Resolution analysis for imaging with noise

We analyze the resolution of imaging functionals that migrate the cross-correlation matrices of passive sensor arrays. These matrices are obtained by cross-correlating signals emitted by ambient noise sources and recorded by the passive sensor array. They contain information about reflectors in the surrounding medium. Therefore, travel time or Kirchhoff migration of the cross-correlations can, under favorable circumstances, produce images of such reflectors. However, migration should be carried out appropriately depending on the type of illumination provided by the ambient noise sources. We present here a detailed resolution analysis of these functionals in a homogeneous medium. Resolution depends on the sensor array diameter, the distance from the array to the reflector and the central frequency, as is the case in active array imaging. When imaging with passive sensor arrays and ambient noise, resolution also depends on the space and time coherence of the noise sources because it determines an effective noise bandwidth