Analysis of the Variation in Bearing Estimation Error with Frequency Bands for a Source Beneath the Arctic Ice Using a Geophone

Abstract

To obtain better frequency bands for source bearing estimation, experiments using an ice-mounted geophone were performed at three sites on the Arctic ice cap. By transforming to the frequency domain, errors of the bearing estimation in a number of frequency bands within 1000 Hz and the horizontal peak displacements received by the geophone in the corresponding frequency bands were obtained. After comparing the variation in errors to the peak displacements in the same frequency band, it was found that the errors are related to the peak displacements, and higher peak displacement values mean smaller errors. When the incident angle of the acoustic source and the ice thickness meet certain conditions, some modes of the Lamb waves of the ice plate are excited, the peak displacements in the same frequency band are increased, the errors of bearing estimation are reduced, and the effective frequency band for bearing estimation is broadened. These results provide some new ideas for the bearing estimation of acoustic sources beneath the Arctic ice.

1. Introduction

In recent years, with the warming of the climate, the range of human activities in the Arctic region has been continuously expanding [1,2,3,4]. Therefore, there is increasing research on the Arctic ice region, such as the environmental characteristics of the Arctic Ocean [3], the thickness of the ice [5,6,7,8,9,10], sound propagation under the ice [11,12,13,14], the localization of underwater sound sources [15], and so on.

Sea ice cover in Arctic regions can provide a stable platform for deploying geophones that can measure three-component (3C) particle motion. There is a long history of deploying a single geophone or multiple geophones on the ice surface for wave signal detection. Some studies have investigated the characterization of elastic waves in sea ice [16,17,18,19], including the types and speeds of wave propagation in a floating ice sheet. Some studies have reported on source bearing or location, such as that of Miller and Schmidt [20], who located the acoustic source using a set of geophones and hydrophone arrays. Becklehimer [21] used a geophone array to conduct beamforming experiments and simulated and calculated the azimuth response. Arvelo [22] believed that the range to an acoustic source can be estimated using the arrival-time differences of seismic waves at an ice-mounted geophone and proposed that mammals could be monitored and tracked using ice-mounted geophones. The location of acoustic sources beneath the Arctic ice was studied using ice-mounted geophones, and the approach of source bearing was presented by maximizing the radial signal power as a function of the horizontal look angle; for frequencies up to 250 Hz, the average absolute error of bearing estimation to the source was within 10° [15,23,24]. By combining passive seismology approaches with specific array processing methods, Moreau et al. [18,19] demonstrated that the multimodal dispersion curves of sea ice can be calculated without an active source and then used to infer sea ice properties. From the abovementioned studies, we can see that by deploying geophones mounted on ice, much acoustic information about ice and underwater acoustic sources can be obtained. However, it is also found that the studied frequency band of signals received by geophones was mostly under 200 Hz [15,17,18,19,20,23,24].

Verrall and Ganton [25] noticed that the reflectivity at a given angle was strongly influenced by the pulse for frequencies above 1 kHz. Yang et al. [26] measured sonic reflectivity below 1 kHz beneath large smooth ice floes in the Arctic Ocean and found that the reflectivity was strongly dependent on frequency as well as grazing angles. Hobæk and Sagen [27] computed the reflection coefficient as a function of the incidence angle and frequency and found that at some incidence angles and frequencies, the reflection coefficient had very low values and was related to the generation of Lamb waves in ice. From these studies, we know that Arctic ice often has different responses to acoustic waves with different frequencies up to 1 kHz. But there have been many studies on signals with frequencies only under 200 Hz using ice-mounted geophones. The effect on source bearing estimation when the signals received by geophones are in the frequency bands that are above 200 Hz is not well known. Which frequency band is better for source bearing estimation is also unknown.

In this study, we report on cross-ice detection experiments with underwater acoustic sources for bearing and an ice-mounted geophone that were performed during the 11th Chinese National Arctic Research Expedition. Section 2 introduces the experiments in detail. A 3C geophone was used for bearing estimation. Section 3 briefly describes the methods for source bearing. In Section 4, the bearing estimation results are compared with the peak displacements received by the ice-mounted geophone. The relationship between the errors of bearing estimation and the horizontal peak displacement is studied. The relationship between the Lamb waves and the horizontal peak displacement and bearing estimation error is also studied. Finally, Section 5 summarizes the results.

2. Experimental Description

Bearing estimation experiments with an underwater acoustic source were performed at three floating ice cap sites (named S1, S2 and S3) in the central Arctic Ocean. During the experiment, at each site, a 3C geophone (named G1) mounted on the ice was used to receive the cross-ice signals. G1 is a wireless vibration sensor, and the brand is iSensor. Its ID number is 701. It is self-contained and can directly measure the vibration velocity and acceleration for particle motion in three dimensions. The receiving frequency band of G1 is 0.01–1000 Hz, and the A/D resolution is 20 bits. The working temperature range is −20–60 °C. During the experiment, the sampling frequency of G1 was set to 4 kHz. In addition, an underwater signal recorder (USR) beneath the ice was used to receive the acoustic pressures in the water at the same time. The USR was manufactured by the Institute of Acoustics of the Chinese Academy of Sciences. The model used (USR-2000) has a maximum operating depth of 2000 m. The sampling frequency of the USR was set to 24 kHz, and the analog-to-digital (A/D) resolution was 24 bits. The sensitivity responses to the frequency of G1 and the USR are shown in Figure 1. It can be seen from Figure 1a,b that the sensitivity curves are rather flat. This means that G1 and the USR are ideal for low-frequency measurement.

The field trial geometry is shown in Figure 2. D is the depth of the acoustic source. The source is a fixed–depth explosion source, which can generate broadband signals. The depth D was 100 m at each of the three sites. R is the horizontal distance between the source and the geophone. At the three different sites, it was 70, 340 and 100 m, respectively. Based on the depth D and horizontal distance R of the source, the three different incident angles θ could be calculated as 35°, 73.6° and 45°, respectively. The ice thickness was mainly 1–2 m. It was roughly measured using a meter ruler. But the ice thickness at site S1 was relatively thin. During the experiment, the x direction of the geophone was toward the source, and the bearing was 0°. The basic information includes site coordinates, experimental time, real source bearing, R, D and number of sources, as shown in

Table 1. Basic information of bearing estimation experiments.

Site Name	Site Coordinate	Experimental Time	Real Bearing (°)	Horizontal Distance R (m)	Source Depth D (m)	Source Quantity
S1	84.5125° N 168.6950° W	16 August 2020	−5	70	100	2
S2	86.0430° N 160.8985° W	18 August 2020	−5	340	100	2
S3	85.4917° N 179.9095° E	24 August 2020	90	100	100	2

.

3. Bearing Estimation Methods

When an acoustic wave is incident on a planar water/ice interface, ice seismic waves propagate in three fundamental models, the L_P wave (longitudinal plate wave), S_H wave (horizontally polarized shear wave) and F_L wave (flexural wave), if the frequencies are low and the wavelengths are greater than the ice thickness [16,17,18,19,23]. The L_P wave and F_L wave are composed of the P wave (compressional wave) and S_V wave (vertically polarized shear wave), i.e., P-S_V wave. The particle motion of the L_P wave and F_L wave mainly exists in the vertical radial plane parallel to the incident wave, while the particle motion of the S_H wave is perpendicular to this vertical radial plane. According to these characteristics of seismic waves in ice, a rotational analysis for source-bearing estimation based on maximizing the radial signal power has been developed [23]. Moreover, so has a straightforward and effective set of polarization filters that can be adapted to bearing estimation [28,29]. The approaches are briefly introduced below.

3.1. Rotation Method of Maximum Radial Power

The rotational method of maximum radial power is based on measuring ice seismic waves for which the direction of particle motion is oriented radially outward from the source [23]. Therefore, the maximum radial signal power as a function of the horizontal look angle is built. By continuously rotating the horizontal azimuth from 0° to 360°, the maximum value is obtained. The angle of maximum power provides the optimal estimate of the source bearing. The maximum radial power function [23] is

$$\psi \left(\theta \right)={\displaystyle {\sum }_{t=1}^T{r}_t^2}\left(\theta \right)={\cos }^2\theta {\displaystyle \sum x_t^2}+{\sin }^2\theta {\displaystyle \sum y_t^2}+2\cos \theta \sin \theta {\displaystyle \sum x_t}{y}_t$$

(1)

In Equation (1), θ is the incident angle in the horizontal plane, t stands for a certain time, and x_t and y_t denote the discrete time series of particle displacement recorded in the x- and y-directions of a geophone, respectively. r_t is the horizontal (radial) particle motion at the time. By calculating the derivative of the maximum radial power function, the maximum value is obtained when the derivative is zero. The angle θ of maximum power, as shown in Equation (2), is the estimated bearing [23].

$${\theta }_{\max }=1/2{\tan }^{-1}\left[\frac{2{\displaystyle \sum x_t{y}_t}}{{\displaystyle \sum x_t^2-{\displaystyle \sum y_t^2}}}\right]$$

(2)

3.2. Vertical Polarization Filtering Method

The vertical polarization filtering method uses the phase difference between the vertical and horizontal components for various wave types. Using the vertical component signal and/or its time derivative as time-domain filters for the horizontal signals, the horizontal polarization S_H waves and noise are suppressed [23,28,29]. The vertical polarization P waves and shallow-angle S_V waves are enhanced, which provides primary information regarding source bearing. Applying the vertical polarization filter on the rotational analysis, the maximum radial power obtained through vertical filtering is as follows [23]:

$${\mathsf{\Psi }}_z\left(\theta \right)=\mathrm{c}\mathrm{o}{\mathrm{s}}^2\theta \sum (x_t{z}_t{)}^2+\mathrm{s}\mathrm{i}{\mathrm{n}}^2\theta \sum (y_t{z}_t{)}^2+2\mathrm{c}\mathrm{o}\mathrm{s}\theta \mathrm{s}\mathrm{i}\mathrm{n}\theta \sum \left(x_t{z}_t\right)\left(y_t{z}_t\right)$$

(3)

4. Results and Discussion

4.1. Acoustic Signals Received and Particle Displacement

At site S1, after an explosion source was released, the cross–ice acoustic signals were received by an ice–mounted geophone, and the particle displacements normalized in three directions are shown in Figure 3a, with some translation in the vertical coordinate direction for a better view. In Figure 3a, it can be seen that the signals generated by the explosion source have significant impact characteristics in the time domain. A detailed explanation of the explosion source can be found in reference [30]. To study the bearing estimation on cross-ice acoustic signals in different frequency bands, the signals were filtered in the frequency domain according to the 1/3 octave. Fifteen signals in the 1/3 octave frequency band centered at frequencies from 40 Hz to 1000 Hz were obtained. The particle displacement caused by the signal wave in each frequency band received by the geophone in the x-, y- or z-directions can be obtained, and the results are shown in Figure 3b–d, with some translation in the vertical coordinate direction. The unit of particle displacement is meters. In order to better understand the signal characteristics of each frequency band, the same translation was performed in the vertical coordinate direction.

It can be seen from Figure 3b–d that the particle displacement varies with the frequency.

Peak displacement (the maximum displacement during the sampling time) is an important characteristic point of energy distribution and plays an important role in research. The peak displacements at each center frequency of the 1/3 octave in the three directions of received signals at site S1 are shown in

Table 2. Peak displacements at each center frequency of the received signals at site S1.

Frequency/Hz	1000	800	630	500	400
x peak/10−7 m	1.1376	1.2432	5.295	13.085	38.113
y peak/10−7 m	0.6745	1.0727	1.6269	1.712	4.252
z peak/10−7 m	1.5068	2.6327	3.9844	8.7499	44.337
Frequency/Hz	315	250	200	160	125
x peak/10−7 m	29.355	28.626	43.977	49.736	42.540
y peak/10−7 m	11.638	8.931	24.205	32.477	28.067
z peak/10−7 m	16.462	17.636	24.518	26.595	29.062
Frequency/Hz	100	80	63	50	40
x peak/10−7 m	39.758	34.733	29.084	21.995	16.103
y peak/10−7 m	21.433	15.521	10.426	6.158	3.557
z peak/10−7 m	31.986	36.409	40.675	38.246	32.068

.

It can be seen in Table 2 that the particle peak displacements in each frequency band are different.

As shown in Figure 3b–d and Table 2, the particle peak displacements in each frequency band are different at site S1. When the frequency band is below 630 Hz (i.e., f < 630 Hz), the value of the x-direction peak displacement is higher and greater than 10 × 10⁻⁷ m. When the frequency is greater than or equal to 630 Hz (i.e., f ≥ 630 Hz), the value of the x-direction peak displacement is lower and less than 10 × 10⁻⁷ m, as shown in Figure 3b. The y- or z-direction peak displacement in each frequency band also has similar characteristics, as shown in Figure 3c,d and Table 2. Therefore, the value of the peak displacement in the x-, y- or z-direction is related to the frequency band of the received signals. Similarly, this feature can also be found at sites S2 and S3.

4.2. Source Bearing Estimation Results in Each Division Frequency Band

According to the bearing estimation method described in Section 3, the maximum power rotation method combined with the vertical filtering method was used. The estimated bearing of 15 different frequency bands of the first explosion acoustic source at site S1 is shown in Figure 4.

As shown in Figure 4, the estimated bearing of the 15 frequency bands to the same acoustic source at the same site is not completely consistent. The true bearing value of the site is −5°, as shown in Table 1. By considering prograde particle motion in the vertical–radial plane, the 180° bearing ambiguity can be solved [23], but it can still be found that some bearing estimation errors (difference from the true value, without considering 180° ambiguity.) are large and some slightly changed with the frequency band of the acoustic signal. Combined with the previous three-direction displacements, which are shown in Figure 3b–d, it is found that the bearing estimation error of the frequency band corresponding to small displacement is large (f ≥ 630 Hz), and the error of the frequency band corresponding to large displacement is small (f < 630 Hz). It seems that the bearing estimation error of different frequency bands is related to the peak displacement in the same frequency band. More details will be provided in the next section.

4.3. Relationship between Bearing Estimation Error and Horizontal Peak Displacement

The results of the bearing estimation of each 1/3 octave frequency band average centered at frequencies 40–1000 Hz for two acoustic sources at site S1 are shown in Figure 5a, where the asterisks indicate the bearing estimation for each frequency band for the first source, the circles indicate the bearing estimation for each frequency band for the second source, the dotted line represents the real bearing angle of −5°, and the upper and lower solid lines represent the bearing angle that deviates from the real value by 20°. If the bearing estimation errors exceed 20°, they will fall outside these two lines. Combined with the previous analysis on the relationship between bearing estimation error and peak displacement, the horizontal x- or y-direction peak displacements in different frequency bands are extracted. The relationship between the x-direction peak displacements and 1/3 octave frequencies is shown in Figure 5b, and the relationship between the y-direction peak displacements and 1/3 octave frequencies is shown in Figure 5c.

As shown in Figure 5a, when the frequencies are in the 630–1000 Hz band, the bearing estimation errors significantly increase and are greater than 20°. A threshold line is drawn near the value of the x- or y-direction peak displacement at 630 Hz in Figure 5b,c, and the threshold values are x = 5.3 × 10⁻⁷ m and y = 1.63 × 10⁻⁷ m, respectively. The x- and y-direction peak displacements in the 630–1000 Hz frequency band are all near or below the threshold. Comparing Figure 5a to Figure 5b,c, it can be found that in the frequency band of 630–1000 Hz, the x- and y-direction peak displacements are small and lower than the threshold, while the bearing estimation errors clearly increase and are almost greater than 20°.

The results of the bearing estimation for each 1/3 octave frequency band for two acoustic sources at site S2 are shown in Figure 6a, where the dotted line represents the real bearing of –5°, and the upper and lower solid lines represent the bearing angle that deviates from the real value by 25°. Because the horizontal distance between the source and the geophone is larger and exceeds 300 m, the bearing estimation error range set in Figure 6a is increased by 5° compared to that in Figure 5a. Similarly, the relationship between the x- or y-direction peak displacements and 1/3 octave frequencies is shown in Figure 6b,c; the threshold value is x = 2.5 × 10⁻⁷ m in Figure 6b and y = 1.5 × 10⁻⁷ m in Figure 6c.

As shown in Figure 6a, the bearing estimation errors in the two frequency bands, 40–63 Hz and 630–1000 Hz, are mostly greater than 25°. Furthermore, the bearing estimation error at the frequency of 315 Hz is greater than 25°. Similarly, it can be seen in Figure 6b,c that in the same two frequency bands, 40–63 Hz and 630–1000 Hz, the x- or y-direction peak displacements are small, mostly near or lower than the threshold, and the x-direction peak displacement at 315 Hz is near the threshold.

The results of the bearing estimation in each frequency band for two acoustic sources at site S3 are shown in Figure 7a, where the dotted line represents the real bearing of 90°, and the upper and lower solid lines represent the bearing that deviates from the true value by 20°. The relationship between the x- or y-direction peak displacements and 1/3 octave frequencies is shown in Figure 7b,c. The threshold value is x = 5 × 10⁻⁷ m in Figure 7b and y = 1 × 10⁻⁶ m in Figure 7c.

As shown in Figure 7, when the frequency is in the range of 400 Hz to 1000 Hz, the bearing estimation errors significantly increase and are almost greater than 20°, except at 1000 Hz. Similarly, in the same frequency band, the x- or y-direction peak displacements are small and lower than the threshold. In the case of small peak displacement, the bearing estimation error at 1000 Hz is still small and remains to be studied further.

By comparing the experimental results of the peak displacement and bearing estimation error in different frequency bands at the three sites, it can be found that the bearing estimation error is related to the x- or y-direction peak displacement.

This occurs partly because in the bearing estimation method mentioned in Section 3, the maximum radial power in Equation (1) is closely related to the horizontal displacement in the x and y-directions of the particle motion. The other reason is that the low values of the x- or y-direction peak displacements mean the maximum radial power is small, which increases the bearing estimation errors in this frequency band. For this reason, if the horizontal peak displacements of the received signal in some frequency bands are too low, the reliability of the bearing estimations for the corresponding frequency band will be reduced.

Through these analyses, it can be determined that the peak displacement, error and the size of the corresponding frequency band are closely related. In this way, we can use these basic relationships and further experiments to analyze the causes of bearing errors at three different sites.

4.4. Lamb Wave and Bearing Estimation

4.4.1. Relationship between the Lamb Wave and x-Direction Peak Displacement

The relationship between the x-direction peak displacements and frequencies at the three sites is shown in Figure 8a. Simultaneously, taking the frequency band width Δf = 47.875 Hz as the processing interval, the energy level of the acoustic sources recorded using the USR was calculated for the three sites, and the results are shown in Figure 8b.

As shown in Figure 8a, the peak displacement distribution structure shows a bimodal distribution at sites S1 and S2, while it shows a single peak distribution at site S3. In Figure 8b, the energy level received by the USR shows a single peak distribution at sites S1, S2 and S3, and there is no second peak at any site. By comparing Figure 8a to Figure 8b, it can be seen that the peak distribution structure is changed from the singlet structure to the bimodal structure for the same source at sites S1 and S2 but maintains the same singlet structure at site S3. Why is the peak distribution changed at site S1 or S2 but remains unchanged at site S3? This may be attributed to the Lamb wave. If an acoustic source is in the seawater beneath the ice, given an incident angle, certain frequencies of the Lamb modes can be excited [26]. When some Lamb modes of the ice plates were excited at sites S1 and S2, the horizontal displacement in the frequency band of the mode was higher, and the second peak was produced in the peak distribution structure. When the Lamb mode of the ice plate was not excited at site S3, the horizontal displacement in the frequency band of the mode was not higher, and there was no second peak in the displacement distribution structure. This idea will be further confirmed below.

4.4.2. Relationship between the Lamb Wave and the Second Peak

When a Lamb wave is excited, it takes away energy from the incident beam in certain frequency bands, which induces a resonance structure in reflectivity, and the dips in the reflection coefficient diagram correspond to some Lamb modes of the ice plate [27]. Using the full wave integration model OASES, let the longitudinal wave velocity c_p of the ice layer be 3600 m/s, the shear wave velocity c_s be 1800 m/s, the density ρ be 0.9 g/cm³, the longitudinal wave attenuation coefficient α_p be 0.216 dB/λ (λ is wavelength), the shear wave attenuation coefficient α_s be 0.648 dB/λ [31], the density of seawater be 1000 kg/m³, the sound velocity of seawater be 1480 m/s and the frequency band be 10–1000 Hz. The reflection coefficient is calculated for the water/ice interface with 2 m smooth sea ice, as shown in Figure 9a. Using Snell’s Law, the incident angle can be changed to phase velocity, and the reflection coefficient can be shown by the phase velocity and frequency. The Lamb modes of the ice plate can be calculated [27]. The reflection coefficient and the Lamb modes are shown in Figure 9b.

In Figure 9a, four obvious dips with low reflection coefficients are marked. The dips in the reflection coefficient diagram correspond to some modes of the Lamb waves of the ice plate [27]. It can be seen in Figure 9b that the vibration frequency of the Lamb waves is connected with the incident angle (phase velocity) of the acoustic wave and the thickness of the ice layer.

When the ice thickness is 1, 2 and 4 m, the incident angles are 35°, 73.6° and 45°, respectively, in the Arctic experiment at the three sites, and the computed reflection coefficients are shown in Figure 10a–c.

At site S1, the incident angle is 35°, the ice thickness d is relatively small, near 1 m, and the obvious dip in the reflection coefficient diagram is in the frequency band of 200–400 Hz, as shown in Figure 10a. Comparing Figure 10a to Figure 8a, the frequency corresponding to the second peak at site S1 is near 400 Hz. Therefore, the frequency band corresponding to the peak is consistent with the frequency band corresponding to the dip in the diagram of the reflection coefficient. This is also consistent with the hypothesis that at site S1, some modes of the Lamb waves were excited, and the second peak was produced.

At site S2, the incident angle is 73.6°, the ice thickness d is near 2 m and the obvious dip in the reflection coefficient diagram is in the frequency band of 400–600 Hz, as shown in Figure 10b. Comparing Figure 10b to Figure 8a, the frequency corresponding to the second peak at site S2 is near 400 Hz. Therefore, the frequency band corresponding to the peak is also consistent with the frequency band corresponding to the dip in the diagram of the reflection coefficient. This is also consistent with the hypothesis that at site S2, some modes of the Lamb waves in the ice were excited, and the second peak was produced.

At site S3, the incident angle is 45°, the ice thickness d is near 2 m and there is no obvious dip in the reflection coefficient diagram, as shown in Figure 10c. This means that no modes of the Lamb waves of the ice plate were excited at this site. As we can see from Figure 8a, at site S3, there is no bimodal structure but a single peak structure, which is consistent with the fact that the Lamb waves were not excited in the ice layer; thus, the second peak cannot be generated.

4.4.3. Relationship between the Lamb Waves and Bearing Estimation Error

At sites S1 and S2, in the excitation frequency band near 400 Hz, which corresponds to the second peak, the error is relatively smaller, within 25°, as shown in Figure 5a and Figure 6a, and the bearing estimation is efficient. At site S3, there is no excited second peak, the bearing estimation errors in the frequency band near 400 Hz are larger, more than 25°, as shown in Figure 7a, and the bearing estimation is bad. According to the previous analysis in this study, the bearing estimation errors are connected with the value of peak displacement, and the excited modes the of Lamb waves are connected with the excited second peak in Figure 8a. Thus, it can be presumed that if some modes of the Lamb waves of the ice plate are excited, the bearing estimation error in the frequency band of the excited peak would be relatively smaller, and the frequency band for the bearing estimation would be efficient. In other words, if some modes of the Lamb waves are excited, the efficient frequency band for the bearing estimation would be widened.

Normally, the thickness of the ice layer cannot be changed. If the ice thickness is constant, the excitation of the Lamb wave is related to the incident angle. Therefore, the bearing estimation error is related to the incident angle. However, we can adjust the incident angle by moving the received distance to excite some modes of the Lambs wave so that more energy can enter the ice layer and the frequency band with a good bearing estimation effect will be widened.

If the incident angle is constant and some modes of the Lamb waves are excited, there will be a dip in the reflection coefficient diagram, as shown in Figure 10a. The thinner the ice layer, the higher the frequency of the dip. That is, if the ice layer is thinner, the Lamb waves will be excited at a higher frequency, which means that a relatively higher and wider frequency band of acoustic signals may be obtained for good bearing estimation. Therefore, if we want to bear an acoustic source in a higher frequency band, a thinner ice layer would be selected, and some modes of the Lamb waves can be excited, letting more energy enter the ice layer, which is conducive to the bearing.

4.5. Better Bearing Estimation and Some Questions

Through the analysis of the relationship between the bearing estimation error and the value of the horizontal peak displacement, it can be seen that to obtain a good bearing estimation of the source, it is necessary to select an appropriate frequency band of the acoustic source. It is better to avoid some frequency bands with low horizontal displacement peaks. If the value of the horizontal peak displacement is too small, the acoustic energy entering the ice is often too small, which is unfavorable to the bearing estimation for the underwater acoustic source, and the bearing estimation error will be larger. Second, it is necessary to make good use of the Lamb waves. When the incident angle and ice thickness meet certain conditions, some modes of the Lamb waves of the ice plate will be excited, and the acoustic energy entering the ice will be increased, which is conducive to bearing estimation of the source.

In the results of the experiments, we also found that some peak displacements are larger, but the bearing estimation errors are also slightly larger in the corresponding frequency bands. For example, at site S1, when the frequency is 200 Hz, the value of the x-direction peak displacement is greater than the threshold, but the bearing estimation error is close to 20°, as shown in Figure 5a. In addition, during the experiments at sites S1 and S2, no obvious bimodal distribution was observed in the y-direction displacement. This may be caused by the ice being inhomogeneous or the fact that the real bearing is too small (the real bearing is −5° at sites S1 and S2), which makes the y component of the corresponding angle relatively small; thus, the y-direction peak displacement is too small to be observed. These problems will be further explored in future research work.

5. Conclusions

During the Chinese National Arctic Research Expedition, source bearing estimation experiments using an ice-mounted geophone and a USR were performed at three sites in the central Arctic Ocean. The relationship between the errors of bearing estimation and frequency bands was studied.

It was found that the bearing estimation errors for an acoustic source in different frequency bands are related to the x- or y-direction peak displacements received by the ice-mounted geophone. The higher the peak displacement, the smaller the bearing estimation error. When the value of the x- or y-direction peak displacement in some frequency band is lower than a certain threshold, the bearing estimation error corresponding to the frequency band becomes larger, almost larger than 25°.

Moreover, when the incident angle of the acoustic source and the thickness of the ice meet certain conditions, some modes of the Lamb waves in the ice layer will be excited, and the peak distribution structure of the horizontal displacement will be changed. The bearing estimation errors in the frequency band corresponding to the Lamb waves are reduced, and the efficient frequency band of the signal for the bearing estimation will be widened.

The study of acoustic signals detected on the surface of ice is not only related to geophones, but also to sound sources. Due to the difficulty in obtaining underwater sound sources and the complex physical characteristics of the ice layer, it has been difficult to obtain variations in cross-ice sound signals with frequency. In experiments at three sites, the x-, y- and z-direction displacements and bearing estimation were measured by using an ice-mounted geophone, and the analysis frequency band was 40–1000 Hz. At same time, the underwater data were received by the USR. By comparing data obtained on the ice with data obtained underwater, we could partly discover the conversion and mechanism of signal energy across ice layers in different frequency bands.

Considering that there are still some problems with source bearings caused by the anisotropy of the ice layer or small real bearing angles in the experiment, Arctic acoustic experiments and research will need to be continuously performed. Underwater acoustic source bearing estimation and the coupling propagation mechanism of underwater acoustic signals across ice-to-ice surfaces will be further studied.