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 of the largest displacement from zero on a Wood–Anderson torsion seismometer output. 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 limit of measurement for local magnitude $M_{L}$ is about 6.8.

Though still widely used, the Richter scale has been superseded by the moment magnitude scale, which gives generally similar values.

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 of 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 decimal numbers were used later. 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 (0.00001in) 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 upper or lower limit, and sensitive modern seismographs now routinely record quakes with negative magnitudes.

Because M_L is derived from measurements taken from a single, band-limited seismograph, its values saturate when the earthquake is larger than 6.8. To overcome this shortcoming, Gutenberg and Richter later developed a magnitude scales 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 traditional magnitude scales have been superseded by the implementation of methods for estimating the seismic moment and its associated moment magnitude scale, although the former are still widely used because they can be calculated quickly.

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:

$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.

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. This table 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	Microearthquakes, 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.

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

Richter Approximate Magnitude	Approximate TNT for Seismic Energy Yield	Joule equivalent	Example
0.0	1 kg (2.2 lb)	4.2 MJ
0.5	5.6 kg (12.4 lb)	23.5 MJ	Large hand grenade
1.0	32 kg (70 lb)	134.4 MJ	Construction site blast
1.5	178 kg (392 lb)	747.6 MJ	WWII conventional bombs
2.0	1 metric ton	4.2 GJ	Late WWII conventional bombs
2.5	5.6 metric tons	23.5 GJ	WWII blockbuster bomb
3.0	32 metric tons	134.4 GJ	Massive Ordnance Air Blast bomb
3.5	178 metric tons	747.6 GJ	Chernobyl nuclear disaster, 1986
4.0	1 kiloton	4.2 TJ	Small atomic bomb
4.5	5.6 kilotons	23.5 TJ
5.0	32 kilotons	134.4 TJ	Nagasaki atomic bomb (actual seismic yield was negligible since it detonated in the atmosphere) Lincolnshire earthquake (UK), 2008
5.4	150 kilotons	625 TJ	2008 Chino Hills earthquake (Los Angeles, United States)
5.5	178 kilotons	747.6 TJ	Little Skull Mtn. earthquake (NV, USA), 1992 Alum Rock earthquake (CA, USA), 2007
6.0	1 megaton	4.2 PJ	Double Spring Flat earthquake (NV, USA), 1994
6.5	5.6 megatons	23.5 PJ	Caracas (Venezuela), 1967 Rhodes (Greece), 2008 Eureka Earthquake (Humboldt County CA, USA), 2010
6.7	16.2 megatons	67.9 PJ	Northridge earthquake (CA, USA), 1994
6.9	26.8 megatons	112.2 PJ	San Francisco Bay Area earthquake (CA, USA), 1989
7.0	32 megatons	134.4 PJ	Java earthquake (Indonesia), 2009, 2010 Haiti Earthquake
7.1	50 megatons	210 PJ	Energy released is equivalent to that of Tsar Bomba, the largest thermonuclear weapon ever tested 1944 San Juan earthquake
7.5	178 megatons	747.6 PJ	Kashmir earthquake (Pakistan), 2005 Antofagasta earthquake (Chile), 2007
7.8	600 megatons	2.4 EJ	Tangshan earthquake (China), 1976
8.0	1 gigaton	4.2 EJ	San Francisco earthquake (CA, USA), 1906 Queen Charlotte earthquake (BC, Canada), 1949 México City earthquake (Mexico), 1985 Gujarat earthquake (India), 2001 Chincha Alta earthquake (Peru), 2007 Sichuan earthquake (China), 2008 (initial estimate: 7.8) 1894 San Juan earthquake
8.5	5.6 gigatons	23.5 EJ	Toba eruption 75,000 years ago; the largest known volcanic event Sumatra earthquake (Indonesia), 2007
9.0	32 gigatons	134.4 EJ	Lisbon Earthquake (Lisbon, Portugal), All Saints Day, 1755
9.1	67 gigatons	477 EJ	Indian Ocean earthquake, 2004 (40 ZJ in this case)
9.2	90.7 gigatons	379.7 EJ	Anchorage earthquake (AK, USA), 1964
9.5	178 gigatons	747.6 EJ	Valdivia earthquake (Chile), 1960 (251 ZJ in this case)
10.0	1 teraton	4.2 ZJ	Never recorded by humans
13.0	108 megatons = 100 teratons	5x1030 ergs = 500 ZJ	Yucatán Peninsula impact (causing Chicxulub crater) 65 Ma ago.

See also

• Earthquake
• Seismic scale
• Seismite
• Moment magnitude scale
• Japan Meteorological Agency seismic intensity scale
• Order of magnitude

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.