Richter scale

The Richter magnitude scale, also known as the local magnitude ($M_{L}$) scale, assigns a single number to quantify the amount of seismic energy released by an earthquake. It is a base-10 logarithmic scale obtained by calculating the logarithm of the combined horizontal amplitude (shaking amplitude) of the largest displacement from zero on a particular type of seismometer (Wood–Anderson torsion). So, for example, an earthquake that measures 5.0 on the Richter scale has a shaking amplitude 10 times larger than one that measures 4.0. The effective upper limit of measurement for local magnitude $M_{L}$ is just below 9 for local magnitudes and just below 10 for moment magnitude when applied to large earthquakes.

The Richter scale has been superseded by the moment magnitude scale, which is calibrated to give generally similar values for medium-sized earthquakes (magnitudes between 3 and 7). Unlike the Richter scale, the moment magnitude scale reports a fundamental property of the earthquake derived from instrument data, rather than reporting instrument data which is not always comparable across earthquakes, and does not saturate in the high-magnitude range. Since the Moment Magnitude scale generally yields very similar results to the Richter scale, magnitudes of earthquakes reported in the mass media are usually reported without indicating which scale is being used.

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.

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 seismometer. 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 separate the vastly larger number of smaller earthquakes from the few larger earthquakes observed in California at the time.

His inspiration was the apparent magnitude scale used in astronomy to describe the brightness of stars and other celestial objects. 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 seismograph recorded using a Wood-Anderson torsion seismometer 100 km (62 mi) from the earthquake epicenter. This choice was intended to prevent negative magnitudes from being assigned. However, the Richter scale has no actual lower limit, and sensitive modern seismographs now routinely record quakes with negative magnitudes.

Because M_L was not designed to to be applied to data with distances to the hypocenter of the earthquake greater than 600 km, its values become unreliable when the earthquake is larger than 7 and Richter's original method is no longer applied.

To overcome this shortcoming, 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. M_S and m_b can still saturate when the earthquake is big enough.

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.

Richter magnitudes

Graph showing frequency (per century; blue line) and energy (brown bars) for the Richter scale. The graph is doubly logarithmic and both axes are numerically identical.

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:

$M_{\mathrm {L} }=\log _{10}A-\log _{10}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 of about 4.6 or greater are strong enough to be recorded by any of the seismographs in the world, given that the seismograph's sensors are not located in an 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).

Richter magnitudes	Description	Earthquake effects	Frequency of occurrence
Less than 2.0	Micro	Micro earthquakes, not felt.	About 8,000 per day
2.0–2.9	Minor	Generally not felt, but recorded.	About 1,000 per day
3.0–3.9		Often felt, but rarely causes damage.	49,000 per year (est.)
4.0–4.9	Light	Noticeable shaking of indoor items, rattling noises. Significant damage unlikely.	6,200 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.	800 per year
6.0–6.9	Strong	Can be destructive in areas up to about 160 kilometres (100 mi) across in populated areas.	120 per year
7.0–7.9	Major	Can cause serious damage over larger areas.	18 per year
8.0–8.9	Great	Can cause serious damage in areas several hundred miles across.	1 per year
9.0–9.9		Devastating in areas several thousand miles across.	1 per 20 years
10.0+	Epic	Never recorded; see below for equivalent seismic energy yield.	Extremely rare (Unknown)

(Based on U.S. Geological Survey documents.)

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 (M_W) of 9.5.

Richter magnitudes examples

The following table lists the approximate energy equivalents in terms of TNT explosive force – though note that the energy is that released underground (i.e. a small atomic bomb blast will not simply cause light shaking of indoor items) rather than the overground energy release. Most energy from an earthquake is not transmitted to and through the surface; instead, it dissipates into the crust and other subsurface structures.

Richter Approximate Magnitude	Approximate TNT for Seismic Energy Yield	Joule equivalent	Example
0.0	15.0 g (0.529 oz)	63.1 kJ
0.5	84.4 g (2.98 oz)	355 kJ	Large hand grenade
1.0	474 g (1.05 lb)	2.00 MJ	Construction site blast
1.5	2.67 kg (5.88 lb)	11.2 MJ	World War II conventional bombs
2.0	15.0 kg (33.1 lb)	63.1 MJ	Late World War II conventional bombs
2.5	84.4 kg (186 lb)	355 MJ	World War II blockbuster bomb
3.0	474 kg (1.05×103 lb)	2.00 GJ	Massive Ordnance Air Blast bomb
3.5	2.67 metric tons	11.2 GJ	Chernobyl nuclear disaster, 1986
4.0	15.0 metric tons	63.1 GJ	Small atomic bomb
4.3	42.3 metric tons	117.0 GJ	Kent Earthquake (Britain), 2007
4.5	84.4 metric tons	355 GJ	Tajikistan earthquake, 2006
5.0	474 metric tons	2.00 TJ	Seismic yield of Nagasaki atomic bomb (Total yield including air yield 21 kT, 88 TJ) Lincolnshire earthquake (UK), 2008 Ontario-Quebec earthquake (Canada), 2010
5.5	2.67 kilotons	11.2 TJ	Little Skull Mtn. earthquake (Nevada, USA), 1992 Alum Rock earthquake (California, USA), 2007 Chino Hills earthquake (Los Angeles, USA), 2008
5.6	3.77 gigacalories	15.8 TJ	Newcastle Earthquake Australia, 1989
6.0	15.0 kilotons	62.7 TJ	Double Spring Flat earthquake (Nevada, USA), 1994
6.3	42.3 kilotons	178 TJ	Rhodes earthquake (Greece), 2008 Christchurch earthquake (New Zealand), 2011
6.4	59.7 kilotons	251 TJ	Kaohsiung earthquake (Taiwan), 2010
6.5	84.4 kilotons	355 TJ	Caracas earthquake (Venezuela), 1967 Eureka earthquake (California, USA), 2010
6.6	119 kilotons	501 TJ	San Fernando earthquake (California, USA), 1971
6.7	168 kilotons	708 TJ	Northridge earthquake (California, USA), 1994
6.8	238 kilotons	1.00 PJ	Nisqually earthquake (Anderson Island, WA), 2001 Gisborne earthquake (Gisborne, NZ), 2007
6.9	336 kilotons	1.41 PJ	San Francisco Bay Area earthquake (California, USA), 1989 Pichilemu earthquake (Chile), 2010
7.0	474 kilotons	2.00 PJ	Java earthquake (Indonesia), 2009 Haiti earthquake, 2010
7.1	670 kilotons	2.82 PJ	San Juan earthquake (Argentina), 1944 Canterbury earthquake (New Zealand), 2010
7.2	938 kilotons	3.98 PJ	Vrancea earthquake (Romania), 1977 Baja California earthquake (Mexico), 2010
7.5	2.67 megatons	11.2 PJ	Kashmir earthquake (Pakistan), 2005 Antofagasta earthquake (Chile), 2007
7.8	7.52 megatons	31.6 PJ	Tangshan earthquake (China), 1976 Hawke's Bay earthquake (New Zealand), 1931 Luzon earthquake (Philippines), 1990 Sumatra earthquake (Indonesia), 2010
8.0	15.0 megatons	63.1 PJ	Mino-Owari earthquake (Japan), 1891 San Juan earthquake (Argentina), 1894 San Francisco earthquake (California, USA), 1906 Queen Charlotte Islands earthquake (British Columbia, Canada), 1949 México City earthquake (Mexico), 1985 Gujarat earthquake (India), 2001 Chincha Alta earthquake (Peru), 2007 Sichuan earthquake (China), 2008
8.1	21.2 megatons	89.1 PJ	Guam earthquake, August 8, 1993
8.35 (approx.)	50 megatons	210 PJ	Tsar Bomba - Largest thermonuclear weapon ever tested
8.5	84.4 megatons	355 PJ	Toba eruption 75,000 years ago; among the largest known volcanic events. Sumatra earthquake (Indonesia), 2007
8.7	168 megatons	708 PJ	Sumatra earthquake (Indonesia), 2005 1883 eruption of Krakatoa
8.8	238 megatons	1.00 EJ	Chile earthquake, 2010
8.9	336 megatons	1.41 EJ	Japan earthquake, 2011
9.0	474 megatons	2.00 EJ	Lisbon Earthquake (Portugal), All Saints Day, 1755
9.2	946 megatons	3.98 EJ	Anchorage earthquake (Alaska, USA), 1964
9.3	1.34 gigatons	5.62 EJ	Indian Ocean earthquake, 2004
9.5	2.67 gigatons	11.2 EJ	Valdivia earthquake (Chile), 1960
10.0	15.0 gigatons	63.1 EJ	Never recorded
12.55	100 teratons	422 ZJ	Yucatán Peninsula impact (creating Chicxulub crater) 65 Ma ago (108 megatons; over 4x1030 ergs = 400 ZJ).
32.0	1×1021 yottatons	4.2×1030 YJ	Approximate magnitude of the starquake on the magnetar SGR 1806-20, registered on December 27, 2004.

See also

• Earthquake
• Seismic scale
• Seismite
• Moment magnitude scale
• Japan Meteorological Agency seismic intensity scale
• Order of magnitude
• Rohn Emergency Scale for measuring the magnitude (intensity) of any emergency

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.