Passive Sensor Imaging Using Cross Correlations of Noisy Signals in a Scattering Medium

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.