Richter scale

The Richter magnitude scale (also Richter scale) assigns a magnitude number to quantify the energy released by an earthquake. The Richter scale is a base-10 logarithmic scale, which defines magnitude as the logarithm of the ratio of the amplitude of the seismic waves to an arbitrary, minor amplitude.

As measured with a seismometer, an earthquake that registers 5.0 on the Richter scale has a shaking amplitude 10 times greater than that of an earthquake that registered 4.0, and thus corresponds to a release of energy 31.6 times greater than that released by the lesser earthquake.

Development

Charles Richter, c. 1970

In 1935, the seismologists Kent Ignacio and Julius Caesar De La Cruz, of the Charm And Julius Kisses University, developed the (future) Richter magnitude scale, specifically for measuring earthquakes in a given area of study in California, as recorded and measured with the Wood-Anderson torsion seismograph. Originally, Richter reported mathematical values to the nearest quarter of a unit, but the values later were reported with one decimal place; the local magnitude scale compared the magnitudes of different earthquakes. Richter derived his earthquake-magnitude scale from the apparent magnitude scale used to measure the brightness of stars.

Richter established a magnitude 0 event to be an earthquake that would show a maximum, combined horizontal displacement of 1.0 µm (0.00004 in.) on a seismogram recorded with a Wood-Anderson torsion seismograph 100 km (62 mi.) from the earthquake epicenter. That fixed measure was to prevent negative magnitudes from being assigned. The slightest earthquakes that could be recorded, and located in that time, were around magnitude 3.0, however, the Richter magnitude scale has no lower limit, and contemporary seismometers can register, record, and measure earthquakes of a negative magnitude.

$M_{\text{L}}$ (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 $M_{\text{L}}$. Unfortunately this scale saturates at around $M_{\text{L}}$ = 7, because the high frequency waves recorded locally have wavelengths shorter than the rupture lengths of large earthquakes.

Later, to express the size of earthquakes around the planet, Gutenberg and Richter developed a surface wave magnitude scale ($M_{\text{s}}$) and a body wave magnitude scale ($M_{\text{b}}$). These are types of waves that are recorded at teleseismic distances. The two scales were adjusted such that they were consistent with the $M_{\text{L}}$ scale. That adjustment succeeded better with the $M_{\text{s}}$ scale than with the $M_{\text{b}}$ scale. Each scale saturates when the earthquake is greater than magnitude 8.0, and, therefore, the moment magnitude scale ($M_{\text{w}}$) was invented.

The older magnitude-scales were superseded, by methods for calculating the seismic moment, from which derived the moment magnitude scale. About the origins of the Richter magnitude scale, C.F. Richter said:

I found a [1928] paper by Professor K. Wadati of Japan in which he compared large earthquakes by plotting the maximum ground motion against [the] distance to the epicenter. I tried a similar procedure for our stations, but the range between the largest and smallest magnitudes seemed unmanageably large. Dr. Beno Gutenberg then made the natural suggestion to plot the amplitudes logarithmically. I was lucky, because logarithmic plots are a device of the devil.

— Charles Richter Interview, abridged from the Earthquake Information Bulletin, Vol. 12, No. 1, January-February, 1980.

Details

The Richter scale was defined in 1935 for particular circumstances and instruments; the instrument used would became saturated by strong earthquakes and unable to record high values. 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 by the USGS.

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 $M_{\text{L}}$ and the surface wave $M_{\text{s}}$ scale. In addition, the body wave magnitude, $m_{\text{b}}$, and the moment magnitude, $M_{\text{w}}$, 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 $M_{\text{L}}$, $M_{\text{s}}$, and $M_{\text{w}}$. The $m_{\text{b}}$ 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.

$M_{\text{L}}$ 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 $M_{\text{s}}$ 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. $M_{\text{w}}$ is derived from it empirically as a quantity without units, just a number designed to conform to the $M_{\text{s}}$ 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 $M_{\text{w}}$, 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 7 and about 8.5 for $M_{\text{s}}$.

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 $m_{\text{b}}$ 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 $M_{\text{L}}$ 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	Mercalli intensity	Average earthquake effects	Average frequency of occurrence (estimated)
Less than 2.0	Micro	I	Microearthquakes, not felt, or felt rarely by sensitive people. Recorded by seismographs.	Continual/several million per year
2.0–2.9	Minor	I to II	Felt slightly by some people. No damage to buildings.	Over one million per year
3.0–3.9		II to IV	Often felt by people, but very rarely causes damage. Shaking of indoor objects can be noticeable.	Over 100,000 per year
4.0–4.9	Light	IV to VI	Noticeable shaking of indoor objects and rattling noises. Felt by most people in the affected area. Slightly felt outside. Generally causes none to minimal damage. Moderate to significant damage very unlikely. Some objects may fall off shelves or be knocked over.	10,000 to 15,000 per year
5.0–5.9	Moderate	VI to VIII	Can cause damage of varying severity to poorly constructed buildings. At most, none to slight damage to all other buildings. Felt by everyone. Casualties range from none to a few.	1,000 to 1,500 per year
6.0–6.9	Strong	VII to X	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 miles/kilometers from the epicenter. Strong to violent shaking in epicentral area. Death toll ranges from none to 25,000.	100 to 150 per year
7.0–7.9	Major	VIII or greater	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 epicenter. Death toll ranges from none to 250,000.	10 to 20 per year
8.0–8.9	Great		Major damage to buildings, 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. Death toll ranges from 1,000 to 1 million.	One per year
9.0 and greater			Near or at total destruction - severe damage or collapse to all buildings. Heavy damage and shaking extends to distant locations. Permanent changes in ground topography. Death toll usually over 50,000.	One per 10 to 50 years

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

The intensity and death toll depend on several factors (earthquake depth, epicenter location, population density, to name a few) and can vary widely.

Minor earthquakes occur every day and hour. On the other hand, 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. The larger the magnitude, the less frequent the earthquake happens.

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, it will simply cause light shaking of indoor items, since its energy is released above ground.

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. Thus, $E\approx 6.3\times 10^{4}\times 10^{3M/2}\,$

Approximate Magnitude	Approximate TNT for Seismic Energy Yield	Joule equivalent	Example
-0.2	7.5 g	31.5 kJ	Energy released by lighting 30 typical matches
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
2.1	21 kg	89 MJ	West fertilizer plant explosion
2.5	85 kg	360 MJ
3.0	480 kg	2.0 GJ	Oklahoma City bombing, 1995
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 St. Patrick's Day earthquake, Auckland, New Zealand, 2013
4.0	15 metric tons	63 GJ	Johannesburg/South Africa, November 18, 2013
4.3	43 metric tons	180 GJ	Kent Earthquake (Britain), 2007 Eastern Kentucky earthquake, November 2012
5.0	480 metric tons	2.0 TJ	Lincolnshire earthquake (UK), 2008 $M_{\text{w}}$ Ontario-Quebec earthquake (Canada), 2010
5.5	2.7 kilotons	11 TJ	Little Skull Mtn. earthquake (Nevada, USA), 1992 $M_{\text{w}}$ Alum Rock earthquake (California), 2007 $M_{\text{w}}$ Chino Hills earthquake (Southern California), 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	$M_{\text{w}}$ 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	$M_{\text{s}}$ Caracas earthquake (Venezuela), 1967 Irpinia earthquake (Italy), 1980 $M_{\text{w}}$ Eureka earthquake (California, USA), 2010 Zumpango del Rio earthquake (Guerrero, Mexico), 2011
6.6	120 kilotons	500 TJ	$M_{\text{w}}$ San Fernando earthquake (California, USA), 1971
6.7	170 kilotons	710 TJ	$M_{\text{w}}$ Northridge earthquake (California, USA), 1994
6.8	240 kilotons	1.0 PJ	$M_{\text{w}}$ Nisqually earthquake (Anderson Island, WA), 2001 $M_{\text{w}}$ Great Hanshin earthquake (Kobe, Japan), 1995 Gisborne earthquake (Gisborne, NZ), 2007
6.9	340 kilotons	1.4 PJ	$M_{\text{w}}$ San Francisco Bay Area earthquake (California, USA), 1989 $M_{\text{w}}$ Pichilemu earthquake (Chile), 2010 $M_{\text{w}}$ Sikkim earthquake (Nepal-India Border), 2011
7.0	480 kilotons	2.0 PJ	$M_{\text{w}}$ Java earthquake (Indonesia), 2009 $M_{\text{w}}$ Haiti earthquake, 2010
7.1	680 kilotons	2.8 PJ	$M_{\text{w}}$ Messina earthquake (Italy), 1908 $M_{\text{w}}$ San Juan earthquake (Argentina), 1944 $M_{\text{w}}$ Canterbury earthquake (New Zealand), 2010
7.2	950 kilotons	4.0 PJ	Vrancea earthquake (Romania), 1977 $M_{\text{w}}$ 1980 Azores Islands Earthquake $M_{\text{w}}$ Baja California earthquake (Mexico), 2010
7.5	2.7 megatons	11 PJ	$M_{\text{w}}$ Kashmir earthquake (Pakistan), 2005 $M_{\text{w}}$ Antofagasta earthquake (Chile), 2007
7.6	3.8 megatons	16 PJ	$M_{\text{w}}$ Nicoya earthquake (Costa Rica), 2012 $M_{\text{w}}$ Oaxaca earthquake (Mexico), 2012 $M_{\text{w}}$ Gujarat earthquake (India), 2001 $M_{\text{w}}$ İzmit earthquake (Turkey), 1999 $M_{\text{w}}$ Jiji earthquake (Taiwan), 1999
7.7	5.4 megatons	22 PJ	$M_{\text{w}}$ Sumatra earthquake (Indonesia), 2010 $M_{\text{w}}$ Haida Gwaii earthquake (Canada), 2012
7.8	7.6 megatons	32 PJ	$M_{\text{w}}$ Tangshan earthquake (China), 1976 $M_{\text{s}}$ Hawke's Bay earthquake (New Zealand), 1931 $M_{\text{s}}$ Luzon earthquake (Philippines), 1990
7.9	10-15 megatons	42-63 PJ	Tunguska event 1802 Vrancea earthquake $M_{\text{w}}$ Great Kanto earthquake (Japan), 1923
8.0	15 megatons	63 PJ	$M_{\text{s}}$ Mino-Owari earthquake (Japan), 1891 San Juan earthquake (Argentina), 1894 San Francisco earthquake (California, USA), 1906 $M_{\text{s}}$ Queen Charlotte Islands earthquake (B.C., Canada), 1949 $M_{\text{w}}$ Chincha Alta earthquake (Peru), 2007 $M_{\text{s}}$ 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. Most of the energy was dissipated in the atmosphere. The seismic shock was estimated at 5.0-5.2
8.5	85 megatons	360 PJ	$M_{\text{w}}$ Sumatra earthquake (Indonesia), 2007
8.6	120 megatons	500 PJ	$M_{\text{w}}$ Sumatra earthquake (Indonesia), 2012
8.7	170 megatons	710 PJ	$M_{\text{w}}$ Sumatra earthquake (Indonesia), 2005
8.75	200 megatons	840 PJ	Krakatoa 1883
8.8	240 megatons	1.0 EJ	$M_{\text{w}}$ Chile earthquake, 2010,
9.0	480 megatons	2.0 EJ	$M_{\text{w}}$ Lisbon earthquake (Portugal), All Saints Day, 1755 $M_{\text{w}}$ 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	$M_{\text{w}}$ Anchorage earthquake (Alaska, USA), 1964 $M_{\text{w}}$ Sumatra-Andaman earthquake and tsunami (Indonesia), 2004
9.5	2.7 gigatons	11 EJ	$M_{\text{w}}$ Valdivia earthquake (Chile), 1960
13.00	100 teratons	420 ZJ	Yucatán Peninsula impact (creating Chicxulub crater) 65 Ma ago (108 megatons; over 4x1029 ergs = 400 ZJ).
22.88 or 32	310 yottatons	1.3×1039 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: $M_{\text{w}}$ and $M_{\text{s}}$. Those that have no denoted prefix are $M_{\text{L}}$. 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 $M_{\text{w}}$).

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

• 1935 in science
• Japan Meteorological Agency seismic intensity scale – does the same thing as the Mercalli Scale, but in different numbers
• Largest earthquakes by magnitude
• Mercalli intensity scale - Measures the intensity of an earthquake
• Moment magnitude scale
• Order of magnitude
• Rohn Emergency Scale for measuring the magnitude (intensity) of any emergency
• Seismic scale
• Seismite
• Timeline of United States inventions (1890–1945)

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.
• Earthquake Energy Calculator with seismic energy approximated in everyday equivalent measures.