Lee Van Cleef

See also: Richter

The magnitude of an earthquake measurement the energy released at the time of a seism. The more the magnitude is raised, the more the seism released from energy. It is about a logarithmic scale, i.e. an increase magnitude of 1 corresponds to a multiplication by 30 of energy.

The media general public often indicate it on the scale of Richter or on the open scales of Richter . These terminologies are unsuitable: the scale of Richter, strictly speaking, is a scale exceeded and only adapted to the Californian earthquakes. The magnitudes usually quoted nowadays are in fact of the magnitudes of moment (noted M_w ).

The magnitude and the intensity (as the scale of Mercalli) are two different measurements. The intensity is a measurement of the damage caused by an earthquake. There exist relations connecting the felt maximum intensity and the magnitude but they is very dependant on the local geological context. These relations are in general used to give a magnitude to the historical earthquakes.

History

It was developed in 1935 by Charles Francis Richter. This last developed this measurement to be able to classify the Sismogramme S recorded locally in California. This scale in the beginning is the measurement of the amplitude in Micromètre S on a Sismographe of the Wood-Anderson type of a earthquake being at 100 km. This measurement is reliable only at very short distance and is now called local magnitude.

The following year, in 1936, Gutenberg and Richter propose a magnitude which bases on the amplitude of the waves of surface for telesismic distances (distance higher than 30°) and for one 20 seconds period (natural period of the seismographs used). Gutenberg in 1945 defines this measurement better. This magnitude is still used today, especially in the first estimates of the power of the seism. Its acronym is ms.

Gutenberg and Richter proposes a new magnitude in 1956, this time based to a measure taken on the waves of volume. Its acronym is Mb (B for body waves, waves of volume in English).

Magnitudes ms and Mb have limitations. It is not a question of a direct measurement of the energy released by the seism. Another problem was raised at the time of large the Earthquake of 1960 in Chile. The duration of the seismic source was quite higher than 20 seconds, at which time the magnitude of surface ms is gauged. The estimate magnitude of the seism, and the great seisms in general under is thus estimated with this type of measurement. This phenomenon is even stronger with Mb for which the base period is of about a second.

In 1977, Hiroo Kanamori introduces a new magnitude gauged on the seismic Moment. Although less immediate to estimate, this magnitude is directly connected to a physical quantity, itself, associated with the energy emitted by the earthquake. This magnitude known as of moment, has as an acronym MW and is employed nowadays.

Principle

The magnitude known as of Richter is based to the measure of the maximum amplitude of the seismic waves on a Sismogramme. The magnitude is defined like the logarithmic curve decimal of this value. This very general definition shows well the empirical character of this measurement which depends on the one hand type of Sismomètre and on the other hand graphic type of development used for the realization of the seismogram on which measurement is done. The latter is also very variable from one seismic station to another because the seismic radiation of a seism is not homogeneous (see Mécanisme with the hearth).

The original definition given by Richter in 1935, called from now on local magnitude or $M\_l$, is a simple logarithmic scale form $M\_l=log\; (A)\; -\; log\; (A\_0)\; +clog\; (\backslash \; Delta)$ where $A$ represents the maximum amplitude measured on the seismogram, $A\_0$ is an amplitude of reference corresponding to a seism magnitude 0 to 100 km, $\backslash \; Delta$ is the distance épicentrale (km) and $c$ is a constant of calibration. In addition to the inhomogeneousness of this equation only locally, marking even more its empirical character, the constants of calibration ($A\_0$ and $\backslash \; Delta$) make this definition valid. For example, in the original definition where the calibration is carried out on moderate seisms of the California of the South recorded with a Sismographe of the Wood-Anderson type, $c=2,76$ and $log\; (A\_0)\; =2,48$.

In order to improve this measurement while making it more total, a new magnitude called $M\_S$ or magnitude of the waves of surface , is introduced in 1936. This magnitude is based to the measure of the maximum amplitude of the waves of surface (in general the wave of Rayleigh on the vertical component of the seismometer) at one period of 20 S. The formulation is almost identical to the preceding one: $M\_S=log\; (A\_\; \{20\})\; +b+clog\; (\backslash \; Delta)$ where $A\_\; \{20\}$ is the measured amplitude, $\backslash \; Delta$ is the distance épicentrale expressed in degree, $b$ and $c$ is constants of calibrations. This measurement is always used today. However, in addition to its empirical character and the problem of saturation (see below), it has two weak points. The first is its uselessness for the major seisms (depth higher than 100 km) which do not generate waves of surface. The second problem comes owing to the fact that the waves of surface are the last wave trains to arrive. Within the framework of a network of alarm, it is paramount to be able to estimate the magnitude of the seism as soon as possible.

The magnitude of the waves of volume noted $m\_b$ (B for " body waves") is thus a measurement which is done on the first wave train P and allows a fast estimate of the importance of the seism. Its formulation is dependant on the dominant period $T$ signal: $m\_b=log\; (A/T)\; +Q\; (\backslash \; Delta,\; H)$ where $A$ is the measured maximum amplitude, $\backslash \; Delta$ is the distance épicentrale (always in degree) and $h$ is the depth hypocentrale. $Q$ is a function of calibration depending on the two preceding parameters. In general the dominant period $T$ is around 1 dryness, period minimum of the waves P for telesismic distances ($\backslash \; Delta>30^o$). The problem of this measurement is fast saturation with the magnitude.

Other magnitudes are employed, especially with the local scales or regional. The magnitude of duration is often used for the micro seismicity and is obtained as its name indicates it by measuring the duration in second of the signal on the seismogram. An abundant literature exists on the regressions between these various measurements in order to try to create relations of passage of the one with the other. This is always a difficult exercise. The disparity of these measurements, that it is due to the type of wave, the type of sensor and its Eigen frequency, at the distance, the type of magnitude used, rather easily explains the great variability of the measurement magnitude of a seism in the hours which follow its occurrence.

To complicate this panorama, it is essential to add that the majority of measurements magnitude, once a certain time passed after the seism, do not correspond to what is described previously. The study of the seism will pass by an inversion of the seismograms in order to find jointly its Localization, its Mécanisme with the hearth and its seismic Moment. From this last, he is deduced a magnitude called magnitude from moment or $M\_w$. It is about the magnitude most used today.

Saturation magnitude

The main issue of the magnitudes $M\_S$ and $m\_b$ is that of saturation. This phénomème is associated with at which time measurement is carried out. It is imperative that this measurement is made at one period which is higher than the duration of emission of the seismic source. However for the great seisms, this time can be very long. The extreme case is that of the earthquake of Sumatra of 2004 where the emission of the source lasted at least 600 S.

If one considers:

• the simplified relation of the seismic moment $M\_0$ with the length of the fault $L$ in km: $M\_0=2,5\; 10^\; \{15\}\; L^3$
• a speed of rupture on the fault of about 3 $km.s^\; \{-\; 1\}$
• the relation between moment and magnitude (see seismic Moment)

then a duration of emission of 1 S corresponds to a magnitude 4,6 and one duration of emission of 20 S corresponds to a magnitude 7,2. Thus any measurement magnitude with $m\_b$ (measured on the waves P) starts under to be estimated with the top a magnitude 4,6 and the same applies to $M\_S$ for seisms magnitude higher than 7,2.

This problem of saturation was highlighted during the estimate magnitude of the earthquake of Chile of 1960, magnitude exceeding 9,0. The magnitude of moment was thus created to mitigate this difficulty. However, the estimate very great magnitudes pose a problem. The seism of Sumatra of 2004 also put in difficulty the methods which calculate the seismic moment and thus by consequence the magnitude. The duration of the very long source obliges to look at signals with low frequencies very. An estimate magnitude was thus made starting from the clean mode most serious of the ground (₀S₂ - period of 53,9 min). This estimate (seismic moment of 6,5 10²² N.m corresponding to a magnitude of 9,15) has an uncertainty of a factor 2, due mainly to the complexity and the dimension of the seismic source.

Graduation

The scale being the logarithm of an amplitude, it is open and unbounded higher known. In practice the seisms magnitude 9 are exceptional and the effects the higher magnitudes are not described any more separately. The most powerful seism ever measured reached the value of 9,5, was the Earthquake of 1960 in Chile.

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