II. Audio-Signal Transmission in Natural Hard-Pack Snow Slab

This experiment to measure relative signal decay in natural snow slabs was conducted in the Bridger Mountain Range near Bozeman, Montana, at 2 200 m elevation on midwinter snow-pack. Nominal snow weight per unit volume was 3 000 N m⁻³ and average snow temperature varied between — 2 and — 5°C over the three-week testing period. The work supplements that of Reference IshidaIshida (1965) who considered acoustic attenuation in snow blocks up to 0.1 m thick under controlled material and boundary conditions. Signal decay reported herein is over snow spans up to 4.0 m in natural snow-pack, for which neither material homogeneity nor boundary conditions were strongly controllable.

The test set-up consisted of a permanent-magnet induction speaker supported next to the side wall of a snow pit (Fig. 1). An aluminum rod connected to the voice coil extended to a 5 cm × 5 cm square aluminum plate which was implanted in the snow wall. Approximately 2.5 cm in front of the plate a contact microphone was embedded in the snow-pack with silica gel. An identical transducer was imbedded similarly at different field locations. Signals from the two transducers were amplified, filtered (pass band 100-100 000 Hz), and measured using a digital voltmeter. The 8 W speaker voice coil was driven sinusoidally over a frequency range 100 to 30 000 Hz at approximately 75% saturation amplitude. The speaker and transducers were placed approximately 0.5 m below the snow surface in nominally 2.0 m deep snow.

Fig. 1. Test set-up to measure audio-signal decay in snow-pack.

The testing sequence involved sweeping the frequency range for successive 1.0 m steps in the spacing between the fixed and the field transducers. To check configuration stability with time, the field transducer was returned to the 1.0 m and 2.0 m spacings occasionally, which accounts for the greater number of data points at these separations.

From the test set-up described it is apparent that signal decay involves mechanisms of attenuation as well as geometric signal spreading, or diffusion. For a line source normal to a plate of transmitting material, geometric diffusion amounts to 6 dB per doubling of radius, with any greater decay attributable to signal attenuation. In the results presented, lack of sufficient accuracy precludes definite separation of diffusion and attenuation components; however certain trends are significant. A summary of data points recorded and average signal-decay curves for sound transmission over distances of 1.0, 2.0 and 3.0 m are shown in Figure 2. At a transmission distance of 4.0 m, no measurable sound was detected at any frequency, indicating signal decay in excess of 70 dB. For signal frequencies greater than 3 000 Hz, signal decay is high, with significant decrement over 1.0 m. The frequency range 100-3 000 Hz was divided into a number of sub-ranges, as listed in Table I, and average signal decays were computed using ail data points in each sub-range. Nominal signal diffusion is in evidence between 1.0, 2.0 and 3.0 m, with a trend toward signal attenuation at the higher frequencies. However, the dominant characteristic is the high signal loss between the source and 1.0 m. This indicates that any attempt to induce high levels of acoustic or vibration excitation of snow results in large localized energy dissipation which is attributable to the non-linear viscous behavior of snow at high deformation rates. The conclusion from this is that any system for monitoring a snow slab acoustically using high-frequency signals must itself be distributed, as transmission from acoustic sources can be expected to be to a maximum of 1.0 to 3.0 m. It is noted further from the data in Table I, that, at 3.0 m, signals in the range 1 000-3 000 Hz have decayed to the threshold level (70 dB), whereas signals in the range 100-200 Hz show greatest persistence.

Fig. 2. Acoustic signal decay versus frequency in snow-pack.

Table I. Average signal attenuation for various transmission distances and frequency ranges

The large scatter of the data points of Figure 1 should be anticipated in acoustic field tests. Reception at the transducers is influenced by a number of factors including signal reflection from natural material layering and local material inhomogeneities, lack of reproducibility in implanting the transducers in silica gel in the snow-pack, and variations in material configurations between test sites. These reported results are for a particular snow-pack with its attendant deposition and aging characteristics, averaged somewhat by the fact that the experiments were conducted at several locally spaced sites (within a 50 m radius). The omission of data in the frequency range 0-100 Hz is significant, and further experimentation is warranted.

III. Low-Frequency Acoustic Emission Spectra of Snow Columns Under Deformation

Snow columns measuring nominally 7.0 cm × 7.0 cm × 20.0 cm were cut from a natural snow block of weight per unit volume 3 300 N m⁻³, then frozen to the load platens of a standard lnstron testing machine in a —5°C test chamber. The range of strain-rates imposed along the 20 cm axis were 0.003 2-0.032 min⁻¹ in compression, and 0.000 27-0.002 8 min⁻¹ in tension, up to a 10% total strain. Sound pressures within the specimen caused by grain and grain-boundary slip and fracture were monitored by a PZT transducer mounted on the side of the specimen and separated from it by a thin layer of silica gel. The signal from the transducer was amplified and recorded on magnetic tape. Because of noise from the testing machine, the useful frequency band was nominally 500-14 000 Hz. Selected 4.0 s segments of the recorded tape were made into loops, and these data played into a 7 Hz spectrum analyzer with variable center-frequency band-pass and plotted. Background spectra were obtained from noise recordings of the complete system, including test specimen, with the testing machine running but not loading the test specimen. Separately, it was determined that engaging the testing machine drive generates additional low-frequency noise which has significant amplitudes only below the low-frequency cut-off (500 Hz) of the experiment.

Typical low-frequency spectra of acoustic bursts in snow in tension and compression are shown in Figures 3 and 4. By overlaying the background and signal spectra, the dominant acoustic frequencies and amplitudes can be identified. Comparing the spectra of Figures 3 and 4, it is seen that emissions in tension are stronger than emissions in compression, particularly when it is noted that the strain-rates differ by an order of magnitude. The spectra shown were taken during the time of initial rapid loading when emissions are frequent compared with activity during the secondary stage of loading. Acoustic activity also intensifies as strain-rates are increased, particularly at rates leading to brittle fracture in tension. If the frequency range from 500 to 14 000 Hz is divided into 500 Hz increments, and the dominant emission amplitudes counted, the distribution of emission amplitudes in tension and compression are as shown in Figure 5. The concentration of counts is in the 1 000 to 10 000 Hz range. This is in evidence in Figure 5 where the amplitude-weighted-average frequency is a minimum of 30% less than the average frequency of amplitudes.

Fig. 3. Acoustic emission spectra and loading of a snow column in compression at a strain-rate of 0.006 7 min^-1 (note that decade amplitude increases at certain frequencies).

Fig. 4. Acoustic emission spectra find loading of a snow column in tension at a strain-rate of 0.000 69 min^-1 (note that decade amplitude increases at certain frequencies).

Fig. 5. Summary of frequency Figure averages and amplitude distributions of acoustic emissions in tension and compression.

It cannot be concluded from the results given that acoustic emission generation in snow is a low-frequency phenomenon. The rapid decay of high-frequency signals, as noted in Section II, means that the volume of snow column contributing to the high-frequency content at the transducer is smaller than the volume contributing to the low-frequency content. Thus, for adequate interception of sound sources in field applications of acoustic emission techniques, a collecting or waveguide concept may be needed.

IV. Waveguide Evaluation for Sound Interception in Snow

Several possible waveguide geometries and materials were tested in the laboratory to determine their sound interception and transmission characteristics. Waveguides were selected for ease of deployment on snow slopes, and minimization of expense in fabrication; thus, simple cross-sections were selected. Although the waveguide is intended to intercept acoustic bursts, a vibration source was used in the laboratory evaluation. Waveguide configurations tested, all 1.0 m in length, include the following:

1. 1. Steel rod: diameter 4.13 mm.

2. 2. Steel plate, rigid: cross-section 6.0 mm × 63.0 mm.

3. 3. Steel plate, flexible: cross-section 0.81 mm × 63.0 mm.

4. 4. Steel sheet: cross-section 0.81 mm × 300 mm.

5. 5. Steel rod with welded 90° corner: diameter 4.13 mm.

6. 6. Steel rod with 50 mm radius, 90° bend: diameter 4.13 mm.

7. 7. Steel wire mesh: wire spacing 8.5 mm, wire diameter 0.81 mm.

8. 8. Wood plate: cross-section 6.0 mm × 63.0 mm.

9. 9. Ice plate: cross-section 15.0 mm × 63.0 mm.

The individual waveguides were mounted at the center of a block of sifted and re-sintered snow of weight per unit volume 3 000 N m^-3 as shown in Figure 6. For all waveguides the surface temperature was above freezing (or wet surface) when emplaced, and loose snow was leveled at the mid-height interface before the block was re-assembled and allowed to set for 72 h at — 20°C. A driving PZT transducer was mounted 0.2 m from one end of the waveguide with a separation of 0.14 m of snow from the waveguide surface. A similar monitoring transducer was mounted onto a small steel block, which in turn was either welded, glued or frozen to the waveguide. The driving transducer was excited from a signal generator and power supply, and the monitoring transducer output was measured with a digital voltmeter.

Fig. 6. Waveguide test configuration.

The intent of the evaluation is to compare the relative attenuation characteristics of the various waveguides. Thus, for each test, frequency and amplitude settings were made the same, and the frequency was, swept from 2.0 to 60 kHz although not all waveguides responded over the entire range.

The curves of attenuation versus frequency of the various waveguides, having subtracted the experimentally measured attenuation of o. 14 m of the snow block from each, are shown in Figures 7 and 8. The attenuation of the various steel waveguides, excepting the wire mesh, is generally less than the wood and ice plates. The insertion of a sharp corner in a steel waveguide has a significant degrading effect on signal transmission, particularly at higher frequencies. The ice plate, which has the advantage of easy emplacement in remote sites, shows relatively high attenuation compared to the metallic types. A waveguide not tested, but which may have the greatest utility in monitoring snow-pack emissions, is the basal layer of rock. Testing of this configuration is most readily carried out by direct field measurements.

Fig. 7. Attenuation versus frequency of steel waveguides with different cross-sections.

Fig. 8. Attenuation versus frequency of miscellaneous waveguide configurations.

Acknowledgement

The comments and criticisms by Dr Richard Sommerfeld and Mr William St. Lawrence during the course of this work are gratefully acknowledged. This work was supported by the National Science Foundation (Grant No. NSF GA-3943) and the Office of Army Research-Durham (Grant No. DA-ARO-D-31-124-71-G59).