Title Page Geophysical Letters-- Recent Measurements of Air-Coupled Flexural Waves in a Thin Layer of Sea Ice

Title Air-Coupled Flexural Wave Measurements if longer than 38 characters, provide a 2nd shortened title of 38 characters or less

Author Roger Turpeningco-Authors Carol Asiala

Author Affiliations, emails Michigan Technological University

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Date of submission of revised paper

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ABSTRACTFlexural waves were first observed in 1934 by Ewing and Crary on thin sheets of lake ice. The waves were generated by explosive sources on the ice or in the water and were recorded with a conventional refraction spread of geophones plus a microphone. The waves were dispersive in nature and theoretical work at the time supported this observation. However, when the source was placed in the air a simple monochromatic flexural waveform was observed that terminated abruptly with the arrival of the air wave. Seventeen years later, theoretical work, and additional lake ice data, confirmed that this was an air-coupled flexural wave. The theoretical work also provided a simple expression for the thickness of the ice given the frequency of the non-dispersive wave and the velocity of the longitudinal wave in the ice (not to be confused with the compressional wave velocity). The acoustic and seismic traces that accompanied those papers were not very clear. Recently (2016), during operational tests of a new, stand-

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alone, instrumentation package on thin sea ice near Barrow, Alaska we obtained excellent air-coupled, flexural wave data. The instrumentation package contained geophones, hydrophones, and a microphone and the tests used various acoustic, seismic, and underwater sources. Ground truth measurements of ice thickness (approx. 1 m) were provided by holes at every source and receiver position. Using longitudinal wave velocities found in the literature we obtained surprisingly good estimates of the ice thickness. This note does not address the interesting question of how variations in ice thicknesses affect the propagation of air-coupled flexural waves.

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INTRODUCTIONThe measurement of ice thickness has always been of interest (Holt, et. al., 2009) and in the past measurements could be made using radar if the ice was thick. Today, however, it is necessary to obtain estimates of the thickness of thin sea ice, therefore, other techniques are needed. Measurements of flexural waves in ice offer an alternative.

Flexural wave observations and supporting theory were first obtained in 1934 when Ewing and Crary (1934) conducted seismic experiments on thin sheets of lake ice using conventional refraction spreads of geophones with explosive sources in the water and on the ice In addition to seismic waves in the ice they also observed flexural waves. In the same paper they supplied the theory governing the propagation of those flexural waves along with a simple expression for the thickness of the ice.

Flexural waves, in contrast to seismic waves, use gravity instead of elasticity as the restoring force after a disturbance. Thus, flexural waves are similar to gravity waves in water. Ewing and Crary also showed that the flexural waves have a dispersive wave train with a group velocity that increases with frequency.

Later Press, Crary, Oliver, and Katz conducted additional seismic experiments on lake ice (Press et al, 1951) but here in addition to sources on the ice and in the water they

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added shots in the air. These shots generated a non-dispersive wave train with a group velocity greater than the speed of sound in air which terminated abruptly with the air-wave arrival. Similar to air-coupled Rayleigh waves these waves were called air-coupled flexural waves. They developed the theory for the propagation of air-coupled flexural waves (Press and Ewing, 1951) which contained a simple expression for the frequency of the non-dispersive wave train as a function of the thickness of the ice and the longitudinal wave velocity (not to be confused with the compressional wave velocity), The longitudinal wave is the long wavelength compressional wave arrival seen at large distances in very thin ice ( i.e. its wavelength is much greater than the thickness of the ice.).

This work gave us the hint that one might be able to estimate the thickness of a region of thin ice using only an acoustic source(s) in the air and the new, wireless, stand-alone instrumentation package on the ice.

In April 2016 three, stand-alone, instrumentation packages of acoustic and seismic sensors were deployed on the sea ice near Barrow, Alaska. A microphone, a 3-C geophone and four hydrophones were in each package. Simple seismic and acoustic sources were deployed amongst these instruments for operational tests. One of the acoustic sources was a propane “gun” that produced a low power, low frequency “pop” in the atmosphere. (This “gun” in conventional service is used to scare away pigeons.) Despite its humble origin the device produced usable air-coupled flexural waves out to a few hundred meters even in very high, wind-noise conditions.

Five sets (vertical geophone and microphone) of data were obtained by recording the propane gun at various ranges (50 m to 850 m) from the three instrument packages. The air-coupled flexural wave was easily identified and its spectrum obtained. Three shots from the propane “gun” were stacked. Estimates of the velocity of the longitudinal wave were obtained from the literature. These data yielded ice thicknesses ranging from 0.7 m to 1.8 m which compare favorably with the data from holes drilled in the ice at each station.

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(4) describe the method of investigation; and (5) describe the principal results of the investigation.

DATA ACQUISITION and PROCESSING In April 2015, we deployed three wireless sensor (3-C geophone, microphone, and hydrophones) packages on the sea ice near Barrow, Alaska. (Figures 1-2). During the shakedown operations we recorded various small sources at three source points. The three instrumentation packages were not all recording simultaneously. Figure 2 shows

Figure 1 Location of stand-alone instrumentation packages on the sea ice near Barrow, Alaska.

Figure 2 Location of stand-alone, receiver, instrumentation packages (Sites 1, 2, and 3) and source locations (Sites 4, 5, and 6).

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the source/receiver pairs that produced data for this short paper. Holes were drilled through the ice at all sites for the deployment of hydrophones and underwater acoustic sources. Thus the thickness of the ice is known at six points (approx. 1 m). The depth of the water (approx. 11 m) is known from bathymetric charts . The topography of the bottom of the ice is not known and in areas such as seen in Figure 4 it might touch the bottom.

Instrumentation

The Source The acoustic source was a device (Figure 5) that fires a small charge of propane. . Propane is loaded into the 0.61 m long roughly horizontal tube and ignited. The result is a pure acoustic pulse, i.e. the source applies no traction to the snow surface. In conventional service it is used to scare away pigeons, therefore it has an automatic repetition rate, we chose 90 seconds as the repetition rate for these data.

Data ProcessingZero time for each shot was obtained from a microphone at each source location. The microphone traces at the receiver locations were then used in the initial search for the flexural waves. The propane “gun” was fired three times at each site and vertical geophone traces were stacked then filtered ( Hz to Hz). In like manner the microphone traces were also stacked and filtered.

Figure 3 Photograph of receiver Site 1 taken from source Site 4., distance between sources and receivers is 50.4 m. Note the flat ice in this area in contrast to ice ridges in the background.. All source

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and recording locations were in similar large flat areas of ice. Therefore, it is assumed that the topography of base of the ice is alsoflat (compared to the topography of the base of the ice in Figure 4.)

Figure 4 Photograph from Site 1 looking past the microphone at the ice ridges.

Figure 5 Propane “gun”.

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Figure 6 Air-coupled flexural waves on the vertical geophone trace displayed as a function of distance of propagation. The air wave is seen on the co-located microphone which in most cases is also seen in the seismic trace. The approximate zero time is given by the acoustic wavelet at the bottom of the plot.

Frank Press et. al (1951) collected seismic, acoustic data from explosive air shots on two freshwater lakes. They observed a non-dispersive wave that culminated with the arrival of the air-wave. They interpreted these waves to be air-coupled flexural waves. We used those two criteria here in our identification of the air-coupled flexural wave. Figure 6 displays four (4) excellent acoustic and seismic arrivals from 50 m out to 177 m that have those attributes.

The air-coupled flexural wave terminates with the arrival of the air-wave in different ways. In one case (Site 3 Site 6 source) the waveform is abruptly terminated and in other cases it appears that another wave begins at the air-wave arrival time (air-coupled seismic wave?). In this short note we focus on the air-coupled flexural wave. In Figure 7 the traces at the range of 853 m have been added to Figure 6 with a corresponding change in the time scale.

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Figure 7 Air-coupled flexural waves on the vertical geophone trace and the accompanying microphone trace from 50.4 m out to 853.2 m. Common amplitude scale for all seismic traces and a common amplitude scale for all acoustic traces except for the traces in the large red box.

The spectrum of flexural wave at each site is obtained after stacking. A window is applied to the stacked trace starting ……..and ending with arrival of the air-wave.

Figure 8 Spectra of the air-coupled flexural wave at site 1, source 50 m away at site 4. Note the simple peak at approximately 40 Hz.

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Figure 9 Spectra of air-coupled flexural wave at site 3 , source 105 m away at site 6. Note the simple spectra peak at approximately 30 Hz.

Figure 10 Spectra of the air-coupled flexural wave at site 1, source 164 m away at site 5. As the propagation distance increases the spectra becomes more complex. Here the peak is again approximately 40 Hz. but two other peaks (approx. 44 Hz and 35 Hz).

Figure 11 Spectra of the air-coupled flexural wave at site 2, source 177 m away at site 6.

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Figure 12 Spectra of air-coupled flexural wave at site 3, source 853 m away at site 5.

Theory

The theory for flexural waves in thin sheets of ice was first given by Ewing and Crary (1934) Then the theory governing the propagation of air-coupled flexural waves in ice was given by Press and Ewing (1951, op. cit.) and Press, Crary, Oliver, and Katz (1951, op. cit). Press and Ewing do restate the general surprise that air-coupling in any kind wave propagation contributes any energy. One would, of course, think that the density contrast between air and earth or water is so great that an air-coupling mechanism could not contribute a useful amount of energy. However, the fact that the coupling occurs when the phase velocity of the flexural wave (in this case) is equal to the speed of sound in air is the mechanism which makes the energy transfer significant. In other words the coupling is continuous all along the path of propagation. In fact this is how Lamb (1932) set up the theoretical problem. He used a series of infinitesimal impulses with each impulse generating a dispersive wave, then the constructive interference of those waves, in the direction of propagation, generated the “coupled wave”.

The Press et al (1951) expression for the phase velocity of flexural waves given here

started with Ewing and Crary (1934) work.

Their formulation involves several parameters one of which is a dimensionless parameter, gamma, the ratio of the thickness of the ice to the wavelength (gamma = H/lambda). The full expression for the phase velocity of the flexural wave is given in Press and Ewing (1951) and need not be repeated here. When the known parameters of water and air (and the gravity constant g) are inserted a simple equation for the phase velocity of a flexural

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wave is obtained. The elastic properties of the ice enter through the longitudinal wave velocity in ice, (not to be confused with the compressional wave velocity in ice). When the flexural wave phase velocity is chosen to be the speed of sound in air an expression for the frequency of that wave is obtained which depends only on the thickness of the ice, the longitudinal wave velocity of the ice, and the speed of sound in air :

fa = gammaaVa/H

Where: fa= frequency of air-coupled flexural waveGamma a = parameter derived from longitudinal velocity Vp

H = thickness of iceVa = speed of sound in air

We obtained gamma a from the longitudinal wave velocity using the Press and Ewing’s (1951) Vp vs. gamma a curve (Figure 13).

Figure 13 Parameter gamma a as a function of longitudinal wave velocity (from Press, et. al. 1951)

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RESULTS

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As mentioned above the unique features of an air-coupled flexural wave were used to find and extract five waveforms from our data set. The frequency of those waves was found to be 40 Hz. 30 Hz. and 18 Hz. Given these frequencies, the speed of sound in air (331 m/sec (1,086 ft./sec)) and a longitudinal wave velocity, (to obtain gamma a.) from the literature. Table 1 Ice Thickness Along Various Air-Coupled Flexural Wave Propagation Paths

Location Ice Thickness

Between Site 4 and Site 1 0.8 m

Between Site 5 and Site 1 0.8 m

Between Site 6 and Site 2 1.1 m

Between Site 6 and Site 3 1.1 m

Between Site 5 and Site 3 1.8 m

The measurements of longitudinal wave velocities found in the literature were measured on thin layers of ice on freshwater lakes thus they are not optimal for this study. They are given in the papers of Press and Ewing (1951); Press, et. al.(1951); Ewing and Crary (1934); and Ewing, Crary and Thorne (1934). The values ranged from 3,505 m/sec to 3,048 m/sec with the low velocities observed in the thickest layers of ice. (approx. 0.6 m).

Therefore we chose those lower values of longitudinal wave velocities in our choice of gamma a (0.099).

Figure 14 Thickness of the ice between the various source and receiver locations. Note that over the long distance (854 m) between site 5 and site 3 the view was blocked by ice ridges thus thicker ice probably did exist there. In fact only over the short distances did a single clear frequency peak exist in the air-coupled flexural wave spectra. .

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Note that the Vp vs. gamma a curve in Figure 13 is a very steep curve, i.e. a wide range of Vp yields a small range of gamma a values. Thus even though we must use longitudinal wave velocities selected from the literature the error in ice thickness that we are forced to accept is small.

Using the peaks in each of the spectra we find that the ice thicknesses vary from 0.8 m to 1.8 m as displayed in Table 1 and Figure 14.

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DISCUSSION

Figure 14 presents a coherent display of ice thickness values with the thinner values (0. 7 m to 0.8 m) around the eastern sites and slightly thicker ice (1.1 m) around the western sites. Note that because of steep slope of the Vp vs. gamma curve in Figure 13 any Vp selected from the entire range of longitudinal wave velocities in the literature (3,500 m/sec to 3050 m/sec) would produce only a few centimeters difference for the ice in this range of thickness (0.7 m to 1.1 m)

It is encouraging to see that the ice thickness (1.8 m) on the long path between site 5 and site 3 is greater than that seen over the short propagation paths. There was no clear line of sight between those two sites (i.e. modest ice ridges existed) therefore it is expected that the ice thickness was greater than 1 m in several places along that path. Now, for ice in this range of thickness (1.8 m) we see that we need to be more careful to narrow our selection of longitudinal wave velocities to those for the thickest layers of ice (0.34 m to 0.64 m) in the literature. If we do this then again our errors in thickness are again a few centimeters.

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This leads to an interesting question about future research, namely how are thickness variations expressed in the air-coupled flexural waveform? We see in multiple peaks some in some of the spectra. Does this mean that an additional path of propagation existed around an ice ridge? Moreover, how does wave propagation along a given path “average” variations in thickness along that path? Numerical modeling of the propagation of air-coupled flexural waves is one path of investigation that could answer these questions.

Longitudinal wave velocities must be investigated. How much variation is there between lake ice and sea ice? What is the relationship between ice thickness, and irregular interfaces (scattering) and measured velocities? What accuracy is necessary in the sea ice community? Are the differences in longitudinal wave velocities so great that one must measure longitudinal wave velocities every time air-coupled flexural wave technique is used? The discussion section should be separate from the conclusion section. If they are combined, the copy editor of your manuscript is instructed to ask you to separate them. This can result in delays in production. See below for a description of the conclusion section.Some papers may not require a discussion section. If this is the case with your paper, do not include a discussion section.

CONCLUSION

Modern measurements of air-coupled flexural waves on a thin sheet of sea ice have been made using new, stand-alone, wireless instrumentation packages. Data was obtained out to a distance of 854 m using multiple shots of a simple propane “gun”.

Using air-coupled flexural wave theory developed by Press, Ewing, Oliver, Crary, and Katz and longitudinal wave velocities from their literature we obtained ice thicknesses that compared favorably direct measurements from holes in the ice.

The steep slope of the longitudinal wave velocity vs. gamma a curve means that errors in measuring or selecting a longitudinal wave velocity are not penalized very heavily. .

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ACKNOWLEDGMENTSThis work was supported by the Defense Advanced Research Projects Agency under contract……………….. We also acknowledge and appreciate the support of the UIC Lands Department for allowing us access to lands in the Barrow, Alaska area. If the author includes an acknowledgments section, it is placed after the conclusion and before the appendices (if any) and reference list.

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REFERENCESThe reference list is placed last in a manuscript, after the acknowledgments and appendices (if any). See the "References" section under "Manuscript Preparation" below for details on reference style.

Ewing, M., A. Crary, and A.Thorne, Jr. (1934), Propagation of Elastic Waves in Ice. Part I, Physics, Volume 5 pp 165-168

Ewing, M., A. Crary (1934) Propagation of Elastic Waves in Ice. Part II, Physics, Vol. 5, pp 181-184

Holt, B, P. Kanagaratnam, S. P. Gogineni, V.C. Ramasami, A. Mahoney, V. Lytle, 2009, Sea ice thickness measurements by ultrawideband penetrating radar: First Results, Cold Regions Science and Technology, Elsevier, pp 33-46

Lamb, H. (1932), Hydrodynamics, pp 413-415, Dover Publications, Sixth Edition

Press, F., A. Crary, J. Oliver, and S. Katz (1951), Air-Coupled Flexural Waves in Floating Ice, Trans., American Geophysical Union, Vol. 32, No. 2 pp 166-172

Press, F., M. Ewing, (1951) Theory of Air-Coupled Flexural Waves, Jour, Applied Physics, Vol. 22 No. 7, pp 892-899

Ewing, M., W. Jardetzky, and F. Press, (1957), Elastic Waves, in Layered Media, McGraw-Hill Book Company Inc.

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