Year: 2016
Communications in Computational Physics, Vol. 19 (2016), Iss. 5 : pp. 1191–1220
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.scpde14.26s
Communications in Computational Physics, Vol. 19 (2016), Iss. 5 : pp. 1191–1220
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 30