Observations and modeling of angular compression and vertical spatial coherence in sea surface forward scattering

Abstract

Measurements and modeling of spatial coherence and related angular spreading associated with forward scattering from the sea surface are presented. The measurements were taken in waters 80 m deep off the New Jersey coast in August 2006. Acoustic signals from a source at depth 40 m were recorded on a vertical line array of length 1.4 m, centered at depth 25 m, and at range 200 m. Measurements in the 14-20-kHz frequency range are reported; the rms waveheight H was 0.16 m, setting kH as approximately 10 where k is acoustic wavenumber. A systematic study of measurements taken over four source-receiver bearing angles separated by 90 degrees suggests a null influence of changing bearing angle or equivalently directional wave effects. Sound speed was characterized by a downward-refracting profile. Refraction modifies the vertical angular spread due to rough sea surface scattering, which can be understood from Snell's law. The Snell mapping is smooth, so an approximation based on the mean grazing angle provides a functional relation between the angular variance near the surface and that at the receiver. The latter is measurably reduced owing to refraction, the effect called angular compression, and a parameter that quantifies this effect is defined.

Spatial coherence considerations for the phase center approximation

“…Analytic Model for Ping-to-Ping Coherence: The van Cittert-Zernike theorem was developed in the field of statistical optics, and it relates the spatial distribution of the intensity of a incoherent radiator to the coherence of the radiated field measured between two points [20]. This theorem has been adapted to address the spatial coherence of scattered acoustic fields [21,22]. It has recently been extended to consider the impact of temporal windowing for seabed scattering of pulsed active sonar systems [23].…”

Near range breakdown of the phase centre approximation

“…The van Cittert-Zernike theorem was developed in the field of statistical optics, and it relates the spatial distribution of the intensity of an incoherent radiator to the coherence of the radiated field measured between two points [20]. This theorem has been adapted to address the spatial coherence of scattered acoustic fields [21,22]. It has recently been extended to consider the impact of temporal windowing for seabed scattering of pulsed active sonar systems [23].…”

Spatial Coherence Comparisons between the Acoustic Field and Its Frequency-Difference and Frequency-Sum Autoproducts in the Ocean

“…As such, (10) and (11) are used to generate error estimates for the genuine acoustic field coherence calculated from (3), and the frequency-difference and frequency-sum autoproduct coherence calculated from (8) and (9). The error estimates of (10) and (11) have been used previously in ocean acoustic coherence studies [16,17] and are expected to be a good approximation of the true variance for a large ensemble, Q [30].…”

“…Coherence length has been studied in a variety of simulation and experimental geometries and scenarios, including with both vertical and horizontal arrays [9], in the presence of internal waves [10][11][12], with varying channel depth [4], in the presence of multipath propagation [3], and at long ranges [13,14], to understand the influence of various ocean environmental characteristics. The coherence of acoustic waves scattered from the ocean surface [15][16][17] and floor sediment [18,19] has also been investigated.…”