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Abstract. It is well known that the travel time or even the full Green's function between two passive sensors can be estimated from the cross correlation of recorded signal amplitudes generated by ambient noise sources. It is also known that the direction of the energy flux from the noise sources affects the estimation of the travel time. Using the stationary phase method we show here that the travel time can be effectively estimated when the ray joining the two sensors continues into the noise source region. We extend this analysis to passive sensor imaging of reflectors with different ambient noise source configurations by suitably migrating the cross correlations. If in addition there is multiple scattering in the medium then reflectors can be imaged with passive sensor networks or arrays by migrating suitable fourth-order cross correlations. Fourth-order cross correlations can also be used with auxiliary passive sensors in order to enhance travel time estimation in a scattering medium.Key words. Travel time estimation, passive sensor imaging, noise sources, random media. AMS subject classifications. 35R30, 35R60, 86A15, 78A461. Introduction. The travel time between two sensors in an inhomogeneous medium can be estimated using the coherent signals emitted by an impulse point source and recorded by them. It can also be estimated using the ambient incoherent noise by computing the cross correlation of noisy signals recorded by the sensors. The ambient noise is generated by sources that are randomly distributed in space and are statistically stationary in time. The cross correlation of signal amplitudes contains information about the Green's function of the wave equation from which the travel time can be obtained. The background propagation velocity can then be estimated from the travel times between sensors in a network covering the region of interest.The first application of this technique was carried out in seismology where the sensors were seismic stations recording velocity fluctuations, the noise sources came from the nonlinear interaction of the ocean swell with the coast that generates surface waves [34], and the goal was to obtain an estimate of the background surface wave velocity map of a large part of the Earth. The idea of exploiting the ambient noise and using the cross correlation of noisy signals to retrieve information about travel times was first proposed in helioseismology and seismology [18,24,31]. It has been applied to background velocity estimation from regional to local scales [21, 32, 20], volcano monitoring [29, 12, 11], and petroleum prospecting [17]. In randomly layered media, correlation methods for imaging are analyzed in [19]. When the support of the random noise sources extends over all space and they are uncorrelated, that is, their spatial correlation is a delta function, it has been shown that the derivative of the cross correlation of the recorded signals is the symmetrized Green's function between the sensors [26]. This is also true with spatially localized noise source dist...

Abstract. We consider the problem of locating perfectly conducting cracks and estimating their geometric features from multi-static response matrix measurements at a single or multiple frequencies. A main objective is to design specific crack detection rules and to analyze their receiver operating characteristics and the associated signal-to-noise ratios. In this paper we introduce an analytic framework that uses asymptotic expansions which are uniform with respect to the wavelength-to-crack size ratio in combination with a hypothesis test based formulation to construct specific procedures for detection of perfectly conducting cracks. A central ingredient in our approach is the use of random matrix theory to characterize the signal space associated with the multi-static response matrix measurements. We present numerical experiments to illustrate some of our main findings.