Earth oscillations

After a large earthquake, the Earth oscillates with natural, resonant frequencies like the tones of a bell. This phenomenon was theoretically predicted in the nineteenth century and was actually discovered after the 1960 magnitude-9.5 Chilean earthquake, the largest tremor of the twentieth century. These so-called free oscillations are now commonly observed after earthquakes of about magnitude 6.5 and larger because of improved seismometers with high sensitivity.

Just as each bell has its own particular tone, the Earth has particular free-oscillation periods. After different earthquakes, the same periods (modes) of oscillations are generated, although amplitudes vary from earthquake to earthquake and from seismic station to seismic station. During the last 20 years, these oscillation periods and their amplitudes have been studied in detail and have given great insight into the interior structure of the Earth.

 

Discovery of background oscillations

 

Until 1997, all observable free oscillations were assumed to be generated by earthquakes or by so-called slow earthquakes. Slow earthquakes are mysterious seismic events that are thought to release energy gradually, without the sudden rupturing of faults. Whether the oscillations are caused by typical earthquakes or slow earthquakes, their occurrence should be transient; such oscillations should decay within a few days after excitation, because of energy loss due to the inelastic properties of the Earth.

However, it was shown in 1997 and repeatedly thereafter, by using different seismic instruments, that the Earth is oscillating continuously, regardless of earthquake occurrence. Observed free oscillations are the type of modes called fundamental spheroidal modes, for frequencies between 2 and 7 millihertz (mHz). Spheroidal modes of free oscillations contain vertical as well as horizontal motions, but detection of oscillations has been done exclusively from vertical seismometers.

Fundamental modes contain most of their energy close to the surface, although fundamental-mode oscillations at 2 mHz shake more than 1000 km (600 mi) down into the Earth, moving approximately the outer one-sixth of the Earth. These continuous oscillations are called background oscillations and contain only fundamental modes. Overtone modes which have energy at greater depths have not been observed in the data, suggesting that the source of excitation is close to the surface of the Earth.

Background oscillations were detected by conventional Fourier analysis of seismic records. This was initially demonstrated by selecting seismically quiet days, meaning days with no earthquakes larger than magnitude 5.5, and examining spectral peaks of fundamental spheroidal modes in data. Although fundamental spheroidal mode peaks for frequencies below 7 mHz should not be excited on such seismically quiet days, spectral peaks persisted. It was shown later that the spectral peaks exist continuously, regardless of earthquake occurrence (Fig. 1). The manner in which the background oscillations were discovered is surprising in that all it required was conventional Fourier analysis for ordinary broadband seismometer records.

 

 

Fig. 1  Three years of acceleration spectral amplitude at Canberra, Australia. Frequency range is between 3 and 4 mHz. Continuous background oscillations are clearly seen as horizontal stripes. These stripes are exactly at the frequencies of spheroidal fundamental modes from 0S22 to 0S32.

 

 

 

 

 

 

The amplitudes of observed modes are about 0.4 nanogal (1 ngal = 10−11 m/s2) and are approximately constant in acceleration (Fig. 1). At a frequency of 3 mHz, these observed amplitudes are equivalent to about 10−6 cm in displacement; the ground goes up and down by this amount in about 300 seconds.

The observed spectral amplitudes are approximately constant as long as there are no earthquakes larger than magnitude 6. When a large earthquake occurs, amplitudes of oscillations increase linearly with size of earthquakes, overwhelming the amplitudes of background oscillations. But in the absence of such large earthquakes, the amplitudes of background oscillations are constant and persistent.

It was shown in 1999 that these amplitudes contain seasonal variations with two maximum peaks in a year, one in December–February and the other in June–August. The peak-to-peak amplitude variation is approximately 8 (+/− 4%).

 

Cause of oscillations

 

The cause of the oscillations is hard to determine because, like a bell, the Earth vibrates much the same regardless of what sets it going. The three-dimensional patterns of oscillations depend mainly on the shape of the Earth, its composition, and its thermal state—not on what excites them. So, free oscillations reveal the interior structure of the Earth but do not reveal very much about the source of oscillations. Three possible sources are (1) cumulative effects of small earthquakes, (2) slow earthquakes, and (3) atmospheric pressure variations.

 

Cumulative effects of small earthquakes

 

Since the Earth is a tectonically active planet, it seems natural to consider the effects from many small earthquakes to be the cause of these continuous oscillations. However, an order of magnitude estimated by this effect to be at the level of excitation was shown to be too small. A more detailed argument goes as follows: The statistics on the number of small earthquakes follows the Gutenberg-Richter law quite well. This empirical law says that for a reduction of magnitude by one, the number of earthquake increases tenfold. However, energy emitted by an earthquake reduces by a factor of 30 for a reduction of magnitude by one. In total, the energy emitted by earthquakes becomes about one-third for a reduction of magnitude by one. Even if all the energy from the small earthquakes is summed up for the excitation of oscillations, it would not reach a sufficient level to explain the observed amplitudes of continuous oscillations.

Constancy of amplitudes for days without earthquakes larger than magnitude 6 also argues against this hypothesis. Even if there are no earthquakes larger than magnitude 6, there are variations of earthquakes below magnitude 6. The amplitudes of background oscillations are constant and do not seem to be affected by such variations. This observation suggests strongly that these oscillations are controlled by some other mechanism.

 

Slow earthquakes

 

Earthquakes are not the only tectonic motions in the Earth. There are perhaps much larger aseismic tectonic motions in the Earth; examples include slow and silent earthquakes, the creeping motions of tectonic plates, and magmatic processes under active volcanoes. Among those possibilities, slow earthquakes are considered to be a serious candidate. Although these earthquakes are not well known, there are some reports from oceanic fracture zones, a little-studied remote part of the Earth. Some of these slow earthquakes may be large enough to excite background oscillations. But quantitative tests have not been possible, and it is uncertain whether or not they can explain various characteristics of the observed amplitude behaviors in background oscillations.

 

Atmospheric pressure variations

 

The atmosphere is a serious candidate for the excitation of background oscillations. This mechanism is considered to work in the following way: The atmosphere in the frequency band between 2 and 7 mHz is turbulent, and there are vigorous motions in the atmosphere which cause pressure fluctuations at the surface of the Earth. When the pressure rises, the atmosphere presses down on the ground or sea beneath it. When the pressure drops, the surface rebounds. The Earth is then like a bell being constantly hit by atmospheric pressure changes (Fig. 2). While this effect may be small locally, the atmosphere applies this process on the solid Earth everywhere, constantly in time. Integrated effects from the whole Earth have been shown to be sufficiently large to excite background oscillations.

 

 

Fig. 2  Atmospheric excitation hypothesis. Atmospheric pressure fluctuations exert force on the solid Earth, which leads to ringing of the Earth with its natural resonant frequencies.

 

 

 

 

 

 

This hypothesis is favored not only because the atmosphere seems to have sufficient energy to explain the observed amplitudes of background oscillations but also because seasonal variation is reported in the background oscillations. Amplitudes of the background oscillations become higher in June–August and in December–February. The variation of amplitude is about 8% from peak to peak throughout a year and is proportional to variations of atmospheric pressure. The real cause of this pattern may be the occurrence of winter in some parts of the world, either in the Northern Hemisphere or in the Southern Hemisphere, since the average atmospheric pressure variation in each hemisphere is known to have a maximum in winter and a minimum in summer.

Other hypotheses that attribute the cause to some processes in the ocean are also being considered for the excitation of the background oscillations. It remains to be seen whether ocean processes have sufficient energy in the frequency band between 2 and 7 mHz, and whether they can maintain constancy of amplitudes and show seasonal variations. Currently, the most favored hypothesis is the atmospheric excitation, but it seems likely that processes in the solid Earth are not the cause of the background oscillations because solid Earth processes do not usually have seasonal variations.

 

 

Application in planetary seismology

 

If the atmospheric excitation hypothesis turns out to be true, other planets with atmospheres may be oscillating by the same mechanism. This could provide a new approach for studying the interior of these planets. It may be an important approach since a planet such as Mars is thought to have very low tectonic activity and probably has few quakes. If so, even if a seismic instrument is installed on Mars's surface, waiting for quakes to be recorded, researchers may never get a sufficient amount of quake data to study the planet's interior. However, if the whole planet is oscillating by the atmospheric excitation mechanism, researchers can observe free oscillations of Mars. Resonant oscillation periods could then give information on the interior structure of Mars. This approach may work for Mars as well as for Venus, although the technical challenge of installing seismometers on these planets may be enormous.

 See also: Earthquake; Fourier series and transforms; Oscillation; Plate tectonics; Seismographic instrumentation; Seismology; Tone (music and acoustics)

Toshiro Tanimoto

 

Bibliography

 

 

  • N. Kobayashi and K. Nishida, Continuous excitation of planetary free oscillations by atmospheric disturbances, Nature, 395:357–360, 1998
  • N. Suda, K. Nawa, and Y. Fukao, Earth's background free oscillations, Science, 279:2089–2091, 1998
  • T. Tanimoto et al., Earth's continuous oscillations observed on seismically quiet days. Geophys. Res. Lett., 25:1553–1556, 1998
  • T. Tanimoto and J. Um, Cause of continuous oscillations of the Earth, J. Geophys. Res., 104:28723–28739, 1999
  • Alifazeli=egeology.blogfa.com

 

 

Additional Readings

 

 

  • Article on free oscillations of the Earth
  •  lower mantle  
  • Alifazeli=egeology.blogfa.com