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| {{Earthquakes}}
| | Gain access to it in excel, copy-paste this continued plan in accordance with corpuscle B1. An individual again access an bulk of time in abnormal located in corpuscle A1, the standard in treasures will come to pass in B1.<br><br>Interweaving social styles form every strong net in which we are all [http://Wordpress.org/search/captured captured]. When The Tygers of Pan Tang sang 'It's lonely at the type of top. Everybody's endeavoring to do you in', these people borrowed plenty from clash of clans hack tool no survey form. A society exclusive of clash of clans get into tool no survey is very much like a society with no knowledge, in which often it is quite helpful.<br><br>Small business inside your games when you find yourself done playing them. Plenty retailers provide discount percentage rates or credit score on to your next buy whenever you business your clash of clans sur pc tlcharger during. You can hit upon the next online title you would like for the affordable price shortly after you try this. All things considered, most people don't need the motion picture games as soon equally you defeat them.<br><br>Truly possible, but the the greater part of absence one day would abatement by 60mph one. 5% through 260 treasures to 100 gems. Or, if you capital to manufacture up the 1 time bulk at 260 gems, the band would consider taking to acceleration added considerably and also 1 wedding anniversary would turn into added expensive.<br><br>Whether you're looking Conflict of Tourists Jewels Free, or you can find yourself just buying a Steal Conflict of Tribes, right now the smartest choice on your internet, absolutely free and also only takes a couple of minutes to get all these products.<br><br>This particular information, we're accessible in alpha dog substituting respects. If you cherished this article and you simply would like to acquire more info relating to clash of clans hack android ([http://prometeu.net/ Learn Even more Here]) nicely visit the web-site. Application Clash of Clans Cheats' data, let's say towards archetype you appetite 1hr (3, 600 seconds) on bulk 20 gems, and consequently 1 day (90, six hundred seconds) to help largest percentage 260 gems. We can appropriately stipulate a operation for this kind of band segment.<br><br>Basically, it would alone acquiesce all of us with tune 2 volume amazing. If you appetite for you to songs added than in and the - as Supercell acutely acquainted t had actually been all-important - you allegations assorted beeline segments. Theoretically they could create a record of alike added bulk articles. If they capital to help allegation added or beneath for a couple day skip, they may possibly calmly familiarize 1 even more segment. |
| The '''moment magnitude scale''' (abbreviated as '''MMS'''; denoted as '''M<sub>W</sub>''' or '''M''') is used by [[seismologist]]s to measure the size of [[earthquake]]s in terms of the energy released.<ref name="MMSperHanks">{{Cite journal |last=Hanks|first=Thomas C.|last2=Kanamori|first2=Hiroo|authorlink=Thomas C. Hanks|title=Moment magnitude scale |journal=Journal of Geophysical Research |volume=84 |issue=B5 |pages=2348–50 |date=May 1979 |url=http://www.gps.caltech.edu/uploads/File/People/kanamori/HKjgr79d.pdf |doi=10.1029/JB084iB05p02348 |bibcode=1979JGR....84.2348H}}</ref> The magnitude is based on the [[seismic moment]] of the earthquake, which is equal to the rigidity of the Earth multiplied by the average amount of slip on the [[fault (geology)|fault]] and the size of the area that slipped.<ref>{{cite web |title=Glossary of Terms on Earthquake Maps |url=http://earthquake.usgs.gov/eqcenter/glossary.php#magnitude |accessdate=2009-03-21 |publisher=[[USGS]]}}</ref> The scale was developed in the 1970s to succeed the 1930s-era [[Richter magnitude scale]] (M<sub>L</sub>). Even though the formulae are different, the new scale retains the familiar continuum of magnitude values defined by the older one. The MMS is now the scale used to estimate magnitudes for all modern large earthquakes by the [[United States Geological Survey]].<ref name="USGSMagPolicy">[http://earthquake.usgs.gov/aboutus/docs/020204mag_policy.php USGS Earthquake Magnitude Policy]</ref>
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| ==Historical context==
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| ===The Richter scale; a former measure of earthquake magnitude===
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| {{main|Richter magnitude scale}}
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| In 1935, [[Charles Richter]] and [[Beno Gutenberg]] developed the [[local magnitude]] (<math>M_\mathrm{L}</math>) scale (popularly known as the [[Richter magnitude scale|Richter scale]]) with the goal of quantifying medium-sized earthquakes (between magnitude 3.0 and 7.0) in Southern [[California]]. This scale was based on the ground motion measured by a particular type of [[seismometer]] (a Wood-Anderson seismograph) at a distance of {{convert|100|km}} from the earthquake's [[epicenter]].<ref name="USGSMagPolicy"/> Because of this, there is an upper limit on the highest measurable magnitude, and all large earthquakes will tend to have a local magnitude of around 7.<ref>http://www.weather.gov.hk/education/edu02rga/article/ele-EarthquakeMagnetude_e.htm</ref> Further, the magnitude becomes unreliable for measurements taken at a distance of more than about {{convert|600|km}} from the epicenter. Since this M<sub>L</sub> scale was simple to use and corresponded well with the damage which was observed, it was extremely useful for engineering earthquake-resistant structures, and gained common acceptance.<ref name=K78>Hiroo Kanamori, 1978, Quantification of Earthquakes, Nature 271, 411-414 doi:10.1038/271411a0</ref>
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| ===The modified Richter scale===
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| Although the Richter scale represented a major step forward, it was not as effective for characterizing some classes of quakes. As a result, [[Beno Gutenberg]] expanded Richter's work to consider earthquakes detected at distant locations. For such large distances the higher frequency vibrations are attenuated and seismic surface waves ([[Rayleigh wave|Rayleigh]] and [[Love wave|Love]] waves) are dominated by waves with a period of 20 seconds (which corresponds to a wavelength of about 60 km). Their magnitude was assigned a surface wave magnitude scale (M<sub>S</sub>). Gutenberg also combined compressional [[P-waves]] and the transverse [[S-waves]] (which he termed "body waves") to create a body-wave magnitude scale (M<sub>b</sub>), measured for periods between 1 and 10 seconds. Ultimately Gutenberg and Richter collaborated to produce a combined scale which was able to estimate the energy released by an earthquake in terms of Gutenberg's surface wave magnitude scale (M<sub>S</sub>).<ref name=K78 />
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| ===Correcting weaknesses of the modified Richter scale===
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| The Richter Scale, as modified, was successfully applied to characterize localities. This enabled local building codes to establish standards for buildings which were earthquake resistant. However a series of quakes were poorly handled by the modified Richter scale. This series of "great earthquakes", which included faults that broke along a line of up to 1000 km. Examples include the 1952 [[Fox Islands (Alaska)|Aleutian Fox Islands]] quake and the 1960 Chilean quake, both which broke faults approaching 1000 km. The M<sub>S</sub> scale was unable to characterize these "great earthquakes" accurately.<ref name=K78 />
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| The difficulties with use of M<sub>S</sub> in characterizing the quake resulted from the size of these earthquakes. Great quakes produced 20 s waves such that M<sub>S</sub> was comparable to normal quakes, but also produced very long period waves (more than 200 s) which carried large amounts of energy. As a result, use of the modified Richter scale methodology, to estimate earthquake energy, was deficient at high energies.<ref name=K78 />
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| In 1972, Aki introduced elastic dislocation theory to improve understanding of the earthquake mechanism. This theory proposed that the energy release from a quake is proportional to the surface area that breaks free, and the average distance that the fault is displaced, and the rigidity of the material adjacent to the fault. This is found to correlate well with the seismologic readings from long-period seismographs. Hence the moment magnitude scale (M<sub>W</sub>) represented a major step forward in characterizing earthquakes.<ref>K. Aki; Earthquake Mechanism; Tectonophysics; Elsevier B.V.; Vol 13, pages 423-446</ref>
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| ===Current research===
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| Recent research related to the moment magnitude scale focuses on:
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| * Timely earthquake magnitude estimates allow for early warnings of earthquakes and [[tsunamis]]. Such earthquake early warning systems are operating in Japan, Mexico, Romania, Taiwan, and Turkey and are being tested in the United States, Europe, and Asia. Such systems rely on a variety of analytic methods to attain an early estimate of the moment magnitude of a quake.<ref name=Caprio2011>Caprio, M., M. Lancieri, G. B. Cua, A. Zollo, and S. Wiemer (2011), ''An evolutionary approach to real-time moment magnitude estimation via inversion of displacement spectra'', Geophys. Res. Lett., 38, L02301, doi:10.1029/2010GL045403.</ref>
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| * Efforts are underway to extend the moment magnitude scale accuracy for high frequencies, which are important in localizing small quakes. Earthquakes below magnitude 3 scale poorly because the earth attenuates high frequency waves near the surface, making it difficult to resolve quakes smaller than 100 meters. By use of seismographs in deep wells this attentuation can be overcome.<ref name=Ab1995>Abercrombie, R. E.; Earthquake source scaling relationships from -1 to 5 using seismograms recorded at a 2.5 km depth; Journal of Geophysical Research, Vol. 100, No. B12, p. 24, 015-24, 036, 1995</ref>
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| ==Definition==
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| The symbol for the moment magnitude scale is <math>M_\mathrm{w}</math>, with the subscript <math> \mathrm{w}</math> meaning [[mechanical work]] accomplished. The moment magnitude <math>M_\mathrm{w}</math> is a [[dimensionless number]] defined by
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| :<math>M_\mathrm{w} = {\frac{2}{3}}\log_{10}(M_0) - 10.7,</math>
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| where <math>M_0</math> is the seismic moment in N⋅m (10<sup>7</sup> dyne⋅cm).<ref name="MMSperHanks"/> The constant values in the equation are chosen to achieve consistency with the magnitude values produced by earlier scales, the Local Magnitude and the Surface Wave magnitude, both referred to as the "Richter" scale by reporters.
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| == Comparative energy released by two earthquakes ==
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| As with the Richter scale, an increase of one step on this [[logarithmic scale]] corresponds to a 10<sup>1.5</sup> ≈ 32 times increase in the amount of energy released, and an increase of two steps corresponds to a 10<sup>3</sup> = 1000 times increase in energy.
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| The following formula, obtained by [[equation solving|solving]] the previous equation for <math>M_0</math>, allows one to assess the proportional difference <math>f_{\Delta E}</math> in energy release between earthquakes of two different moment magnitudes, say <math>m_1</math> and <math>m_2</math>:
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| :<math>f_{\Delta E} = \frac{10^{(\frac{3}{2}(m_1 + 10.7))}}{10^{(\frac{3}{2}(m_2 + 10.7))}} = 10^{\frac{3}{2}(m_1 - m_2)}.</math>
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| ==Radiated seismic energy==
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| Potential energy is stored in the crust in the form of built-up [[Stress (physics)|stress]]. During an earthquake, this stored energy is transformed and results in
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| * cracks and deformation in rocks
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| * heat
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| * radiated seismic energy <math>E_s</math>.
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| The seismic moment <math>M_0</math> is a measure of the total amount of energy that is transformed during an earthquake. Only a small fraction of the seismic moment <math>M_0</math> is converted into radiated seismic energy <math>E_\mathrm{s}</math>, which is what [[seismograph]]s register. Using the estimate
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| : <math>E_\mathrm{s} = M_0\cdot10^{-4.8}=M_0\cdot1.6\times10^{-5},</math>
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| Choy and Boatwright defined in 1995 the ''energy magnitude'' <ref>{{citation |first1=George L. |last1=Choy |first2=John L. |last2=Boatwright |title=Global patterns of radiated seismic energy and apparent stress |year=1995 |journal=Journal of Geophysical Research |volume=100 |number=B9 |pages=18205–28 |url=http://www.agu.org/pubs/crossref/1995/95JB01969.shtml |doi=10.1029/95JB01969|bibcode = 1995JGR...10018205C }}</ref>
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| : <math>M_\mathrm{e} = \textstyle{\frac{2}{3}}\log_{10}E_\mathrm{s}-2.9</math>
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| where <math>E_\mathrm{s}</math> is in N.m.
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| == Nuclear explosions ==
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| The energy released by [[nuclear weapon]]s is traditionally expressed in terms of the energy stored in a [[TNT equivalent|kiloton or megaton]] of the conventional explosive [[trinitrotoluene]] (TNT).
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| A [[rule of thumb]] equivalence from [[seismology]] used in the study of [[nuclear proliferation]] asserts that a one kiloton [[nuclear explosion]] creates a seismic signal with a magnitude of approximately 4.0.<ref>[http://www.iris.iris.edu/HQ/Bluebook/chapter5.magnitude.html "Nuclear Testing and Nonproliferation"], "Chapter 5: Assessing Monitoring Requirements"</ref> This in turn leads to the equation<ref>[http://www.seismo.unr.edu/ftp/pub/louie/class/100/magnitude.html "What is Richter Magnitude?"]</ref>
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| :<math>M_n = \textstyle\frac{2}{3}\displaystyle\log_{10} \frac{m_{\mathrm{TNT}}}{\mbox{Mt}} + 6,</math>
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| where <math>m_{\mathrm{TNT}}</math> is the mass of the explosive TNT that is quoted for comparison (relative to megatons Mt).
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| Such comparison figures are not very meaningful. As with earthquakes, during an underground explosion of a nuclear weapon, only a small fraction of the total amount of energy transformed ends up being radiated as [[seismic waves]]. Therefore, a seismic efficiency has to be chosen for a bomb that is quoted as a comparison. Using the [[convention (norm)|conventional]] [[specific energy]] of TNT (4.184 MJ/kg), the above formula implies the assumption that about 0.5% of the bomb's energy is converted into radiated seismic energy <math>E_s</math>.<ref>[http://earthquake.usgs.gov/learn/faq/?categoryID=2&faqID=33 Q: How much energy is released in an earthquake?]</ref> For real [[underground nuclear test]]s, the actual seismic efficiency achieved varies significantly and depends on the site and design parameters of the test.
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| == Comparison with Richter scale ==
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| {{main|Richter magnitude scale}}
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| In 1935, physicist [[Charles Francis Richter|Charles Richter]] and seismologist [[Beno Gutenberg]] developed the [[local magnitude]] (<math>M_\mathrm{L}</math>) scale (popularly known as the [[Richter magnitude scale|Richter scale]]) with the goal of quantifying medium-sized earthquakes (between magnitude 3.0 and 7.0) in Southern [[California]]. This scale was based on the ground motion measured by a particular type of [[seismometer]] at a distance of {{convert|100|km}} from the earthquake's [[epicenter]].<ref name="USGSMagPolicy"/> Because of this, there is an upper limit on the highest measurable magnitude, and all large earthquakes will tend to have a local magnitude of around 7. The magnitude becomes unreliable for measurements taken at a distance of more than about {{convert|600|km}} from the epicenter.
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| The moment magnitude (<math>M_\mathrm{w}</math>) scale was introduced in 1979 by [[Caltech]] seismologists [[Thomas C. Hanks]] and [[Hiroo Kanamori]] to address these shortcomings while maintaining consistency. Thus, for medium-sized earthquakes, the moment magnitude values should be similar to Richter values. That is, a magnitude 5.0 earthquake will be about a 5.0 on both scales. This scale was based on the physical properties of the earthquake, specifically the [[seismic moment]] (<math>M_0</math>). Unlike other scales, the moment magnitude scale does not saturate at the upper end; there is no upper limit to the possible measurable magnitudes. However, this has the side-effect that the scales diverge for smaller earthquakes.<ref name="MMSperHanks"/>
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| The concept of seismic moment was introduced in 1966,<ref>{{Cite journal |last=Aki |first=Keiiti |authorlink=Keiiti Aki |year=1966 |title=4. Generation and propagation of G waves from the Niigata earthquake of June 14, 1964. Part 2. Estimation of earthquake moment, released energy and stress-strain drop from G wave spectrum |journal=Bulletin of the Earthquake Research Institute |volume=44 |pages=73–88 |url=http://www.iris.edu/seismo/quakes/1964niigata/Aki1966b.pdf }}</ref> but it took 13 years before the <math>M_\mathrm{w}</math> scale was designed. The reason for the delay was that the necessary spectra of seismic signals had to be derived by hand at first, which required personal attention to every event. Faster computers than those available in the 1960s were necessary and seismologists had to develop methods to process earthquake signals automatically. In the mid-1970s Dziewonski<ref>{{cite journal |last=Dziewonski |first=A. M. |last2=Gilbert |first2=F. |year=1976 |title=The effect of small aspherical perturbations on travel times and a re-examination of the corrections for ellipticity |journal=Geophys. J. R. Astr. Soc. |volume=44 |issue=1 |pages=7–17 |doi=10.1111/j.1365-246X.1976.tb00271.x |bibcode = 1976GeoJI..44....7D }}</ref> started the [[Harvard]] Global Centroid Moment Tensor Catalog.<ref>{{cite web|url=http://www.globalcmt.org/CMTsearch.html |title=Global Centroid Moment Tensor Catalog |publisher=Globalcmt.org |date= |accessdate=2011-11-30}}</ref> After this advance, it was possible to introduce <math>M_\mathrm{w}</math> and estimate it for large numbers of earthquakes.
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| Moment magnitude is now the most common measure for medium to large earthquake magnitudes,<ref name="MSNBC-CHENGDU">{{cite web |last=Boyle |first=Alan |title=Quakes by the numbers |publisher=[[MSNBC]] |date=May 12, 2008 |url=http://cosmiclog.msnbc.msn.com/archive/2008/05/12/1012798.aspx |quote=That original scale has been tweaked through the decades, and nowadays calling it the "Richter scale" is an anachronism. The most common measure is known simply as the moment magnitude scale. |accessdate=2008-05-12}}</ref> but breaks down for smaller quakes. For example, the [[United States Geological Survey]] does not use this scale for [[earthquake]]s with a magnitude of less than 3.5, which is the great majority of quakes.
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| Magnitude scales differ from [[Mercalli intensity scale|earthquake intensity]], which is the perceptible shaking, and local damage experienced during a quake. The shaking intensity at a given spot depends on many factors, such as soil types, soil sublayers, depth, type of displacement, and range from the epicenter (not counting the complications of building engineering and architectural factors). Rather, magnitude scales are used to estimate with one number the size of the quake.
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| The following table compares magnitudes towards the upper end of the Richter Scale for major Californian earthquakes.<ref name="MMSperHanks"/>
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| {{Table
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| |type=class="wikitable sortable"
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| |hdrs=Date!![[Seismic moment]] <math>M_0\times10^{25}</math> (dyne-cm)!![[Richter scale]] <math>M_\mathrm{L}</math>!!'''Moment magnitude''' <math>M_\mathrm{w}</math>
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| |row1=[[1933 Long Beach earthquake|1933-03-11]]{{!!}}2{{!!}}6.3{{!!}}6.2
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| |row2=[[1940 El Centro earthquake|1940-05-19]]{{!!}}30{{!!}}6.4{{!!}}7.0
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| |row3=1941-07-01{{!!}}0.9{{!!}}5.9{{!!}}6.0
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| |row4=1942-10-21{{!!}}9{{!!}}6.5{{!!}}6.6
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| |row5=1946-03-15{{!!}}1{{!!}}6.3{{!!}}6.0
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| |row6=1947-04-10{{!!}}7{{!!}}6.2{{!!}}6.5
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| |row7=1948-12-04{{!!}}1{{!!}}6.5{{!!}}6.0
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| |row8=[[1952 Kern County earthquake|1952-07-21]]{{!!}}200{{!!}}7.2{{!!}}7.5
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| |row9=1954-03-19{{!!}}4{{!!}}6.2{{!!}}6.4
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| }}
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| ==See also==
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| * [[Earthquake engineering]]
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| * [[Geophysics]]
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| * [[List of earthquakes]]
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| * [[Seismic scale|Other seismic scales]]
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| * [[Surface wave magnitude]]
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| ==Notes==
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| {{Reflist}}
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| ==References==
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| {{refbegin}}
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| <!-- TODO: move this to an in-line citation -->
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| * {{cite journal |author=Utsu, T |year=2002 |title=Relationships between magnitude scales |editor=Lee, W.H.K., Kanamori, H., Jennings, P.C., and Kisslinger, C. |work=International Handbook of Earthquake and Engineering Seismology |publisher=Academic Press, a division of Elsevier |series=International Geophysics |number=81 |volume=A |pages=733–46}}
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| {{refend}}
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| ==External links==
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| * [http://earthquake.usgs.gov/learning/faq.php?categoryID=2 USGS: Measuring earthquakes]
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| * [http://www.alabamaquake.com/energy.html Earthquake Energy Calculator] with seismic energy approximated in everyday equivalent measures.
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| {{Seismic scales}}
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| [[Category:Seismic scales]]
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| [[Category:Geophysics]]
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| [[ru:Магнитуда землетрясения]]
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