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Recently reported declines in the population of Atlantic cod have led to calls for additional survey methods for stock assessments. In combination with conventional line-transect methods that may have ambiguities in sampling fish populations, Ocean Acoustic Waveguide Remote Sensing (OAWRS) has been shown to have a potential for providing accurate stock assessments (Makris N.C., ^{2.4} frequency dependence below roughly 2 kHz in typical continental shelf environments along the US northeast coast. We then find that it is possible to robustly detect cod aggregations across frequencies at and near swim bladder resonance for observed spawning configurations along the U.S. northeast coast, roughly the two octave range 150–600 Hz for water depths up to roughly 100 m. This frequency range is also optimal for long-range ocean acoustic waveguide propagation, because it enables multimodal acoustic waveguide propagation with minimal acoustic absorption and forward scattering losses. As the sensing frequency moves away from the resonance peak, OAWRS detection of cod becomes increasingly less optimal, due to a rapid decrease in cod scattering amplitude. In other environments where cod depth may be greater, the optimal frequencies for cod detection are expected to increase with swim bladder resonance frequency.

Reported declines [

Both OAWRS detection range and minimum detectable fish population density are limited by scattered returns from the seafloor in the same resolution cell as the fish. Efficient and reliable estimates of seafloor scattering are then necessary to determine OAWRS fish detection limitations. Here, we use a Rayleigh–Born volume scattering approach, where multimodal propagation effects, which appear only in the waveguide Green function, can be mathematically separated from seafloor scattering effects. Our approach differs from traditional investigations of seafloor scattering using free-space plane-wave approaches [

We used OAWRS seafloor scattering data acquired in 2003 on the New Jersey continental shelf [^{3} and 1700 m/s, respectively [

We used cod body length distributions and aggregation densities measured during recent spring surveys conducted from New Hampshire during May–June, 2011, described in [^{2} [

The expected magnitude squared of the Rayleigh–Born seafloor scattering amplitude, 〈|A_{S}^{2}〉, is estimated by minimizing the mean squared error between the measured and modeled scattered field (^{th}^{th}_{m}_{Si}_{0}, _{c}^{th}_{Si}_{ref}_{S}_{c}^{2}〉 for each source frequency, _{c}

We restrict our analysis to beams that are not contaminated by bio-clutter or ship noise and to regions that are within approximately 30 km of the receiver array (

Comparisons between the measured and modeled scattered field level in the New Jersey continental shelf and Georges Bank for various source frequencies are shown in

For a given fish aggregation density of _{F}_{F}^{2}〉, should be greater than that from the seafloor, 〈|Φ_{S}^{2}〉, over the same area:
_{min}, above which fish scattering is greater than seafloor scattering is:

As a direct consequence of

Using OAWRS measurements of long-range seafloor scattering in typical sandy continental shelf waveguide environments along the US northeast coast, we estimate the magnitude squared of seafloor scattering amplitude per coherence volume (^{2.4} frequency dependence, varying as ^{2.7} in the New Jersey continental shelf and as ^{2.1} in Georges Bank (

We find that at swim bladder resonance frequencies, robust detection and imaging of cod spawning aggregations with OAWRS is possible (^{2}, can be detected roughly 20–27 dB above seafloor scattered returns at swim bladder resonance, roughly 300 Hz in this case, when cod are neutrally buoyant close to the seafloor (

The spawning aggregation density then would be roughly 1–2 orders of magnitude higher than the minimum density required for OAWRS detection above seafloor scattering, again enabling robust OAWRS detection. At spawning sites with denser cod aggregations [^{2}. This aggregation density then would be roughly 1–2 orders of magnitude higher than the minimum density required for OAWRS detection above seafloor scattering, again enabling robust OAWRS detection. The scattering amplitude of Atlantic cod is modeled as a function of frequency using the Love model [

Spawning cod aggregations in the coastal waters under investigation here have recently been shown to produce sounds in the 50–500 Hz frequency range [

The seafloor scattered field at center frequency, _{c}_{S}_{S}_{0}, _{c}_{0}, a scattering seafloor region centered on _{S}_{k}_{d}_{S}_{c}/c_{t}_{0}, _{c}_{t}_{S}_{t}_{c}

Since the mean scattered field from diffuse inhomogeneities in a fluctuating waveguide vanishes [_{c}_{d}_{c}

The variance of the seafloor scattered field can also be written as:
_{t}_{t}

Detailed derivations of the broadband seafloor scattered field and its moments and approximations that enable efficient wide-area estimation of seafloor scattering using the Rayleigh–Born approach are provided in

A lower frequency OAWRS system [

It may be possible to remotely classify cod by OAWRS spectral analysis, since they have such a strong response at their swim bladder resonance, which is not found in seafloor scattering. Ground truth from capture, as well as behavioral analysis to set the context would still likely be necessary, since a number of other species of large fish, such as haddock, hake and pollock [

We find that Ocean Acoustic Waveguide Remote Sensing (OAWRS) is capable of instantaneously and robustly detecting spawning cod aggregations over wide areas spanning thousands of square kilometers for observed spawning cod densities and configurations in US northeast continental shelf waters at cod swim bladder resonance frequencies. At swim bladder resonance, OAWRS can also be used to detect individual cod within a few kilometers of the OAWRS system. Such robust detections of cod are possible, because the cod scattering amplitude has a strong low frequency resonance peak spanning the roughly two-octave range of 150–600 Hz within water depths of roughly 100 m, in contrast to the relatively uniform seafloor scattering frequency dependence of roughly ^{2.4}, which we find below roughly 2 kHz in US northeast continental shelf environments. This cod resonance frequency range is also optimal for long-range ocean acoustic waveguide propagation, because it enables multimodal acoustic waveguide propagation with minimal acoustic absorption and forward scattering losses. As the sensing frequency moves away from the resonance peak, OAWRS detection of cod becomes increasingly less optimal, due to a rapid decrease in cod scattering amplitude. In other environments where cod depth may be greater, the optimal frequencies for cod detection are expected to increase with swim bladder resonance frequency.

This research was supported by the National Oceanographic Partnership Program, the Office of Naval Research and the National Oceanic and Atmospheric Administration (NOAA). We would like to thank Christopher W. D. Gurshin, W. Huntting Howell and J. Michael Jech for inviting us to take part in the cod surveys conducted in Ipswich Bay in May–June, 2011, and for providing us with raw echogram data.

The authors declare no conflict of interest.

Bathymetric map of (

Comparison between the measured normalized seafloor scattering and the modeled normalized scattered level in the New Jersey continental shelf at (

Comparison between the measured normalized seafloor scattering and the modeled normalized seafloor scattering in the Georges Bank at (

We consider an ocean waveguide consisting of a water layer, located between an air half-space above and a bottom half-space below (_{0}=(x_{0}, y_{0}, z_{0}), the receiver at _{t}_{t}_{t}_{t}

(_{t}_{t}_{t}_{t}_{w}_{w}_{w}_{b}_{b}_{b}

To derive the broadband scattered field from random volume inhomogeneities, we use the Rayleigh–Born approach [_{t}_{t}_{κ}

Γ_{d}

Applying Green’s theorem [_{S}_{S}_{0}, _{s}_{S}

Green function _{t}_{t}_{t}_{i}_{t}_{0}, _{S}_{t}

We normalize the source level by letting Φ_{i}_{t}_{0}, _{t}_{0}, _{t}_{i}

We derive the scattered field for a source that transmits a broadband waveform, _{c}_{M}_{0} = ∫ |^{2}

We provide expressions for the mean, variance and second moment of the matched filtered scattered field in

We find that the second moment of the broadband field (

In order to account for random fluctuations in the ocean environment, we vary the sound speed profile with the range [

The modeled (

Here, we derive full analytical expressions for the total moments of the matched filtered scattered field in terms of the statistical moments of fractional changes in compressibility and density and in terms of Green functions and their gradients in a randomly fluctuating ocean waveguide. We assume the bottom inhomogeneities to vary randomly in space, following a stationary random process within the region, _{S}_{κ}_{d}

The magnitude of the square of the mean matched filtered scattered field, then, is:

To model the statistics of the density and compressibility variations, we use a delta correlation function and assume the parameters to be correlated in all three dimensions within a coherence volume [

Similarly:

Then,

After integrating one of the delta functions over the volume, _{S}

The total variance can be expressed in terms of the total second moment and the squared of the mean field as:

Although

In this section, we present a computationally efficient approximation to the matched filtered scattered intensity derived in _{S}

In Section A.2, we show, using Monte Carlo simulations in a standard Pekeris waveguide, that the matched filtered scattered intensity derived in

Echograms showing cod aggregations on (^{3}. Black regions represent seafloor sediment.

(

Frequency dependence of the experimentally estimated magnitude squared of seafloor scattering amplitude, |_{S}^{2} (^{2.4}. In water, _{ref}^{3} and _{ref}

The Ocean Acoustic Waveguide Remote Sensing (OAWRS) fish-to-seafloor scattering ratio (FSR) (^{−4} cod/m^{2} for bottom-dwelling cod and roughly 1 × 10^{−5} cod/m^{2} for mid-water column cod. Cod are assumed to be neutrally buoyant at the shallowest limit of their assumed occupancy depth range in each case. The aggregation density in (^{2}, similar to that observed during spawning in Ipswich Bay [^{2}, similar to that observed during feeding [

The fish-to-seafloor scattering ratio (FSR) (

(

(