TY - JOUR
T1 - Analyses and Applications of the Second-Order Cross Correlation in the Passive Imaging
AU - Lingdi Wang, Wenbin Chen & Jin Cheng
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 - <p style="text-align: justify;">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 <span style="color: #111F2C; font-family: &quot;Microsoft YaHei&quot;, &quot;Segoe UI&quot;, system-ui, Roboto, &quot;Droid Sans&quot;, &quot;Helvetica Neue&quot;, sans-serif, Tahoma, &quot;Segoe UI SymbolMyanmar Text&quot;, 微软雅黑; font-size: 14px; white-space: pre-wrap; background-color: #FFFFFF;">$\mathcal{O}$</span>($T^{−1+α}$), with 0&lt;α&lt;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.</p>