Broadband Characteristics of Target Strength of Pacific Chub Mackerel

Abstract

Broadband backscattering measurements of Pacific mackerel (Scomber japonicus) can improve acoustic surveys of the species for the management of its fisheries throughout the Pacific Ocean. The determination of its target strength (TS), the logarithmic form of the backscattering cross-section, is the aim of this work. It was measured for fourteen individual specimens, eight in a freshwater tank and six in a seawater tank, using calibrated broadband echosounders spanning the frequency band 24–84 kHz. The TS is expressed as a function of frequency and tilt angle, with fish length as a parameter. The individual broadband TS patterns with the tilt angle of fish showed size and frequency dependencies. The fish length-normalized TS of mackerel decreased with increasing fish length-to-acoustic wavelength ratio (l/λ) in the small l/λ range (approximately 2–6) but was flat in the larger l/λ range (>6). This variation in the normalized TS indicates that a pair of regression equations is necessary to span the range of commercially important mackerel relative to the acoustic wavelength. The relative l/λ characteristic of the normalized TS showed constant values with tilt-angle distributions over a large l/λ range and can be used as a characteristic of acoustic backscattering for discrimination among species.

1. Introduction

In acoustic surveys for fisheries resource management, the acoustic backscattering characteristics of target species are key to correctly estimating abundance. Broadband echosounders using a frequency-modulated (FM) chirp signal provide a continuous frequency response of acoustic backscattering from a target that represents the characteristics of organisms, attributed to their morphological and size differences [1,2].

The genus Scomber is a group of small pelagic fish that are distributed globally [3]. The species of this group are an important fishery resource in several regions. The combined acoustic–trawl method, which obtains acoustic backscattering data with echosounders and biological data from trawl catches, is commonly used to estimate fish biomass [4], and has also been used for stock assessments of Scomber spp. [5,6,7]. To estimate fish abundance using this method, the target strength in dB re. 1 m² (TS), which is the acoustic backscattering intensity from a single target, is essential for converting the volume backscattering coefficient into absolute fish densities [4]. The TS for estimating fish densities is usually derived from functions of fish length in cm, which is estimated from biological data as follows [8]:

TS = alog₁₀l + b,

(1)

where a and b are the slope and intercept, respectively. TS is often assumed to be proportional to the square of l (i.e., a = 20) and is represented by the following:

TS = 20log₁₀l + b₂₀.

(2)

Generally, the results of previous studies that investigated TS with respect to fish length were used to determine the coefficients of the function. However, the values of the coefficients used in some Scomber species are considered insufficient, owing to the lack of data on the TS of the group. A value of b₂₀ = −68.7 at 38 kHz was used for surveys of the Atlantic chub mackerel, S. colias [7], and values of a = −15.44 and b = 7.75 (for estimating dB kg⁻¹) at 38 kHz were used for the Pacific chub mackerel, S. japonicus [6,9]. These values were estimated from another species of jack mackerel, Trachurus murphyi [10], and the Cape horse mackerel, T. capensis [11], respectively. Although the TSs of the genera Scomber and Trachurus are considered similar [12], the fish density estimated by the acoustic method greatly depends on TS and should be estimated based on the species concerned.

Pacific chub mackerel (hereafter referred to as mackerel) also play an important role as a fisheries resource worldwide. However, there is no appropriate reference for the TS of mackerel to estimate their densities using acoustic methods [6]. Although recent studies have estimated the TS of mackerel using an acoustic backscattering model [13,14,15] and tank experiment with free swimming fish [16], the b₂₀ values estimated in these studies had a difference of 6–8 dB at various frequencies; the reason for this discrepancy is uncertain. As TS changes in a complicated manner, depending on multiple morphological and physiological factors, more studies are needed to accurately estimate the TS of mackerel. Specifically, the dependence of the TS on frequency is scarcely researched by measurements in situ or ex situ. Traditional single frequency echosounders provide discrete frequency data that are limited in information to understand the frequency dependence. The investigation of the relationships between the frequency response and other factors affecting the TS collected by broadband measurement may help to better understand the acoustic backscattering characteristics of mackerel. The idea of representing TS-normalized fish length as a function of the fish length-to-wavelength ratio (l/λ) was used to represent the size and frequency dependence of TS in two-dimensional graphs [17,18,19]. This representation has been used historically to summarize TS data obtained by discrete frequencies, fish length, and species [20,21,22]. The broadband acoustic measurement provides a specific relationship between TS and a wide l/λ range and may have an advantage in obtaining the general characteristics of acoustic backscattering for species. Yan et al. [23] used this idea to obtain the different TS characteristics among three fish species without swim bladders. In addition, the fish orientation, with respect to the incident angle of the acoustic signal, is also a critical factor affecting TS. The tilt-angle distribution of fish must be considered to determine the TS because the signal emitted from the echosounder hits the dorsal side of fish. The data on tilt-angle distribution in natural conditions are very scarcely measured but the standard deviation of it is close to 15° in general [21].

The frequency response of acoustic backscattering is also expected to enhance the acoustic discrimination among species [24,25]. As mackerel is widely distributed, not only horizontally but also vertically [26], overlaps between its distribution and that of other pelagic species can frequently occur. Therefore, the findings on the broadband backscattering of mackerel will also be useful for acoustic discrimination. The relative l/λ TSs represent the acoustic backscattering characteristics [27]. This idea is based on the relative frequency response, which is defined as the ratio of the target strength at a frequency to a reference frequency [28]. The relative frequency response of discrete multi-frequency can represent differences in backscattering characteristics among species groups, but it is difficult to discriminate among species that have similar frequency responses, such as swim bladder fish species [29,30]. The potential for discrimination among swim bladder fish species using the broadband frequency response remains a challenge in this field. The relative l/λ characteristic can represent the frequency and fish length dependence of acoustic backscattering, and it may improve the quality of acoustic discrimination [27].

The objective of this study was to derive the dependence of the TS of mackerel on the parameters of frequency, fish length, and tilt angle of fish. The measurements were conducted in experimental tanks to measure the dorsal-aspect TS patterns of mackerel related to the tilt angle by broadband frequency, and the results were compared with the modeled values. Additionally, we suggest the use of l/λ characteristics for estimating the TS of mackerel and for acoustic discrimination among species.

2. Materials and Methods

2.1. Fish Samples for Measurements

The mackerel used for the TS measurements were caught by angling in the coastal area around Hakodate, Japan, from July to October 2021. The fish samples were kept in two cylindrical tanks (a 2.6 m diameter × 0.9 m high tank, and a 1.8 m diameter × 0.6 m high tank) until measurement. The water temperature and the salinity of the two tanks were maintained at approximately 20 °C and 33 psu, respectively. Frozen krill was supplied to the fish as food once every two days. A total of 14 individuals, which were 14.8–23.4 cm in fork length (FL), were used for the measurements (

Table 1. Morphological information of Pacific chub mackerel used in this study, range of l/λ, and measurement location and date.

No.	Fork Length (cm)	Swim Bladder Length (cm)	Swim Bladder Angle (°)	l/λ	Location	Date
1	15.5	4.3	11	2.5–7.2	HU	30 August 2021
2	21.2	6.1	9	3.4–9.8		30 August 2021
3	19.4	5.5	6	3.1–9.0		1 September 2021
4	14.8	4.0	8	2.4–6.8		1 September 2021
5	16.2	4.4	8	2.6–7.5		2 September 2021
6	23.0	7.1	6	3.7–10.6		2 September 2021
7	23.4	6.5	9	3.8–10.8		3 September 2021
8	15.6	4.2	11	2.5–7.2		3 September 2021
9	22.9	6.7	10	7.0–12.6	HRCFO	4 August 2021
10	23.4	5.2	9	7.2–12.8		5 August 2021
11	14.9	3.8	8	4.6–8.3		23 October 2021
12	22.7	5.0	9	7.1–12.6		23 October 2021
13	18.2	4.4	7	5.7–10.1		24 October 2021
14	15.9	3.8	13	4.9–8.8		24 October 2021

). In this paper, fork length was used as the length of the mackerel and “l” was assigned as the variable.

2.2. Design of Measurements in Experimental Tanks

The TS measurements of each mackerel were conducted in two experimental tanks: a 5 m × 5 m × 5 m freshwater tank, located at Hokkaido University (HU), and a 5 m × 10 m × 6 m saltwater tank at the Hakodate Research Center for Fisheries and Oceans (HRCFO). Eight individuals were measured at the former from 30 August to 3 September in 2021, and the others were measured at the latter from 4 to 5 August and 23 to 24 October in 2021 (Table 1).

For the measurements at HU, a bistatic custom-made broadband system based on that described by Amakasu et al. [31] was used. Two single-beam transducers were deployed at a depth of 2.5 m near the wall of the tank so that the acoustic signals were transmitted horizontally (Figure 1). The beam width of the transducers is 40° at 30 kHz and 17° at 70 kHz. Linear FM chirp pulses sweeping 20–70 kHz for 2 ms were generated with a function generator (WF1946, NF, Kanagawa, Japan), amplified by a power amplifier (PRO-50, Accuphase, Kanagawa, Japan), and applied to the transducer for transmission. Echoes from a target were detected by the receiving transducer, amplified by a differential preamplifier (LI-75A, NF, Kanagawa, Japan), and the received signal was recorded by an oscilloscope (WaveJet312A, Teledyne LeCroy, New York, NY, USA). The sampling rate of the recording was set to 20 MHz.

For the measurements at HRCFO, a Simrad EK80 echosounder system (Kongsberg Maritime, Kongsberg, Norway) consisting of a wideband transceiver (WBT) and a split-beam transducer (ES70-7C) was used. The transducer was placed in a box-shaped frame and deployed at a depth of 3 m (Figure 1). FM chirp pulses of 45–90 kHz, a 2.048 ms long duration, and a fast-ramping mode [32] were transmitted from the transducer horizontally, and echoes from the target were recorded using Simrad EK80 software (ver. 2.0.1).

Each mackerel was suspended in an experimental tank after being anesthetized with eugenol (FA100, Sumitomo Pharma Animal Health, Osaka, Japan). Four monofilament nylon fishing lines (0.15 mm in diameter) were used to suspend each mackerel in the water, by connecting a suspension system consisting of two flames connected by four multifilament polyethylene fishing lines (0.70 mm in diameter), so that the dorsal side of the fish could face the transducers. The fish were suspended at a distance of 2.8 m (tank in HU) and 5.0 m (tank in HRCFO) from the transducer. The suspended position was out of the near field of the transducer; it was at a distance from which the fish body can be assumed as a point target, and fish was within the first Fresnel zone [33]. All activities, from the anesthetic to the suspension procedure, were carefully conducted with the fish in water to prevent air bubbles from attaching to their bodies. The incident angle of the acoustic pulse was adjusted manually by rotating the suspension system. The echo from each mackerel was measured in the angle range of −40° to +40° in increments of 1° (the plus degree indicates the fish’s head was pointed up towards the transducer). For each angle, a waveform averaging eight pings was recorded in the measurement at HU, and more than ten ping echoes were recorded in the measurements at HRCFO.

2.3. Calibration of Echosounder Systems

Each system was calibrated using standard spheres made of tungsten carbide with 6% cobalt binder. Each sphere was suspended in a net bag made from monofilament nylon line (0.4 mm in diameter), according to Foote et al. [34]. The available frequency range of each system was evaluated by calibration.

A 38.1 mm diameter sphere was used for the calibration of the custom-made system. As the single-beam system could not measure the direction of the target, the position where the received echo level of the sphere was at its maximum at a frequency of 70 kHz was assumed to be on the beam axis of the transmitter and receiver transducers. After the echoes of the sphere were collected, echoes of another 22.2 mm diameter sphere were recorded at the same position as the 38.1 mm diameter sphere to confirm the calibration results using the following method. Each mackerel was suspended in the same position as the spheres by observing their position using a digital camera (TG-4, Olympus, Tokyo, Japan) deployed in the tank.

The EK80 system was calibrated using its calibration mode and a 25.0 mm diameter sphere. The echo data of the sphere were recorded until the center coverage, and the overall coverage was more than 80%, as displayed in the calibration mode. After recording, the outliers were removed manually using the software, and the parameters were updated.

2.4. Processing of Acoustic Data

The acoustic data from the custom-made system were recorded as time-series voltage waveforms received by the system. The Fourier transformation of the voltage V_r(f) is defined by the following equation [31]:

V_r(f) = V_t(f)S_t(f)S_r(f)G(f)D(f)L(f)F_bs(f),

(3)

where f is the frequency (Hz), S_t(f) and S_r(f) are the system responses of the transmitter and receiver transducers, respectively, D(f) is the directivity of the combination of the transmitter and receiver transducers, G(f) is the system gain, L(f) is the two-way acoustic attenuation, and F_bs is the backscattering amplitude of the target. The response of the entire system is defined as follows:

$$K(f)={\displaystyle \frac{V_{\mathrm{r}}(f)}{L(f)F_{\mathrm{bs}}(f)}},$$

(4)

A matched filter for processing the cross-correlation was applied to the recorded signals to increase the signal-to-noise ratio [35,36]. The compressed pulse cp(t) is given by the cross-correlation between the received voltage v_r(t) and replica v_rep(t), which was defined as the signal applied to the transmitter transducer in this study, as follows [2,37]:

$$cp(t)=R_{\mathrm{rep}}^{-1}(0)v_{\mathrm{t}}(t)\otimes v_{\mathrm{rep}}(t),$$

(5)

$$R_{\mathrm{rep}}(t)=v_{\mathrm{rep}}(t)\otimes v_{\mathrm{rep}}(t),$$

(6)

where the term ⊗ denotes the correlation and R_rep(t) represents the output of the autocorrelation between the replicas, which reaches a maximum value when the time lag of the two signals is zero (t = 0). The system response associated with the compressed pulse K_cp(f) is given by

$$K_{\mathrm{cp}}(f)={\displaystyle \frac{C{P}^{*}(f)}{L(f)F_{\mathrm{bs}}(f)}},$$

(7)

where CP(f) is the Fourier transformation of the compressed pulse and the superscript * denotes the complex conjugate. Then, the backscattering amplitude of the target and target strength is given by

$$F_{\mathrm{bs}}(f)={\displaystyle \frac{C{P}_{\mathrm{tar}}^{*}(f)}{K_{\mathrm{cp}}(f)L(f)}},$$

(8)

$$TS(f)=10\log \left|F_{\mathrm{bs}}(f)\right|,$$

(9)

K_cp(f) was derived from the calibration with a 38.1 mm standard sphere and the result was evaluated by comparing the measured and predicted F_bs(f) of a 22.2 mm standard sphere. In this study, the compressed pulse was not tapered for Fourier transformation to ensure that the available bandwidth was as wide as possible [25]. A 250 μs long rectangular window was applied to calculate the spectrum of the compressed pulse (Figure 2).

The acoustic data recorded by the EK80 were processed using Echoview ver. 10.0.271 (Echoview Software, Hobert, TAS, Australia). The TS spectrum of the target was calculated using a single target detection (wideband) algorithm. The configuration of the algorithm parameters is listed in

Table 2. Parameters used in the single target detection algorithm of Echoview.

Parameter	Value
Compensated TS threshold (dB)	−90
Maximum beam compensation (dB)	6.0
Pulse length determination level (dB)	6.0
Minimum normalized pulse length	0.5
Maximum normalized pulse length	1.5
Window size (m)	0.4

. For each incident angle, the spectrum of the TS calculated for all the pings was averaged on a linear scale.

2.5. Target Strength Estimated by Acoustic Backscattering Model

The Kirchhoff Ray Mode (KRM) backscattering model [38,39] was used to estimate the TS of the mackerel. The model assumes that the fish body is a series of fluid-like cylinders, and that the swim bladder is a series of gas-filled cylinders. The backscattering amplitude from the whole body of the fish is calculated by summing the backscattering amplitudes from the fish body and the swim bladder coherently (see Clay and Horne [38] for a detailed derivation). The coordinates of the fish body and swim bladder were traced from X-ray photographs taken after the measurements using a radiographic instrument (SOFTEX CMB-2, SOFTEX Co., Ltd., Tokyo, Japan) (Figure 3). The photographs were scanned, and the shapes of the body and swim bladder were traced. The body of the fish was traced, except for the fins and tail. The traced images were rotated, so that the anteroposterior axis of the fish body was horizontal (i.e., on the x-axis), and digitized in increments of 1 mm along the x-axis. The acoustic parameters of the fish body, swim bladder, and water are listed in

Table 3. Parameters used in KRM model.

Parameter	No. 1–8	No. 9–10	No. 11–14
Sound speed in water (m s−1)	1492	1530	1513
Sound speed in fish body (m s−1)	1570	1570	1570
Sound speed in swim bladder (m s−1)	345	345	345
Density of water (kg m−3)	1000	1025	1025
Density of fish body (kg m−3)	1070	1070	1070
Density of swim bladder (kg m−3)	1.24	1.24	1.24

. The fish body and swim bladder parameters were obtained from Clay and Horne [38]. The sound speeds of water were calculated by Medwin [40] for freshwater and Mackenzie [41] for saltwater, based on the temperature, salinity, and depth of the fish in the tank experiments. Water densities of 1000 kg m⁻³ and 1025 kg m⁻³ were used for freshwater and saltwater, respectively. The frequency range used in the model was 20–90 kHz. The TS(f) of each mackerel was predicted in a tilt-angle range of −40° to +40° in increments of 0.5°.

The length and angle of the swim bladders were also measured by X-ray photos viewed from lateral. The length between the front and end edge of the swim bladder was determined as the swim bladder length. The angle between the x-axis of the image and the line used to measure the swim bladder length was defined as the swim bladder angle.

2.6. Target Strength Representation

The TS pattern related to the tilt angle θ was averaged following the approach of Foote [42] for each frequency, assuming that the probability distribution of the angle was Gaussian:

$$TS{(f)}_{ave}=10\log \left\{{\displaystyle \frac{{\displaystyle {\int }_{-40}^{40}{\sigma }_{\mathrm{bs}}(f,\theta )g(\theta )d\theta }}{{\displaystyle {\int }_{-40}^{40}g(\theta )d\theta }}}\right\},$$

(10)

where σ_bs(f, θ) is the backscattering cross-section in square meters, and g(θ) is the function for the tilt-angle distribution of fish, defined by

$$g(\theta )={\displaystyle \frac{1}{\sqrt{2\pi s^2}}}\exp \left\{-{\displaystyle \frac{{\left(\theta -m\right)}^2}{2s^2}}\right\},$$

(11)

where m and s are the mean and standard deviation of the distribution, respectively. To evaluate the dependence of the distribution on the tilt-averaged TS, four combinations of the m and s of Gaussian, (m, s) = (−5, 10), (−5, 15), (0, 10), and (0, 15), were used to calculate TS(f)_ave. The slope and the intercepts of Equations (1) and (2) were estimated from the TS(f)_ave results for each tilt-angle distribution.

In addition to the regression using Equations (1) and (2), the TS related to l/λ was used to represent the specific characteristics of the acoustic backscattering of the mackerel. Backscattering cross-sections of the fish were normalized by fish length to compare the individual results with non-dimensional values. The regression equations for the normalized backscattering cross-section are as follows [19]:

$$10\log {\displaystyle \frac{{\sigma }_{\mathrm{bs}}(l/\lambda )}{l^2}}={\beta }_1\log {\displaystyle \frac{l}{\lambda }}+{\beta }_0,$$

(12)

$$T{S}_{\mathrm{norm}}=10\log {\displaystyle \frac{{\sigma }_{\mathrm{bs}}}{l^2}},$$

(13)

where TS_norm is the normalized TS by the square of fish length. The average TS derived from Equation (10) for each angle distribution was used to calculate the normalized TS. The acoustic wavelength was calculated from the sound speed of each water tank and the frequency in increments of 1 kHz.

The relative TS normalized by fish length for l/λ was calculated by [27]

$$r\left({\displaystyle \frac{l}{\lambda }}\right)=T{S}_{\mathrm{norm}}\left({\displaystyle \frac{l}{\lambda }}\right)-T{S}_{\mathrm{norm}}\left\{{\left({\displaystyle \frac{l}{\lambda }}\right)}_0\right\},$$

(14)

where r is the relative TS normalized by fish length and (l/λ)₀ is the reference l/λ. r(l/λ) was calculated in the case of (l/λ)₀ = 7.1, according to the range of each l/λ for the individual fishes (Table 1). However, the l/λ of two fish could not be within the range (No. 4 and No. 10), and the two were excluded from the analysis.

3. Results

3.1. Calibration Results and Frequency Bands for Analyses

The calibration of the custom-made system was performed three times, and the system response K_cp was stable (Figure 2). The predicted and measured TSs of the 22.2 mm diameter sphere were compared, and the results showed good consistency (within a 0.5 dB difference) at most frequencies (Figure 4). The difference was larger in some frequency ranges, where K_cp was relatively lower. Therefore, the frequency ranges (20–23, 52–54, 64–66, and 69–70 kHz) in which K_cp was less than 68 dB were judged as having a low signal-to-noise ratio and removed from the analyses.

The calibration results of the Simrad EK80 echosounder system with a split-beam transducer (ES70-7C) showed that the gain of the system was almost stable for each measurement in August and October, with a difference of up to 0.9 dB, except in the range of 45–47 kHz and 84–90 kHz (Figure 5). The data obtained in these frequency ranges were likely to be insufficiently accurate and were removed from the analyses.

3.2. Target Strength Pattern with Respect to Tilt Angle

The broadband TS patterns related to the tilt angle were obtained by tank measurements and modeled by KRM (Figure 6 and Figure 7). The TS patterns were more complex at higher frequencies, including sharp peaks, lobes, and dips. Size dependence was also observed, as the larger samples had a relatively larger TS and slightly sharper peaks than the smaller ones. Similar TS patterns were observed between the measured and modeled results, but the peaks of the modeled TS tended to be broader than the measured TS. The TS patterns had an offset with respect to the tilt angle and the peak of TS appeared to be less than 0°. At higher frequencies, the peak was observed at an angle of approximately −10° to −5°, which was a larger offset than that at lower frequencies. As the TS of the fish body was significantly lower than that of the swim bladder (Figure 8), the whole TS patterns were strongly affected by the swim bladder and the peak of TS generally appeared to correspond to the swim bladder angle relative to the body axis, as shown (Table 1). However, the modeled results also showed that the peak of the TS for the fish body near 0° was relatively large at some frequency ranges, which was enough to affect the entire TS pattern. In the lower-frequency band, the width of the peak was relatively variable with respect to the frequency.

3.3. Target Strength Related to Fish Length

The average TS was calculated using four tilt-angle distributions, and the regression lines related to the fork length in cm at discrete frequencies of 38 kHz, 50 kHz, and 70 kHz are listed in

Table 4. The coefficients of the regression equations calculated from the relationship between the target strength and fish length (cm) by tilt-angle distributions.

System	Frequency (kHz)	(−5, 10)			(−5, 15)			(0, 10)			(0, 15)
		a	b	b20	a	b	b20	a	b	b20	a	b	b20
Custom	38	15.0	−60.4	−66.7	14.7	−61.0	−67.7	12.9	−58.5	−67.4	13.9	−60.4	−68.1
Model		16.8	−62.8	−66.9	16.0	−62.7	−67.8	14.3	−60.0	−67.3	14.8	−61.4	−68.1
Custom	50	18.7	−66.1	−67.7	18.5	−66.7	−68.7	17.4	−65.3	−68.6	18.0	−66.6	−69.1
EK80		19.4	−66.8	−67.6	20.1	−68.6	−68.5	17.0	−64.7	−68.6	19.1	−67.8	−69.0
Custom and EK80		19.2	−66.5	−67.6	19.3	−67.7	−68.6	17.3	−65.1	−68.6	18.6	−67.3	−69.1
Model		20.3	−67.9	−67.5	19.1	−67.3	−68.5	17.9	−65.6	−68.3	18.3	−66.8	−68.9
EK80	70	25.4	−74.1	−67.1	24.5	−74.0	−68.2	24.2	−73.7	−68.3	24.0	−73.9	−68.8
Model		26.8	−75.9	−67.3	25.0	−74.8	−68.4	28.4	−79.0	−68.3	26.0	−76.6	−69.0

. The coefficient of b₂₀ agreed between the measured and modeled values within a difference of 0.3 dB. The b₂₀ was highest at the three frequencies when the tilt-angle distribution was assumed to be (−5, 10) and lowest when it was assumed to be (0, 15). The difference in b₂₀ was 1.4–1.7 dB between the two tilt-angle distributions. The data obtained at 50 kHz showed no discrepancy between the results from the two systems. The slope a of the regression line did not vary noticeably with the tilt-angle distribution at any frequency. However, the slope and intercept of the regression calculated over the frequency band showed that the coefficients varied significantly with frequency (Figure 9). The slope a and intercept b of the measured TS agreed with those of the modeled TS at frequencies higher than 40 kHz, while the values exhibited large differences at the lower frequency. The coefficients calculated from the modeled TS were more variable with the tilt-angle distribution than the measured TS. The values of b₂₀ decreased slightly with the increase in frequency.

3.4. Fish Length-to-Wavelength Ratio Characteristics

The TS normalized by fish length or acoustic wavelength were calculated using each tilt-angle distribution. The l/λ characteristics of the normalized TS were dependent on size and frequency (Figure 10 and Figure 11). The fish length-normalized TS showed an obvious change in characteristics at approximately l/λ = 6, and the single regression lines of Equation (12) did not explain the entire characteristic (the determination coefficient R² was between 0.32 and 0.42 for each tilt-angle distribution). Then, a pair of lines was derived such that the residual error was the lowest (

Table 5. Equations of TS as a function of fish length and acoustic wavelength by tilt-angle distribution.

Tilt-Angle Distribution	Equation for TS	Range of l/λ	Residual Sum of Squares
(−5, 10)	16.4 log l + 3.6 log λ − 24.1	2.4 < l/λ < 12.8	4.1
	11.1 log l + 8.9 log λ − 20.7	2.4 < l/λ ≤ 6.2	2.5
	22.8 log l − 2.8 log λ − 30.0	6.2 ≤ l/λ < 12.8
(−5, 15)	16.2 log l + 3.8 log λ − 25.0	2.4 < l/λ < 12.8	3.3
	11.0 log l + 9.0 log λ − 21.7	2.4 < l/λ ≤ 6.1	1.8
	22.0 log l − 2.0 log λ − 30.3	6.1 ≤ l/λ < 12.8
(0, 10)	14.7 log l + 5.3 log λ − 23.7	2.4 < l/λ < 12.8	6.4
	8.9 log l + 11.1 log λ − 20.0	2.4 < l/λ ≤ 6.2	4.5
	22.0 log l − 2.0 log λ − 30.5	6.2 ≤ l/λ < 12.8
(0, 15)	15.6 log l + 4.4 log λ − 25.0	2.4 < l/λ < 12.8	4.1
	10.2 log l + 9.8 log λ − 21.5	2.4 < l/λ ≤ 6.3	2.5
	21.8 log l − 1.8 log λ − 30.7	6.3 ≤ l/λ < 12.8

). The boundaries of the lines were in the range of l/λ = 6.1–6.3 for the four tilt-angle distributions. A difference in the normalized TS among the tilt-angle distributions was observed.

The relative l/λ characteristics of the four tilt-angle distributions are shown in Figure 11. The average characteristics, in dB units, were calculated by linearly interpolating the relative fish length-normalized TS of each fish in increments of 0.01 of log(l/λ). The average characteristics were different among the tilt-angle distributions by up to 1 dB at small l/λ, whereas the relative normalized TS was almost the same for each tilt-angle distribution at a large l/λ. The results showed that the TS of mackerel decreased with increasing l/λ from 3 to 6 and was flat in the range of l/λ > 6.

4. Discussion

4.1. Target Strength for Estimating Abundance of Mackerel

Several equations for TS related to fish length and the acoustic wavelength of mackerel for each tilt-angle distribution were derived from the results of the broadband TS measurements. The b₂₀ values at a frequency of 38 kHz, which are commonly used for acoustic surveys of swim bladder fish, were −66.7 to −68.1 dB, which agreed with the modeled values (Table 4). These values were included in the range of −65.8 to −73.5 dB as estimated by previous studies [13,14,15,16,43] (

Table 6. List of coefficients for TS equations related to fish length published in previous studies.

Frequency (kHz)	Method (Angle Distribution)	Slope a	Intercept b	b20	Fish Length (cm)	Reference
38	Model (−5, 15)	11.4	−54.4	−66.0	15.4–26.2	Park et al., 2022 [13]
	Model (−5, 10)	23.6	−77.9	−73.5	13.0–22.2	Tong et al., 2022 [14]
	Model (3, 4)	40.4	−92.4	−65.8	14.8–26.9	Zhu et al., 2024 [15]
	Free Swimming (−1.2, 11.5)	27.4	−77.9	−67.9	17.4–34.0	Zhu et al., 2024 [16]
	In situ			−71.0	26–30	Gutiérrez et al., 1998 [43]
50	Ex situ (−5, 15)	27.9	−79.5	−67.2	26.2–38.3	Lee and Shin, 2005 [44]
70	Model (−5, 15)	7.2	−49.2	−66.5	15.4–26.2	Park et al., 2022 [13]
	Model (−5, 10)	24.9	−79.7	−73.8	13.0–22.2	Tong et al., 2022 [14]
	Model (3, 4)	19.4	−64.5	−65.3	14.8–26.9	Zhu et al., 2024 [15]
75	Ex situ (−5, 15)	28.6	−83.2	−69.9	26.2–38.3	Lee and Shin, 2005 [44]

). Lee and Shin [44] obtained similar b₂₀ values of −67.2 dB at 50 kHz and −69.9 dB at 75 kHz that were estimated using the ex situ approach. These values were within a 2 dB difference from those found in this study, although the range of the fish lengths used in the measurements was completely different. The results of these two studies indicated that the b₂₀ of mackerel could be shared over a wide fish length range. However, Tong et al. [14] obtained the b₂₀ of −73.5 dB at 38 kHz and that of −73.8 dB at 70 kHz using the KRM model, which were 6.6–6.7 dB lower than the values determined in this study. This discrepancy was likely caused by the difference in the swim bladder condition, because the acoustic backscattering from a swim bladder usually contributes more than 90% to the TS of fish with a swim bladder [45]. Comparing the two studies in terms of the ratio of swim bladder length to fish length, our samples had a relatively larger ratio, although the range of fish lengths was similar. Therefore, the size difference in the swim bladder was the most probable cause of this discrepancy.

The b₂₀ is a simple parameter for estimating the TS. However, the slopes and intercepts of the regression lines best fitted for the relationship between TS and fish length varied with frequency (Figure 9). These results imply that the b₂₀ values are not appropriate for estimating the TS of mackerel in cases where the slope is significantly different from a = 20. In particular, the estimation error can be larger if the range of fish lengths is not close to the average length used in this study. Dorsal-aspect TS mainly varies with frequency, tilt angle, and fish size (or swim bladder size), and we need to understand the relationship between the factors to estimate TS correctly. The idea of using the equation derived from the l/λ characteristics of the normalized TS can express the dependence on both fish length and frequency and may improve the TS estimation. The characteristics of fish length-normalized TS should be incorporated into the estimations of TS. The l/λ characteristics of the fish length-normalized TS obviously changed l/λ = 6.1 to 6.3, owing to the frequency dependence (Figure 10). The pair of regression equations for the range of l/λ was proposed by Love [18] as TS = 15.8logL + 0.42logλ − 32.0 (L/λ is 0.7 to 14) and TS = 27.5logL − 0.75logλ − 45.4 (L/λ is 14 to 90), where L is the fish length in meters. Note that the regression lines were obtained by integrating the maximum TSs of several species.

In this study, the TS values were estimated using four assumptions regarding the tilt-angle distributions. The variance in the tilt-angle distribution had a slight effect on the normalized TS in the small l/λ range, whereas the difference among the distributions was larger for a large l/λ. The results indicated that the normalized TS varied at high frequencies or for large fish lengths. This was caused by the frequency and size dependence of the TS pattern with tilt angle, which was more complicated at high frequencies or large fish lengths, including sharp peaks and nulls (Figure 6 and Figure 7). Therefore, the TS in the small l/λ range was more accurate for estimating abundance. Mackerel have a wide vertical distribution and show diel vertical migration (DVM), with fish occurring in deep water during the day and moving to the surface of the water at night [26]. It should therefore be noted that the tilt-angle distribution is not stable and varies at different times of the day. In particular, the tilt-angle distribution can tend toward fish having their head down or up during vertical movements around dawn and dusk. In these times, the TS may be lower than that in the daytime or night, assuming that the average of the tilt angle can be tens of degrees. DVM also affects swim bladder volume and shape due to the rapid change in water pressure. These times should be avoided when conducting acoustic surveys for mackerel. Unfortunately, there is no reliable data available for the tilt-angle distribution of mackerel for the estimation of TS. The broadband techniques also had potential to measure the tilt angles of fish with their high range resolution [46]. The additional data in this aspect will improve TS estimations. The angle distribution of (−5, 15) was favorable for the estimation of TS because it was within the general range of the tilt-angle distribution [21].

4.2. Application in Acoustic Discrimination

Obtaining the frequency response of acoustic backscattering provided by broadband echosounders is easily available through commercial system developments. Recent studies that addressed the acoustic classification from broadband acoustic data succeeded in dividing acoustic backscattering into specific groups, including swim bladder fish [47,48,49]. The availability of the frequency response for classification is uncontestable, but there are still limited detailed data available on measured TSs connected with species validation. The tank experiment is a useful method for collecting basic acoustic backscattering related to some parameters for specific fish, although it has some problems in ensuring the quality of the data, such as unnatural fish conditions [4]. The datasets of broadband measurements in tanks can also be valuable for acoustic discrimination.

The relative l/λ of the normalized TS was derived to express the specific characteristics of the mackerel. Furusawa and Amakasu [27] estimated the l/λ characteristics using a prolate-spheroid model series [50] given some swim bladder types and suggested the probability of using the data for acoustic discrimination. Their results also included variations in the characteristics with tilt-angle distribution and indicated that the normalized TS was relatively flat above l/λ = 5 (noting the reference l/λ = 5 in their study). Our results also showed that the relative normalized TS was almost completely consistent among the four tilt-angle distributions in the large l/λ range (Figure 11) and could be a reliable parameter for acoustic discrimination even when measurements are conducted in situ. However, it should be noted that the characteristic varies depending on the reference l/λ, which was limited to the selection in this study owing to the individual range of l/λ.

For the discrimination among fish species with a swim bladder, the morphological difference in the swim bladder is likely to be a key parameter. The frequency response of the TS may extract its dependence. However, the TS pattern with tilt angle also depends on the size of the swim bladder, which is usually proportional to fish length We demonstrated that its effect is not negligible but indeed significant. The idea of using relative l/λ characteristics may improve the accuracy of the extraction of acoustic-specific characteristics by including size dependency. The relative l/λ characteristics of some fish species with a swim bladder were demonstrated, which showed that two or three species had different acoustic backscattering characteristics with relative l/λ while the relative frequency response of those almost overlapped (recalculated by Furusawa and Amakasu [27], using the data of Fassler et al. [51], and Pedersen and Korneliussen [52]). Although these results were obtained from a discrete frequency response, the relative l/λ characteristic provides an available index for acoustic discrimination. Additionally, no data are presently available to compare our results with those of other species to demonstrate the discriminatory power of this approach. Data collection for other swim bladder fish species is therefore needed to confirm the performance of the relative l/λ characteristics.

5. Conclusions

The dorsal-aspect TS of mackerel has been applied to other species’ values in acoustic surveys and the values are considered insufficient. This study obtained the TS relationship between frequency, fish size, and tilt angle using broadband acoustic techniques. The results revealed some considerable characteristics in the TS, such as the limitation of the coefficient b₂₀ due to the variation in the size dependence with frequency. The use of the l/λ characteristic may improve the application of a more precise TS for acoustic abundance estimation. TS data, with respect to a continuous and wide range of l/λ, can be easily obtained, owing to the recent widespread availability of broadband acoustic systems, and it provides useful data to discuss the detailed characteristics of TS, which is complex and variable.

The l/λ characteristic may also improve the extraction of specific characteristics that contribute to the progress in acoustic discrimination. The relative value of fish length-normalized TS with respect to l/λ derived from the measurements showed a flat response in a large l/λ range, regardless of the tilt-angle distributions for averaging the TS. As the tilt-angle distribution of fish such as mackerel may be variable in nature rather than constant, owing to their behavioral pattern, such flat characteristics should provide reliable data for acoustic discrimination.