Emergence rate of the time-domain Green’s function from the ambient noise cross-correlation function

• DOI: 10.1121/1.2109059
• Publication Date: 2005-12-09T19:03:28Z
• Authors: Karim G. Sabra; Philippe Roux; W. A. Kuperman
• Keywords: 01 natural sciences; 0105 earth and related environmental sciences

It has been demonstrated experimentally and theoretically that an estimate of the Green’s function between two receivers can be obtained from the time derivative of the long-time average ambient noise function cross-correlation function between these two receivers. The emergence rate of the deterministic coherent arrival times of the cross-correlation function, which yield an estimate of the Green’s function, from the recordings of an isotropic distribution of random noise sources is studied by evaluating the amplitude of the variance of the cross-correlation function. The leading term in the expression of the variance depends on the recorded energy by both receivers and the time-bandwidth product of the recordings. The variance of the time derivative of the correlation function has a similar dependency. These simple analytic formulas show a good agreement with the variance determined experimentally for the correlation of ocean ambient noise for averaging time varying from 1 to 33min. The data were recorded in shallow water at a depth of 21-m water depth in the frequency band [300–530Hz] for receivers separation up to 28m.