Proceedings of the Institute of Acoustics

 

Geometry of acoustic communication links in the Arctic

 

G. Hope, Nansen Environmental and Remote Sensing Center, Bergen, Norway

H. Hobæk, Nansen Environmental and Remote Sensing Center, Bergen, Norway

H. Sagen, Nansen Environmental and Remote Sensing Center, Bergen, Norway

 

 

1 INTRODUCTION

 

The Arctic is characterized by strong vertical stratification of the water column. A fresh water layer traps the acoustic energy against the sea-ice and the steep sound speed gradient below creating a surface channel. The stratification varies throughout the Arctic, and the amount of energy trapped in the surface channel varies with it.

 

The amount of energy trapped in the surface duct is dependent on the source position, in these proceedings two locations in the Arctic are surveyed using an acoustic model: the Fram Strait and the Beaufort Sea.

 

An acoustic model with a rough sea-ice layer will be used in the OASES package¹ to calculate transmission loss and signal structure for a frequency of 900 Hz. Sea-ice elastic parameters are derived from Laible et. al. (1996)^2,3 and agree quite well with previous and historical measurements of the sound speed for sea-ice. Table 1 summarizes the elastic parameters used for the sea-ice layer for the acoustic model.

 

 

Table 1: ​ Average sea-ice elastic values based on Rajan (1993)³, ​ as estimated by Laible, et. al. (1993)².

 

Figure 1 shows the reflection coefficient calculated for the water-ice interface for a smooth ice layer with the parameters described in Table 1. It shows that there is generally total reflection for incidence angles above 60^o. Waves traveling any distance are usually above this angle, meaning that the roughness is the most important parameter for the interaction with the sea-ice. The plot can be scaled vertically with frequency and ice thickness, the right hand side of the plot (above 60^o) will nonetheless be close to total reflection.

 

 

Figure 1: Reflection coefficient for 2 m homogeneous, smooth, ice. For angles of incidence greater than 60^o there is generally total reflection. Most of the waves traveling any distance have incidence angles greater than 60^o and the interaction with the sea-ice is therefore mainly defined by the roughness.

 

The roughness of the sea-ice is parameterized into RMS thickness and characteristic correlation length. These are used for a statistical model of the internal ice thickness distribution. The OASES model is capable of modeling RMS roughness of up to about 0.6 m with frequencies of 900 Hz. Unfortunately, the limited measurements available of RMS thickness indicate that the values of about 1.5 m are more realistic⁴. This will lead to an under estimation of the scattering from the sea-ice. The correlation length has been found to be of less importance for values greater than 5 m. A characteristic correlation length of 20 m is used in this model. For both locations a sea-ice thickness of 2 m is used, which corresponds to the mean thickness in the Fram Strait in the summer⁵.

 

For the locations: Fram Strait and Beaufort Sea, the transmission loss is calculated using OASES with a rough sea-ice layer on top of the respective measured sound speed profiles. Different transmitter-receiver geometries are simulated for smooth to increasingly rough sea-ice to determine the effect of a rough sea-ice layer for different geometries. The sound speed profiles are presented below in Section 1.1 while the results from the numerical modeling is presented in Section 2. Finally, the results are summarized and implications for communication and navigation systems are discussed in Section 3.

 

1.1 Sound speed profiles

 

Figure 2 shows the sound speed profiles for the Fram Strait (left) and the Beaufort Sea (right). The profile from the Fram Strait is a mean of the calculated sound speeds from a section of XBTs along 82^o N. The Beaufort Sea profile was measured from an ice tethered profiler. The Fram Strait profile was discretized into 14 piecewise linear segments, while the Beaufort Sea profile was discretized into 12 segments. A generic reflecting sea-floor is used in both cases, based on Jokat et. al. (1995)⁶.

 

 

Figure 2: Sound speed profiles for the Fram Strait (left) along 82N, and the Beaufort Sea (right).

 

 

2 NUMERICAL RESULTS

 

The different sound channels permit sound waves to travel long distances in the Arctic, some however, interact more with the sea ice and are more sensitive to its roughness.

 

 

Figure 3: Transmission loss for a 900 Hz signal in the Beaufort Sea (top) and the Fram Strait (bottom) with 2 m smooth sea ice, source depth: 50 m.

 

Figure 3 shows the transmission loss for a source placed at 50 m depth with smooth ice (almost total reflection). For a source this shallow, placed within the surface channel, the propagation pattern in the upper 150 - 250 m are fairly similar for both locations, although the surface channel is somewhat deeper in the Beaufort Sea. For both profiles convergence and focus zones are visible at approximately each 35 km resulting from the deep refracted rays. These rays are also sensitive to the sea-ice roughness since they are reflected at the surface.

 

 

Figure 4: ​ Beaufort Sea (top) and Fram Strait (bottom): roughness increased to 0.6 m RMS, otherwise the same situation as in Figure 3. Source depth: 50 m.

 

Figure 4 shows the transmission loss as for Figure 3, but with a roughness of 0.6 m RMS added. It is apparent that the waves travelling in the surface channel and the deeper refracted waves are dampened significantly. This is at the limit of the roughness level that is possible to model with the statistical method applied in the OASES model, and is an underestimation of the damping that can be expected.

 

By increasing the depth of the source to 100 m in the Beaufort Sea a more persistent channel emerges. Figure 5 shows how a narrow channel forms ​ below the first sound speed maximum. As the source is moved further down it fails to fill the narrow channel with energy and a pattern similar to that in the Fram Strait forms. This consists of a surface channel bounded by the sound speed gradient located at roughly 250 m. The energy in this channel is dampened by rough sea-ice in the same way as in the Fram Strait in Figure 4.

 

 

Figure 5: ​ The Beaufort Sea (top) and Fram Strait (bottom) with a source depth of 100 m and a roughness of 0.6 m RMS.

 

In the Fram Strait a narrow channel unaffected by the sea-ice roughness does not form until the source is moved well below the steep sound speed gradient to roughly 450 m depth (Figure 6). This channel is less sharply defined than the channel in the Beaufort Sea. At this source depth the Beaufort Sea no longer forms long range propagating channels that do not interact with the sea-ice.

 

 

Figure 6: ​ Beaufort Sea (top) and Fram Strait (bottom) transmission loss for a source located at 450 m with sea-ice roughness of 0.6 m RMS.

 

In effect the arrivals that would be expected to travel in the surface channels are greatly influenced by the sea-ice roughness, and modeling not taking the roughness into account would overestimate their strength. By moving the source further down below the surface channel, narrower, and perhaps less persistent, sound channels can be reached that are less sensitive to the sea-ice roughness and may be more suitable for long range propagation in the Arctic. These are strongly dependent on location since the sound speed profile differs in the upper 500 m for the two locations.

 

 

3 CONCLUSIONS

 

Since reflection at these frequencies is almost total for relevant incidence angles of incidence, the sea-ice roughness is more important for the acoustic transmission loss than the thickness and the elastic parameters of the ice.

 

The sea-ice thickness is often thought to increase transmission loss. However, this happens indirectly since older, thicker, multi-year ice tends have undergone more deformation, and is therefore rougher.

 

Placing a source in a well defined propagation channel that interacts with the surface may not provide the intuitive increased propagation range when it is covered by rough sea-ice. Rather, deeper propagation channels that are bounded by the sound speed gradient above may provide a better option. These channels seem to be quite narrow in depth, and may be sensitive to small perturbations in the sound speed profile. The Beaufort Sea provides the most clearly defined secondary sound speed channel at roughly 250 m, however it is created by very detailed stratifications in the upper water layers and may be less robust than wider channel present at roughly 450 m depth in the Fram Strait.

 

 

4 ACKNOWLEDGEMENTS

 

The Beaufort Sea sound speed profile has kindly been provided from the CANAPE project by P. Worcester and M. Dzieciuch at the Scripps Institution of Oceanography. This work was funded by the Office of Naval Research (Global) project Under-ice Acoustic Propagation NERSC-WHOI, and supported by the Research Council of Norway through the project: UNDER-ICE: Arctic Ocean under melting ice. Additional support has been provided from Trond Mohn via Frank Mohn ASA.

 

 

5 REFERENCES

 

1. Schmidt, H., & Jensen, F. B. (1985). A full wave solution for propagation in multilayered viscoelastic media with application to Gaussian beam reflection at fluid-solid interfaces. The Journal of the Acoustical Society of America, 77(3), 813. http://doi.org/10.1121/1.392050

2. Laible, H., & Rajan, S. D. (1996). Temporal evolution of under ice reflectivity. The Journal of the Acoustical Society of America, 99(2), 851. http://doi.org/10.1121/1.414661

3. Rajan, D., Frisk, G. V., Doutt, J. A., & Sellers, J. (1993). Determination of compressional wave and shear wave speed profiles in sea ice by crosshole tomography – Theory and experiment, 93 (February).

4. National Snow and Ice Data Center. (1998). Submarine Upward Looking Sonar Ice Draft Profile Data and Statistics, Version 1. Boulder, Colorado, USA: NSIDC: National Snow and Ice Data Center. http://doi.org/http://dx.doi.org/10.7265/N54Q7RWK

5. Hansen, E., Gerland, S., Granskog, M. A., Pavlova, O., Renner, A. H. H., Haapala, J., & Tschudi, M. (2013). Thinning of Arctic sea ice observed in Fram Strait: 1990-2011. Journal of Geophysical Research: Oceans, 118(10), 5202–5221. http://doi.org/10.1002/jgrc.20393

6. Jokat, W., Weigelt, E., Kristoffersen, Y., Rasmussen, T., & Schöne, T. (1995). New geophysical results from the south-western Eurasian Basin (Morris Jesup Rise, Gakkel Ridge, Yermak Plateau) and the Fram Strait. Geophysical Journal International, 601–610.