In the past century, extensive research has been done regarding the sound propagation in Arctic ice sheets. The majority of this research has focused on low-frequency propagation over long distances. Due to changing climate conditions in these environments, experimentation is warranted to determine sound propagation characteristics in, through, and under first-year, thin ice sheets, in shallow water, over short distances. In April 2016 several experiments were conducted approximately 2 km off the coast of Barrow, Alaska on shore-fast, first-year ice, approximately 1 m thick. To determine the propagation characteristics of various sound sources, frequency response functions were measured between a source location and several receiver locations at various distances from 1 m to 1 km. The primary sources used for this experiment were, an underwater speaker with various tonal outputs, an instrumented impact hammer on the ice, and a propane cannon that produced an acoustic blast wave in air. The transmission loss (TL) characteristics of the multipath propagation (air, ice, water) are investigated and reported. Data indicate that TL in frequency bands between 125 and 2000 Hz varied from approximately 3–6 dB per doubling of distance which is consistent with geometrical spreading losses, cylindrical and spherical, respectively.

In the past century, there has been a great deal of research conducted regarding acoustic propagation in multilayered media such as air, ice, and water. In floating ice sheets, the theory of wave propagation is well developed1–10 and has been corroborated by several experiments.11–18 With the exception of a few studies,10,15 the majority of this research focuses on low frequency (approximately less than 100 Hz) propagation over long-ranges (generally greater than 1 km).

It is well known that the global climate change is affecting the Arctic ice layers.19–22 In general, the ice layer formations are much different than those which were studied in early acoustic experiments. The majority of multi-year pack ice, which has been extensively studied, is now melting between seasons giving rise to an increase of annually formed first-year ice.19,20 The shore-fast ice sheet has previously been composed of multi-year ice that travels to shore on currents and gets trapped in the first year ice. Due to the overwhelming loss of multi-year ice in the Arctic as a whole, the near-shore environment is now composed of predominantly first year ice. First-year, shore-fast ice is thinner, more saline, and of different density and strength than multi-year ice23 and is deserving of specific study into its acoustic properties.

In addition, this changing Arctic environment warrants new investigation into the acoustic detection, identification, and tracking of anthropogenic sources. Because there is less ice in the Arctic environment for longer time periods during the year, there is expected to be increased near-shore anthropogenic activity.22,24–26 This activity may come in the form of Arctic shipping through the Northwest Passage, natural resource exploration, and tourism. It is of interest to determine the location and type of these anthropogenic sources. Sensing of sources in the first-year shore-fast ice environment is non-trivial due to ice ridging and ever-changing ice movements. Furthermore, first-year, near-shore ice is not well understood in terms of acoustic properties. Therefore, new data are required to understand the acoustic transmission paths in the first-year, near-shore ice environment and to validate algorithms for detection, identification, and tracking of anthropogenic sources in shallow water (less than 50 m) with thin, irregular ice sheets.

Typically, acoustic transmission loss (TL) data have been measured using arrays of geophones on the ice surface, arrays of hydrophones underwater, or microphones in the air. Sometimes combinations of either geophones and hydrophones, or geophones and microphones have been used to better understand acoustic propagation.12,13 However, the combination of all three sensor modalities is uncommon. Combining a small number of sensors of all three modalities may enhance source detection, identification, and tracking using lower cost sensor nodes. For this reason, this study investigates the simultaneous acquisition of data from all three sensing modalities.

Early experiments often excited layered media with explosives.1,2,12,15,17 This excitation method is now less common due to environmental regulation on explosive acoustic sources.27 Due to these regulations, new excitation methods are necessary. Recent techniques for ice excitation include freezing a wooden or steel post into the ice and hitting the post with a sledgehammer.16,28 For underwater excitation, light bulbs, or other crushable containers, have been placed at depth and imploded to create an acoustic source.27,28 While some studies take care to control the source excitation levels in some manner,10,28 source levels have not been systematically quantified or measured.

This set of experiments is conducted in Arctic environments regarding the multimodal, short range, and shallow water response to calibrated and measured sources. In the industrial noise and vibration field, a common method for determining acoustic path characteristics in response to a known source level is the calculation of frequency response functions (FRFs).29–31 The FRF is a spectral frequency domain ratio of a response measurement to a source measurement. This method is not commonly used in the seismo-acoustic or Arctic-acoustic fields. In this paper, FRFs are used to quantify the multipath characteristics in the Arctic environment. Using FRF calculations, spectral frequency domain ratios are determined between microphone, geophone, and hydrophone responses to various measured source inputs, namely, a small propane cannon, an instrumented impact hammer, and an underwater speaker.

The primary focus of this paper is the data which were collected in Barrow, AK, in April 2016. The data are analyzed in terms of temporal propagation, TL, and FRFs over short ranges in the first-year ice, near-shore Arctic environment.

Acoustic propagation measurements were recorded during April 8–15, 2016. All measurements were conducted approximately 2 km offshore of Barrow, Alaska, on first-year, shore-fast ice that was between 1.05 and 1.15 m thick at the test sites. Water depth below the ice was 8–12 m deep. A total of 6 sites were identified: three were used to collect data and three were used for acoustic excitation into the air, ice, or water. Sites 1, 2, and 3 were receiver locations and sites 4, 5, and 6 were source locations (Fig. 1). Acoustic propagation distances between source and receiver sites are seen in Table I.

FIG. 1.

(Color online) Site layout approximately 2 km off the coast of Barrow, AK.

FIG. 1.

(Color online) Site layout approximately 2 km off the coast of Barrow, AK.

Close modal
TABLE I.

Distance between source and receiver sites in meters.

Receiver sites
Site 1Site 2Site 3
Source sites Site 4 50.3 929.9 743.2 
Site 5 164.3 1034.7 853.2 
Site 6 703.5 117.5 105.3 
Receiver sites
Site 1Site 2Site 3
Source sites Site 4 50.3 929.9 743.2 
Site 5 164.3 1034.7 853.2 
Site 6 703.5 117.5 105.3 

The sea ice conditions varied significantly throughout the test area (Fig. 2). At the cluster of sites 1, 4, and 5, the ice was relatively flat, without any large ridges. At the cluster of sites 2, 3, and 6, the ice was also flat but was surrounded on all sides by large ice ridges. The largest of these ridges was near site 3 and was approximately 5 m high. It was suspected that some of the large ice ridges may have been bottom-fast because the water was only 8–12 m deep at all sites, however, this was not confirmed. The space between the two site clusters was moderately covered with smaller ice ridges 2–3 m high. Test sites were chosen where there was flat ice to facilitate deployment of equipment and where they were sufficiently close to shore to commute via snowmobile on a daily basis. Ice ridges were avoided as much as possible; however, large open areas of ice, without ridges, were sparse in the shore-fast environment. The rugged ice conditions made it difficult to locate reasonable test locations and limited the number of test locations that could effectively be measured. In addition, the weather during the test window limited the data gathering to 3 days (April 9, 12, and 13) out of the 8 days window. Although this is expected for testing in the harsh environment of the Arctic, it severely limited the collected data set spatially and only priority locations were able to be collected.

FIG. 2.

(Color online) Shore-fast sea ice conditions near the test sites: (A) Site 1 looking seaward. (B) Photograph from cluster of sites 2, 3, and 6 looking east towards sites 1, 4, and 5. (C) Large ice ridge near site 3. (D) Scale of large ice ridges compared to a person. Large ice ridges were approximately 5 m high. (E) Site 2 looking towards site 3.

FIG. 2.

(Color online) Shore-fast sea ice conditions near the test sites: (A) Site 1 looking seaward. (B) Photograph from cluster of sites 2, 3, and 6 looking east towards sites 1, 4, and 5. (C) Large ice ridge near site 3. (D) Scale of large ice ridges compared to a person. Large ice ridges were approximately 5 m high. (E) Site 2 looking towards site 3.

Close modal

Generally speaking, each experiment measured the acoustic path characteristics between source sites and receiver sites. Each experiment used either a propane cannon, instrumented force hammer, or underwater speaker to create an acoustic excitation of the environment. The excitation level of the source was quantified at the source location by a microphone in the air, geophone on the ice, and a hydrophone underwater. The receiver sites measured the acoustic responses down range with microphones, hydrophones, and geophones. The variation in distances between source and receiver sites facilitated estimation of TL as a function of distance. In addition, spectral analysis of the drive point (source and receiver co-located) transducers allowed for calculations of FRFs. It was the intent to characterize the TL and FRFs between all source–receiver combinations. However, in the case of a few source–receiver combinations, there was not sufficient signal to noise ratio (SNR) to allow for analysis.

At source sites, data were collected with a headless, 4-slot, National Instruments (NI) cRIO-9024. The data acquisition modules used were NI-9234, NI-9269, NI-9467, and NI-9344. These modules were used for acoustic data collection, signal output (as necessary), global positioning satellite (GPS) location and timing signal acquisition, and system control, respectively. At receiver sites, data were collected with a 4-slot, cRIO-9031. Three NI-9234 modules were used to collect acoustic data and one NI-9467 module was used for GPS location and timing signal acquisition. All acoustic data were sampled at 51 200 Hz in blocks of 120 s (in subsequent sections, each 120 s data collect is referred to as one experiment). GPS time and position data were sampled once at the beginning of every data collection. Source and receiver data collections were time synchronized in post-processing via GPS timing signals.

Three types of acoustic sources were used to excite the air, ice, or water for various experiments (Fig. 3). The acoustic responses to each source were then measured down range at receiver sites. Several experiments were conducted using each source type to increase the number of potential averages that could be acquired during post-processing. Only one type of source per experiment was used for excitation.

FIG. 3.

(Color online) Source site schematic of various acoustic sources and receivers. Arrows indicate drive point measurements between source and receiver with adequate signal-to-noise ratio. Units of output signal over input signal are indicated.

FIG. 3.

(Color online) Source site schematic of various acoustic sources and receivers. Arrows indicate drive point measurements between source and receiver with adequate signal-to-noise ratio. Units of output signal over input signal are indicated.

Close modal

A propane cannon (Zon Mark 4) was used as an in-air acoustic source. The detonation of propane created an impulsive pressure wave originating at the source location. The cannon did not shoot a projectile. A mechanical regulator was used to automatically fire the cannon one time approximately every 30 s. The regulator was set so that as many shots as possible could be recorded during the 120 s measurement period.

A 12 lb instrumented force hammer (PCB Model 086D50, 0.23 mV/N) was used to input energy to the ice sheet. The hammer was used to excite the ice sheet with an impact while it measured the force input to the ice sheet using an onboard force gage. The ice was struck directly since it was hard and flat at the source locations after removing a few inches of surface snow. The location of the hammer impact in relation to the source transducers changed slightly between experiments. This was necessary to find a relatively smooth and solid patch of ice to impact. At source sites where multiple hammer experiments were conducted, the ice would inevitably become chipped and non-uniform after one experiment. Therefore, it was necessary to move locations slightly (less than 1 m) between experiments. During the 120 s measurement period, the ice was impacted with the force hammer as many times as was feasible (usually between 30 and 40 times). Any hits that were of poor quality (double hits and overloaded signals) were removed during post-processing. This resulted in 10–20 “good” hammer impacts per recording that could be used for spectral averaging per experiment.

An underwater speaker (Lubell Labs Model LL916) was used as an underwater acoustic sound source. The speaker produced tones at various frequencies (200, 400, 800, 1600, 6400 Hz) and short chirps across frequency ranges (40–2500 Hz and 4000–25 000 Hz). The tones and chirps were played over the 120 s measurement period. Each tone duration was 10 s and each chirp duration was 0.01 s. An amplifier (PylePro PZR 600) was used to drive the underwater speaker and maintain consistent sound levels between experiments. The underwater speaker was deployed through a drilled hole in the ice to a depth of 2 m.

In order to quantify the source levels, one microphone (PCB 377B02, 50 mV/Pa), one single-axis, vertically oriented, geophone [Mark Products 19.7 V/(m/s)], and one hydrophone (Teledyne Reson TC 4032, −170 dB re 1 V/μPa) were placed near the source (Fig. 3). At source sites, the hydrophone was placed at a depth of 2.5 m through a drilled hole in the ice. The distance between the hydrophone and the underwater speaker source (when used) was between 1 and 2 m. Precise distances between the underwater speaker and the hydrophone for each experiment were computed in post processing using time delays and measured sound speed in the water column. The microphone was placed on a tripod 70 cm above the ice and within 1 m of the hydrophone hole, opposite the underwater speaker hole. The microphone was 2.8 m from the muzzle of the propane cannon. The geophone was placed between the two holes which were drilled for the underwater source and the hydrophone. For all experiments, the hammer impact location was between approximately 1 and 3 m from the source geophone.

It should be noted for experiments when the cannon was used, the pressure wave overloaded the in-air microphone at the source site. Because of limited spare equipment at the test site, a hydrophone (TC 4032) replaced the microphone in the air. The hydrophone was used at the source site only to record the in-air acoustic wave for the cannon experiments because its sensitivity was much lower than that of the microphones. For simplicity, and to avoid confusion, any in-air measurements will be referred to as microphone measurements.

At each receiver site, several transducers were placed to simultaneously record the acoustic response from the source excitation (Fig. 4). One microphone (PCB 378B02, 50 mV/Pa), one three-axis geophone [GS-One 3-C, 85.8 V/(m/s)], and five hydrophones (Teledyne Reson TC 4013, −211 dB re 1 V/μPa) were used at each receiver location to measure the in-air sound pressure level (SPL), ice vibrational velocity, and underwater SPL, respectively. The microphone, geophone, and one hydrophone were centrally located at the site. Four additional hydrophones were placed at cardinal directions of North, East, South, and West, 3 m from the center of the site. The microphones were placed 2 m above the ice and the hydrophones were placed at a depth of 5 m underwater through drilled holes in the ice. For purposes of this paper, only the centrally located receiver hydrophone and vertical orientation of the receiver geophone are analyzed.

FIG. 4.

(Color online) Receiver site transducer layout. Site 1 shown.

FIG. 4.

(Color online) Receiver site transducer layout. Site 1 shown.

Close modal

At the outset of this analysis, it was necessary to determine the source–receiver combinations which had adequate SNR for any given experiment. Examining the spatial and temporal propagation, also gave an indication of which frequency ranges and distances could be used for future detection and tracking applications. Figures 5–7 show the power spectral densities (PSD) as a function of both frequency and time measured at the source location and at selected receiver locations. The time scale on these plots is zoomed in to focus on only a few source inputs from the 120 s acquisition time. This was done for greater clarity of the temporal propagation.

FIG. 5.

(Color online) Ice-to-ice and ice-to-water temporal propagation. Source (site 4) to receiver (site 1) distance approximately 50 m. (A) Hammer force input [dB re 1 N/rt(Hz)] at site 4 source location. (B) Geophone response [dB re 1 m/s/rt(Hz)] at site 4 source location. (C) Hydrophone response [dB re 1 Pa/rt(Hz)] at site 4 source location. (D) Geophone response [dB re 1 m/s/rt(Hz)] at site 1 receiver location. (E) Hydrophone response (dB re 1 Pa/ rt(Hz)) at site 1 receiver location.

FIG. 5.

(Color online) Ice-to-ice and ice-to-water temporal propagation. Source (site 4) to receiver (site 1) distance approximately 50 m. (A) Hammer force input [dB re 1 N/rt(Hz)] at site 4 source location. (B) Geophone response [dB re 1 m/s/rt(Hz)] at site 4 source location. (C) Hydrophone response [dB re 1 Pa/rt(Hz)] at site 4 source location. (D) Geophone response [dB re 1 m/s/rt(Hz)] at site 1 receiver location. (E) Hydrophone response (dB re 1 Pa/ rt(Hz)) at site 1 receiver location.

Close modal
FIG. 6.

(Color online) Air-to-air temporal propagation from the cannon source to the microphones at various receiver distances. (A) In air sound level at source location (site 5) normalized to 1 m. (B) In air sound level at site 1 approximately 164 m from source. (C) In air sound level at site 3 approximately 853 m from source. (D) In air sound level at site 2 approximately 1035 m from source. All levels: dB re 1 Pa/Hz.

FIG. 6.

(Color online) Air-to-air temporal propagation from the cannon source to the microphones at various receiver distances. (A) In air sound level at source location (site 5) normalized to 1 m. (B) In air sound level at site 1 approximately 164 m from source. (C) In air sound level at site 3 approximately 853 m from source. (D) In air sound level at site 2 approximately 1035 m from source. All levels: dB re 1 Pa/Hz.

Close modal
FIG. 7.

(Color online) Air-to-ice-to-water temporal propagation from the cannon source to the hydrophones at various receiver distances. (A) Underwater sound level at site 5. (B) Underwater sound level at site 1 approximately 164 m from source. (C) Underwater sound level at site 3 approximately 853 m from source. All levels: dB re 1 Pa/Hz.

FIG. 7.

(Color online) Air-to-ice-to-water temporal propagation from the cannon source to the hydrophones at various receiver distances. (A) Underwater sound level at site 5. (B) Underwater sound level at site 1 approximately 164 m from source. (C) Underwater sound level at site 3 approximately 853 m from source. All levels: dB re 1 Pa/Hz.

Close modal

For the hammer source experiment (Fig. 5), the force input to the ice, as well as the geophone and hydrophone responses at the source location are investigated. Note that microphone data in response to hammer excitation was not included due to lack of SNR at receiver sites. At 50 m from the source [Fig. 5(d)], the geophone has some detectable response especially at low frequencies (less than 200 Hz). It comes as no surprise that low frequencies propagate well in the ice and mid-high frequencies are attenuated quite rapidly. Beyond 50 m, there was no detectable signal in the geophone. By comparison, mid-high frequencies propagate better through the water and can be seen much more clearly in both the 50 and 164 m sites. In general, it can be said that the water path transmits energy farther than the ice path for a direct force input to the ice.

The in-air temporal propagation of the cannon blast is seen in Fig. 6. In Figs. 6(c) and 6(d), two large signal indications are visible between 1.4 and 3.3 s, before the arrival of the in air pressure wave at approximately 4.5 and 5.1 s, respectively. During the cannon experiment, a hand-held two-way radio was held near the cannon and near the receiver microphones. As the cannon was about to fire, the transmitting (push-to-talk) feature of the source radio was activated. This transmitted the cannon sound via radio waves, which arrived much earlier than the in-air pressure wave. Following the radio start indication, the in-air pressure wave can be seen at the receiver locations. Based on the time delay between the source and receiver sites, the in-air sound speed was determined to be 331 m/s. This is approximately 4 m/s faster than the speed of sound determined from Eq. (1),32 which is based on the ratio of specific heats (γ=1.4), the specific gas constant [R=287J/(kgK)], and the average air temperature (Tk=266.7K). The higher measured speed of sound is due to the receivers being down-wind from the cannon source, decreasing the time of flight (i.e., increasing sound speed). Wind speeds varied between 3.9 and 22.8 m/s during this testing:

c=γRTk.
(1)

The low frequency (40–2500 Hz) chirps produced by the underwater source were detectable at the 164 and the 853 m site hydrophones with 60 and 29 dB of SNR, respectively. Similar results were seen for the high frequency (4000–25000 Hz) chirps and tonal frequencies. The signal from the underwater speaker was not detectable by the microphone or geophone receivers. Based on the time delay between the source and receiver sites for the underwater speaker chirps, the average underwater sound speed was determined to be approximately 1441 m/s. The hydrophone responses to the cannon blast in air (Fig. 7) also confirm an average underwater sound speed of 1441 m/s. It is interesting to note in Fig. 7(c), that there are signals which are present before the arrival of the underwater sound wave. These indicate sound waves which traveled through the ice. Additionally, there are several signals after the arrival of the underwater sound wave which indicate reflections and scattering from the underwater environment. These reflections and scattering are expected due to the irregular ice ridges near sites 2 and 3.

In order to verify the time of flight sound speed measurement, the average sound speed was also measured directly with a SonTek CastAway conductivity, temperature, and depth (CTD) probe (Fig. 8). From the CTD data, the sound speed underwater ranged from 1433 to 1446 m/s for various depths. For the hydrophone depths used at source and receiver sites, the mean speed of sound is close to 1441 m/s. Therefore, the time of flight measurement of a sound speed of 1441 m/s is reasonable and represents direct path propagation. The underwater sound speed profile was calculated by a CastAway CTD using the Chen–Millero method.33,34

FIG. 8.

Sound speed profiles measured with conductivity, temperature, and depth (CTD) probe for sites 1 and 2. Measurements taken on 12/04/16 at UTC 15:53:32 and UTC 17:07:47 for sites 1 and 2, respectively.

FIG. 8.

Sound speed profiles measured with conductivity, temperature, and depth (CTD) probe for sites 1 and 2. Measurements taken on 12/04/16 at UTC 15:53:32 and UTC 17:07:47 for sites 1 and 2, respectively.

Close modal

For purposes of processing beyond this point, data which does not have at least 10 dB of signal-to-noise ratio based on the average ambient background noise is not included.

From the calibrated time series data for each experiment, the linear spectra of the source (Sx) and the linear spectra of the receivers (Sy) were determined by computing the fast Fourier transform (FFT) in Matlab. Using the linear spectra, the autopower spectra (Gxx), crosspower spectra (Gyx), and FRF between source and receiver were determined [Eqs. (2)–(4)].30,35

The FRF is defined as the output signal (response) divided by the input signal (source) in the frequency domain.30,35 Since the crosspower spectra averages out uncorrelated components, the noise on the response is minimized in the FRF calculations:30,35

Gxx(ω)=Sx*(ω)Sx(ω),
(2)
Gyx(ω)=Sy*(ω)Sx(ω),
(3)
FRF(ω)=Gyx(ω)Gyy(ω).
(4)

To determine the effectiveness of the FRF, an accompanying function, coherence (COH), was calculated.30,35 Coherence represents the amount of the output signal that is linearly related to the input signal. The coherence function ranges from zero to one, where one represents 100% of the output signal being linearly related to the input signal and zero represents 0% of the output signal being linearly related to the input signal. In general, it is preferable to see coherence which is close to one at frequencies where the FRF is to be investigated. Coherence less than one can be caused by non-linearity in the system, unmeasured inputs to the system (noise), an anti-resonance in the system, bias errors in the measurement, or some combination of all of these reasons.30,35 The coherence for the measurements is investigated alongside the FRFs to provide validation that the received signal is linearly related to the source signal:

COH(ω)=Gxy(ω)Gyx(ω)Gxx(ω)Gyy(ω).
(5)

For hammer experiments, there were 30–40 hammer hits over the 120 s measurement period with 3–4 s between hits and various impact force with the hammer. Various impact force was used intentionally because data could not be inspected on-site due to the harsh environmental conditions. The designed variation in impact force provided the best likelihood of generating impacts with high SNR that was not overloaded. Only “good” hammer hits were used for post-processing (10–20 per experiment). Hammer hits were not included if the signal was overloaded or if there was a double hit. Note that a double hit was registered any time that the hammer struck the ice more than one time per swing. Double hits were not included because they can provide unequal excitation in the frequency range of interest. Blocks of data, 1 s in duration and containing a good hammer hit signal, were used to compute the autopower spectra. All of the autopower spectra for a given experiment were then averaged. The averaged autopower spectra for the hammer experiments can be seen in Fig. 9. There is effective input energy between 1 and 200 Hz because the autopower spectra is high enough to excite a system response and there is good coherence in this frequency range. At 200 Hz and above the autopower spectra begins to roll off at a rate of −11.6 dB per octave. Beyond 2 kHz, the input autopower spectra is too low to excite any system responses. Additionally, coherence between the source and receiver begins to suffer due to low input energy above 2 kHz.

FIG. 9.

Source input levels from instrumented force hammer (left-hand scale) and propane cannon (right-hand scale).

FIG. 9.

Source input levels from instrumented force hammer (left-hand scale) and propane cannon (right-hand scale).

Close modal

The drive point FRF and COH between the hammer input and the geophone response at the source site (drive point mobility) is shown in Fig. 10. It can be seen that there is a large peak in the FRF at approximately 800 Hz and a corresponding harmonic at 1600 Hz. The 800 Hz peak and its harmonic are believed to correspond to the through-thickness compressional mode of the ice sheet.

FIG. 10.

(A) Drive point FRFs and (B) COH measured between the hammer and the geophone (left-hand scale) or hydrophone (right-hand scale) at the source location. Theoretical infinite plate mobility for sea ice conditions in Barrow (−66 dB re 1 m/s/N) is indicated.

FIG. 10.

(A) Drive point FRFs and (B) COH measured between the hammer and the geophone (left-hand scale) or hydrophone (right-hand scale) at the source location. Theoretical infinite plate mobility for sea ice conditions in Barrow (−66 dB re 1 m/s/N) is indicated.

Close modal

It is well known for quarter-wavelength resonators, that frequency (f) is related to the wave velocity (vp) and the wavelength by Eq. (6).36 The parameter L can be set equal to the ice thickness which was 1.05 m at the drive point locations. Also, for the 800 Hz mode, n can be set equal to 1:

f=(2n1)vp4L.
(6)

Solving for the compressional wave velocity in the ice, vp is determined to be approximately equal to 3360 m/s. This is similar to the compressional wave speed reported by several other sources.11,13,16

To confirm that the measured drive point mobility is reasonable, the theoretical infinite plate mobility is plotted for comparison. To approximate the theoretical mobility, the ice elastic properties are needed. Assumptions for these properties were made based on referring to several papers23,37–41 in aggregate to determine reasonable values for first-year ice in Barrow. Poisons ratio (v) was assumed to be 0.295 and the ice density (ρ) was assumed to be 910 kg/m.23,37–39 Also, the volume of brine in the ice (Vb) was assumed to be 20 ppt which results in an elastic modulus (E) of 2.98 GPa from Eq. (7).23,40,41 From these elastic properties, the flexural rigidity (D) and the infinite plate mobility can then be determined [Equations (8) and (9)].42 It is seen in Fig. 10(a) that the theoretical infinite plate mobility is approximately −66 dB (re 1 m/s/N) based on Eq. (9). This is very similar to the measured FRF level between 20 and 500 Hz where there is little modal response in the ice:

E=100.351Vb,
(7)
D=EH312(1v2),
(8)
x¨Finf=18DρH.
(9)

By comparison, the drive point FRF between the hammer and the hydrophone (Fig. 10) indicates that the hydrophone response is not affected by the modal properties of the ice.

The coherence for both the geophone and hydrophone are very close to one for the frequency ranges of 20–1000 Hz. This indicates that for this frequency range the input signal is linearly related to the output signal. Below 10 Hz, there is little response from the ice for the given input signal, causing coherence to be low. Above 1 kHz, the coherence also begins to drop off because the amount of energy input to the system (Fig. 9) is decreasing. Low coherence could also be caused by non-linear ice stiffness and damping properties at these frequencies and variation in excitation amplitudes.

During all experiments, the wind speed varied between 3.9 and 22.8 m/s. The average wind speed was 15.0 m/s (34 mph). This caused significant background noise at the microphone (despite using an environmental windscreen) that was not easily overcome by most of the sources (excluding the cannon). The in-air acoustic levels produced by the hammer hitting the ice was not loud enough to produce a coherent response at the microphone. Therefore, the drive point FRF between the hammer and the microphone are not reported.

The input autopower spectra for the cannon source (Fig. 9) was calculated by normalizing the microphone response at the source to 1 m distance. This was done assuming hemispherical spreading. There is input energy from the cannon in the frequency range of 1 Hz–2 kHz.

The cannon FRFs were normalized to the cannon sound power. The cannon sound power (W) was computed with Eq. (10) (Ref. 32) assuming hemispherical spreading. The air density (ρ0=1.324kg/m3) and speed of sound (c=327m/s) were approximated based on the average air temperature, −6.45 °C, and standard pressure, 101.3 kPa. The autopower spectra of the receiver was then divided by the sound power of the source to compute the FRF:

W=p2ρ0c2πr2.
(10)

In the drive point FRF between the cannon and the geophone in Fig. 11(a), two dominant peaks are seen: one at 29 Hz and one at 800 Hz. The 800 Hz peak corresponds with the through-thickness mode previously identified in the hammer drive point mobility. In this instance, the through-thickness mode is excited by the cannon pressure wave.

FIG. 11.

(a) Drive point FRFs and (b) COH between the cannon source and the geophone (left-hand scale) or hydrophone (right-hand scale) at the source location.

FIG. 11.

(a) Drive point FRFs and (b) COH between the cannon source and the geophone (left-hand scale) or hydrophone (right-hand scale) at the source location.

Close modal

The 29 Hz mode is due to an air-coupled flexural wave in the ice layer. Since air-coupled flexural waves are non-dispersive,3,11 it is expected that the majority of its energy would appear at a single frequency. This is supported by Fig. 11(a). Press et al.3,11 describe air coupled flexural waves in detail. The dimensionless parameter γ relates the ice thickness (H) to the speed of sound in air and to the air-coupled wave frequency, f:

γ=Hλ=Hfc.
(11)

It has been shown11 that γ can also be expressed as a function of the compressional wave velocity in ice. Since the compressional wave velocity in the ice was previously determined, a γ value of approximately 0.092 from Fig. 6 of Press et al.11 can also be determined. As previously mentioned, the sound speed in air (c) was 331 m/s during the measurements and the ice thickness (H) was 1.05 m. By rearranging Eq. (11), the air-coupled flexural wave frequency is computed to be 29 Hz. This indicates that the observed 29 Hz peak is an air-coupled flexural wave in the ice.

As shown by Press et al.3,11 the air-coupled flexural wave can be observed in the time domain signals of the microphones and geophones in response to a cannon blast (Fig. 12). Due to a higher group velocity in ice, the flexural wave in ice arrives before the pressure wave in air for an air-coupled flexural wave. Upon arrival of the in-air wavefront (i.e., when the speed of sound in air matches the phase velocity of the flexural wave), the flexural wave amplitude is immediately reduced and/or terminated.3,11 This termination of amplitude is seen in the geophone data in Fig. 12(c).

FIG. 12.

(A) Propane cannon blast measured at the source location microphone. (B) Microphone measurements at 50 and 100 m receiver locations. (C) Geophone measurements at 50 and 100 m locations. The flexural wave amplitude in the ice (C) is significantly reduced upon arrival of the in-air wavefront (B) indicating the detection of an air-coupled flexural wave at 29 Hz.

FIG. 12.

(A) Propane cannon blast measured at the source location microphone. (B) Microphone measurements at 50 and 100 m receiver locations. (C) Geophone measurements at 50 and 100 m locations. The flexural wave amplitude in the ice (C) is significantly reduced upon arrival of the in-air wavefront (B) indicating the detection of an air-coupled flexural wave at 29 Hz.

Close modal

Analysis of the hydrophone FRF in Fig. 11 shows the air–ice–water path is behaving as a low-pass filter at the drivepoint location. This comes as no surprise when comparing to the previous evaluation of Figs. 5 and 7. The modal properties of the ice do not seem to have an effect on the hydrophone response. The coherence in Fig. 11 show that between 20 and 300 Hz and at specific frequencies of interest (29 and 800 Hz) the system response and excitation are linearly related. Low coherence in frequency bands less than 20 Hz and greater than 300 Hz are likely due to low input signal amplitude from the cannon or non-linear stiffness and damping ice properties.

1. Tonal underwater transmission loss

To quantify the underwater transmission loss (TLUW) for the underwater tones, the mean-squared pressure of each tone was determined at the source hydrophone, psUW2¯, and receiver hydrophone, prUW2¯, locations. For each tonal frequency, the source and receiver hydrophone data were time domain filtered with bandpass cutoffs at plus/minus 5% of the center frequency. The mean-squared pressure at the source and receiver was then determined in the filtered band. The ratio of receiver mean-squared pressure to source mean-squared pressure was then calculated for each experiment in every frequency band [Eq. (12)]. Figure 13 shows TLUW as a function of distance:

TLUW(f)=prUW2¯(f)psUW2¯(f).
(12)
FIG. 13.

(Color online) Measured underwater acoustic transmission loss data shown with theoretical cylindrical and spherical spreading curves for reference.

FIG. 13.

(Color online) Measured underwater acoustic transmission loss data shown with theoretical cylindrical and spherical spreading curves for reference.

Close modal

2. In-air transmission loss

To quantify the in-air transmission loss (TLAA), the ratio of autopower spectra between the source microphone and receiver microphones were computed for the cannon experiments (Fig. 14). The source microphone autopower spectra was normalized to 1 m distance from the source. The ratio of autopower spectra between the receiver microphone and source microphone were then filtered into octave bands to determine the mean-squared pressure ratio in each respective band. The ratio of received mean-squared pressure, prA2¯, to source mean-squared pressure, psA2¯, at 1 m in each frequency band was then converted to dB as shown in Eq. (13):

TLAA(f)=10log10prA2¯(f)psA2¯(f).
(13)
FIG. 14.

(Color online) Measured in air transmission loss data and theoretical spherical spreading curve shown for reference.

FIG. 14.

(Color online) Measured in air transmission loss data and theoretical spherical spreading curve shown for reference.

Close modal

3. Air–ice–water transmission loss

The transmission loss between the cannon source and the down-range hydrophones was computed using an autopower spectra ratio. The source microphone autopower spectra was normalized to 1 m. The ratio between the hydrophone sound pressure at the receiver location and the microphone sound pressure 1 m from the cannon was then filtered into octave bands to determine the transmission loss through the air, ice, and water (TLAIW) shown in Fig. 15. It should be noted that the difference in reference pressures between air and water was not accounted for. Only a ratio of mean-squared pressure at the receiver hydrophone, prUW2¯, to mean-squared pressure of the source microphone, psA2¯, was computed. The TL in each frequency band was then converted to dB as shown in Eq. (14):

TLAIW(f)=10log10prUW2¯(f)psA2¯(f).
(14)
FIG. 15.

(Color online) Measured transmission loss data through the combined air-ice-water path.

FIG. 15.

(Color online) Measured transmission loss data through the combined air-ice-water path.

Close modal

The FRFs in Figs. 10 and 11 are useful for determining the various acoustic path contributions between the air, ice, and the water. The through-thickness resonance in the ice at 800 Hz and the increase in attenuation at the same frequency are suspected to be related. This relationship should be proven with further investigation on the effect of various ice thicknesses and bottom reflection loss on the additional attenuation.

The majority of the underwater TL data (Fig. 13) falls between the theoretical cylindrical and spherical spreading curves. This is similar to the transmission loss results determined by Pecknold et al. for open water in Barrow Strait.43 Granted, Pecknold's study was conducted over longer ranges, greater depths, and lower frequency than the data presented in this paper.

The measured in-air transmission loss is less than theoretical spherical spreading (Fig. 14) which indicates a downward refracting atmosphere over the course of this test. The propagation conditions (temperature and wind velocity profiles, humidity, and atmospheric turbulence) were not recorded with enough resolution to make any conclusion on the relative contributions of different path effects.

The offset of the TLAIW data (Fig. 15) represents 11.3–24.8 dB of transmission loss through the air and ice at the source location. Upon coupling into the water, the TLAIW data appears to follow the trend of cylindrical spreading.

Due to the variation on the transmission loss data, there are loss mechanisms which are not accounted for in this data set. Underwater absorption, additional attenuation, and acoustic mode coupling are all factors which should be addressed in future studies.

The underwater absorption coefficient was not directly measured in Barrow, but can be estimated from Eq. (15) as shown by Urick.44 The underwater absorption coefficient was computed to be 1.8916e-5 dB/m from Eq. (15) where ρo is the nominal density of sea water 1.029 g/cm3, c is the measured underwater sound speed 1.441e5 cm/s, and f is the highest frequency of interest 6400 Hz. At the longest range of interest, 1035 m, the underwater absorption is less than 0.02 dB and therefore underwater absorption can be neglected for short range TL problems,

α=20log10(e)16π23ρoc3(0.0311)f2100cm1m.
(15)

Additional attenuation accounts for loss mechanisms which are not related to geometric spreading. In general, additional attenuation increases as propagation distance increases due to absorption in the sea bed and scattering from the complex under-ice surface. In this study, under-ice surveys of the seabed and ice layer were not carried out. Therefore, it was not possible to characterize the reflection losses of the bottom and undersurface of the ice as a function of frequency and grazing angle. In subsequent studies, it is recommended that all additional attenuation mechanisms be individually quantified in the under-ice environment to better understand loss mechanisms. Also, the effect of underwater acoustic modes on the transmission loss in the shore-fast, shallow water realm has not been considered. It is of interest to study acoustic modes in this unique environment and compare to the measured data presented here.

To build upon the results presented above, there are several additional areas where further investigation is necessary on first-year, shore-fast, thin ice sheets.

The transmission loss data are somewhat sparse in spatial resolution because weather and ice conditions on-site limited the number of receiver locations that were possible to measure. Due to the harsh environmental conditions encountered in the shore-fast Arctic region (high winds, large ice ridges, etc.), the quantity of experiments originally anticipated while in Barrow, AK were not possible to be conducted. The presence of ice ridges provided special challenges for deployment of hardware. The measurement methods for Arctic transmission loss, and similar Arctic measurements over long ranges, in the shore-fast region require significant improvement to provide more spatial resolution and a greater number of spectral averages.

At the test locations, holes were drilled in the ice to deploy the hydrophones. Ideally, none of the acoustic energy from the cannon would pass through the hole in the ice to the hydrophone, however, this was not likely the case because the sensors were not frozen in the holes. It is unclear if the ice borehole acts as an acoustic short circuit for the sound to travel between the air and the water. Further investigation is required to determine how much of the acoustic energy is passing through the hole in the ice rather than directly through the ice sheet since this will have some effect on the hydrophone FRF measurement in Fig. 11.

Finally, due to the changing climate, anthropogenic activity is expected to increase in the Arctic realm where this study has been conducted. Acoustic methods should be developed to detect, identify, and track anthropogenic sources in this new environment.

Acoustic data were collected 2 km offshore of Barrow, Alaska during April 2016. Experiments were conducted on first-year, shore-fast ice approximately 1.05 m thick and in shallow water between 8 and 12 m deep. At the test sites chosen, the surrounding ice was rough with many ice ridges 1–5 m in height. These conditions are typical of annually formed shore-fast ice and offshore first-year ice in the Arctic. Methods were developed to characterize the Arctic sound propagation in these shallow, thin, ice-covered waters including FRF and transmission loss. A propane cannon, instrumented force hammer, and underwater speaker were used as acoustic sources and microphones, geophones, and hydrophones were used as receivers.

FRF were computed between the various sources and receivers to further define the multi-modal response of the Arctic environment in the frequency domain. An air-coupled flexural wave at 29 Hz was identified in the FRF between the geophone and the cannon source. A through-thickness compressional mode was identified at 800 Hz in the geophone response to the hammer source. The 800 Hz mode was used to compute the compressional speed of sound in the ice which was 3360 m/s.

The transmission loss was determined through the air, the ice, and the water paths and combined multi-modal paths. Underwater, the transmission loss varied between the theoretical limits of cylindrical and spherical acoustic spreading (−3 to −6 dB per doubling of distance, respectively). The variation in the data is suspected to be due to the complex ice-ridged environment causing reflections and scattering and bottom attenuation. In the air, the transmission loss was measured to be less than theoretical spherical spreading indicating the possibility of a downward refracting atmosphere. The computation of transmission loss through the combined air, ice, and water path in response to the cannon source led to the observation of 11.3–24.8 dB of TL through the air and 1.05 m of ice.

This work was funded by DARPA under contract number W15QKN-16-C-0018. The DARPA Program Manager for this project was Dr. John Kamp, Strategic Technology Office (STO). Upon his retirement from DARPA during the project, Dr. Kamp was replaced by Dr. Lisa Zurk (STO). Thanks to Dr. Joseph Burns, Christopher Roussi, Brian Wilson, and Benjamin Hart at Michigan Technological Research Institute for help with facilitating data collection in Barrow. Thanks to Dr. Roger Turpening at Michigan Technological University for his advice on seismo-acoustics, especially relating to air-coupled flexural waves.

1.
M.
Ewing
and
A. P.
Crary
, “
Propagation of elastic waves in ice. Part II
,”
J. Appl. Phys.
5
,
181
184
(
1934
).
2.
M.
Ewing
,
A. P.
Crary
, and
A. M.
Thorne
, Jr.
, “
Propagation of elastic waves in ice. Part I
,”
J. Appl. Phys.
5
,
165
168
(
1934
).
3.
F.
Press
and
M.
Ewing
, “
Theory of air-coupled flexural waves
,”
J. Appl. Phys.
22
,
892
899
(
1951
).
4.
M.
Ewing
,
W. S.
Jardetzky
, and
F.
Press
,
Elastic Waves in Layered Media
(
McGraw-Hill
,
New York
,
1957
).
5.
A.
Langley
, “
The sound fields of an infinite, fluid-loaded plate excited by a point force
,”
J. Acoust. Soc. Am.
83
,
1360
1365
(
1988
).
6.
T. C.
Yang
and
T. W.
Yates
, “
Flexural waves in a floating ice sheet: Modeling and comparison with data
,”
J. Acoust. Soc. Am.
97
,
971
(
1995
).
7.
W. S.
Jardetzky
and
F.
Press
, “
Rayleigh wave coupling to atmospheric compression waves
,”
Seismol. Soc. Am.
42
(
2
),
135
144
(
1952
).
8.
R. E.
Sherrif
, “
Introduction to seismic methods
,” in
Geophysical Methods
(
Prentice Hall
,
Englewood Cliffs, NJ
,
1989
), pp.
209
227
.
9.
W. I.
Futterman
, “
Dispersive body waves
,”
J. Geophys. Res.
67
(
13
),
5279
5291
, (
1962
).
10.
F. E.
Francios
and
T.
Wen
, “
Propagation of sound generated on the ice surface into water
,” in
Oceans
, Seattle,
1989
.
11.
F.
Press
,
A. P.
Crary
,
J.
Oliver
, and
S.
Katz
, “
Air-coupled flexural waves in floating ice
,”
Am. Geophys. Union
32
(
2
),
166
172
(
1951
).
12.
F.
Press
and
M.
Ewing
, “
Propagation of elastic waves in a floating ice sheet
,”
Am. Geophys. Union
32
(
5
),
673
678
(
1951
).
13.
A. R.
Milne
, “
Shallow water under-ice acoustics in Barrow Strait
,”
J. Acoust. Soc. Am.
32
,
1007
1016
(
1960
).
14.
K.
Hunkins
and
K.
Henry
, “
Shallow-water propagation in the Arctic Ocean
,”
J. Acoust. Soc. Am.
35
,
542
551
(
1963
).
15.
A. R.
Milne
, “
A 90 km sound transmission test in the Arctic
,”
J. Acoust. Soc. Am.
35
,
1459
1461
(
1963
).
16.
T. C.
Yang
and
G. R.
Giellis
, “
Experimental characterization of elastic waves in a floating ice sheet
,”
J. Acoust. Soc. Am.
96
,
2993
3009
(
1994
).
17.
B. E.
Miller
and
H.
Schmidt
, “
Observation and inversion of seismo-acoustic waves in a complex Arctic ice environment
,”
J. Acoust. Soc. Am.
89
,
1668
1685
(
1991
).
18.
R. W.
Knapp
, “
Observations of the air-coupled wave as a function of depth
,”
Geophysics
51
(
9
),
1853
1857
(
1986
).
19.
J.
Maslanik
,
J.
Stroeve
,
C.
Fowler
, and
W.
Emery
, “
Distribution and trends in Arctic sea ice age through Spring 2011
,”
Geophys. Res. Lett.
38
,
L13502
, (
2011
).
20.
J. C.
Stroeve
,
T.
Markus
,
L.
Boisvert
,
J.
Miller
, and
A.
Barrett
, “
Changes in Arctic melt season and implications for sea ice loss
,”
Geophys. Res. Lett.
41
,
1216
1225
, (
2014
).
21.
J.
Rodrigues
, “
The rapid decline of the sea ice in the Russian Arctic
,”
Cold Reg. Sci. Technol.
54
,
124
142
(
2008
).
22.
R.
Lei
,
H.
Xie
,
J.
Wang
,
M.
Lepparanta
,
I.
Jonsdottir
, and
Z.
Zhang
, “
Changes in sea ice conditions along the Arctic Northeast Passage from 1979–2012
,”
Cold Reg. Sci. Technol.
119
,
132
144
(
2015
).
23.
G. W.
Timco
and
W. F.
Weeks
, “
A review of the engineering properties of sea ice
,”
Cold Reg. Sci. Technol.
60
,
107
129
(
2010
).
24.
S.
Somanathan
,
P. C.
Flynn
, and
J.
Szymanski
, “
The Northwest Passage: A simulation
,” in
Winter Simulation Conference
,
2006
.
25.
L. C.
Smith
and
S. R.
Stephenson
, “
New Trans-Arctic shipping routes navigable by midcentury
,”
Proc. Natl. Acad. Sci. U.S.A.
110
(
13
),
1191
1195
(
2013
).
26.
S. R.
Stephenson
,
L. W.
Brigham
, and
L. C.
Smith
, “
Marine accessibility along Russia's Northern Sea route
,”
Polar Geogr.
37
(
2
),
111
133
(
2014
).
27.
G. J.
Heard
,
M.
McDonald
,
N. R.
Chapman
, and
L.
Jaschke
, “
Underwater lightbulb implosions: A useful acoustic source
,” in
IEEE/Oceans
,
1997
.
28.
S. E.
Dosso
,
G. J.
Heard
, and
M.
Vinnins
, “
Seismo-acoustic propagation in an ice-covered arctic ocean environment
,” in
MTS/IEEE Oceans
Honolulu,
2001
.
29.
D. L.
Brown
and
R. J.
Allemang
, “
Review of spatial domain modal parameter estimation procedures and testing methods
,” in
IMAC
2009
.
30.
W.
Heylen
,
S.
Lammens
, and
P.
Sas
,
Modal Analysis Theory and Testing
(
K.U. Leuven
,
2013
).
31.
C. V.
Karsen
, “
Averaging for improved frequency response functions
,”
S.V. Sound and Vibration
18
(8),
18
24
(
1984
).
32.
H. W.
Lord
,
W. S.
Gatley
, and
H. A.
Evensen
,
Noise Control for Engineers
(
Krieger
,
Malabar, CA
,
1980
).
33.
CastAway User Manual—CTD Principles of Operation
,”
2010
, p.
74
.
34.
N. P.
Fofonoff
and
R. C.
Millard
, “
Algorithms for computation of fundamental properties of seawater
,” Unesco Technical Papers in Marine Science, no. 44,
1983
.
35.
J. S.
Bendat
and
A. G.
Piersol
,
Random Data: Analysis and Measurement Procedures
, 3rd ed. (
Wiley
,
New York
,
2000
).
36.
L. E.
Kinsler
,
A. R.
Frey
,
A. B.
Coppens
, and
J. V.
Sanders
,
Fundamentals of Acoustics
(
Wiley
,
New York
,
1999
).
37.
G. W.
Timco
and
R. M. W.
Frederking
, “
A review of sea ice density
,”
Cold Reg. Sci. Technol.
24
,
1
6
(
1996
).
38.
N. K.
Sinha
, “
Effective Poisson's ratio of isotropic ice
,” in
International Offshore Mechanics and Arctic Engineering Symposium
, Houston, TX,
1987
, Vol. IV, pp.
189
195
.
39.
J. R.
Murat
and
L. M.
Lainey
, “
Some experimental observations on the Poisson's ratio of sea ice
,”
Cold Reg. Sci. Technol.
6
,
105
113
(
1982
).
40.
A.
Traetteberg
,
L. W.
Gold
, and
R.
Frederking
, “
The Strain rate and temperature dependence of Young's modulus of ice
,” in
IAHR International Symposium on ICE Problems
, Hanover, New Hampshire,
1975
, Vol. 3.
41.
M. P.
Langleben
, “
Young's modulus for sea ice
,”
Can. J. Phys.
40
(
1
),
1
8
(
1962
).
42.
S. A.
Hambric
,
S. H.
Sung
, and
D. J.
Nefske
,
Engineering Vibroacoustic Analysis: Methods and Applications
, 1st ed. (
Wiley
,
New York
,
2016
).
43.
S. P.
Pecknold
,
N.
Pelavas
, and
G. J.
Heard
, “
Measurements and modeling of transmission loss variability in Barrow Strait
,” in
ICA
, Montreal (
Acoustical Society of America
,
New York
,
2013
), Vol. 19.
44.
R. J.
Urick
, “
Propagation of sound in the sea: Transmission loss, I and II
,” in
Principles of Underwater Sound
, 3rd ed. (
Peninsula
,
Los Altos, CA
,
1996
).