Normal modes of the Earth

Abstract

Abstract. The free oscillations of the Earth were observed for the first time in the 1960s. They can be divided into spheroidal modes and toroidal modes, which are characterized by three quantum numbers n, l, and m. In a spherically symmetric Earth, the modes are degenerate in m, but the influence of rotation and lateral heterogeneities within the Earth splits the modes and lifts this degeneracy. The occurrence of the Great Sumatra-Andaman earthquake on 24 December 2004 provided unprecedented high-quality seismic data recorded by the broadband stations of the FDSN (Federation of Digital Seismograph Networks). For the first time, it has been possible to observe a very large collection of split modes, not only spheroidal modes but also toroidal modes.

Impact excitation of a seismic pulse and vibrational normal modes on asteroid Bennu and associated slumping of regolith

“…We ignore torsional modes because they do not give radial displacements, so they would not be strongly excited by impacts or tidal perturbations. For the non-rotating homogeneous sphere, the mode frequencies are independent of m. In a spinning body, the normal modes are split and the frequencies depend on m (Montagner and Roult, 2008). However, as the spin rate of Bennu is small (1000 times smaller than the characteristic frequency f char = V p /R), the frequency splitting in Bennu and other nearly spherical asteroids should be small.…”

Real-time earthquake warning for astronomical observatories

“…They also tend to have larger amplitudes than body waves. Large-amplitude earthquakes are capable of driving up the normal modes of the Earth [24]. Earth's slowest normal-mode oscillation occurs at about 0.3 mHz, and distinct modes can still be identified up to a few millihertz.…”

Imaging the solid Earth with seismic noise

“…At 8s surface waves are mostly sensitive to the upper crust (5)(6)(7)(8). The Alpine arc is associated with high velocities that can reach 3.2km.s −1 as well as the Bohemian Massif.…”

“…For periods between 1s and 20s, the ambient vibrations are called microseismic noise. At very low frequencies where fundamental modes of the Earth are observed (100s-1000s period range), this ambient noise is referred to as "hum" [4,5]. It should be noted that in all frequencies, the exact origin of seismic noise is not clearly established, and the mechanism of noise generation remains unknown.…”