^{1}, Andone C. Lavery

^{1}and Timothy K. Stanton

^{1}

### Abstract

A controlled laboratory experiment of broadband acoustic backscattering from live squid (*Loligo pealeii*) was conducted using linear chirp signals (60–103 kHz) with data collected over the full 360° of orientation in the lateral plane, in <1° increments. The acoustic measurements were compared with an analytical prolate spheroid model and a three-dimensional numerical model with randomized squid shape, both based on the distorted-wave Born approximation formulation. The data were consistent with the hypothesized fluid-like scattering properties of squid. The contributions from the front and back interfaces of the squid were found to dominate the scattering at normal incidence, while the arms had a significant effect at other angles. The three-dimensional numerical model predictions out-performed the prolate spheroid model over a wide range of orientations. The predictions were found to be sensitive to the shape parameters, including the arms and the fins. Accurate predictions require setting these shape parameters to best describe the most probable squid shape for different applications. The understanding developed here serves as a basis for the accurate interpretation of *in situ*acoustic scatteringmeasurements of squid.

The authors would like to thank Benjamin Jones in the Naval Postgraduate School for providing the computer program for the three-dimensional DWBA numerical model and comments on the manuscript. We thank Dr. Roger Hanlon at the Marine Biological Laboratory (MBL) for providing information on the life history and behavior of squid, Dr. Aran Mooney at the Woods Hole Oceanographic Institution (WHOI) and Justine Allen at MBL for their assistance and suggestions on the sedation and handling of squid, and Dr. Michael Jech at the Northeast Fisheries Science Center for suggestions on the experimental setup. We also thank Ed Enos at MBL for providing live squid and Keenan Ball at WHOI for providing the linear power amplifier. Funding for this research was provided by the Taiwan Merit Scholarship (NSC-095-SAF-I-564-021-TMS) and the Academic Program Office at WHOI.

I. INTRODUCTION

II. EXPERIMENTAL METHODS

A. Squid used in the experiment

B. Tank and instrument setup

C. Experimental procedure

D. Acoustic signal analysis and calibration

E. Subtraction of background reverberation

III. THEORY AND MODELING

A. Basic definitions

B. Distorted-wave Born approximation formulation: Application to squid

1. Analytical DWBA prolate spheroid model

2. Three-dimensional DWBA numerical model

3. Modeling parameters

C. Model predictions

1. Comparison of model predictions for the analytical DWBA prolate spheroid model and the three-dimensional DWBA numerical model

2. Contribution of individual body parts

3. Randomized squid shape

IV. DATA-MODEL COMPARISON

A. Time domain CPO characteristics

1. CPO at normal incidence

2. Angular dependence of the CPO

B. Angular variation of TS at fixed frequencies

C. Model predictions of TS averaged over angle-of-orientation distribution

V. DISCUSSION

A. Model performance

B. Squid tissue material properties

C. Scattering contribution from other potential sources

D. Squid size estimation

E. Squid shape

F. Modeling squid aggregations

VI. SUMMARY AND CONCLUSIONS

### Key Topics

- Numerical modeling
- 83.0
- Acoustic scattering
- 34.0
- Mantle
- 28.0
- Materials properties
- 18.0
- Acoustic modeling
- 17.0

##### G01H

## Figures

(a) The pulse-echo system and experimental setup. The shaded box represents the NI system containing the central labview control program. (b) Tethering system used in the experiment and the definition of angle of orientation relative to incident acoustic signal. Solid lines represent monofilament lines outside of the squid body. Dashed lines represent monofilament lines running through the mantle cavity.

(a) The pulse-echo system and experimental setup. The shaded box represents the NI system containing the central labview control program. (b) Tethering system used in the experiment and the definition of angle of orientation relative to incident acoustic signal. Solid lines represent monofilament lines outside of the squid body. Dashed lines represent monofilament lines running through the mantle cavity.

(a) Transmit signal measured at the output of the power amplifier. (b) Received calibration signal. (c) Spectrum of the received calibration signal. (d) Envelope of the autocorrelation function of the received calibration signal, normalized to the maximum value at 0 *μ*s.

(a) Transmit signal measured at the output of the power amplifier. (b) Received calibration signal. (c) Spectrum of the received calibration signal. (d) Envelope of the autocorrelation function of the received calibration signal, normalized to the maximum value at 0 *μ*s.

TS prediction versus angle of orientation at four frequencies (60, 70, 85, and 100 kHz) for the three-dimensional DWBA numerical model using arms-folded squid shapes with and without the fins, and the analytical DWBA prolate spheroid model. The arrow indicates the scattering contribution from the fins.

TS prediction versus angle of orientation at four frequencies (60, 70, 85, and 100 kHz) for the three-dimensional DWBA numerical model using arms-folded squid shapes with and without the fins, and the analytical DWBA prolate spheroid model. The arrow indicates the scattering contribution from the fins.

TS predictions versus frequency for the three-dimensional DWBA numerical model using arms-folded squid shape and the analytical DWBA prolate spheroid model at four angles of orientation (0°, 45°, 90°, 135° from normal incidence). The usable band (gray area) in the experiment lies entirely in the geometric scattering region.

TS predictions versus frequency for the three-dimensional DWBA numerical model using arms-folded squid shape and the analytical DWBA prolate spheroid model at four angles of orientation (0°, 45°, 90°, 135° from normal incidence). The usable band (gray area) in the experiment lies entirely in the geometric scattering region.

Compressed pulse output envelope of the three-dimensional DWBA numerical model using two fixed squid shapes through two full rotations (720°): (a) arms-folded configuration and (b) arms-splayed configuration. The CPO envelopes are normalized to the maximum envelope value in each of the plots. The strong sinusoidal pattern in both plots corresponds to the location of the squid arms during the rotation.

Compressed pulse output envelope of the three-dimensional DWBA numerical model using two fixed squid shapes through two full rotations (720°): (a) arms-folded configuration and (b) arms-splayed configuration. The CPO envelopes are normalized to the maximum envelope value in each of the plots. The strong sinusoidal pattern in both plots corresponds to the location of the squid arms during the rotation.

Temporal characteristics of the scattering at normal incidence. (a) Model predictions given by the three-dimensional DWBA numerical model with arms-folded and arms-splayed squid shapes and the analytical DWBA prolate spheroid model. (b) Experimental data from 15 individual pings overlaid at normal incidence. All CPO envelopes (model prediction and data) were normalized to the maximum value in each model prediction or each ping.

Temporal characteristics of the scattering at normal incidence. (a) Model predictions given by the three-dimensional DWBA numerical model with arms-folded and arms-splayed squid shapes and the analytical DWBA prolate spheroid model. (b) Experimental data from 15 individual pings overlaid at normal incidence. All CPO envelopes (model prediction and data) were normalized to the maximum value in each model prediction or each ping.

Compressed pulse output envelope of (a) the experimental data and (b) the three-dimensional DWBA numerical model using a hybrid squid shape with randomized arms over two full rotations (720°). The CPO envelopes are normalized to the maximum envelope value in each of the plots. Faint vertical lines in the experimental data are due to noise not effectively eliminated by the background reverberation subtraction.

Compressed pulse output envelope of (a) the experimental data and (b) the three-dimensional DWBA numerical model using a hybrid squid shape with randomized arms over two full rotations (720°). The CPO envelopes are normalized to the maximum envelope value in each of the plots. Faint vertical lines in the experimental data are due to noise not effectively eliminated by the background reverberation subtraction.

Data-model comparison of TS versus angle of orientation at four frequencies (60, 70, 85, and 100 kHz). Hybrid randomized squid shapes with three fin shapes were used in the three-dimensional DWBA numerical model: (A) original asymmetric fins, (B) artificial symmetric fins, (C) no fins. The experimental data are represented by dots. The gray area indicates the range of ±1 standard deviation from the mean of the model predictions. The arrow indicates the scattering contribution of the fins. The cut-off pattern near the bottom of each plot is resulted from omitting experimental data and model predictions lower than the noise threshold.

Data-model comparison of TS versus angle of orientation at four frequencies (60, 70, 85, and 100 kHz). Hybrid randomized squid shapes with three fin shapes were used in the three-dimensional DWBA numerical model: (A) original asymmetric fins, (B) artificial symmetric fins, (C) no fins. The experimental data are represented by dots. The gray area indicates the range of ±1 standard deviation from the mean of the model predictions. The arrow indicates the scattering contribution of the fins. The cut-off pattern near the bottom of each plot is resulted from omitting experimental data and model predictions lower than the noise threshold.

Averaged TS versus frequency for the experimental data, the analytical DWBA prolate spheroid model, and the three-dimensional DWBA numerical model using both fixed and hybrid randomized squid shapes in two planes (data only available in the lateral plane). All averages were done in the linear domain over ±2 standard deviations (*σ*) from the mean angle (*μ*) and converted to TS. (a) Averages in the dorsal-ventral plane. (b) Averages in the lateral plane.

Averaged TS versus frequency for the experimental data, the analytical DWBA prolate spheroid model, and the three-dimensional DWBA numerical model using both fixed and hybrid randomized squid shapes in two planes (data only available in the lateral plane). All averages were done in the linear domain over ±2 standard deviations (*σ*) from the mean angle (*μ*) and converted to TS. (a) Averages in the dorsal-ventral plane. (b) Averages in the lateral plane.

Noise addition procedure for model predictions. (a) The frequency dependent background noise profile (including reverberation) across the usable band of the experiment. (b) TS predictions with noise added (top row) and without noise added (bottom row) based on the three-dimensional DWBA numerical model. The solid line is the mean of the measured or added noise. The gray or white area between the two dashed lines indicates the range between ±1 standard deviation from the mean. The brackets indicate regions where the effect of noise addition is more prominent. Model predictions below the noise threshold were omitted.

Noise addition procedure for model predictions. (a) The frequency dependent background noise profile (including reverberation) across the usable band of the experiment. (b) TS predictions with noise added (top row) and without noise added (bottom row) based on the three-dimensional DWBA numerical model. The solid line is the mean of the measured or added noise. The gray or white area between the two dashed lines indicates the range between ±1 standard deviation from the mean. The brackets indicate regions where the effect of noise addition is more prominent. Model predictions below the noise threshold were omitted.

Comparison of the performance of the three-dimensional DWBA numerical model and the analytical DWBA prolate spheroid model at two frequencies. Frequency-dependent noise was added to both models to enable valid comparison with the data. Dots represent the ping-by-ping experimental data. The gray area indicates the range of ±1 standard deviation from the mean of the models. Note that the experimental data and model predictions lower than the background noise threshold (black lines) were not omitted to illustrate the difference clearly.

Comparison of the performance of the three-dimensional DWBA numerical model and the analytical DWBA prolate spheroid model at two frequencies. Frequency-dependent noise was added to both models to enable valid comparison with the data. Dots represent the ping-by-ping experimental data. The gray area indicates the range of ±1 standard deviation from the mean of the models. Note that the experimental data and model predictions lower than the background noise threshold (black lines) were not omitted to illustrate the difference clearly.

## Tables

Dimensions and ranges of angle of orientation for the squid used in the acoustic backscattering measurements. All dimensional measurements were conducted when the animal was dead after the acoustic experiment was completed. The total length is the length from the tip of the mantle to the tip of the arms when the squid is placed flat on a surface. The mantle width is the width of the widest portion of the mantle on the dorsal side. The mantle length is the length between the two ends of the mantle on the dorsal side. Two numbers in the measured angle of orientation indicate that acoustic measurements were conducted twice on the same individual. The calculated weight was calculated using the published length-weight relationship for *L. pealeii* (Lange and Johnson, 1981).

Dimensions and ranges of angle of orientation for the squid used in the acoustic backscattering measurements. All dimensional measurements were conducted when the animal was dead after the acoustic experiment was completed. The total length is the length from the tip of the mantle to the tip of the arms when the squid is placed flat on a surface. The mantle width is the width of the widest portion of the mantle on the dorsal side. The mantle length is the length between the two ends of the mantle on the dorsal side. Two numbers in the measured angle of orientation indicate that acoustic measurements were conducted twice on the same individual. The calculated weight was calculated using the published length-weight relationship for *L. pealeii* (Lange and Johnson, 1981).

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