The effect of saturated transmission scintillation on ocean acoustic intensity measurements

Abstract

Coherence theory is used to analyze the statistical properties of ocean-acoustic intensity fluctuations measured after saturated multipath propagation. Previous analyses in this area have been implicitly limited to certain special cases for which the time-bandwidth product of the field received from a given source is unity. In this paper, the statistical description is extended and generalized to be a function of measurement time and temporal coherence. As a result, the well known 5.6-dB transmission loss ͑TL͒ standard deviation of Dyer is found to be a special case of a more general TL standard deviation that approximates 4.34 sqrt͑1/͒ dB when the time-bandwidth product is large. Therefore, the TL standard deviation approaches zero for increasing , as it must in the deterministic limit of an arbitrarily large sample size. A similar generalization is obtained for the TL mean, from which it is found that the sonar equation must be corrected for a-dependent bias that vanishes in the deterministic limit of large. Additionally, asymptotic analysis shows that intensity statistics in the saturated region converge to a log-normal distribution, where Ͼ4 is typically sufficient for the log-normal approximation to be made.

Feasibility of Acoustic Remote Sensing of Large Herring Shoals and Seafloor by Baleen Whales

“…Black vertical lines represent the variation of the measured mean ambient noise levels for given wind speed. Instantaneous measurements of ambient noise fluctuate around each mean ambient noise level with 5.6 dB standard deviation [26].…”

“…In Equation (4), Φ re f = 1 µPa is the reference acoustic pressure in water, SL is the whale call source level with mean and standard deviation [1,2] given in Table 1 consistent with circular complex Gaussian random fields fluctuations [26], TLA is the depth-averaged two-way transmission loss to individual targets integrated over one resolution footprint area [23] given in Equation (5), TS = 10 log 10 S r re f k 2 is the expected target strength of a single herring, S is the plane wave scatter function of a single herring, k is the acoustic wavenumber, r re f = 1 m is the reference length, n A,re f = 1 fish/m 2 is the reference areal fish population density, and n A = N/A R (ρ C ) is the expected areal density of the targets within a spatially varying resolution cell centered at horizontal location ρ C . When the instantaneous bandwidth BW of baleen whale vocalizations [1,2] is greater than the one-third octave bandwidth BW 1/3 given in Table 1, an adjusted whale call source level SL adj = SL + 10 log 10…”

“…The coefficients n, α, and β given in Table 1 are empirically determined [2] by least-square fitting between the measured and the modeled ambient noise levels as a function of measured wind speed during the OAWRS 2006 experiment [22] ( Figure A1). The instantaneous measurements of ambient noise vary with 5.6 dB standard deviation [26]. For target detection under seafloor scattering limited detection conditions, the expected magnitude square of the scattered field from herring shoals should be greater than that of the scattered field from the seafloor by a factor that corresponds to detection threshold DT given in Table 1: 10 log 10…”

“…The detection threshold DT is determined by requiring that the scattered returns from fish targets stand at least one standard deviation [26,36] above background levels from seafloor scattering or ambient noise.…”

“…Detection of large herring shoals and the seafloor is then investigated using theoretical and numerical methods developed for analyzing Ocean Acoustic Waveguide Remote Sensing (OAWRS) of fish shoals [21][22][23][24][25] given these active sensing parameters. Sensing resolution in cross-range is determined by spatial array theory and in range by incoherent energy analysis [1,2,[21][22][23][24][25][26], since evidence suggests temporally coherent auditory processing is unlikely [27,28].…”