Modal Analysis of a Freestanding Sandstone Monolith (Castleton Tower, Utah)

We determined key dynamic properties of Castleton Tower, a 120 m high sandstone monolith located near Moab, Utah, from a limited-duration ambient vibration data set. The tower exhibits mutually-perpendicular, sub-horizontal modal displacement with low damping ratios at its first two eigenmodes, results which we successfully reproduced in 3D eigenfrequency simulation. The average Young's modulus resolved from our simulation is ~30% lower than we measured on core samples, consistent with past scaling estimates. Our analysis shows that the pattern of deformation for the first eigenmodes closely resembles that of a cantilever beam. The results of this study can be used to assess the vibration response and vulnerability of Castleton Tower and other freestanding rock monoliths in the region.