# Richter scale

Charles Richter, co-inventor and namesake of the Richter scale

The Richter scale is a magnitude scale . It is based on amplitude measurements from seismogram recordings that were obtained at a relatively short distance of a few hundred kilometers from the epicenter . It is therefore also known under the term local earthquake magnitude .

To determine the strength of earthquakes , records from measuring devices are used today, which are distributed over the entire surface of the earth. The value determined from this is usually indicated on the torque magnitude scale as the torque magnitude . The press often mistakenly speak of values ​​on the Richter scale. ${\ displaystyle M _ {\ mathrm {w}}}$

## Emergence

The scale was developed by Charles Francis Richter and Beno Gutenberg at the California Institute of Technology in 1935 and was initially referred to as the M L scale (Magnitude Local). In his seminal publication An instrumental Earthquake Magnitude Scale in the Bulletin of the Seismological Society of America , Charles Francis Richter applied the basic idea of ​​an instrumental earthquake scale first published by K. Wadati in 1931 to California earthquakes.

## Basics

Due to its definition, the Richter scale has no upper limit, but the physical properties of the earth's crust make an earthquake of magnitude 9.5 or higher almost impossible, since the rock cannot store enough energy and discharges before it reaches this strength. The term “open to the top”, which is often used in the media, is intended to distinguish the instrumental Richter scale from the intensity scales, which are often used to characterize the strength and destructive power of an earthquake.

Most magnitude scales reach saturation in the upper value range: If the energy released during the quake increases further, the magnitude changes only slightly and the scale loses its linearity . The Richter scale is also subject to this phenomenon, so it is not suitable for values ​​above magnitude 6.5. Values ​​beyond this generally refer to other magnitude scales.

## Derivation

The specified value, the magnitude or size class, is derived from the decadic logarithm of the maximum amplitude (deflection) in the seismogram . The magnitude is determined according to the following relationship:

${\ displaystyle M _ {\ mathrm {L}} = \ log _ {10} \ left ({\ frac {A _ {\ max}} {A_ {0}}} \ right)}$,

where A max indicates the maximum deflection in micrometers (μm) with which a short-period standard seismometer (Wood-Anderson seismograph ) would record an earthquake at a distance of 100 km from the epicenter . For the purpose of correction, the reference may have to be adapted to the conditions for earthquakes at different distances. For this purpose, the damping of the amplitude is taken into account, which in turn depends on the regional velocity and damping structure, the age of the earth's crust and its composition, the depth of the focal point and the heat flow conditions. Strictly speaking, these calibration functions according to Richter are only valid for southern California and must be determined separately for other regions of the world. ${\ displaystyle A_ {0}}$

Because of the decadic logarithm, the increase in magnitude by one point on the scale means an approximately ten times higher deflection (amplitude) in the seismogram and approximately 32 times the energy release ( exponential growth ) in the earthquake focus. A magnitude of two or less is called a micro-earthquake because it often cannot be perceived by humans and is only recorded by local seismographs. Quakes around 4.5 and higher in magnitude are strong enough to be captured by seismographs around the world. However, the magnitude must be greater than 5 to be considered a moderate earthquake.

## Classification of the scale values

Typical effects in the area of ​​the epicenter can be assigned to the magnitude values. It should be noted that the intensity and thus the ground effects depend not only on the magnitude, but also on the distance to the epicenter, the depth of the earthquake focus below the epicenter and the local geological conditions.

Richter magnitudes Classification of the earthquake strength Earthquake effects Frequency of events worldwide released energy
(TNT equivalent in t (energy in J))
<2.0 Micro Micro earthquake ** , not noticeable ≈ 8000 times per day (> magnitude 1.0) up to 1 t
(<4.2 GJ)
2.0 ... <3.0 extremely light Generally not noticeable, but measured ≈ 1500 times a day 1 to 32 t
(4.2 to 135 GJ)
3.0 ... <4.0 very easy Often noticeable, but damage is very rare ≈ 49,000 times per year (estimated) 32 to 1,000 t
(135 to 4,200 GJ)
4.0 ... <5.0 light Visible movement of room objects, vibration noises; mostly no damage ≈ 6200 times per year (estimated) 1 to 32 kt
(4.2 to 135 TJ)
5.0 ... <6.0 medium strength Serious damage to fragile buildings, slight or no damage to robust buildings ≈ 800 times a year 32 to 1,000 kt
(135 to 4,200 TJ)
6.0 ... <7.0 * strong Destruction within a radius of up to 70 km ≈ 120 times a year 1 to 50 Mt
(4.2 to 210 PJ)
7.0 * ... <8.0 * big Destruction over large areas ≈ 18 times a year 50 to 1,000 Mt
(210 to 4,200 PJ)
8.0 * ... <9.0 * very large Destruction in areas of a few hundred kilometers ≈ once a year 1 to 5.6 Gt
(4.2 to 23.5 EJ)
9.0 * ... <10.0 * extremely big Destruction in areas of a thousand kilometers ≈ every 20 years 5.6 to 1,000 Gt
(23.5 to 4,200 EJ)
≥ 10.0 * global catastrophe Never registered unknown > 1,000 Gt
(> 4,200 EJ)

* The Richter scale is metrologically limited to an upper limit of magnitude 6.5. Higher magnitudes of stronger earthquakes are determined with the moment magnitude scale (M W ).

**The term micro-earthquake or microquake is used inconsistently. It generally describes low-intensity tremors. The United States Geological Survey (USGS) defines microquakes as earthquakes up to a magnitude of 3.0. Other sources define them as earthquakes with a magnitude of up to 2.0. Microquakes are usually imperceptible to humans.

### Negative values

At that time, Richter had related the magnitude 0 to a value of the ground vibration that appeared to him to be the smallest possible value that could ever be measured, so he set a seismometer reading of one micrometer 100 kilometers from the center of the earthquake as the zero point. Today, modern electronic seismographs can measure ground movements that are 1000 times smaller than in the 1930s. This means, however, that very weak earthquakes that can still be measured locally today can have negative magnitudes (up to around −2 to −3).

## Relation to other scales

Despite the fundamentally different approach of the Richter scale, attempts are often made to relate it to the intensity scales, such as the modified and repeatedly further developed Mercallis scale by the Italian Giuseppe Mercalli (1850–1914). On a further intensity scale, the so-called MSK scale (Medvedev-Sponheuer-Karnik scale), the strength of an earthquake is given in twelve degrees of strength, for example. The gradation is based on both subjective and objective criteria . In Japan, the JMA scale is widely used as the intensity scale , while the JMA magnitude scale is used as the magnitude scale .

For some time now, the moment magnitude scale (abbreviation M W ) has also been specified in many cases , the determinants of which are based on the physical parameters in the earthquake focus.

The logarithmic relationship between energy and magnitude can be roughly summed up with

${\ displaystyle M = 2 + {\ frac {2} {3}} \ log _ {10} W \ quad {\ textrm {or}} \ quad W = 10 ^ {{\ frac {3} {2} } (M-2)} = \ left ({\ frac {A _ {\ max}} {100 \, A_ {0}}} \ right) ^ {3/2} \ approx {\ frac {31.6 ^ {M }} {1000}} \ ,,}$

where M is the magnitude and W is the equivalent (explosive) energy in tons of TNT .

## literature

• Charles F. Richter: An instrumental earthquake magnitude scale . In: Bulletin of the Seismological Society of America . Vol. 25, No. 1 , January 1935, ISSN  0037-1106 , p. 1-32 .
• B. Gutenberg , CF Richter : Seismicity of the Earth and Associated Phenomena . Princeton University Press, Princeton NJ 1949 (English).