Global lattice models of a rotating planet -- view on shake, rattle and roll

TL;DR

This paper introduces a spectral approach using gyroscopic lattice models to simulate Earth's vibrations and earthquake phenomena on a rotating planet, providing new insights into core motion and tectonic boundary oscillations.

Contribution

It presents a novel spectral method based on gyroscopic 3D lattices for modeling seismic activity and Earth's core dynamics, advancing discrete approximation techniques.

Findings

Eigenmodes of gyroscopic lattices model Earth's vibrations.

New results on Earth's core motion derived from the model.

Numerical examples align with observed earthquake resonances.

Abstract

A new approach, based on the analysis of a spectral problem for a discrete gyroscopic system, to modelling earthquakes on a rotating planet is presented in this paper. The eigenmodes of gyroscopic three-dimensional icosahedron-dodecahedron lattices are used for the discrete approximations of Earth's vibrations. Related model of the gyroscopic centred icosahedron lattice reveals new results about the motion of Earth's core. The vibrations of the tectonic plate boundaries, inducing shear and longitudinal motions of the ground, are described through the oscillations of the nodal elements within the discrete gyroscopic models. The theoretical analysis is complemented with the illustrative numerical examples linked to natural resonant vibrations observed during large earthquakes.