Analyses and Applications of the Second-Order Cross Correlation in the Passive Imaging (Communications in Computational Physics, 2020)
The first-order cross correlation and corresponding applications in the passiveimaging 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 thesecond-order cross correlation. The second-order cross correlation is proven to be astatistically stable quantity, with respective to the random ambient noise sources. Specially,with proper time scales, the stochastic fluctuation for the second-order crosscorrelation converges much faster than the first-order one. Indeed, the convergent rateis of order $\mathcal{O}$($T^{−1+α}$), with 0