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

• Published in: The Journal of the Acoustical Society of America 2005-12, Vol.118 (6), p.3524-3531
• Main Authors: SABRA, Karim G, ROUX, Philippe, KUPERMAN, W. A
• Format: Article
• Language: English
• Subjects: Acoustics; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Marine; Physics
• ISSN: 0001-4966; 1520-8524
• DOI: 10.1121/1.2109059

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.