Analyses and Applications of the Second-Order Cross Correlation in the Passive Imaging. (17th May 2016)

• Record Type: Journal Article
• Authors: Wang, Lingdi; Chen, Wenbin; Cheng, Jin
• Is Part Of: Communications in computational physics. Volume 19:Number 5(2016:May)
• Page Start: 1191
• Page End: 1220
• Publication Date: 2016-05-17
• Subjects: 35L10, -- 35R30, -- 35R60, -- 78A46; Second-order cross correlation, -- ambient noise sources, -- stationary phase method, -- passive imaging; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.scpde14.26s
• Languages: English
• ISSNs: 1815-2406

Abstract

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, 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; Another method is based on the geometric property, and can improve the bad range resolution of the imaging results.