Richter scale

The Richter magnitude scale is any of 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 ≈ 31.6227 times greater than one that measures 4.0.

Since the mid 20th century, the use of the Richter magnitude scale has largely been supplanted by the moment magnitude scale in many countries. However, the Richter scale is still widely used in Russia and other CIS countries.

Development

Charles Richter, c. 1970

Developed in 1935 by Charles Richter in partnership with Beno Gutenberg, both from 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. Richter, who since childhood had aspirations in astronomy, drew inspiration from the apparent magnitude scale used to account for the brightness of stars lost due to distance. 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 (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. 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.

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 classified 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 $M_{w}$. 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. 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 $M_{s}$.

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, the other is based on a recently discovered channel wave.

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. 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:

$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 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'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, the location of the epicenter and geological conditions (certain terrains can amplify seismic signals).

Magnitude	Description	Average maximum Mercalli intensity	Average earthquake effects	Average frequency of occurrence (estimated)
Less than 2.0	Micro	I to II	Microearthquakes, not felt, or felt rarely by sensitive people. Recorded by seismographs.	Continual/several million per year
2.0–2.9	Minor	I to III	Generally felt by few to many up to several miles/kilometers from the epicenter. Weak shaking in the felt area. Recorded by seismographs.	Over one million per year
3.0–3.9		II to V	Often felt in the area by many to all, but very rarely causes damage. Can be felt tens of miles/kilometers from the epicenter.	Over 100,000 per year
4.0–4.9	Light	III to VII	Noticeable shaking of indoor items, rattling noises. Many to everyone feel it with slight to strong intensity. Slightly felt outside. Generally causes none to slight damage. Moderate, heavy, major, or significant damage unlikely. Some falling of objects.	10,000 to 15,000 per year
5.0–5.9	Moderate	IV to VIII	Can cause moderate to major damage to poorly constructed buildings. At most, none to slight damage to well-designed buildings. Can be felt hundreds of miles/kilometers from the epicenter at low/lower intensity. People can report it as very strong to violent intensity tens of miles from the epicenter.	1,000 to 1,500 per year
6.0–6.9	Strong	VI to X	Can be damaging/destructive in populated areas. Damage to many to all buildings, poorly designed structures receive moderate to severe. Earthquake-resistant structures survive with slight to moderate damage. Most likely felt hundreds of miles/kilometers from the epicenter. Death toll usually is between none to more than 25,000.	100 to 150 per year
7.0–7.9	Major	VII to XII	Can cause great/greater damage over larger areas. Damage to all buildings; many to all receive moderate to very heavy damage, or collapse partially to completely. Death toll is usually between none to more than 150,000.	10 to 20 per year
8.0–8.9	Great	VIII to XII	Can cause major damage across very wide, large areas. Many to all buildings in epicentral area severely damaged or destroyed. Buildings further from the epicenter most likely will receive damage, also. Very strong shaking up to a few hundred miles/kilometers away. Death toll is usually between 50 to more than 500,000, however some earthquakes this magnitude have killed none.	One per year (rarely none, two, or over two per year)
9.0–9.9			Destructive to very devastating in extremely large areas. Many to all buildings severely damaged to completely destroyed up to even tens of miles from the epicenter. Easily felt and/or damaging at extremely distant points. Ground changes. Death toll usually is between 250 and one million.	One per 5 to 50 years
10.0+	Massive/Epic	IX to XII	Heavy, widespread, colossal damage/devastation across enormous areas. Large ground changes. Never recorded; see below for equivalent seismic energy yield. Death toll is usually at least 1,000 to over 10 million.	None per year (unknown, extremely rare, or impossible/may not be possible)

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

The intensity and death toll can vary a lot because it depends on several factors (earthquake depth, epicenter location, and damage to name a few).

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.

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. 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, 31.6227 to the power of 0 equals 1, 31.6227 to the power of 1 equals 31.6227 and 31.6227 to the power of 2 equals 1000. Therefore, an 8.0 on the Richter scale releases 31.6227 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
1.2	1.1 kg	4.9 MJ	Single stick of dynamite [DynoMax Pro]
1.4	2.2 kg	9.8 MJ	Seismic impact of typical small construction 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, Henderson, Nevada, 1988 Dallas, Texas earthquake, September 30, 2012
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	Maine/New England, October 16, 2012
4.3	43 metric tons	180 GJ	Kent Earthquake (Britain), 2007
5.0	480 metric tons	2.0 TJ	Lincolnshire earthquake (UK), 2008 $M_{W}$ Ontario-Quebec earthquake (Canada), 2010
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, Australia, 1989 Oklahoma, 2011 Pernik, Bulgaria, 2012
6.0	15 kilotons	63 TJ	Double Spring Flat earthquake (Nevada, USA), 1994 Approximate magnitude of Virginia/Washington, D.C./East Coast earthquake, 2011 Approximate yield of the Little Boy Atomic Bomb dropped on Hiroshima (~16 kt)
6.3	43 kilotons	180 TJ	$M_{W}$ Rhodes earthquake (Greece), 2008 Jericho earthquake (British Palestine), 1927 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
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	$M_{W}$ Nicoya earthquake (Costa Rica), 2012 $M_{W}$ Oaxaca earthquake (Mexico), 2012 $M_{W}$ Gujarat earthquake (India), 2001 $M_{W}$ İzmit earthquake (Turkey), 1999 $M_{W}$ Jiji earthquake (Taiwan), 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
7.9	10-15 megatons	42-63 PJ	Tunguska event 1802 Vrancea earthquake
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
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
8.6	-	-	$M_{W}$ Sumatra earthquake (Indonesia), 2012
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 $M_{W}$ The Great Japan earthquake, March 2011
9.15	800 megatons	3.3 EJ	Toba eruption 75,000 years ago; among the largest known volcanic events.
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, equivalent to an earthquake rupturing a very large, massive, lengthy fault, or an extemely rare/impossible megaquake
12.55	100 teratons	420 ZJ	Yucatán Peninsula impact (creating Chicxulub crater) 65 Ma ago (108 megatons; over 4x1030 ergs = 400 ZJ).
32.0	1.5×1043 tons	6.3×1052 J	Approximate magnitude of the starquake on the magnetar SGR 1806-20, registered on December 27, 2004.

• 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 $M_{W}$).

Magnitude empirical formulae

These formulae are an alternative method to calculate Richter magnitude instead of using Richter correlation tables based on Richter standard seismic event ($M_{\mathrm {L} }$=0, A=0.001mm, D=100 km).

The Lillie empirical formula:

$M_{\mathrm {L} }=\log _{10}A-2.48+2.76\log _{10}\Delta$

Where:

• A is the amplitude (maximum ground displacement) of the P-wave, in micrometers, measured at 0.8 Hz.
• $\Delta$ is the epicentral distance, in km.

For distance less than 200 km:

$M_{\mathrm {L} }=\log _{10}A+1.6\log _{10}D-0.15$

For distance between 200 km and 600 km:

$M_{\mathrm {L} }=\log _{10}A+3.0\log _{10}D-3.38$

where A is seismograph signal amplitude in mm, D distance in km.

The Bisztricsany (1958) empirical formula for epicentral distances between 4˚ to 160˚:

$M_{\mathrm {L} }=2.92+2.25\log _{10}(\tau )-0.001\Delta ^{\circ }$

Where:

• $M_{\mathrm {L} }$ is magnitude (mainly in the range of 5 to 8)
• $\tau$ is the duration of the surface wave in seconds
• $\Delta$ is the epicentral distance in degrees.

The Tsumura empirical formula:

$M_{\mathrm {L} }=-2.53+2.85\log _{10}(F-P)+0.0014\Delta ^{\circ }$

Where:

• $M_{\mathrm {L} }$ is the magnitude (mainly in the range of 3 to 5).
• $F-P$ is the total duration of oscillation in seconds.
• $\Delta$ is the epicentral distance in kilometers.

The Tsuboi, University of Tokio, empirical formula:

$M_{\mathrm {L} }=\log _{10}A+1.73\log _{10}\Delta -0.83$

Where:

• $M_{\mathrm {L} }$ is the magnitude.
• $A$ is the amplitude in um.
• $\Delta$ is the epicentral distance in kilometers.

See also

• Earthquake
• Largest earthquakes by magnitude
• Seismic scale
• Seismite
• Mercalli intensity scale
• 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.