Source depth and the spatial coherence of ambient noise in the ocean

Abstract

An analytical model is developed for the vertical coherence of the ambient noise field generated by a plane of sources at a finite depth beneath the ocean surface. To clarify the effects of source depth on the noise field, the relatively simple case of a semi-infinite ocean with an isovelocity profile is considered. The expression derived for the coherence is exact; it depends on the source depth explicitly, and it includes the homogeneous and inhomogeneous components of the field. When the sources are shallow, that is, the source depth is much less than a wavelength and the source–image pairs act as dipoles, the coherence is an oscillatory function of frequency, consistent with an earlier theory of noise coherence in deep water. With deeper sources, the dipole description fails and the coherence function becomes approximately independent of frequency. This change of character suggests that the spatial structure of the noise field at depth in the ocean could be inverted to yield information on the acoustic properties of the bubble sources associated with breaking surface waves.

Arrival-time structure of the time-averaged ambient noise cross-correlation function in an oceanic waveguide

“…24,25 For instance, this depth was estimated to be 1.5 m, based on inversion of wave-breaking sound measured at wind speed of 10 m/s or greater in the sea-surface bubble layer. 26 Only the arrival times, s ϭͱL 2 ϩ(z 2 Ϯz 1 Ϯ2z s ϩ2(nϮp)H) 2 /c 0 of the time derivative of the cross correlation dC 1,2 ()/d, that do not exactly match the arrival times of the TDGF ͓see Eq. ͑1͔͒, depend on the spatial distribution of z s ͑i.e., the depth dependency of the acoustically active noise bubbles͒.…”

“…͑19͔͒ for the vertical coherence of seasurface ambient noise has been previously reported. 26 The expression depends on various combinations depth differences z 2 Ϯz 1 and z 2 Ϯz 1 Ϯ2z s .…”

“…Thus, the NCF is independent of the source spectrum when normalized by the energy of the recorded signals at each receiver location. 26 In practice, the NCF is constructed from ensemble averages, denoted by ͗ ͘, over realizations of the noise source amplitude S(r s ;t s ). We assume that the random impulse noise sources have the same amplitude Q (Pa m 3/2 s), have a creation rate 29 ͑m Ϫ2 s Ϫ1 ͒ per unit time per surface area, and are temporally and spatially incoherent 13 in the limit of infinite recording time and infinite bandwidth ͑due to the impulsive nature of the sources͒; then…”

“…Surface noise model At frequencies above several hundred hertz, ambient noise is mostly generated at the ocean's surface. 12,17,[22][23][24] A simple model for the surface-generated ambient noise field 13,19,[25][26][27] is a random distribution, in space and time, of individual point noise sources located in a plane lying beneath the sea surface at a constant depth z s . The signal recorded at the two receivers locations from a single random noise source is fully determined by the TDGF for the oceanic waveguide of interest, between this random source and the receivers.…”

Vertical coherence of ambient noise in shallow water

“…However, noise coherence which is normalized with respect to power spectral density is expected to be stable over a wide range of environmental conditions [2]. Since spatial structure of time averaged ambient noise is largely dependent on seabed properties, coherence can be used to estimate geoacoustic properties of the sea bed [1][2][3][4].…”