At what frequency does the earth vibrate?

The hum of the earth: natural vibrations

Earthquakes and other phenomena ensure that the earth keeps making strange movements. The planet swings like a steel ball, it rocks like a top. These natural vibrations help to understand the interior of the earth.

If a freely suspended steel ball is struck briefly with a hammer, it will reverberate for some time: the impact stimulates the ball to free elastic natural vibrations. Their shifts lead to the emission of acoustic waves on the surface. The associated natural frequencies are characteristic of the sphere and depend on its size, density and elasticity. If you replace the ball with the earth, the hammer with a strong earthquake and our ears with sensitive seismometers, then you have the geophysical counterpart of the laboratory experiment in front of you. Nature often makes this attempt - unfortunately, often with catastrophic results. One of the tasks of seismology is to detect the natural elastic vibrations of the earth and to determine the typical properties of the earth from them. The frequencies are between 0.3 and about 20 mHz (Millihertz). The upper limit is only given by the limits of the evaluation process.

There are other natural vibrations besides the elastic ones. An example: If a game top is set into rapid rotation and its figure axis is briefly pushed, then the top executes circular oscillations around its axis - the top natural oscillations. They are also called free nutations. Their properties are determined by moments of inertia, deformability, etc. This experiment is also carried out continuously by nature with the earth as a top. The vibrations are stimulated by torques in the atmosphere and oceans and by the tidal forces of the moon and sun.

Natural vibrations after an earthquake

There are two simple methods that can be used to determine the mechanical resonances of a system such as the earth. On the one hand, the system of a spring can be deflected straight away from its rest position and released; it then returns with free, damped natural oscillations. On the other hand, the system can be excited harmoniously with a variable frequency and the natural vibrations can be found due to the resonant effect. The type of excitation must match the natural oscillation. If one has a theory for these vibrations, then from the observations properties of the system can be determined, from which the natural vibrations can be explained.

Of course, the following must be taken into account: In addition to the free vibrations, the solid earth carries out a whole series of forced (quasi) periodic vibrations, e.g. B. the general precession of the earth's axis with a period of 25,765 years, the annual polar fluctuation and the tides of the solid earth.

Elastic natural vibrations

Observing natural vibrations of the earth with various long-period seismographs was possible for the first time after the extremely strong earthquake on May 22, 1960 in Chile. On March 28, 1964, another strong quake in Alaska stimulated the vibrations again measurably. These two events mark the beginning of a new research direction in seismology: terrestrial spectroscopy was born. The observed frequencies of many natural oscillation types were equally very close to those that had been calculated with earth models. This, in turn, had been determined from the transit times of seismic waves.

In order to determine natural vibrations, one must first measure the symptoms. Seismometers and gravimeters are used for this. These instruments consist of inert masses that are suspended from springs. The displacements of the inertial masses in relation to the housings are recorded with displacement or speed sensors and then processed further electronically. The devices react to accelerations and changes in the gravitational field associated with seismic signals. The so-called strain seismometers (also: extensometers) work differently. They measure the changes in distance between two points caused by elastic deformation of the rock, which can be between 1 cm and 1 km apart.

Earthquake seismograms are composed of various pulse-like signals that originate from the elastic compression and shear waves. These waves reach the station as so-called space waves through the earth's interior. This is followed by waves that spread across the surface. Then the so-called coda becomes noticeable, which consists of waves that are reflected and scattered several times as well as waves that have traveled around the earth several times. Similar to how a standing wave is created on a string by the superposition of a wave running to the left with a wave running to the right, the constructive interference of these waves leads to the natural vibrations of the earth. The different types of natural oscillation arise from different types of running waves.

Pattern of natural vibrations after quakes

So that seismograms of natural vibrations can be evaluated, they must cover a period of at least 20 hours. There are several restoring forces with these vibrations. On the one hand there are the elastic tensions that arise from deformation from the equilibrium state, on the other hand the gravitational effect of the displaced masses (self-gravity). The gravitational effect only plays a major role in the natural oscillation types with the lowest frequencies. The shape of the displacement fields and the frequencies of these "seismic" wave types follow from their geometry as well as from the distribution of the density r and the elastic parameters in the earth. Therefore, these properties and their distribution on earth can be determined from the observed displacement fields and frequencies.

The natural vibration type with the lowest frequency is called "football mode" in English. It has a period of 54 minutes and is only demonstrably excited by the most powerful earthquakes. The earth swings back and forth - greatly exaggerated - between the shapes of an American football (egg-shaped) and a pumpkin. That of a breathing ball (English breathing mode) corresponding vibration type has a period of 20 minutes, which is approximately equal to the transit time of a compression wave from the earth's surface to the center of the earth and back. Since it could be observed for up to a month after very strong earthquakes, its frequency is known very precisely. A homogeneous steel ball with the same radius as the earth would have a period of 30 minutes for this type of wave.

So far only earthquakes have been mentioned as a mechanism for stimulating natural vibrations of the earth. As shear fractures, earthquakes have a very short duration compared to the decay times of the waves. This allows the waves to vibrate freely until they disappear in the noise.

But volcanoes also stimulate natural vibrations. In 1991 it was observed that the eruption of Mount Pinatubo in the Philippines produced harmonic waves with two frequencies for about eight hours. They ran around the earth several times and could constructively interfere with each other. The volcano supplied the energy for two vertical natural oscillations of the atmosphere. Due to their pressure fluctuations on the earth's surface, they generated the seismic waves observed in the distance.

Then in 1998 it was proven for the first time that the natural vibrations of the earth are demonstrably excited even in times without tremors. These so-called natural background vibrations are in the 2-7 mHz band and have an acceleration amplitude of 10-12 m / s2. The excitation mechanism is still controversial. The most promising candidates are processes in the oceans or in the atmosphere. As with the signals of the Pinatubo eruption, it is also assumed here that a temporally variable air or water pressure in the solid earth below can lead to the excitation of seismic waves.

Gyroscopic vibrations

If the earth is viewed as a flattened top, then it executes precession movements due to the external forces and torques from the moon and sun. In addition, the earth can execute superimposed free movements that correspond to those of a force-free top. A flattened top can rotate stably around its figure axis. If the axis of rotation deviates from the axis of the figure, a so-called free nutation occurs at the same time. This tumbling motion of the top (English wobble) is counted among the natural vibrations.

The tumbling of the earth

The American astronomer Seth Carlo Chandler discovered as early as 1891 during astronomical observations a fluctuation in the earth's latitude with a period of 435 sidereal days. The axis of rotation moves cyclically at the poles of the earth within a circle with a 10 m radius. This movement is made up of the so-called Chandler wobble and the somewhat stronger annual period forced by the atmosphere. The Chandler movement was quickly associated with the movement already predicted by Euler with the period 305 sidereal days. The difference between the periods (435 and 305 sidereal days), however, required a technical explanation.

The Chandler wobble is continuously excited. The atmosphere and oceans, but occasionally also earthquakes (changes in the moments of inertia) are discussed as energy sources. The atmosphere seems to be able to supply only about a third of the necessary energy, the other two thirds come from the ocean. So far, earthquakes could not be reliably identified as sources.

Summary

What we know today about the long-wave structure of the deep interior of the earth is largely based on observations of the earth's natural vibrations. Further and improved observations, together with theoretical-numerical developments, will help to refine this picture. The three-dimensional distribution of density in the earth's mantle, for example, is currently a challenge. It can only be moved against the body by means of natural vibrations. The latest discoveries of the constantly excited elastic and low-frequency vibration types, the first approaches to a time-dependent seismology, as well as the increasing resolution in the observation of free nutations show that this research area always holds surprises in store. They will further improve our view towards the center of the earth.