Magnitude (earthquake)

The magnitude is a measure of the strength of earthquakes . Magnitudes are mainly determined from the amplitudes , and more rarely from other parameters of seismograms . These are in turn recorded worldwide at earthquake measuring stations with seismographs . In contrast to this, the intensity of earthquakes - i.e. their effects on people, buildings and the landscape - can be observed without instruments.

Historical developments

The oldest magnitude scale is the Richter scale , well known from the media , which was developed by Charles Francis Richter in the 1930s to quantify California earthquakes. Richter had recognized that there was a connection between the maximum deflection in the seismogram and the distance from the epicenter . The logarithmic relationship found in this way was suitable for inferring the strength of the earthquake from the decay behavior of the amplitude. However, this magnitude scale refers to seismic waves , the beam paths of which mostly run through the earth's crust . As a result, the Richter scale can only be used up to a maximum distance of 600 to 1000 km from the epicenter. It is therefore also known as the local earthquake magnitude (M _L ).

In order to be able to compare earthquakes further away, Beno Gutenberg introduced the so-called surface wave magnitude (M _S ) in 1945 . In the same year he also presented the sky wave magnitude (m _B ). Various framework conditions, which were given partly by the focal processes of the earthquakes and partly by the limits of technical feasibility, led to the development of further magnitude scales.

Due to the limited dynamics and the overdrive during strong local events, a correct determination of the maximum deflections was not always possible with the earlier analog recording devices. As a makeshift, the code magnitude (M _d ) was developed for such cases , for which the decay time of the wave coda , in particular the S _g phase, was used. In modern science, the moment magnitude scale , which was developed in 1977 by Hiroo Kanamori and Tom Hanks , is used in particular .

Methodological basics

Historical definition

Richter looked at maximum amplitudes in seismograms (measured in micrometers , i.e. 1/1000 mm) recorded by standard Wood-Anderson type seismometers . He presented the decadic logarithm of the amplitude values as a function of the epicentral distance (distance of the measuring instrument from the epicenter). He found that the maximum amplitudes of earthquakes of various strengths decay along more or less parallel curves with distance. He therefore defined the magnitude of an earthquake as the logarithmic maximum deflection of the standard seismometer. For scaling, he used a reference distance of 100 km.

Local restrictions

Strictly speaking, the Richter magnitude only applies to the California area, since the decrease in amplitude depends on the nature of the rock material.

Later development

Further magnitude scales developed later. Their basic principle is largely the same, but different phases of the wave field and their special physical properties are used. For surface waves, the true ground movement is derived from the seismogram and used to calculate the magnitude, while the sky wave magnitude m _{B is} based on theoretically calculated corrections of the amplitudes due to the decrease in energy density with 1 / r² for spherical waves and the damping that occurs along the beam path .

With the introduction of the WWSSN standard seismometer with a natural frequency of one Hertz (corresponds to a natural period of one second), calibration to the short period wave components (English: short period , abbreviation: SP) became common. The change was primarily due to the growing interest in using seismological recordings to detect underground nuclear explosions, which can be identified, among other things, on the basis of their frequency spectrum. To distinguish this short-period sky wave magnitude is referred to as m _b .

A frequently used empirically developed relationship establishes a connection between the surface wave magnitude M _S and the seismic energy E _S (in joules) released during the earthquake .

{\ displaystyle \ log (E_ {S}) \ simeq 1 {,} 5 \ cdot M_ {S} +4 {,} 8}

From this it follows that 1 magnitude unit means about 32 times higher energy release. A difference of 2 magnitude units already corresponds to 1000 times the energy released. An earthquake with the surface wave magnitude M _S = 5.5 then has the seismic energy E _S ≈ 3 GWh, which is released within a few seconds. The same seismic magnitude would be achieved by an underground nuclear explosion with the equivalent of one megaton (Mt) of chemical explosive. However, only about one percent of the seismic wave energy would be generated in the explosion, while the remaining energy would flow into heat generation and the crushing of the rock material.

Error due to saturation problems

Almost all magnitude scales behave problematically when recording particularly strong earthquakes (saturation phenomenon). The reason for this is that the maximum amplitude in the upper range no longer increases significantly due to the increase in energy radiation caused by the earthquake.

In the saturation range, the scale does not correctly reflect the further increase in energy radiation caused by the earthquake. This means that conclusions can no longer be drawn correctly about the energy released by the earthquake, and the strength of earthquakes in this area can practically no longer be distinguished.

Saturation-free scales

The moment magnitude scale is derived solely from the seismic moment and thus from the direct physical parameters of the earthquake focus. It does not reach saturation even for the heaviest earthquakes and is therefore often used for very strong events.

Diversity of the magnitude scales

basis

The different methods for determining magnitudes are based on the amplitudes of different phases of the seismic wave field . However, these differ in terms of the physical basis of their propagation. There is a significant difference, for example, in the energy spectrum, since the wave phases have different dominant frequencies or oscillation periods (see table).

symbol	designation	Period range (s)
M _L	Richter scale	0.1 - 001.0
m _b	Sky wave magnitude	1.0 - 005.0
M _S	Surface wave magnitude	0.0 - P20th
M _W	Moment magnitude	0.0 > 200

comparability

Because of these natural differences in the wave phases, the results of the magnitude determinations of the various methods sometimes differ considerably and are only comparable to a limited extent. This is especially true for very strong earthquakes when the saturation described above comes into play.

This can easily be shown using the Chile earthquake of 1960 : According to the (saturated) surface wave magnitude scale, this event reaches the value M _S = 8.5, while the moment magnitude results in the value M _W = 9.5, which is around 30 - times higher energy release. To correctly classify the magnitude of an earthquake, it is not enough to specify a simple numerical value; the underlying magnitude scale must always be correctly named.

Magnitude information in press media

In press reports on earthquake events, the Richter scale is sometimes incorrectly referred to. In particular, high magnitude values above about 6.5 are generally based on other magnitude scales, since the Richter scale is not designed for higher magnitudes.

Magnitude scales

The name indicates which method was used to determine the magnitude. For this purpose, an index is added to the capital "M" for "magnitude" (exception: the sky wave magnitude m _b ):

Identifier	Surname	description
m	Unity magnitude scale ( unified magnitude )	This scale is formed from the variable m _B calculated from the sky wave magnitude m _B and from the surface wave magnitude M _S as a weighted arithmetic mean .
m _B	Body wave magnitude ( body-wave magnitude )	This scale uses space waves that propagate through the interior of the earth's body. Your decrease in energy depends solely on the distance.
m _b	Short Periodic body wave magnitude (SP) ( body-wave magnitude, short period )	It differs from m _{B in} its calibration to the short-period wave components. As a result, it deviates significantly from smaller values for earthquakes of magnitudes m _B > 5 and also reaches saturation much faster.
M _d	Coda magnitude scale (Abklingmagnitude) ( duration magnitude )	With this scale, the magnitude was determined based on the decay of the signal. The length of time was measured starting with the arrival of the wave up to the end of its wave coda , i.e. until it can no longer be made out in the background noise.
M _E	Energy magnitude scale ( energy magnitude )	This magnitude is another form of the moment magnitude. Here, the seismic moment is not used for the determination, but the released energy. If the Kanamori condition E _S / M ₀ ≈ 5 · 10 ^{−5 is} fulfilled , both scales deliver identical magnitudes.
M _j , M _jma	JMA magnitude scale ( Kishō-chō magunichūdo )	A magnitude scale commonly used by the Japan Meteorological Agency , which combines three different individual scales for strong, weak, near-surface and deep earthquakes.
M _m	Coat magnitude scale ( mantle magnitude )	This scale examines very long-wave surface waves of the Rayleigh type, but also of the Love type, which reach deep into the earth's mantle . Due to the long periods, saturation is avoided.
M _L	Richter Scale , Local Quake Magnitude ( local magnitude )	This scale uses maximum amplitudes of near quakes up to a maximum of 600–1000 km epicentral distance.
M _S	Surface wave magnitude ( surface wave magnitude )	For this scale, the real ground movement at the measuring point is determined from the amplitude, from which the magnitude is in turn calculated. Surface waves that propagate along the earth's surface are examined .
M _W	Moment magnitude scale ( moment magnitude )	This scale uses the distance-independent seismic moment M ₀ to determine the magnitude. It does not reach any saturation.

These magnitude scales represent a selection; for certain purposes, further magnitude relationships or those derived from the mentioned scales are also used.

Others

If the surface wave magnitude (M _S ) and the sky wave magnitude (m _b ) are related to each other, earthquakes can easily be differentiated from sources of explosion (e.g. an atom bomb ): In nuclear explosions, the ratio between the measured weak surface waves and the significantly stronger ground waves is exceptionally high.

Web links

James P. McCalpin Earthquake Magnitude Scales

Lexicon ZAMG: Magnitude

seismo.ethz.ch - Description of the magnitudes

GEOFON (GFZ Potsdam), overview of automatically localized earthquakes worldwide

BGR Hannover, overview of current earthquakes in Germany and worldwide

CSME-EMSC European-Mediterranean Seismological Center - overview of all automatically recorded earthquakes worldwide (superordinate organization of LDG, GFZ, INGV, IGN, BGR etc.)

Estimated values of the magnitude of an earthquake based on the maximum intensity and other focus parameters from earthquake catalogs R. Gutdeutsch, Vienna, D. Kaiser and G. Jentzsch, Jena

Individual evidence

↑ ^a ^b ^c ^d ^e ^f Peter Bormann (Ed.): IASPEI New Manual of Seismological Observatory Practice. 2 volumes. GeoForschungsZentrum Potsdam , Potsdam 2002, ISBN 3-9808780-0-7 .

↑ ^a ^b ^c Peter M. Shearer: Introduction to seismology. Cambridge University Press, Cambridge et al. 1999, ISBN 0-521-66023-8 .

^ ^A ^b ^c Thorne Lay, Terry C. Wallace: Modern global seismology (= International Geophysics Series. Vol. 58). Academic Press, San Diego CA et al. 1995, ISBN 0-12-732870-X .

^ ^A ^b Hans Berckhemer : Fundamentals of geophysics. 2nd, revised and corrected edition. Scientific Book Society, Darmstadt 1997, ISBN 3-534-13696-9 .

↑ Beno Gutenberg , Charles Francis Richter : The energy of earthquakes. In: The Quarterly Journal of the Geological Society of London. Vol. 112, 1965, ISSN 0370-291X , pp. 1-14.

↑ Recommendations of the Joint General Assembly of the IASPEI / IAVCEI on naming magnitudes, Durham, 1977 ( Memento of the original from July 23, 2008 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. @1@ 2

[bormann-1] ↑ ^a ^b ^c ^d ^e ^f Peter Bormann (Ed.): IASPEI New Manual of Seismological Observatory Practice. 2 volumes. GeoForschungsZentrum Potsdam , Potsdam 2002, ISBN 3-9808780-0-7 .

[shearer-2] Peter M. Shearer: Introduction to seismology. Cambridge University Press, Cambridge et al. 1999, ISBN 0-521-66023-8 .

[lay-3] A ^b ^c Thorne Lay, Terry C. Wallace: Modern global seismology (= International Geophysics Series. Vol. 58). Academic Press, San Diego CA et al. 1995, ISBN 0-12-732870-X .

[berckhemer-4] A ^b Hans Berckhemer : Fundamentals of geophysics. 2nd, revised and corrected edition. Scientific Book Society, Darmstadt 1997, ISBN 3-534-13696-9 .

[5] Beno Gutenberg , Charles Francis Richter : The energy of earthquakes. In: The Quarterly Journal of the Geological Society of London. Vol. 112, 1965, ISSN 0370-291X , pp. 1-14.