Richter magnitude scale

Part of a series on earthquakes
Types
Foreshock • Aftershock • Blind thrust Doublet • Interplate • Intraplate Megathrust • Remotely triggered • Slow Submarine • Supershear Tsunami • Earthquake swarm
Causes
Fault movement • Volcanism • Induced seismicity
Characteristics
Epicenter • Hypocenter • Shadow zone Seismic wave • P-wave • S-wave
Measurement
Mercalli scale • Richter scale Moment scale • Surface wave magnitude scale Body wave magnitude scale • Seismometer Earthquake duration magnitude
Prediction
Coordinating Committee for Earthquake Prediction Earthquake sensitive
Other
Shear wave splitting • Adams–Williamson equation Flinn-Engdahl regions • Earthquake engineering Seismite • Seismology

The expression Richter magnitude scale refers to a number of ways to assign a single number to quantify the energy contained in an earthquake.

In all cases, the magnitude is a base-10 logarithmic scale obtained by calculating the logarithm of the amplitude of waves measured by a seismograph. An earthquake that measures 5.0 on the Richter scale has a shaking amplitude 10 times larger and corresponds to an energy release of √1000 ≈ 31.6 times greater than one that measures 4.0.^[1]

1 Development
2 Details
3 Richter magnitudes
- 3.1 Examples
4 See also
5 References
6 External links

Development

Developed in 1935 by Charles Richter in partnership with Beno Gutenberg, both of the California Institute of Technology, the scale was firstly intended to be used only in a particular study area in California, and on seismograms recorded on a particular instrument, the Wood-Anderson torsion seismograph. Richter originally reported values to the nearest quarter of a unit, but values were later reported with one decimal place. His motivation for creating the local magnitude scale was to compare the size of different earthquakes.^[1]

His inspiration was the apparent magnitude scale used in astronomy to describe the brightness of stars and other celestial objects.^[2] Richter arbitrarily chose a magnitude 0 event to be an earthquake that would show a maximum combined horizontal displacement of 1 µm (0.00004 in) on a seismogram recorded using a Wood-Anderson torsion seismograph 100 km (62 mi) from the earthquake epicenter. This choice was intended to prevent negative magnitudes from being assigned. The smallest earthquakes that could be recorded and located at the time were of magnitude 3, approximately. However, the Richter scale has no lower limit, and sensitive modern seismographs now routinely record quakes with negative magnitudes.

M_L (local magnitude) was not designed to be applied to data with distances to the hypocenter of the earthquake greater than 600 km^[3] (373 mi). For national and local seismological observatories the standard magnitude scale is today still M_L. Unfortunately this scale saturates at M6.5, approximately, because the high frequency waves recorded locally have wavelengths shorter than the rupture lengths of large earthquakes.

To be able to measure the size of earthquakes around the globe, Gutenberg and Richter later developed a magnitude scale based on surface waves, surface wave magnitude M_S; and another based on body waves, body wave magnitude m_b.^[4] These are types of waves that are recorded at teleseismic distances. The two scales were adjusted such that they were consistent with the M_L scale. This succeeded better with the M_s scale than with the m_b scale. Both of these scales saturate when the earthquake is bigger than magnitude 8 and therefore the moment magnitude scale, M_w, was invented.^[5]

These older magnitude scales have been superseded by the implementation of methods for estimating the seismic moment, creating the moment magnitude scale, although the former are still widely used because they can be calculated quickly.

Details

The Richter scale proper was defined in 1935 for particular circumstances and instruments; the instrument used saturated for strong earthquakes. The scale was replaced by the moment magnitude scale (MMS); for earthquakes adequately measured by the Richter scale, numerical values are approximately the same. Although values measured for earthquakes now are actually $M_w$ (MMS), they are frequently reported as Richter values, even for earthquakes of magnitude over 8, where the Richter scale becomes meaningless. Anything above 5 is classed as a risk.

The Richter and MMS scales measure the energy released by an earthquake; another scale, the Mercalli intensity scale, classifies earthquakes by their effects, 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 than a much more energetic deep earthquake in an isolated area.

There are several scales which have historically been described as the "Richter scale," especially the local magnitude $M_L$ and the surface wave $M_s$ scale. In addition, the body wave magnitude, $m_b$ , and the moment magnitude, $M_w$ , abbreviated MMS, have been widely used for decades, and a couple of new techniques to measure magnitude are in the development stage.

All magnitude scales have been designed to give numerically similar results. This goal has been achieved well for $M_L$ , $M_s$ , and $M_w$ .^[6]^[7] The $m_b$ 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 different hypocentral depths, and for different earthquake sizes, the amplitudes of different types of elastic waves must be measured.

$M_L$ 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 is most common, although $M_s$ is also reported frequently.

The seismic moment, $M_o$ , 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. $M_w$ is derived from it empirically as a quantity without units, just a number designed to conform to the $M_s$ scale.^[8] A spectral analysis is required to obtain $M_o$ , whereas the other magnitudes are derived from a simple measurement of the amplitude of a specifically defined wave.

All scales, except $M_w$ , saturate for large earthquakes, meaning they are based on the amplitudes of waves which 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 $M_L$ is about 6.5 and about 8 for $M_s$ .^[9]

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,^[10] the other is based on a recently discovered channel wave.^[11]

The energy release of an earthquake, which closely correlates to its destructive power, scales with the ³⁄₂ power of the shaking amplitude. Thus, a difference in magnitude of 1.0 is equivalent to a factor of 31.6 ( $=({10^{1.0}})^{(3/2)}$ ) in the energy released; a difference in magnitude of 2.0 is equivalent to a factor of 1000 ( $=({10^{2.0}})^{(3/2)}$ ) in the energy released.^[12] The elastic energy radiated is best derived from an integration of the radiated spectrum, but one can base an estimate on $m_b$ because most energy is carried by the high frequency waves.

Richter magnitudes

The Richter magnitude of an earthquake is determined from the logarithm of the amplitude of waves recorded by seismographs (adjustments are included to compensate for the variation in the distance between the various seismographs and the epicenter of the earthquake). The original formula is:^[13]

$M_\mathrm{L} = \log_{10} A - \log_{10} A_\mathrm{0}(\delta) = \log_{10} [A / A_\mathrm{0}(\delta)],\$

where A is the maximum excursion of the Wood-Anderson seismograph, the empirical function A₀ depends only on the epicentral distance of the station, $\delta$ . In practice, readings from all observing stations are averaged after adjustment with station-specific corrections to obtain the M_L value.

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 a doubling of the energy released.

Events with magnitudes greater than about 4.6 are strong enough to be recorded by a seismograph anywhere in the world, so long as its sensors are not located in the earthquake's shadow.

The following describes the typical effects of earthquakes of various magnitudes near the epicenter. The values are typical only and should be taken with extreme caution, since intensity and thus ground effects depend not only on the magnitude, but also on the distance to the epicenter, the depth of the earthquake's focus beneath the epicenter, and geological conditions (certain terrains can amplify seismic signals).

Magnitude	Description	Earthquake effects	Frequency of occurrence
Less than 2.0	Micro	Micro earthquakes, not felt.^[14]	Continual
2.0–2.9	Minor	Generally not felt, but recorded.	1,300,000 per year (est.)
3.0–3.9	Minor	Often felt, but rarely causes damage.	130,000 per year (est.)
4.0–4.9	Light	Noticeable shaking of indoor items, rattling noises. Significant damage unlikely.	13,000 per year (est.)
5.0–5.9	Moderate	Can cause major damage to poorly constructed buildings over small regions. At most slight damage to well-designed buildings.	1,319 per year
6.0–6.9	Strong	Can be destructive in areas up to about 160 kilometres (99 mi) across in populated areas.	134 per year
7.0–7.9	Major	Can cause serious damage over larger areas.	15 per year
8.0–8.9	Great	Can cause serious damage in areas several hundred kilometres across.	1 per year
9.0–9.9	Great	Devastating in areas several thousand kilometres across.	1 per 10 years (est.)
10.0+	Massive	Never recorded, widespread devastation across very large areas; see below for equivalent seismic energy yield.	Extremely rare (Unknown/May not be possible)

(Based on U.S. Geological Survey documents.)^[15]

Great earthquakes occur once a year, on average. The largest recorded earthquake was the Great Chilean Earthquake of May 22, 1960, which had a magnitude of 9.5 on the moment magnitude scale.^[16] The Richter scale is open ended. There is no upper limit to the magnitude of an earthquake on the Richter scale.^[17]

Examples

The following table lists the approximate energy equivalents in terms of TNT explosive force – though note that the earthquake energy is released underground rather than overground.^[18] Most energy from an earthquake is not transmitted to and through the surface; instead, it dissipates into the crust and other subsurface structures. In contrast, a small atomic bomb blast (see nuclear weapon yield) will not simply cause light shaking of indoor items, since its energy is released above ground.

Following, 31.623 to the power of 0 equals 1, 31.623 to the power of 1 equals 31.623 and 31.623 to the power of 2 equals 1000. Therefore, an 8.0 on the Richter scale releases 31.623 times more energy than a 7.0 and a 9.0 on the Richter scale releases 1000 times more energy than a 7.0.

Approximate Magnitude	Approximate TNT for Seismic Energy Yield	Joule equivalent	Example
0.0	15 g	63 kJ
0.2	30 g	130 kJ	Large hand grenade
0.5	85 g	360 kJ
1.0	480 g	2.0 MJ	Small construction site blast
1.5	2.7 kg	11 MJ
2.0	15 kg	63 MJ
2.5	85 kg	360 MJ
3.0	480 kg	2.0 GJ
3.5	2.7 metric tons	11 GJ	PEPCON fuel plant explosion, 1988
3.87	9.5 metric tons	40 GJ	Explosion at Chernobyl nuclear power plant, 1986
3.91	11 metric tons	46 GJ	Massive Ordnance Air Blast bomb
4.0	15 metric tons	63 GJ
4.3	43 metric tons	180 GJ	Kent Earthquake (Britain), 2007
4.5	85 metric tons	360 GJ	Tajikistan earthquake, 2006
5.0	480 metric tons	2.0 TJ	Lincolnshire earthquake (UK), 2008 $M_W$ Ontario-Quebec earthquake (Canada), 2010^[19]^[20]
5.5	2.7 kilotons	11 TJ	Little Skull Mtn. earthquake (Nevada, USA), 1992 $M_W$ Alum Rock earthquake (California, USA), 2007 $M_W$ Chino Hills earthquake (Los Angeles, USA), 2008
5.6	3.8 kilotons	16 TJ	Newcastle Earthquake Australia, 1989 Sparks Earthquake (Oklahoma, USA), 2011
6.0	15 kilotons	63 TJ	Double Spring Flat earthquake (Nevada, USA), 1994
6.3	43 kilotons	180 TJ	$M_W$ Rhodes earthquake (Greece), 2008 Christchurch earthquake (New Zealand), 2011
6.4	60 kilotons	250 TJ	Kaohsiung earthquake (Taiwan), 2010 Vancouver earthquake (Canada), 2011
6.5	85 kilotons	360 TJ	$M_S$ Caracas earthquake (Venezuela), 1967 $M_W$ Eureka earthquake (California, USA), 2010 Zumpango del Rio earthquake (Guerrero, Mexico), 2011^[21]
6.6	120 kilotons	500 TJ	$M_W$ San Fernando earthquake (California, USA), 1971
6.7	170 kilotons	710 TJ	$M_W$ Northridge earthquake (California, USA), 1994
6.8	240 kilotons	1.0 PJ	$M_W$ Nisqually earthquake (Anderson Island, WA), 2001 Gisborne earthquake (Gisborne, NZ), 2007
6.9	340 kilotons	1.4 PJ	$M_W$ San Francisco Bay Area earthquake (California, USA), 1989 $M_W$ Pichilemu earthquake (Chile), 2010 $M_W$ Sikkim earthquake (Nepal-India Border), 2011
7.0	480 kilotons	2.0 PJ	$M_W$ Java earthquake (Indonesia), 2009 $M_W$ Haiti earthquake, 2010
7.1	680 kilotons	2.8 PJ	$M_W$ Messina earthquake (Italy), 1908 $M_W$ San Juan earthquake (Argentina), 1944 $M_W$ Canterbury earthquake (New Zealand), 2010
7.2	950 kilotons	4.0 PJ	Vrancea earthquake (Romania), 1977 $M_W$ Baja California earthquake (Mexico), 2010
7.5	2.7 megatons	11 PJ	$M_W$ Kashmir earthquake (Pakistan), 2005 $M_W$ Antofagasta earthquake (Chile), 2007
7.6	3.8 megatons	16 PJ	$M_W$ Gujarat earthquake (India), 2001 $M_W$ İzmit earthquake (Turkey), 1999
7.7	5.4 megatons	22 PJ	$M_W$ Sumatra earthquake (Indonesia), 2010
7.8	7.6 megatons	32 PJ	$M_W$ Tangshan earthquake (China), 1976 $M_S$ Hawke's Bay earthquake (New Zealand), 1931 $M_S$ Luzon earthquake (Philippines), 1990
8.0	15 megatons	63 PJ	$M_S$ Mino-Owari earthquake (Japan), 1891 San Juan earthquake (Argentina), 1894 San Francisco earthquake (California, USA), 1906 $M_S$ Queen Charlotte Islands earthquake (B.C., Canada), 1949 $M_W$ Chincha Alta earthquake (Peru), 2007 $M_S$ Sichuan earthquake (China), 2008 Kangra earthquake, 1905
8.1	21 megatons	89 PJ	México City earthquake (Mexico), 1985 Guam earthquake, August 8, 1993^[22]
8.35	50 megatons	210 PJ	Tsar Bomba - Largest thermonuclear weapon ever tested
8.5	85 megatons	360 PJ	$M_W$ Sumatra earthquake (Indonesia), 2007
8.7	170 megatons	710 PJ	$M_W$ Sumatra earthquake (Indonesia), 2005
8.75	200 megatons	840 PJ	Krakatoa 1883
8.8	240 megatons.	1.0 EJ	$M_W$ Chile earthquake, 2010,
9.0	480 megatons	2.0 EJ	$M_W$ Lisbon earthquake (Portugal), All Saints Day, 1755 $M_W$ 2011 Tōhoku earthquake and tsunami (Japan)
9.15	800 megatons	3.3 EJ	Toba eruption 75,000 years ago; among the largest known volcanic events.^[23]
9.2	950 megatons	4.0 EJ	$M_W$ Anchorage earthquake (Alaska, USA), 1964 $M_W$ Sumatra-Andaman earthquake and tsunami (Indonesia), 2004
9.5	2.7 gigatons	11 EJ	$M_W$ Valdivia earthquake (Chile), 1960
10.0	15 gigatons	63 EJ	Never recorded
12.55	100 teratons	420 ZJ	Yucatán Peninsula impact (creating Chicxulub crater) 65 Ma ago (10⁸ megatons; over 4x10³⁰ ergs = 400 ZJ).^[24]^[25]^[26]^[27]^[28]
32	1.5×10⁴³ tons	6.3×10⁵² J	Approximate magnitude of the starquake on the magnetar SGR 1806-20, registered on December 27, 2004.^[29]

Quakes using the more modern magnitude scales will denote their abbreviations: $M_W$ and $M_S$ . Those that have no denoted prefix are $M_L$ . Please be advised that the magnitude "number" (example 7.0) displayed for those quakes on this table may represent a significantly greater or lesser release in energy than by the correctly given magnitude (example $M_W$ ).

References

^ ^a ^b The Richter Magnitude Scale
^ Hough, S.E. (2007). Richter's scale: measure of an earthquake, measure of a man. Princeton University Press. p. 121. ISBN 9780691128078. http://books.google.co.uk/books?id=rvmDeAxEiO8C&pg=PA121&dq=richter+scale+star+brightness&hl=en&ei=bA7jToe6M4Wc8gOPgJH5Aw&sa=X&oi=book_result&ct=result&resnum=1&sqi=2&ved=0CDQQ6AEwAA#v=onepage&q=richter%20scale%20star%20brightness&f=false. Retrieved 10 December 2011.
^ "USGS Earthquake Magnitude Policy". USGS. March 29, 2010. http://earthquake.usgs.gov/aboutus/docs/020204mag_policy.php.
^ William L. Ellsworth (1991). SURFACE-WAVE MAGNITUDE (M_s) AND BODY-WAVE MAGNITUDE (mb). USGS. http://www.johnmartin.com/earthquakes/eqsafs/safs_694.htm. Retrieved 2008-09-14.
^ Kanamori
^ Richter, C.F., 1936. "An instrumental earthquake magnitude scale", Bulletin of the Seismological Society of America 25, no., 1-32.
^ Richter, C.F., "Elementary Seismology", edn, Vol., W. H. Freeman and Co., San Francisco, 1956.
^ Hanks, T. C. and H. Kanamori, 1979, "Moment magnitude scale", Journal of Geophysical Research, 84, B5, 2348.
^ "Richter scale". Glossary. USGS. March 31, 2010. http://earthquake.usgs.gov/hazards/qfaults/glossary.php.
^ Di Giacomo, D., Parolai, S., Saul, J., Grosser, H., Bormann, P., Wang, R. & Zschau, J., 2008. Rapid determination of the enrgy magnitude Me, in European Seismological Commission 31st General Assembly, Hersonissos.
^ Rivera, L. & Kanamori, H., 2008. Rapid source inversion of W phase for tsunami warning, in European Geophysical Union General Assembly, pp. A-06228, Vienna.
^ USGS: Measuring the Size of an Earthquake, Section 'Energy, E'
^ Ellsworth, William L. (1991). The Richter Scale M_L, from The San Andreas Fault System, California (Professional Paper 1515). USGS. pp. c6, p177. http://www.johnmartin.com/earthquakes/eqsafs/safs_693.htm. Retrieved 2008-09-14.
^ This is what Richter wrote in his Elementary Seismology (1958), an opinion copiously reproduced afterwards 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 metres). 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.
^ [1]
^ USGS: List of World's Largest Earthquakes
^ http://tremor.nmt.edu/faq/how.html
^ FAQs – Measuring Earthquakes
^ "Magnitude 5.0 – Ontario-Quebec border region, Canada". earthquake.usgs.gov. http://earthquake.usgs.gov/earthquakes/recenteqsww/Quakes/us2010xwa7.php#details. Retrieved 2010-06-23.
^ "Moderate 5.0 earthquake shakes Toronto, Eastern Canada and U.S.". nationalpost.com. http://news.nationalpost.com/2010/06/23/tremors-felt-in-toronto-ottawa-reports/. Retrieved 2010-06-23.
^ km al NOROESTE de ZUMPANGO DEL RIO, GRO &regresar=catalogo1 "Zumpango Del Rio Earthquake" (in Mexican). Servicio Sismologico Nacional. http://www.ssn.unam.mx/website/jsp/localizacion.jsp?&archivo=111210_194725.gif&evento=1&fecha=2011-12-10&hora=19:47:25&latitud=17.84&longitud=-99.98&profundidad=58&magnitud=6.5&epicentro=53 km al NOROESTE de ZUMPANGO DEL RIO, GRO &regresar=catalogo1. Retrieved 28 December 2011.
^ "M8.1 South End of Island August 8, 1993.". eeri.org. http://www.eeri.org/site/reconnaissance-activities/64-guam/182-m81southendofisland. Retrieved 2011-03-11..
^ Petraglia, M.; R. Korisettar, N. Boivin, C. Clarkson,4 P. Ditchfield,5 S. Jones,6 J. Koshy,7 M.M. Lahr,8 C. Oppenheimer,9 D. Pyle,10 R. Roberts,11 J.-C. Schwenninger,12 L. Arnold,13 K. White. (6 July 2007). "Middle Paleolithic Assemblages from the Indian Subcontinent Before and After the Toba Super-eruption". Science 317 (5834): 114–116. doi:10.1126/science.1141564. PMID 17615356.
^ Bralower, Timothy J.; Charles K. Paull; R. Mark Leckie (1998). "The Cretaceous-Tertiary boundary cocktail: Chicxulub impact triggers margin collapse and extensive sediment gravity flows". Geology 26: 331–334. Bibcode 1998Geo....26..331B. doi:10.1130/0091-7613(1998)026<0331:TCTBCC>2.3.CO;2. ISSN 0091-7613. http://www.geosc.psu.edu/people/faculty/personalpages/tbralower/Braloweretal1998.pdf. Retrieved 2009-09-03.
^ Klaus, Adam; Norris, Richard D.; Kroon, Dick; Smit, Jan (2000). "Impact-induced mass wasting at the K-T boundary: Blake Nose, western North Atlantic". Geology 28: 319–322. Bibcode 2000Geo....28..319K. doi:10.1130/0091-7613(2000)28<319:IMWATK>2.0.CO;2. ISSN 0091-7613.
^ Busby, Cathy J.; Grant Yip; Lars Blikra; Paul Renne (2002). "Coastal landsliding and catastrophic sedimentation triggered by Cretaceous-Tertiary bolide impact: A Pacific margin example?". Geology 30: 687–690. Bibcode 2002Geo....30..687B. doi:10.1130/0091-7613(2002)030<0687:CLACST>2.0.CO;2. ISSN 0091-7613.
^ Simms, Michael J. (2003). "Uniquely extensive seismite from the latest Triassic of the United Kingdom: Evidence for bolide impact?". Geology 31: 557–560. Bibcode 2003Geo....31..557S. doi:10.1130/0091-7613(2003)031<0557:UESFTL>2.0.CO;2. ISSN 0091-7613.
^ Simkin, Tom; Robert I. Tilling; Peter R. Vogt; Stephen H. Kirby; Paul Kimberly; David B. Stewart (2006). "This dynamic planet. World map of volcanoes, earthquakes, impact craters, and plate tectonics. Inset VI. Impacting extraterrestrials scar planetary surfaces". U.S. Geological Survey. http://mineralsciences.si.edu/tdpmap/pdfs/impact.pdf. Retrieved 2009-09-03.
^ Phil Plait (2009). "Anniversary of a cosmic blast". discovermagazine.com. http://blogs.discovermagazine.com/badastronomy/2009/12/27/anniversary-of-a-cosmic-blast/. Retrieved 2010-11-26.

External links

IRIS Real-time Seismic Monitor of the Earth
USGS: magnitude and intensity comparison
USGS: Earthquake Magnitude Policy
USGS: 2000–2006 Earthquakes worldwide
USGS: 1990–1999 Earthquakes worldwide
Alaska Railroad Earthquake with a table of yield-to-magnitude relations.

Seismic scales

Modern scales

Intensity scales	European Macroseismic Scale (EMS) · INQUA · Liedu · Medvedev-Sponheuer-Karnik (MSK) · Modified Mercalli (MM) · Shindo

Magnitude scales	Body wave magnitude · Local magnitude (Richter scale) · Moment magnitude · Surface wave magnitude

Historical scales

Mercalli-Cancani-Sieberg (MCS) · Mercalli-Wood-Neuman (MWN) · Omori · Rossi–Forel