Estimating the ice thickness and water depth of a frozen lake using flexural waves recorded by distributed acoustic sensing

Information about frozen lakes, including ice rigidity, ice thickness, and water depth, is essential for both 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 offer an alternative 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 under a 1000 m fiber-optic cable installed on Lake Pääjärvi, Finland. To do so, 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 reproduce the observed dispersion curves and agree with independent field measurements, demonstrating that it is possible to obtain first-order information about ice thickness and water depth in frozen lakes. However, the reliability of water depth estimates is limited by the wavenumber content of the flexural waves. In our case, water depth estimates become less robust with increasing water depth because low-wavenumber flexural waves, which are sensitive to the water column, are lacking. 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 may be biased.