Keywords

The need to measure the thickness of the ice cover formed over the water surface at low temperatures may arise as a solution to many practical problems, such as: to ensure the safe movement of people on frozen water bodies and vehicles on ice crossings and winter roads, flood forecasting, assessment of the quality of ice maps created on the basis of satellite methods for remote monitoring of the ice situation, etc.

Among the methods for determining the thickness of the ice cover, the most accurate, but also the most time-consuming, is the direct method, which involves drilling holes and measuring the thickness of ice with an ice gauge.

The most common method for determining the thickness of ice is based on electromagnetic sounding of the ice cover by geo-radar (Kulizhnikov 2016; Singh et al. 2012; Fu et al. 2018). This method is characterized by high productivity and fairly good accuracy, but with large variability of the electrical parameters of ice (for example, in salt-water), it may require periodic calibration of the equipment.

Acoustic methods are also used to determine the thickness of ice. As a rule, these are active methods, for example, echolocation from the ice surface (Kirby and Hansman Jr 1986). The results of applying a passive acoustic method to determine the thickness of ice are presented below. The method is based on the extraction of standing waves from acoustic noise recorded on the ice surface.

This method has been repeatedly used before, for example, in physical modeling and field experiments to determine voids in ground sediments (Kolesnikov et al. 2018). The method is reduced to the registration of acoustic noise on the surface of the investigated limited object and the accumulation of amplitude spectra of a large number of noise records. This makes it possible to distinguish standing waves from the noise formed under its influence in the object.

In our case, such a limited object is an ice layer lying on the surface of water or frozen soil. Depending on the conditions of reflection, either an integer number of half-lengths or an odd number of quarters of the lengths of standing waves (like standing waves in rods that are not fixed or fixed at one end) should be placed in such a layer during the formation of standing waves between its lower and upper boundaries (Khaikin 1971).

The frequencies of standing waves of vertical compression-tension in the layer (natural frequencies of the layer) in these two cases are determined, respectively, by the equations:

$$f_{n} = \frac{{nV_{p} }}{2h} ,$$
(1)

for ice under which there is water or air, or

$$f_{n} = \frac{{nV_{p} }}{2h},$$
(2)

for ice lying on top of frozen ground. Where n is the mode number of standing waves, \(V_{p}\) is the velocity of longitudinal waves, h is the distance between the boundaries of the layer.

To assess the possibility of using a passive acoustic method to determine the ice thickness, based on the extraction of standing waves from acoustic noise, in late January—early February 2019, full-scale experiments were conducted on two reservoirs in the area of Novosibirsk Akademgorodok—on the Zyryanka river and on the beach “Zvezda” on the Ob reservoir. Registration of noise records was carried out on linear profiles with a step of 1 m. On the river, the profile 20 m long was oriented along the banks and was approximately in its middle part, and obviously above the water, since its murmur was clearly heard from under the ice. On Zvezda beach, the observation profile was approximately perpendicular to the coastline and was located partly above the water, partly above the frozen sand.

Acoustic noise was recorded using a digital oscilloscope B-423 with a sampling frequency of 100 kHz. A wide-band piezoceramic piston-type sensor with a vertically directed axis of maximum sensitivity was used as a receiver, which was installed directly on the cleaned ice surface during measurements. The total duration of the noise recordings at each point was 30 s.

During processing, the records were divided into fragments with a duration of 8192 samples, after which the amplitude spectra of these fragments were accumulated. The frequencies of the resonance peaks emitted from the averaged amplitude spectra were used to determine the thickness of the ice cover at the observation points using Eq. (1). It was assumed that the longitudinal wave velocity \(V_{p}\) for ice is known and varies insignificantly at different observation points. Therefore, in the calculations, the value \(V_{p}\) = 4090 m/s, determined by the pulsed method on an ice core obtained by drilling a control hole near the Zvezda beach, was used.

Figure 1 shows examples of averaged spectra of noise recordings recorded at two observation sites. It can be seen, even with a relatively short duration of registration of noise in their spectra, several regular resonant peaks can be confidently distinguished. The regularity of the peaks in the amplitude spectra and the agreement with Eqs. (1) and (2) allow us to identify these peaks as resonances at the frequencies of standing waves.

Fig. 1
figure 1

Examples of normalized averaged amplitude spectra of noise records recorded on the ice sheet of the a river Zyryanka, b near the shoreline of the Ob reservoir on ice above water and c above frozen sand

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Indeed, if ice covers water at a lower speed relative to it, then these peaks are located on the frequency axis with high accuracy in accordance with Eq. (1). For example, in Fig. 1a, the frequencies of the first four modes of standing waves are 17.4 kHz, 34.8 kHz, 52.1 kHz, and 69.5 kHz. At the same time, over the frozen sand (Fig. 1c), the distribution of peaks is consistent with Eq. (2), which indicates its greater acoustic rigidity compared to ice (mainly, apparently, due to the higher density of mineral grains).

The correspondence of the distinguished regular peaks to the standing waves of vertical compression-tension of the ice layer, and not to the standing waves of other types, is due to the use of a sensor that measures mainly the vertical component of acoustic noise during measurements. The thickness of the ice measured above the water by the rail was approximately 10.2 cm. The lowest mode frequency determined from the noise recorded near the hole is \(f_{1} =\) 19.92 kHz, which, at the measured velocity \(V_{p} =\) 4090 m/s, in accordance with Eq. (1), gives almost the same thickness 10.27 cm. This example, in addition, confirms the correctness of the application of the method in question to determine the thickness of the ice cover of water bodies.

The frequencies of the three lowest modes for all observation points of two experiments are shown in Fig. 2. In this figure, it is clearly seen that for observations on the Zyryanka river, the frequencies of the second and third modes exceed the frequency of the first mode by 2 and 3 times, respectively, which is consistent with formula (1). The same pattern is observed for measurements performed on Zvezda beach, but only for a section of a profile of 9–15 m. For a part of a profile from 0 to 8 m, the frequency interval between adjacent modes is equal to twice the frequency of the lowest mode, which is consistent with formula (2). It follows that from 0 to 8 m the profile passes over frozen sand, from 9 to 15 m above water, and between the marks of 8 and 9 m there is a border of these zones.

Fig. 2
figure 2

The frequencies of the first (square markers), second (round markers) and third (triangular markers) modes of standing compression-extension waves for observation profiles on a the river. Zyryanka and b on Zvezda beach

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In summary, it can be noted that the experiments have shown the effectiveness of the use of acoustic noise to determine the thickness of the ice cover of water bodies, as well as to assess the type of underlying medium (water or frozen ground) on which the ice layer lies.