Using flexural waves recorded by distributed acoustic sensing to infer the ice thickness and water depth of a frozen lake

Information about frozen lakes, including ice rigidity, ice thickness, and water depth, is essential for environmental studies and practical applications. Although these properties can be measured in the field, such measurements are labor-intensive and spatially limited, motivating the development of alternative observation methods. Seismic waves provide an effective approach to studying frozen lakes, as their propagation velocity depends on the physical properties of the ice–water system, including the elastic moduli and thickness of the ice, and water column depth. In this study, we investigate the use of wind-driven flexural waves recorded by a distributed acoustic sensing (DAS) system to infer ice thickness and water depth beneath a 1000 m fiber-optic cable installed on Lake Pääjärvi, southern Finland. We identify wind-induced flexural waves in the 0.01-0.5 Hz frequency band, extract their dispersion curves, and invert them using a grid search to estimate effective ice thickness and water depth under four cable intervals. Our estimates indicate effective ice thicknesses ranging from 22 to 34 cm and effective water depths ranging from 0.8 to 31 m. Absolute differences between effective estimates and arithmetic averages of field measurements range from 0.5 to 8.6 cm for ice thickness and 1.2 to 10.3 m for water depth. Our estimates reproduce the observed dispersion curves and agree with field measurements, demonstrating that it is possible to obtain first-order information about ice thickness and water depth in frozen lake environments. However, the robustness of water depth estimates is limited by the wavenumber content of the flexural waves. In our case, the uncertainty of the water depth estimates increases from 0.43 to 12.05 m as water depth increases because low-wavenumber flexural waves, which are most sensitive to the water column, are not resolved by the dispersion curves. Another important observation is that refraction of flexural waves toward shallower water must be considered when converting apparent velocities measured along the cable to true velocities. If this effect is neglected, dispersion curves and the estimated parameters can be biased.