(untitled) (Communications in Computational Physics, 2020)
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 O(T^−1+α), with 0