Microphone recording of flexural waves for estimation of lake ice thickness

Abstract

In this study we took an intentionally low-tech approach, aiming to estimate key physical parameters of lake ice using a single, inexpensive microphone. We consider this approach highly relevant to the issue of transport safety and the relatively high number of accidents involving breakthrough failure of thin ice underlines the importance of this topic. We conducted a range of experiments on three frozen lakes in the Tromsø region of Northern Norway and found that the monochromatic air-coupled flexural wave was a robust feature of impulsively excited frozen lakes. Ice thickness was estimated via a closed form solution that only depends on the measured monochromatic frequency of the air-coupled flexural wave and a set of assumed physical parameters for the ice, air and water. We discuss the impact of uncertainty in the assumed parameters on estimated ice thickness and bearing capacity, finding the uncertainty to be quite small, particularly when physical observation of ice type or drilled thickness are available to constrain the assumed Young's modulus of the ice. Ice thicknesses estimated from air-coupled flexural waves were typically within 5–10% of ice thickness measured in holes drilled in the vicinity of the microphone for both artificial sources including hammer strikes, jumping and tapping with ice skates and natural ice quakes. The thickness estimates were also similarly accurate whether the microphone was resting on the ice, placed on land along the shoreline or handheld. We also showed that it is possible to record the dispersive ice flexural wave using a microphone, particularly when it was resting on the ice surface. Since thickness was constrained by the air-coupled flexural wave, we were able to estimate the propagation distance, corresponding to the horizontal offset between source and microphone, by inversion of the time dispersed arrival of the chirp signal corresponding to the ice flexural wave. We also demonstrated that a microphone can record inharmonic monochromatic overtones of the air-coupled flexural wave, that were linked to the geometry and boundary conditions of the frozen lakes using finite element modal analysis. This study leads us to conclude that a simple microphone can be a powerful tool giving a surprising amount of information on the lake-ice system. Using a microphone to record air-coupled flexural waves appears to be a promising additional tool for evaluation of ice conditions, convenient enough that it could substantially increase the availability of timely and accurate information on ice thickness and thereby contribute to safer travel on floating ice.