with 0<α<1. Besides, by using the stationary phase method in both homogeneous and scattering medium, similar behaviors of the singular components for the second-order cross correlation are obtained. Finally, two imaging methods are proposed to search for a target point reflector: One method is based on the imaging function, and has a better signal-to-noise rate; the other method is based on the geometric property, and can improve the bad range resolution of the imaging results.