This article is about the earthquake magnitude scale introduced by Charles Richter in 1935. For a review of earthquake magnitude scales, seeseismic magnitude scales. For the musical scale used for tuning harmonicas, seeRichter tuning. For the single by EPMD, seeRichter Scale (song).
TheRichter scale[1] (/ˈrɪktər/), also called theRichter magnitude scale,Richter's magnitude scale, and theGutenberg–Richter scale,[2] is a measure of the strength ofearthquakes, developed byCharles Richter in collaboration withBeno Gutenberg, and presented in Richter's landmark 1935 paper, where he called it the "magnitude scale".[3] This was later revised and renamed thelocal magnitude scale, denoted as ML or ML .[4]
Because of various shortcomings of the original ML scale, most seismological authorities now use other similar scales such as themoment magnitude scale (Mw ) to report earthquake magnitudes, but much of the news media still erroneously refers to these as "Richter" magnitudes. All magnitude scales retain thelogarithmic character of the original and are scaled to have roughly comparable numeric values (typically in the middle of the scale). Due to the variance in earthquakes, it is essential to understand the Richter scale usescommon logarithms simply to make the measurements manageable (i.e., a magnitude 3 quake factors 10³ while a magnitude 5 quake factors 105 and has seismometer readings 100 times larger).[5]
The Richter magnitude of an earthquake is determined from thelogarithm of theamplitude of waves recorded by seismographs. Adjustments are included to compensate for the variation in the distance between the various seismographs and theepicenter of the earthquake. The original formula is:[6]
whereA is the maximum excursion of theWood-Anderson seismograph, the empirical functionA0 depends only on theepicentral distance of the station,. In practice, readings from all observing stations are averaged after adjustment with station-specific corrections to obtain the ML value.[6]
Because of the logarithmic basis of the scale, each whole number increase in magnitude represents a tenfold increase in measured amplitude. In terms of energy, each whole number increase corresponds to an increase of about 31.6 times the amount of energy released, and each increase of 0.2 corresponds to approximately a doubling of the energy released.
Events with magnitudes greater than 4.5 are strong enough to be recorded by a seismograph anywhere in the world, so long as its sensors are not located in the earthquake'sshadow.[7][8][9]
The following describes the typical effects of earthquakes of various magnitudes near the epicenter.[10] The values are typical and may not be exact in a future event because intensity and ground effects depend not only on the magnitude but also on (1) the distance to the epicenter, (2) the depth of the earthquake's focus beneath the epicenter, (3) the location of the epicenter, and (4)geological conditions.
Noticeable shaking of indoor objects and rattling noises. Felt by most people in the affected area. Slightly felt outside. Generally causes zero to minimal damage. Moderate to significant damage is very unlikely. Some objects may fall off shelves or be knocked over.
Damage to a moderate number of well-built structures in populated areas.Earthquake-resistant structures survive with slight to moderate damage. Poorly designed structures receive moderate to severe damage. Felt in wider areas; up to hundreds of kilometers from the epicenter. Strong to violent shaking in the epicentral area.
Causes damage to most buildings, some to partially or completely collapse or receive severe damage. Well-designed structures are likely to receive damage. Felt across great distances with major damage mostly limited to 250 km from the epicenter.
10 to 20 per year
8.0–8.9
Great
Major damage to buildings, and structures likely to be destroyed. Will cause moderate to heavy damage to sturdy or earthquake-resistant buildings. Damaging in large areas. Felt in extremely large regions.
One per year
9.0–9.9
Extreme
Near total destruction – severe damage or collapse to all buildings. Heavy damage and shaking extend to distant locations. Permanent changes in ground topography.
The intensity and death toll depend on several factors (earthquake depth, epicenter location, and population density, to name a few) and can vary widely.
Millions of minor earthquakes occur every year worldwide, equating to hundreds every hour every day.[15] On the other hand, earthquakes of magnitude ≥8.0 occur about once a year, on average.[15] The largest recorded earthquake was theGreat Chilean earthquake of May 22, 1960, which had a magnitude of 9.5 on themoment magnitude scale.[16]
Seismologist Susan Hough has suggested that a magnitude 10 quake may represent a very approximate upper limit for what the Earth's tectonic zones are capable of, which would be the result of the largest known continuous belt of faults rupturing together (along the Pacific coast of the Americas).[17] A research at theTohoku University in Japan found that a magnitude 10 earthquake was theoretically possible if a combined 3,000 kilometres (1,900 mi) of faults from theJapan Trench to theKuril–Kamchatka Trench ruptured together and moved by 60 metres (200 ft) (or if a similar large-scale rupture occurred elsewhere). Such an earthquake would cause ground motions for up to an hour, with tsunamis hitting shores while the ground is still shaking, and if this kind of earthquake occurred, it would probably be a 1-in-10,000-year event.[18]
Prior to the development of the magnitude scale, the only measure of an earthquake's strength or "size" was a subjective assessment of the intensity of shaking observed near theepicenter of the earthquake, categorized by variousseismic intensity scales such as theRossi–Forel scale. ("Size" is used in the sense of the quantity of energy released, not the size of the area affected by shaking, though higher-energy earthquakes do tend to affect a wider area, depending on the local geology.) In 1883,John Milne surmised that the shaking of large earthquakes might generate waves detectable around the globe, and in 1899 E. Von Rehbur Paschvitz observed in Germany seismic waves attributable to an earthquake inTokyo.[19] In the 1920s,Harry O. Wood andJohn A. Anderson developed theWood–Anderson seismograph, one of the first practical instruments for recording seismic waves.[20] Wood then built, under the auspices of theCalifornia Institute of Technology and theCarnegie Institute, a network of seismographs stretching acrossSouthern California.[21] He also recruited the young and unknown Charles Richter to measure the seismograms and locate the earthquakes generating the seismic waves.[22]
In 1931,Kiyoo Wadati showed how he had measured, for several strong earthquakes in Japan, the amplitude of the shaking observed at various distances from the epicenter. He then plotted the logarithm of the amplitude against the distance and found a series of curves that showed a rough correlation with the estimated magnitudes of the earthquakes.[23] Richter resolved some difficulties with this method[24] and then, using data collected by his colleagueBeno Gutenberg, he produced similar curves, confirming that they could be used to compare the relative magnitudes of different earthquakes.[25]
Additional developments were required to produce a practical method of assigning an absolute measure of magnitude. First, to span the wide range of possible values, Richter adopted Gutenberg's suggestion of alogarithmic scale, where each step represents a tenfold increase of magnitude, similar to the magnitude scale used by astronomersfor star brightness.[26] Second, he wanted a magnitude of zero to be around the limit of human perceptibility.[27] Third, he specified the Wood–Anderson seismograph as the standard instrument for producing seismograms. Magnitude was then defined as "the logarithm of the maximum trace amplitude, expressed inmicrons", measured at a distance of 100 km (62 mi). The scale was calibrated by defining a magnitude 0 shock as one that produces (at a distance of 100 km (62 mi)) a maximum amplitude of 1 micron (1 μm, or 0.001 millimeters) on a seismogram recorded by a Wood-Anderson torsion seismometer.[28] Finally, Richter calculated a table of distance corrections,[29] in that for distances less than 200 kilometers[30] the attenuation is strongly affected by the structure and properties of the regional geology.[31]
When Richter presented the resulting scale in 1935, he called it (at the suggestion of Harry Wood) simply a "magnitude" scale.[32] "Richter magnitude" appears to have originated whenPerry Byerly told the press that the scale was Richter's and "should be referred to as such."[33] In 1956, Gutenberg and Richter, while still referring to "magnitude scale", labelled it "local magnitude", with the symbol ML , to distinguish it from two other scales they had developed, thesurface-wave magnitude (MS) andbody wave magnitude (MB) scales.[4]
How Richter magnitude is determined – the larger the value on the log graph, the higher the damage caused.
The Richter scale was defined in 1935 for particular circumstances and instruments; the particular circumstances refer to it being defined for Southern California and "implicitly incorporates theattenuative properties of Southern California crust and mantle."[34] The particular instrument used would become saturated by strong earthquakes and unable to record high values. The scale was replaced in the 1970s by themoment magnitude scale (MMS, symbol Mw ); for earthquakes adequately measured by the Richter scale, numerical values are approximately the same. Although values measured for earthquakes now are Mw , they are frequently reported by the press as Richter values, even for earthquakes of magnitude over 8, when the Richter scale becomes meaningless.
The Richter and MMS scales measure the energy released by an earthquake; another scale, theMercalli intensity scale, classifies earthquakes by theireffects, from detectable by instruments but not noticeable, to catastrophic. The energy and effects are not necessarily strongly correlated; a shallow earthquake in a populated area with soil of certain types can be far more intense in impact than a much more energetic deep earthquake in an isolated area.
Several scales have been historically described as the "Richter scale",[citation needed] especially thelocal magnitude ML and the surface wave Ms scale. In addition, thebody wave magnitude, mb , and themoment magnitude, Mw , abbreviated MMS, have been widely used for decades. A couple of new techniques to measure magnitude are in the development stage by seismologists.
All magnitude scales have been designed to give numerically similar results. This goal has been achieved well for ML , Ms , and Mw .[35][36] The mb scale gives somewhat different values than the other scales. The reason for so many different ways to measure the same thing is that at different distances, for differenthypocentral depths, and for different earthquake sizes, the amplitudes of different types of elastic waves must be measured.
ML is the scale used for the majority of earthquakes reported (tens of thousands) by local and regional seismological observatories. For large earthquakes worldwide, the moment magnitude scale (MMS) is most common, although Ms is also reported frequently.
Theseismic moment,M0, is proportional to the area of the rupture times the average slip that took place in the earthquake, thus it measures the physical size of the event. Mw is derived from it empirically as a quantity without units, just a number designed to conform to the Ms scale.[37] A spectral analysis is required to obtain M0 . In contrast, the other magnitudes are derived from a simple measurement of the amplitude of a precisely defined wave.
All scales, except Mw , saturate for large earthquakes, meaning they are based on the amplitudes of waves that have a wavelength shorter than the rupture length of the earthquakes. These short waves (high-frequency waves) are too short a yardstick to measure the extent of the event. The resulting effective upper limit of measurement for ML is about 7 and about 8.5[38] for Ms .[39]
New techniques to avoid the saturation problem and to measure magnitudes rapidly for very large earthquakes are being developed. One of these is based on the long-period P-wave;[40] The other is based on a recently discovered channel wave.[41]
Theenergy release of an earthquake,[42] which closely correlates to its destructive power, scales with the3⁄2 power of the shaking amplitude (seeMoment magnitude scale for an explanation). Thus, a difference in magnitude of 1.0 is equivalent to a factor of 31.6 () in the energy released; a difference in magnitude of 2.0 is equivalent to a factor of 1000 () in the energy released.[43] The elastic energy radiated is best derived from an integration of the radiated spectrum, but an estimate can be based on mb because most energy is carried by the high-frequency waves.
These formulae for Richter magnitude are alternatives to using Richter correlation tables based on Richter standard seismic event In the formulas below, is the epicentral distance inkilometers, and is the same distance represented as sea levelgreat circle degrees.
TheLillie empirical formula is:
where is the amplitude (maximum ground displacement) of theP wave, inmicrometers (μm), measured at 0.8 Hz.
^abEllsworth, William L. (1991)."The Richter Scale ML". In Wallace, Robert E. (ed.).The San Andreas Fault System, California. United States Geological Survey. p. 177. Professional Paper 1515. Archived fromthe original on April 25, 2016. RetrievedSeptember 14, 2008.
^This is what Richter wrote in hisElementary Seismology (1958), an opinion copiously reproduced afterward in Earth's science primers. Recent evidence shows that earthquakes with negative magnitudes (down to −0.7) can also be felt in exceptional cases, especially when the focus is very shallow (a few hundred meters). See: Thouvenot, F.; Bouchon, M. (2008). "What is the lowest magnitude threshold at which an earthquake can be felt or heard, or objects thrown into the air?," in Fréchet, J., Meghraoui, M. & Stucchi, M. (eds),Modern Approaches in Solid Earth Sciences (vol. 2),Historical Seismology: Interdisciplinary Studies of Past and Recent Earthquakes, Springer, Dordrecht, 313–326.
^McCaffrey, R. (2008). "Global frequency of magnitude 9 earthquakes".Geology.36 (3):263–266.doi:10.1130/G24402A.1.
^"Richter scale".Glossary. United States Geological Survey. March 31, 2010.
^Di Giacomo, D., Parolai, S., Saul, J., Grosser, H., Bormann, P., Wang, R. & Zschau, J., 2008. "Rapid determination of the energy magnitude Me," inEuropean Seismological Commission 31st General Assembly, Hersonissos.
^Rivera, L. & Kanamori, H., 2008. "Rapid source inversion of W phase for tsunami warning," inEuropean Geophysical Union General Assembly, pp. A-06228, Vienna.
^Vassiliou, Marius; Kanamori, Hiroo (1982). "The Energy Release in Earthquakes".Bull. Seismol. Soc. Am.72:371–387.
^Lahr, J.C. (1980). HYPOELLIPSE: A computer program for determining local earthquake hypocentral parameters, magnitude, and first-motion pattern.US Geological Survey open-file report (Report). Vol. 80–59.
Gutenberg, B.; Richter, C. F. (1956b), "Earthquake magnitude, intensity, energy, and acceleration (Second Paper)",Bulletin of the Seismological Society of America,46 (2):105–145.
