Eigenoscillations and Stability of Rocking Stones: The Case Study of “The Hus Pulpit” in The Central Bohemian Pluton

Abstract

Stability of precariously balanced rocks is employed in seismic hazard estimates. Standard toppling models of these rocks are based on a rigid body motion, i.e., this approximation assumes that their eigenfrequencies are infinite in any position of a rock. This assumption is, however, questionable in the case of rocking stones oscillating with lowest eigenfrequencies of only several hertz when resonance effects facilitating rolling/wobbling due to a seismic signal cannot be a priori excluded. An example demonstrating existence of such low frequencies is “the Hus Pulpit” rocking stone located in the Central Bohemian Pluton (49.568N,14.363E). The observed lowest frequencies recorded by a Guralp CMG-40T seismometer located on the top of this rocking stone are 3, 7 and 9 Hz with the quality factors of 60, 55 and 77, respectively. Using the COMSOL Multiphysics software package we model the oscillations of this rocking stone numerically and demonstrate that these observed low frequencies and their dampings can be explained by a force interaction between the stone base and the bedrock that can formally be interpreted as the damped elastic response of the bedrock to its surface deformation by the stone. We also numerically study stability of the stone under the presence of such an interaction and conclude that beginning of toppling requires very high horizontal PGV (PGA) for input seismic frequencies even at the resonance frequencies. However, different numerical models, where the seismic displacements are considered as the direct input at the rock base, can result in rock instabilities under a presence of an $\hbox {M}=7$ earthquake at a distance of about 150 km.