# Particle motion polarization of offshore fish vocalizations versus ambient and ship noise

Ian Jones, Julien Bonnel, Julien Flamant

► To cite this version:

Ian Jones, Julien Bonnel, Julien Flamant. Particle motion polarization of offshore fish vocalizations versus ambient and ship noise. Journal of the Acoustical Society of America, 2025, 158 (3), pp.1723-1736. 10.1121/10.0039105. hal-05238780

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Submitted on 3 Sep 2025

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# Particle motion polarization of offshore fish vocalizations versus ambient and ship noise

Ian T. Jones,¹,ª) Julien Bonnel,²) and Julien Flamant³)
sensory hair cells in fish inner ears are directionally tuned for 3D particle motion detection (Fay, 1984; Fay and EddWalton, 1997; Weeg et al., 2002). Additionally, lateral line hair cells (which sense hydrodynamic cues) are directionally sensitive, and their input is theorized to be integrated with that of inner ear organs to aid sound localization in the near field (Cardinal et al., 2018; Radford and Mensinger, 2014). Fishes that have swim bladders might integrate sound pressure and particle motion cues to sense sound direction, e.g., by computing a time-averaged intensity vector (Hawkins and Popper, 2018; Veith et al., 2024). Fishes are also thought to use a vector weighting mechanism to sense direction, which would only require particle motion detection (Sand, 2023). However, sound pressure detection might be necessary to resolve the inherent 180° ambiguity of particle motion cues (Hawkins and Popper, 2018). Behaviorally, plainfin midshipman (*Porichthys notatus*) swim toward con-specific vocalizations in a dipole field by orienting their body to and then following local particle motion vectors, suggesting a fish might not need to “know” where the sound source is as long as they follow the local particle motion vector field (Zeddies et al., 2012).

Acoustic fields of sounds produced by fishes have inherent directionality as well. Fish produce sounds either by beating a “sonic muscle” against the swim bladder (drumming) or rubbing hard bony structures (e.g., pectoral fins) together (stridulation). In the case of drumming, empirical data and models indicate that although a bladder may radiate approximately as a monopole (such as when fully filled), this radiation is not uniformly omnidirectional in the horizontal plane, and increased directivity (e.g., as a dipole) may be achieved with reductions in swim bladder size (Barimo and Fine, 1998; Su et al., 2023). Further, monopole radiation (or nearly so) from the swim bladder of a stationary fish is thought to, instead, radiate as a dipole from swimming fish (Kalmijn, 1988).

Fish acoustic communication often occurs in the near field, and for benthic fishes, this occurs in close proximity (e.g., within 1/4 acoustic wavelength) of the seafloor (Amorim, 2023; Higgs and Radford, 2016). In these scenarios, particle motion magnitudes are not readily predictable from single-hydrophone pressure measurements (Gray et al., 2016; Jansen et al., 2019; Nedelec et al., 2021). Thus, particle motion measurements are strongly recommended for fish bioacoustics studies alongside sound pressure measurements (Popper and Hawkins, 2018). Despite the importance of particle motion to fish hearing and communication, particle motion data on fish vocalizations and ambient soundscapes are limited relative to studies solely measuring sound pressure. However, increased recognition of particle motion's relevance to fishes has driven enhanced effort in the past decade to measure and better understand particle motion of natural and anthropogenic sources in soundscape studies and in the contexts of fish acoustic ecology, behavior, and anthropogenic noise impacts (Dahl et al., 2015; Jones et al., 2022; Jones et al., 2025; Kaplan and Mooney, 2016; Pieniazek et al., 2023; Rogers et al., 2021).

If one is interested in sound levels generated by a single source, particle motion is relevant for short distances from sound sources (i.e., in the near field) and within about 1/4 of a wavelength from the sea surface and seafloor (Oppeneer et al., 2023). For far field and free-field particle motion, models and empirical measurements indicate that particle motion levels can be estimated by dividing pressure by acoustic impedance, at least given sufficiently large frequency bandwidth, e.g., 1/3 octave (Dahl and Bonnel, 2022; Flamant and Bonnel, 2023; Dahl et al., 2024). Importantly, however, particle motion measurement (as opposed to estimation from single pressure sensors) is necessary (even in the far field) to obtain information about the vector field (i.e., polarization; see below), including directional information relevant to fish hearing or bearing estimation by acousticians.

Underwater bioacoustic studies that report *in situ* particle motion measurements often focus on the magnitude of particle motion signals either as a 3D vector norm or along individual sensor axes. However, there is additional useful information to be gained from particle motion when one considers its full vector nature through polarization, rather than just its norm. The notion of polarization originates from optics (Goldstein, 2003) and has been extended to general bivariate signals recently (Flamant et al., 2017, 2019), i.e., signals recorded along two orthogonal spatial axes forming a two-dimensional (2D) plane. Note that polarization can also be defined for 3D vectors (Gil, 2014), although this is less common. Bivariate signals allow measurement of sound polarization properties in a given plane, including the shape of particle motion trajectories, the time-stability of polarization, as well as the primary axis of motion, which may differ from axes of a measurement array (Bonnel et al., 2021; Dahl and Bonnel, 2022; Dall'Osto and Dahl, 2013; Flamant et al., 2017). If two orthogonal axes have particle motion exactly in phase with each other, this motion will be linear, i.e., back and forth in a straight line in the direction of the propagating wave. This pattern would be observed for plane waves or isolated sound sources in the far field not influenced by reflective boundaries, scatterers, or additional sounds arriving from other directions. In many real-world scenarios however, reflection, interference, and scattering of waves can lead to phase differences between particle motion axes, and particle motion will follow an elliptical pattern. The specific shape of the ellipse can vary broadly from narrow to wide (Campbell et al., 2019; Dall'Osto and Dahl, 2013). At the two extreme ends of this shape spectrum, the ellipse can become a line segment or a circle, and in such cases, the polarization is said to be linear or circular (see Sec. II A for more detail).

To the authors' knowledge, polarization properties of *in situ* particle motion signals have not yet been studied in the context of fish sound detection and production, which is the primary focus of the present study. Polarization metrics applied in this study were first described for 2, 3, and 4 kHz pulses in shallow underwater waveguides (Dall'Osto and Dahl, 2013) and have since been quantified for ship noise
and normal mode propagation of combustive sources (Bonnel et al., 2021; Dahl and Bonnel, 2022). These studies discuss applications of these metrics for geoacoustic inversions and physical acoustic oceanography, yet, these metrics have not been applied to marine bioacoustics studies. Similar polarization metrics have been proposed for bioacoustics and applied to quantify particle motion ellipses received by fishes in a tank-based behavioral study (Campbell et al., 2019; Campbell and Nedelec, 2023). Theoretically, particle motion signals with linear polarization and a high degree (high temporal stability) of linear polarization might be easier for fishes to detect and localize amidst noise, compared to signals with circular polarization and low degree of polarization (Campbell et al., 2019). If so, this could be considered a form of masking release. Masking is formally defined as the process by which the threshold for hearing a sound (signal) is raised by the presence of a masking sound (noise), whereas masking release refers to a decrease from expected masking as a result of a specific mechanism (Erbe et al., 2016). One such mechanism present in fishes and mammals (among other animal taxa) is spatial release from masking (SRM), which occurs when signal and noise sources are spatially separated (Chapman and Johnstone, 1974; Erbe et al., 2016).

The objective of this study was to apply established
polarization metrics (Bonnel et al., 2021; Dahl and Bonnel,
2022) to in situ fish vocalizations to better understand parti-
cle motion (acceleration) polarization properties of fish sig-
nals in relation to those of ambient noise and anthropogenic
ship noise. For the present study, “ambient noise” is defined
as natural ambient sounds (e.g., from wind) in the absence
of fish signals and ship noise. Fish vocalizations were
recorded on continental slope waters offshore of Florida.
Specific questions addressed include (1) are these fish sig-
nals linearly polarized and do they have a high degree of
polarization?, and if so, (2) are polarization properties of the

fish signals distinct from those of ship and ambient noise in
ways that could allow SRM for fish hearing? Implications of
particle motion polarization results for fish communication
will be discussed, along with useful applications of the pre-
sented analysis framework for quantifying and visualization
particle motion polarization in fish bioacoustics studies.

II. METHODS

A. Overview of polarization metrics for bivariate
signals

The recorded particle acceleration signals in this study
are 3D vectors, $a_{3D} = [a_x \ a_y \ a_z]$. The polarization metrics
considered here are defined for bivariate, i.e., 2D, signals.
To go from 3D to 2D, the two horizontal components ($a_x$
and $a_y$) are combined into a single component $a_r$, pointing
toward the source (see the Appendix). This results in the [$a_r$
$a_z$] bivariate signal, where one horizontal component points
toward the source ($a_r$) and one vertical component points
upward ($a_z$).

For a narrowband signal [$a_r$, $a_z$], its evolution as a func-
tion of time in the $r-z$ plane is an ellipse, as illustrated in
Fig. 1. Polarization refers to the shape of this ellipse, which
can be described using various sets of parameters. A com-
mon set used for polarization studies is illustrated on Figs. 1
(A) and 1(B), with the following definitions:

* The amplitude $\kappa > 0$ of the ellipse is formally defined as
  $\kappa = \sqrt{H_r^2 + H_z^2}$, where $H_r$ and $H_z$ are the amplitudes of $a_r$ and $a_z$, respectively;

* the orientation angle $\theta$ is the angle between the main axis of the ellipse and the horizontal axis. It ranges from -90° to +90°. For the [$a_r$ $a_z$] signal, $\theta$ is an elevation angle. If one were to consider an [$a_x$ $a_y$] signal, then $\theta$ would be the azimuth. The orientation angle $\theta$ has an inherent 180° ambiguity; and

<figure><img src="image_2.png" /></figure>

FIG. 1. (A) Elliptical trajectory in a plane formed by *x* and *y* shows ellipse orientation angle (θ) and ellipticity angle (χ). κ is the ellipse amplitude, i.e., maximum absolute distance of the ellipse from the origin. The ellipse is bisected by orthogonal semi-major (extending to κ) and semi-minor axes. (B) Elliptical trajectories for different ellipticity angles (columns) and orientation angles (rows) are depicted. Arrows show the rotation direction for particle motion ellipse trajectories (counterclockwise around the ellipse for positive χ and clockwise around the ellipse for negative χ). The *x* axis and *y* axis components each have an amplitude of one and ellipses were synthesized using Eq. (9) of Bonnel *et al.* (2021). Note that the ellipse becomes a circle when ellipticity angle is 45° (or -45°) regardless of the orientation angle. (C) From top to bottom, 3 sets of 50 independent realizations of ellipse width, with high (φ = 0.99), middle (φ = 0.8), and low (φ = 0.1), degrees of polarization. In (C), all ellipses have the same parameters θ and χ.
* the ellipticity angle $\chi$ describes the shape of the ellipse (independently of its size or orientation). It is formally defined through $\tan(\chi) = b/c$, where b is the semi-minor axis and c is the semi-major axis of the ellipse. The ellipticity angle $\chi$ ranges from -45° to +45°, where, by convention, a negative sign indicates clockwise rotation of the ellipse and positive sign indicates counterclockwise rotation (note other conventions for sign and rotation direction may be used elsewhere).

The ellipticity angle $\chi$ is a fundamental parameter to describe polarization. If $|\chi| \approx 0$, then the ellipse becomes a line segment, and the signal is said to be linearly polarized. If $|\chi| \approx 45°$, then the ellipse becomes a circle, and the signal is said to be circularly polarized. In the circularly polarized case, the orientation angle $\theta$ becomes meaningless [Fig. 1(B)].

As mentioned above, the ellipse shape can be described in many ways. As examples, Dahl and Bonnel (2022) used a metric called circularity, which can be directly related to the parameterization used here, employing Stokes parameters (see Sec. II C; Bonnel et al., 2021; Dahl and Bonnel, 2022). Further, Campbell and Nedelec (2023) propose another metric, “eccentricity” $e$. It is directly related to our traditional set of parameters through $e = \sqrt{1 - \tan^2(\chi)}$. A key point here is that neither parameterization is better than the other because a one-to-one mapping exists between $e$ and $\chi$.

In practice, real signals are complex, fluctuating, and random (if only caused by noise). As a result, the polarization ellipse varies across time or experiments. The statistical dispersion of ellipses is usually described through the degree of polarization $\phi$, ranging from 0 to 1. This nondimensional quantity is formally defined for stochastic processes. However, in practice, $\phi$ can be computed by “averaging out” polarization ellipses computed over several overlapping time segments (Bonnel et al., 2021). If the polarization ellipse is consistent over time, then $\phi = 1$; the signal is said to be fully polarized. On the other hand, for $\phi = 0$, no “average” polarization ellipse can be found, and the signal is said to be unpolarized. For intermediate situations in which $0 < \phi < 1$, the signal is said to be partially polarized, where $\phi$ indicates the ratio of polarized signal power over the total signal power. Figure 1(C) illustrates the concept of degree of polarization; see also Dahl and Bonnel (2022) and Flamant et al. (2017) for further details and interpretations on the degree of polarization.

Many real signals, such as those considered in this paper, are broadband, therefore, the narrowband description presented above needs to be extended. For broadband signals, polarization can be described in the frequency domain: an individual polarization ellipse (described by Stokes parameters) is attached to each frequency bin, and Stokes parameters can then be summed over frequency bins as in the present study (see Sec. II C). Another possibility is to describe time-varying polarization by considering the analytic signal after bandpass filtering in a band of interest (Dahl and Bonnel, 2022). However, we chose the

frequency-domain approach as it is a direct extension of spectrogram data usually obtained for soundscape and bioacoustic studies and follows the primary approach of recent studies (Bonnel et al., 2021; Dahl and Bonnel, 2022).

## B. Study site and dataset

Fish signals, ship noise, and ambient noise were recorded from a stationary platform at Blake Escarpment, 29.251° N; 78.351° W, part of the Atlantic Deepwater Ecosystem Observatory Network (ADEON; Miksis-Olds, 2023). This site was 870 m deep and 280 km offshore of Florida. Data were recorded from Acoustic Long Term Observatory (ALTO) landers (JASCO Applied Sciences, Halifax, Nova Scotia, Canada) deployed on the seafloor. The lander included a four-channel array of M36-V35-100 hydrophones (Geospectrum Technologies, Dartmouth, Nova Scotia, Canada; calibrated frequency range, 2–250 000 Hz; nominal sensitivity, -165 dB re 1 V/µPa; spectral noise floor level, 34 dB re 1 µPa²/Hz) connected to an Autonomous Multichannel Acoustic Recorder (AMAR G4; JASCO Applied Sciences; 24-bit, 8 kHz sample rate; 6 dB gain). Four hydrophones were orthogonally spaced at nominally 0.5 m apart to form two horizontal axes and one vertical axis with a center hydrophone at the origin. The lower three hydrophones were approximately 1.25 m above the seafloor and 0.25 cm above the lander surface. The lander was also equipped with a Seabird SBE 37-SMP-ODO MicroCAT (Sea-Bird Scientific, Bellevue, WA) conductivity, temperature, and dissolved oxygen sensor, which sampled every 30 min. Seawater density obtained from this sensor was used for the calculation of particle acceleration (Sec. II C). Further descriptions and images of the lander can be found in Jones et al. (2025) and Martin et al. (2018). Fish signals and ambient noise were sampled June 12–18, 2018 (the same fish signal was present before and after this period, however, temporal occurrence of fish signals is not the focus of the present study). The fish signals were not identified to species, but potentially soniferous species were found via opportunistic video data from other landers in the ADEON network, including conger eels (Conger oceanicus), white hake (Urophycis tenuis), and blackbelly rosefish Helicolenus dactylopterus (Jones et al., 2025). Sounds from these species have not been reported, although the spectrotemporal pattern of fish signals in the present study (Fig. 2) resembles those among members of families Gadidae and Sciaenidae (Kaschner, 2012; Looby et al., 2025). Ship noise was sampled June 11–29, 2018. During the sampled deployment (June 10, 2018–November 6, 2018), the simultaneous four-channel recordings by the AMAR had an irregular duty cycle averaging to 43 min h⁻¹.

## C. Acoustic data processing

All data processing was conducted in MATLAB R2023a (The MathWorks, Natick, MA). The mean of the raw time series was first subtracted from the raw time series to remove any direct current offset. Frequency-specific calibration
<figure><img src="image_3.png" /><figcaption>FIG. 2. Spectrograms of an example fish signal of five pulses (upper row) and example ship pass (lower row). Columns (left to right) show sound pressure (from the top hydrophone of z axis), particle acceleration in the x, y, and z axes of the hydrophone array, and particle acceleration for the horizontal source-receiver axis. On the colorbar labels, $L_{p,f}$= mean square sound pressure spectral density level, and $L_{a,f}$= mean square particle acceleration spectral density level.</figcaption></figure>

curves were applied to convert data to sound pressure units (μPa). This was completed by performing a fast Fourier transform (FFT) on the raw time series, and next applying calibration coefficients for each frequency, using linear interpolation for frequencies between those for which measured coefficients were available. Then, an inverse FFT was used to return now-calibrated data to the time domain. As stated in the Introduction, particle motion data and polarization metrics were expressed using particle acceleration, which is considered to be the most relevant cue for fish hearing (Sand and Karlsen, 2000). Polarization results using particle velocity are not shown but were confirmed as equivalent to those of particle acceleration [velocity and acceleration directly scale with each other in the frequency (f) domain by a factor of $2\pi if$]. Particle acceleration (a) was calculated for each array axis (x, y,z) using the finite-difference approximation

$$a_{21}(t) = \frac{-(p_2(t) - p_1(t))}{\rho d}, \quad (1)$$

where $p_1(t)$ and $p_2(t)$ are pressures (unit, Pa) at two hydrophones at a single time point t, ρ is seawater density determined from SeaBird MicroCAT data (1032 kg/m³), and d is the measured distance (m) between hydrophones. All analyses were limited to a minimum frequency of 25 Hz and a maximum frequency of 750 Hz as directionality above 750 Hz becomes ambiguous with 0.5 m hydrophone spacing (Gray et al., 2016). Particle acceleration data in the horizontal plane were steered to a source-receiver axis (where horizontal particle acceleration amplitude was maximal) to

report polarization metrics for the bivariate signal [$a_r$, $a_z$] in the vertical plane formed by this horizontal source-receiver axis (r) and vertical axis (z). The procedure for steering to the source-receiver axis is detailed in the Appendix.

Level metrics, kurtosis duration (a measure of pulse length), and peak frequency of n = 30 fish signals were calculated for 100 ms windows centered on each fish signal from 200 to 750 Hz, where the 200 Hz cutoff omitted other lower frequency noises (e.g., flow noise and noise from baleen whale calls). Zero-to-peak sound pressure levels of fish signals, $L_{p,0-pk}$, as defined by ISO 18405:2017, were calculated using the center (origin) hydrophone (ISO/DIS, 2017). Maximum frequencies of n = 28 fish signals were below 1600 Hz, and n = 2 fish signals reached 3500 Hz; $L_{p,0-pk}$ calculated in a 200–3500 Hz band exceeded those of the 200–750 Hz band only by 1–2 dB, thus, sound pressure levels were limited to a maximum frequency of 750 Hz, corresponding to the high-frequency limit used for particle motion. Zero-to-peak particle acceleration levels were calculated following the ISO 18405:2017 definition for $L_{p,0-pk}$ but with acceleration (units, μm s⁻²) in place of sound pressure (ISO/DIS, 2017). These values were calculated for the steered horizontal source-receiver axis $a_r$ ($L_{a,r,0-pk}$) and separately for the 3D vector norm of particle acceleration $a_{3D}$ ($L_{a,3D,0-pk}$) as

$$a_{3D} = \sqrt{a_x^2 + a_y^2 + a_z^2}. \quad (2)$$

To measure pulse length of fish signals, kurtosis duration ($T_β$) was calculated on $a_r$ data (Müller et al., 2023). As
defined in Müller et al. (2023), $T_β$ is a measure based on sound pressure kurtosis (a measure of impulsivity), but in the present study, the particle acceleration time series ($a_r$) was input instead of the sound pressure time series. Peak frequencies (frequencies of highest sound energy) of fish signals ($a_r$) were found in 10 Hz frequency bins (FFT size = 800).

Subsequent analyses were performed with two different time-frequency averaging schemes summarized in Table I: one to produce example spectrograms (Fig. 2) and polarization spectrograms (Fig. 3) over longer time windows, and a second with shorter time windows to statistically compare polarization metrics between individual fish pulses, ambient noise, and ship noise (Figs. 4–6). Example spectrograms for ~5 s of fish signals and one ~18 min ship pass were made for sound pressure, each array axis of particle acceleration (x,y,z), and the source-receiver axis of particle acceleration. The polarization spectrograms show how orientation angle $θ$ and ellipticity angle $χ$ change over time and frequency.

Polarization properties were compared between $n=30$ fish signals, $n=30$ ambient noise time windows, and $n=30$ ship passes. All replicates were 100 ms time windows to avoid potential biases from unequal averaging times. The 100 ms window encompassed the maximum fish pulse length (Table II). The ambient time windows were manually selected within ±5 s before or after the fish signal, where there were no noticeable discrete signals in the spectrograms. The ship noise time windows were manually selected within 1 min of the closest point of approach (CPA), i.e., where ship noise had maximum received sound pressure level. Each CPA was auto-detected via an algorithm described in Martin (2013), and the data product of ship CPA times was provided by JASCO Applied Sciences (see Acknowledgments) and manually visually confirmed on spectrograms. The CPA was chosen as this typically is a point of greatest masking potential in terms of amplitude, and we aimed to determine whether polarization differences exist between fish signals and ship noise that could allow SRM even a with low fish signal to ship noise ratio. Note, however, that polarization properties will change across a ship pass, as previously studied (Dahl and Bonnel, 2022).

<table><caption>TABLE I. Summary of time windows and resulting time and frequency resolution for spectrograms and polarization spectrograms and statistical comparisons of polarization metrics between $n=30$ each of fish signal, ambient noise, and ship noise samples.</caption><thead><tr><th></th><th>Spectrograms and polarization spectrograms</th><th>Statistical comparisons of polarization</th></tr></thead><tbody><tr><td>FFT size</td><td>1600</td><td>8000</td></tr><tr><td>Window type</td><td>Hann</td><td>Hann</td></tr><tr><td>Time resolution</td><td>20 ms<sup>a</sup></td><td>100 ms</td></tr><tr><td>Frequency resolution</td><td>5 Hz</td><td>1 Hz<sup>b</sup></td></tr><tr><td>Associated figures</td><td>Figs. 2 and 3</td><td>Figs. 4–6</td></tr></tbody></table>

<figure><img src="image_4.png" /><figcaption>FIG. 3. Polarization spectrograms of the example fish signal [(A), (B)] and ship noise [(C), (D)] displayed in Fig. 2, and ambient noise [(E), (F)]. Left column shows orientation angle $θ$, and right column shows ellipticity angle $χ$. $θ$ and $χ$ are defined for the vertical plane formed by a horizontal steered source-receiver axis and orthogonal vertical axis.</figcaption></figure>

Ellipse orientation angle ($θ$), ellipticity angle ($χ$), and degree of polarization ($φ$) were calculated via Stokes parameters following Bonnel et al. (2021), Dahl and Bonnel (2022), and Flamant et al. (2017). Particle acceleration data were Fourier transformed (using parameters in Table I) to obtain complex spectra $A_r$ and $A_z$. Stokes parameters were then calculated as

$$S_0 = A_r(f, t)A_r^*(f, t) + A_z(f, t)A_z^*(f, t), \quad (3)$$

$$S_1 = A_r(f, t)A_r^*(f, t) - A_z(f, t)A_z^*(f, t), \quad (4)$$

$$S_2 = 2\Re[A_r(f, t)A_z^*(f, t)], \quad (5)$$

$$S_3 = 2\Im[A_r(f, t)A_z^*(f, t)], \quad (6)$$

where $\Re$ extracts only the real component, and $\Im$ extracts the imaginary component. $S_0$ gives the kinetic energy of a

<footnote><sup>a</sup>20 ms time bins had 90% overlap.</footnote>

<footnote><sup>b</sup>Quantities (Stokes parameters) in 1 Hz bins were later summed to decide-cade levels.</footnote>
<figure><img src="image_5.png" /><figcaption>FIG. 4. Bivariate histograms of example particle acceleration signals in the plane formed by the horizontal source-receiver axis and vertical axis, depicted over 100 ms windows for a decidecade band centered at 630 Hz. (A) Fish signal, (B) ambient noise 3 s after the fish signal and steered to the same source-receiver axis as the fish signal, and (C) ship noise at CPA. Colorbars show histogram bin counts. Overlaid on each subplot are values for ellipse amplitude $κ$, ellipticity angle $χ$, ellipse orientation angle $θ$, and degree of polarization $φ$. The fish signal and ship noise windows were sampled from the same signals exhibited in Figs. 2 and 3(A)–3(D). Note the different axis limits for each subplot.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>FIG. 5. Boxplots comparing values of each polarization metric (rows, ellipse orientation angle $θ$, ellipticity angle $χ$, and degree of polarization $φ$) for fish signals, ship noise (at CPA), and ambient noise for three decidecade bands (columns, 400, 500, and 630 Hz center frequencies). Horizontal lines at the top of subplots indicate statistical results (Wilcoxon rank sum tests) for comparisons of fish vs ship and ship vs ambient (lower lines) and fish vs ambient (upper line). $^*p < 0.0167$, $^{**}p < 0.01$, $^{***}p < 0.001$, n.s. = not significant ($p > 0.0167$).</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>FIG. 6. Signal-to-noise ratios (depicted in this figure as SNR) of ellipse amplitude (κ) of fish signals to κ of time-adjacent ambient noise vs polarization metrics of fish signals. Each subplot is for a given polarization metric (|θ|, |χ|, or φ; rows) and decidecade frequency band (400, 500, and 630 Hz; columns). Solid black lines are lines of best fit from regressions, and gray-shaded areas are 95% confidence regions. For |θ| and |χ|, ordinary least squares regression was performed. For φ, exponential asymptotic regression was performed of the form $y = 1 - (1 - b)e^{(-c \times x)}$.</figcaption></figure>

bivariate signal (equal to κ², the ellipse amplitude squared), whereas S₁, S₂, and S₃ describe the polarization state of a bivariate signal.

For statistical comparisons of polarization metrics between fish, ambient, and ship noise, Stokes parameters initially calculated for 1 Hz bins (Table I) were then summed over decidecade bands. Fishes are thought to integrate sounds over critical bandwidths between 1/3 octave and 1 octave, based on experiments estimating critical bands of Atlantic cod, Gadus morhua (likely, between 1/2 octave and 1 octave) and frequency discrimination thresholds of 3%–20% in goldfish Carassius auratus and other species (Fay, 1988; Hawkins and Chapman, 1975). Decidecade bands are approximately equal to 1/3 octave bands and were chosen because of their recent recommendation in best practices for reporting soundscape data (Heaney et al., 2020). Peak frequencies of the fish signals were between 310 and

700 Hz, therefore, three decidecade bands were chosen centered at 400, 500, and 630 Hz to compare fish signal polarization with that of ship noise and ambient noise. Polarization metrics were then calculated using decidecade band-summed Stokes parameters as follows:

$$ \theta = \frac{1}{2} \operatorname{atan} \left( \frac{S_2}{S_1} \right), \qquad (7) $$

$$ \chi = \frac{1}{2} \operatorname{atan} \left( \frac{S_3}{\sqrt{S_1^2 + S_2^2}} \right) = \frac{1}{2} \operatorname{asin} \left( \frac{S_3}{S_0} \right), \qquad (8) $$

$$ \phi = \frac{\sqrt{S_1^2 + S_2^2 + S_3^2}}{S_0}. \qquad (9) $$

Note that for Eq. (7), the four-quadrant inverse tangent (“atan2” in MATLAB) must be used to obtain θ in an interval
of -90° to +90°. Because degree of polarization (φ) requires multiple time samples, Stokes parameters for degree of polarization were calculated for 10 ms sliding windows at intervals of 5 ms, leading to 19 time samples for each full 100 ms window; the average of each Stokes parameter over these 19 samples was then taken and input into Eq. (9) to get a single φ value for each 100 ms window.

Wilcoxon rank sum tests (equivalent to Mann-Whitney U tests) were run to compare values of each polarization metric (θ,χ,φ) between fish signals, ambient noise, and ship noise at CPA. These were run individually for each decade band. The significance threshold, α, was based on a Bonferroni correction for three pairwise tests, i.e., α = 0.05/3 = 0.0167, for fish vs ship, fish vs ambient, and ship vs ambient.

Last, the fish signal to ambient noise ratio (SNR) was found for each decade band to assess whether low SNR signals could be distinguished from noise based on their polarization properties. First, the particle acceleration ellipse amplitude, κ, of each fish signal and time-adjacent (±5 s) ambient noise window was found from S₀ such that

$$ \kappa = \sqrt{S_0}. \qquad (10) $$

Then, the ratio of κ of each fish signal and that of its paired ambient noise sample was taken to get n = 30 SNR values for each decade band. SNR values were plotted against polarization metric values (θ,χ,φ) of the fish signals.

### III. RESULTS

#### A. Time, frequency, and amplitude properties of unidentified fish signals

Fish signals had variable zero-to-peak sound pressure level (Lₚ,₀-pk) zero-to-peak particle acceleration level (Lₐ,₀-pk; Lₐ,₃D,₀-pk), duration, and peak frequency (Table II). Percentile and maximum Lₐ,₀-pk (along the horizontal source-receiver axis) were 1–4 dB below Lₐ,₃D,₀-pk (3D vector norm), indicating mainly horizontal propagation of the fish signals. Based on a previous study of these same fish signals’ measured particle acceleration relative to a free-field plane wave approximation, these signals (particularly those with the highest measured particle motion levels) are thought to have been recorded in the near field (Jones et al., 2025).

#### B. Polarization properties of the fish signals, ship noise, and ambient noise

Particle acceleration spectrograms indicated directionality of fish signals pointing more along horizontal axes (x, y, and source-receiver axis) than the vertical z axis (Fig. 2). Conversely, ship noise had greater particle acceleration levels in the z axis compared to horizontal axes, especially at the CPA around 700 s. Particle acceleration data in the x, y, and z array axes had low frequency transients (<200 Hz) that were less apparent on the source-receiver axis and not observed in the sound pressure data for three out of four

hydrophones; when inspecting spectrograms, all four hydrophone channels (not shown) revealed these transients were only present on the center (origin) hydrophone. Although the source of these transients is unknown, possibly they are a result of flow noise or reflections off the seafloor or lander itself. Subsequent data analyses and figures report data only for frequencies above these transients (>200 Hz).

Polarization spectrograms (Fig. 3) visualize orientation angle (here, elevation), θ, and ellipticity angle, χ, over time and frequency for the same fish and ship noise files displayed in Fig. 2, as well as an example of about 20 min of ambient noise. Orientation angle was close to horizontal (-10° > θ > +10°) for fish signals but closer toward vertical (θ < -30° or θ > +30°) for ambient noise. Ship noise had near vertical |θ| (near 90°) at the CPA and lower (more horizontal) |θ| at times away from the CPA. Ellipticity angle was low for fish signals (0° < χ < 10° in this example), indicating that the fish signals were nearly linearly polarized. Ship noise also had nearly linear polarization (-10° < χ < 10°) near the CPA [around 700 s on Fig. 3(D)]; however, remember that orientation differs (fish signals are mostly horizontal, whereas ship noise near CPA are mostly vertical). At times further away from the CPA, the ship noise polarization was more widely elliptical with various shapes (χ < -10° or χ > +10°). Ellipticity angles for ambient noise were random.

Bivariate histograms provide a view of the respective variance of signals along two axes. In this case, the “footprint” of particle acceleration trajectories over a time window in the vertical plane formed by the horizontal source-receiver axis and z axis (Fig. 4). Examples are shown for a fish signal, ship noise, and ambient noise, each over 100 ms windows on data filtered to the 630 Hz decade band (Fig. 4). The fish bivariate signal [Fig. 4(A)] has near-horizonal orientation (|θ| = 0.97°), a narrow quasi-linear trajectory (|χ| = 3.75°), and stable polarization throughout the 100 ms time window (φ = 0.97). The ambient noise [Fig. 4(B); steered to the same azimuth as the fish signal in Fig. 4(A)] has a close to vertical orientation (|θ| = 78.13°), a trajectory width wider than the fish signal (|χ| = 7.25°), and lower degree of polarization (φ = 0.61) than the fish signal. The ship signal at CPA [Fig. 4(C)] has closer to vertical orientation than the fish signal (|θ| = 62.02°), a trajectory width narrower than the ambient noise but wider than the fish signal (|χ| = 6.80°), and a high degree of polarization that is lower than that of the fish signal (φ = 0.94) but much higher than the ambient noise.

For all three decade bands, fish signals had significantly lower absolute orientation angles (i.e., they were more horizontal) than ship noise at CPA or ambient noise (p < 0.01; see the supplementary material for full statistical results). Ship noise had significantly lower orientation angle than ambient noise only for the 500 Hz decade band (p < 0.0167). Fish signals had significantly lower absolute ellipticity angles than ship noise in the 630 Hz decade band (p < 0.001), indicating closer to linear polarization of fish signals compared to ship noise at CPA in this band.
<table><caption>TABLE II. Descriptive statistics (medians, interquartile ranges, minima, and maxima) of time-frequency and amplitude properties of fish signals (n = 30; 100 ms time windows), including amplitude (zero-to-peak levels), kurtosis duration, and peak frequency. Sound pressure levels ($L_{p,0-pk}$) are from a single hydrophone (at the origin of the array). Zero-to-peak article acceleration levels are shown for a 3D vector norm (using all three axes of the orthogonal hydrophone array; $L_{a,3D,0-pk}$) and the (steered) horizontal source-receiver axis ($L_{a,r,0-p}$). Visualization of waveforms confirmed each fish signal had <100 ms duration, however, kurtosis duration overestimated n = 2 fish signals at >100 ms, possibly because of low SNR; these two values were omitted from kurtosis duration statistics in this table.</caption><thead><tr><th>Metric</th><th>Median</th><th>Interquartile range</th><th>Minima, and maxima</th></tr></thead><tbody><tr><td>$L_{a,3D,0-pk}$ (dB re 1 µm s<sup>-2</sup>)</td><td>47.7</td><td>[47.0,55.3]</td><td>[40.6,83.4]</td></tr><tr><td>$L_{a,r,0-pk}$ (dB re 1 µm s<sup>-2</sup>)</td><td>47.0</td><td>[43.5,53.9]</td><td>[30.2,81.5]</td></tr><tr><td>$L_{p,0-pk}$ (dB re 1 µPa)</td><td>103.3</td><td>[101.2,110.4]</td><td>[95.1,137.6]</td></tr><tr><td>Kurtosis duration, $T_β$ (ms)</td><td>43</td><td>[40,52]</td><td>[22,79]</td></tr><tr><td>Peak frequency (Hz)</td><td>505</td><td>[470,570]</td><td>[310,700]</td></tr></tbody></table>

Median ellipticity angles of fish signals were lower than those for ship noise in each decade band and lower than ambient ellipticity angles for 500 and 630 Hz bands, although these differences were not significant. Interquartile ranges of fish signal ellipticity angles were smaller than for ship or ambient noise in each band. Fish signals had significantly higher degree of polarization than ambient noise in 500 and 630 Hz bands ($p < 0.01$) as did ship noise compared to ambient noise in these bands ($p < 0.01$). Fish signals and ship noise had statistically similar degrees of polarization ($p > 0.0167$). The ellipticity angle and degree of polarization results together indicate almost linear and high degree of polarization of fish signals, further from linear (closer to circular) polarization for ship noise at CPA, and closest to circular and lowest degree of polarization for ambient noise. Note that although all the fish signals had <100 ms pulse length (Table II), ship noise (of individual passes) lasts much longer (minutes to hours), and polarization metrics of ship noise will vary over time as observed in Fig. 3 and as detailed in Dahl and Bonnel (2022).

### C. Dependence of polarization properties on SNR

There was moderate correlation ($0.43 < R^2 < 0.54$) of fish SNR with degree of polarization for each frequency band, where these data follow an exponential asymptotic regression (Fig. 6). Low SNR fish signals (arbitrarily defined as <5 dB) tended to have degree of polarization below median ambient degrees of polarization (Fig. 5), whereas degree of polarization increased exponentially with increasing SNR and plateaued above 20 dB SNR. Fish SNR had weak-to-no correlation ($0.02 < R^2 < 0.14$) with absolute ellipticity angle and no apparent correlation with absolute ellipse orientation angle ($R^2 < 0.04$), and wide confidence intervals for linear regressions. For some replicates, there were low ellipse orientation angles at relatively low SNR ($\theta < 30°$ at SNR < 15 dB, indicating near-horizontal directionality) and low ellipticity angle values ($\chi < 10°$ at SNR < 5 dB, indicating quasi-linear polarization), but there

was wide data spread with a few values of $\theta > 30°$ and $\chi > 10°$ below these SNRs. Thus, there was no clear dependence of ellipse orientation angle or ellipticity angle on SNR.

### IV. DISCUSSION

This study applied a framework for analyzing, visualizing, and comparing polarization of bivariate particle motion signals to fish signals, relative to ship noise (at CPA), and ambient noise. Polarization metrics, including ellipse orientation angle ($\theta$), ellipticity angle ($\chi$), and degree of polarization ($\phi$), describe the spatial axis of motion, ellipse shape, and temporal stability, respectively. Although the fish species producing vocalizations observed was unknown, fish signal amplitudes and time-frequency properties (Table II) were within ranges reported for vocalizations of marine fish species within Gadidae and Sciaenidae families (Amorim, 2006; Roberts and Rice, 2023). Measured zero-to-peak sound pressure levels and particle acceleration levels of fish signals were above sound pressure and particle acceleration hearing thresholds between 200 and 700 Hz for many marine fish species (Ladich and Fay, 2013).

Fish signals had distinct polarization properties from ship noise and ambient noise. The polarization property that best distinguished fish signals from ambient noise was ellipse orientation angle (here, elevation), followed by degree of polarization, and, last, ellipticity angle. Polarization of fish signals was also distinguished from ship noise by orientation angle, where ship noise (again, at CPA) had intermediate elevation between more horizontal fish signals and more vertical ambient noise. Ship noise and fish signals had similar temporal stability of polarization, and ship noise had significantly wider ellipses than fish signals in the highest analyzed frequency band.

Investigations of the utility of polarization metrics to distinguish low SNR fish signals (e.g., <5 dB SNR) from noise had mixed results. For the human observer applying these metrics, discriminating fish signals observed in this study from ambient noise with degree of polarization alone would require at least 5 dB SNR. This result is logical considering, if the fish signal recorded is assumed to be a sum of a deterministic fish signal and unpolarized ambient noise, then degree of polarization is directly given by $\phi = R/(1+R)$, where SNR = $10 \log_{10}(R)$, which goes to zero as R approaches zero and goes to one as R approaches infinity (Flamant et al., 2017). Researchers' ability to detect polarization properties of fish signals (as with polarization of signals, generally) relies on SNR and, thus, may be biased, i.e., lower SNR fish signals may have been missed even if they have distinct polarization properties from noise. Orientation angle and ellipticity angle, instead, had no clear correlation with SNR, hence, it is uncertain whether these metrics alone could aid in detection of signals with low SNR (<5 dB). However, it has long been known that with vector sensors and hydrophone arrays, steering to a source-receiver can enhance SNR given sufficient angular separation of signal and noise (Thode et al., 2016; Thode et al., 2019).
Quantifying particle motion polarization has practical research applications for understanding particle motion signal properties, whether experimentally applied or observational. Further, polarization properties may be useful to fishes themselves to directionally detect and discriminate signals and localize relevant sound sources (e.g., conspecific mating calls). Existing studies on fish directional hearing necessarily report orientation angles (as azimuth or elevation) of sounds, whether this angle refers to the direction of the local particle motion vector (θ in the present study) or a travelling sound pressure wave. Plainfin midshipman orient their bodies to match and swim along local particle motion vectors to swim toward a conspecific mating call, suggesting fishes' use of (in that study, azimuthal) ellipse orientation angle for localizing sound sources (Zeddies et al., 2012). Increased angular separation between an acoustic signal and masking noise allows SRM, which is a common strategy among vertebrate taxa (Erbe et al., 2016). In fishes, SRM has been experimentally demonstrated in Atlantic cod *G. morhua* and haddock *Melanogrammus aeglefinus* with 7 dB decreases in hearing thresholds for 45° angular separation of a pure tone from noise (Chapman and Johnstone, 1974). Cod and haddock can discriminate source elevation angles differing by about 16°, which is well within the elevation differences observed between fish signals and noise in the present study, and discriminate azimuth differences of about 20° (Chapman and Johnstone, 1974; Hawkins and Sand, 1977). Thus, fishes can likely take advantage of the ellipse orientation angle differences observed to discriminate biologically relevant signals and achieve SRM.

Although relative particle motion ellipse orientation angles (or the propagation direction) of signals and masking noise have known implications for fish directional hearing and SRM, it is unknown whether fishes can discriminate between different signals or signals from masking noise based on their ellipticity angle or degree of polarization. Future experiments could manipulate these polarization variables independently and measure behavioral and neurophysiological responses to determine if changes in these properties are detectable by fishes. Such studies could investigate new questions about fishes' directional sound sensitivity. For example, do smaller absolute ellipticity angle values (i.e., narrower particle motion ellipses) of signals or noise for a given orientation angle difference allow lower hearing thresholds (and greater SRM) than the angular separation of the signal and noise alone? One may predict narrower and temporally stable ellipses to have greater effective angular separation (functionally, for fish directional detection) than wider ellipses and temporally unstable ellipses (i.e., a smaller degree of polarization). Mathematically speaking, when ellipses are so wide that $|χ|$ approaches 45°, the orientation (θ) exists but is mostly meaningless, i.e., in this case, for different θ, the ellipse trajectory will appear to be the same as a circle [Fig. 1(B)]. In the present study, ship noise at CPA had statistically similar $|χ|$ and φ to the fish signals for most decadeband; however, significantly different ellipticity angle (in this case, elevation) between fish calls

and ship noise at CPA could allow SRM. In the case of fish signals vs ambient noise, statistically significant differences of $|χ|$ and φ may indicate potential of these properties to further contribute to SRM.

More baseline directional hearing data on fishes is needed, including azimuth and elevation-dependent amplitude hearing thresholds and minimum audible angles; among fishes, minimum audible angles have only been estimated for Atlantic cod (Hawkins and Popper, 2018). Even less is known on mechanisms of how fish localize sound sources, including conspecific signals, although in theory, linear (or nearly so) and high degree of polarization of biologically relevant signals would aid fishes in this task (Campbell et al., 2019). Further, along with orientation angle, ellipticity angle and degree of polarization have utility as data quality checks when experimentally exposing particle-motion-sensitive animals to directional and polarized stimuli, as previously discussed for similar metrics describing the same polarization properties, e.g., eccentricity (Campbell et al., 2019; Campbell and Nedelec, 2023).

Importantly, although the present study indicates quasi-linear polarized horizontal motion along the source-receiver axis, this is not necessarily representative of the radiation pattern of the acoustic field from these fish sources at other azimuths around the fish. Further, the orientations of fishes relative to the hydrophones were unknown. Horizontal directionality and polarization of fish signal particle motion observed in discrete planes reported in the present study does not itself imply non-monopole or monopole radiation. Without sampling known azimuthal and elevation angles relative to the source and ideally at multiple known distances from the source, it cannot be determined with certainty from these data whether fish signals recorded radiated approximately as monopoles, as typically assumed for stationary fishes, or dipoles, typically assumed for swimming fishes, or multipoles (Kalmijn, 1988). Further, in the present dataset, there is uncertainty over to what extent directionality observed is representative of the fish acoustic source alone (direct propagation path) vs the source plus the propagation environment (e.g., reflections off the nearby seabed). Models and measurements of yellow croaker (*Larimichthys crocea*), oyster toadfish (*Opsanus tau*), sea catfish (*Arius felis*), and mulloway (*Argyrosomus japonicus*) demonstrate directional radiation patterns of fish signals, which are dependent on swim bladder shape and frequency (Barimo and Fine, 1998; Parsons et al., 2012; Su et al., 2023; Tavolga, 1977). These studies revealed that fish vocalizations from swim bladders have strongest radiation (highest pressure and particle motion) directly behind and/or in front of the fish. Notably, this discussion of radiation pattern is most relevant to the near field, where much of fish communication occurs, whereas farther from the source, radiation patterns are expected to become more omnidirectional (Amorim, 2006).

## V. CONCLUSIONS

This study provided a first look at polarization of *in situ* fish vocalizations in relation to that of ship and ambient
noise, contributing to understanding of directional particle motion properties of relevance to fish bioacoustics studies and fishes' directional hearing, as well as members of the ocean acoustics community interested in modeling particle motion. The presented analysis framework may be adopted for in situ and laboratory-based studies on fishes, as well as particle motion-sensitive invertebrates, where these metrics help us understand polarization shapes ($\chi$) and directions ($\theta$) of particle motion signals, and how stable (vs fluctuating over time) the polarization properties are ($\phi$). Such metrics are recommended for use in multiple types of studies to describe particle motion signals in greater detail beyond just their magnitudes, such as experiments on fish hearing and sound localization that manipulate the direction (and potentially other polarization properties) of signals and noise; studies tracking how fishes' behavioral or physiological responses to sound and masking effects may depend on polarization properties; or as in the present study, observations on polarization properties of signals vs noise that fishes may experience within natural soundscapes. This case study focused on only one type of fish signal and one measurement location, and it will be interesting to see how polarization properties for other fish signals from known species compare, as well as those of ambient and ship noise across the water column in different regions. As well, polarization properties will be affected by the acoustic propagation environment; for instance, shallow water fish signals (e.g., in estuaries and rivers) and signals from fish that vocalize while resting on the substrate (e.g., toadfish) will likely have specific polarization properties because of interference and scattering from seafloor and sea surface boundaries as compared to the same fish sources in a free-field environment. Polarization metrics could open doors for addressing questions on fishes' directional hearing and use of sound, in validating the polarization of experimental or observed signals and investigating whether polarization properties have consequence on fishes' abilities to detect, discriminate, and respond to natural and anthropogenic particle motion cues.

## SUPPLEMENTARY MATERIAL

See the supplementary material for a table detailing the Wilcoxon rank sum statistical results corresponding to Fig. 5.

## ACKNOWLEDGMENTS

We thank the crews of the RV Endeavor and RV Neil Armstrong and the many students, scientists, and collaborators responsible for data collection during the ADEON project cruises and subsequent data archiving. We thank S. Bruce Martin and JASCO Applied Sciences for providing detector products of ship noise used in the present study to identify CPAs. We also thank Jennifer L. Miksis-Olds for ADEON data access and Theresa Ridgeway and UNH Research Computing Center staff for assistance with data management and processing. We thank two anonymous reviewers whose constructive feedback helped improve our

manuscript. Funding to I.T.J. was provided by the Office of Naval Research (ONR), Code 32, under Grant No. N00014-23-1-2749. Funding was also provided to J.B. by the ONR. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the ONR. J.F. acknowledges the support of the French National Research Agency (ANR) through Grant No. ANR-21-CE48-0013. The ADEON project was funded by the U.S. Department of the Interior, Bureau of Ocean Energy Management, Environmental Studies Program, Washington, DC, under Contract No. M16PC00003. Funding for ADEON ship time was provided by the ONR, Code 32.

## AUTHOR DECLARATIONS

### Conflict of Interest

The authors have no conflicts to disclose.

## DATA AVAILABILITY

The data that support the findings of this study are openly available at https://adeon.unh.edu/data_portal (Miksis-Olds, 2023) and on NCEI databases at https://www.ncei.noaa.gov/maps/passive-acoustic-data. The derived data are available from the corresponding author upon reasonable request.

## APPENDIX: METHODS FOR STEERING FISH SIGNALS AND SHIP NOISE TO SOURCE-RECIEVER AXES

Following Thode et al. (2019), to steer to the azimuth of the source-receiver axis, an acoustic intensity method was used, which required conversion to particle velocity. First, particle velocity was calculated from particle acceleration in the frequency domain using

$$v(f) = \frac{a(f)}{2\pi i f}, \qquad (A1)$$

where $a(f)$ is the Fourier-transformed particle acceleration, $f$ is frequency, $i$ is the imaginary number $\sqrt{-1}$, and $v(f)$ is the Fourier-transformed particle velocity. Particle velocity was then inverse-Fourier-transformed to a time series and additionally bandpass filtered 200–750 Hz for the calculation of azimuth, as this range covered peak frequencies of fish signals and ship noise while avoiding contamination from lower frequency noise. Then, short-time Fourier transforms of sound pressure $P(f, t)$ and $x$ and $y$ particle velocity data $V(f, t)$ were calculated with a FFT size of 800 (100 ms windows, 10 Hz bins) with 90% overlap (leading to 10 ms time bins). Active intensity $I$ was calculated from $P(f, t)$ and $V(f, t)$

$$I_k(f, t) = \Re[P(f, t)V_k^*(f, t)], \qquad (A2)$$

where $k$ is an index for the $x$ or $y$ axis, the asterisk indicates a complex conjugate, and $\Re$ extracts the real part. The azimuth (in degrees) was calculated by
$$azimuth = \arctan2\left(\frac{I_x(f, t)}{I_y(f, t)}\right), \qquad (A3)$$

where arctan2 is defined, by convention, from -180 deg to +180 deg. Azimuth can be simply obtained by adding a 360° value to negative arctan2 values. Consistent azimuth was found across frequencies (200–750 Hz) of fish signals and ship noise for given time windows, therefore, broadband azimuth was subsequently calculated by first bandpassing the pressure and velocity data to 200–750 Hz, then Hilbert-transforming the pressure and velocity data (to get the analytic signal), and plugging these analytic pressure and velocity time series in place of their frequency-domain counterparts in Eq. (A2). For examples in Fig. 3 only, ship noise and ambient noise azimuth was calculated in 5 s bins; otherwise, for data presented in Figs. 4–6, ship and ambient azimuth was calculated for 100 ms samples (at CPA for ship) matching the 100 ms window for fish signal analysis. For 100 ms samples of ambient noise (sampled within ±5 s of each fish signal), the azimuth found for each fish signal was applied to its respective nearby ambient window. This allowed comparison of polarization metrics along the same horizontal source-receiver axis for paired fish signal and ambient noise windows. Finally, 25–750 Hz bandpass-filtered pressure and particle motion data were steered to azimuth to get horizontal source-receiver acceleration $a_r$ following Dahl and Dall'Osto (2020),

$$a_r = a_x \cos(\text{azimuth} - 90^\circ) + a_y \cos(\text{azimuth} - 0^\circ), \quad (A4)$$

where -90° and 0° refer to bearings of X and Y array axes. Although true azimuthal bearings could be estimated, it was not necessary to correct the array to these bearings for the present study.

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