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| {{Earthquakes}}
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| The '''surface wave magnitude''' ('''<math>M_s</math>''') '''scale''' is one of the [[Seismic scale#Magnitude scales|magnitude scales]] used in [[seismology]] to describe the size of an [[earthquake]]. It is based on measurements in [[Rayleigh wave|Rayleigh surface waves]] that travel primarily along the uppermost layers of the earth. It is currently used in [[People's Republic of China]] as a national standard ('''GB 17740-1999''') for categorising earthquakes.<ref name="GB 1740-1999">{{cite web
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| | publisher=General Administration of Quality Supervision, Inspection, and Quarantine of P.R.C.
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| | author=XU Shaokui, LU Yuanzhong, GUO Lucan, CHEN Shanpei, XU Zhonghuai, XIAO Chengye, FENG Yijun (许绍燮、陆远忠、郭履灿、陈培善、许忠淮、肖承邺、冯义钧)
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| | url=http://www.dccdnc.ac.cn/html/zcfg/gfxwj1.jsp
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| | title=Specifications on Seismic Magnitudes (地震震级的规定)
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| | date=1999-04-26
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| | accessdate=2008-09-14
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| | language=Chinese
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| }}
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| </ref> | |
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| Surface wave magnitude was initially developed in 1950s by the same researchers who developed the [[local magnitude scale]] M<sub>L</sub> in order to improve resolution on larger earthquakes:<ref name="Ellsworth">{{cite paper
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| | publisher=USGS
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| | author=William L. Ellsworth
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| | url=http://www.johnmartin.com/earthquakes/eqsafs/safs_694.htm
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| | title=SURFACE-WAVE MAGNITUDE (M<sub>S</sub>) AND BODY-WAVE MAGNITUDE (mb)
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| | year=1991
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| | accessdate=2008-09-14
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| }} {{Dead link|date=October 2010|bot=H3llBot}}
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| </ref>
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| {{Quotation|The successful development of the local-magnitude scale encouraged [[Beno Gutenberg|Gutenberg]] and [[Charles Richter|Richter]] to develop magnitude scales based on teleseismic observations of earthquakes. Two scales were developed, one based on surface waves, <math>M_s</math>, and one on body waves, mb.
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| <p>Surface waves with a period near 20 s generally produce the largest amplitudes on a standard long-period seismograph, and so the amplitude of these waves is used to determine <math>M_s</math>, using an equation similar to that used for <math>M_L</math>.| William L. Ellsworth |The San Andreas Fault System, California (USGS Professional Paper 1515), 1990-1991}} | |
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| Recorded magnitudes of earthquakes during that time, commonly [[Richter magnitude scale|attributed to Richter]], could be either <math>M_s</math> or <math>M_L</math>.
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| ==Definition==
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| The formula to calculate surface wave magnitude is:<ref name="GB 1740-1999" /><ref>It is obvious that the entire formula cannot stand [[dimensional analysis]] without additional qualifications. References here provide no such qualification.</ref>
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| <math>M = \log_{10}\left(\frac{A}{T}\right)_{\text{max}} + \sigma(\Delta)</math>
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| where A is the maximum [[particle displacement]] in surface waves ([[vector sum]] of the two horizontal displacements) in [[micrometre|μm]], T is the corresponding [[Period (physics)|period]] in [[Second|s]], Δ is the [[epicentral distance]] in [[Degree (angle)|°]], and
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| <math>\sigma(\Delta) = 1.66\cdot\log_{10}(\Delta) + 3.5</math> | |
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| According to GB 17740-1999, the two horizontal displacements must be measured at the same time or within 1/8 of a period; if the two displacements have different periods, weighed sum must be used:
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| <math> T = \frac{T_{N}A_{N} + T_{E}A_{E}}{A_{N} + A_{E}}</math>
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| where A<sub>N</sub> is the north-south displacement in μm, A<sub>E</sub> is the east-west displacement in μm, T<sub>N</sub> is the period corresponding to A<sub>N</sub> in s, and T<sub>E</sub> is the period corresponding to A<sub>E</sub> in s.
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| ==Other studies==
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| Vladimír Tobyáš and Reinhard Mittag proposed to relate surface wave magnitude to [[local magnitude scale]] M<sub>L</sub>, using<ref name="Tobyas summary">{{cite paper
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| | publisher=Studia Geophysica et Geodaetica | |
| | author=Vladimír Tobyáš and Reinhard Mittag
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| | url=http://www.springerlink.com/content/lv140444x5m01362/ | |
| | title=Local magnitude, surface wave magnitude and seismic energy | |
| | date=1991-02-06 | |
| | accessdate=2008-09-14
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| }}
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| </ref>
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| :<math> M_s = -3.2 + 1.45 M_{L} </math>
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| Other formulas include three revised formulae proposed by CHEN Junjie et al.:<ref>{{cite paper
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| | publisher=Journal of Seismological Research (《地震研究》) | |
| | author=CHEN Junjie, CHI Tianfeng, WANG Junliang, CHI Zhencai (陈俊杰, 迟天峰, 王军亮, 迟振才)
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| | url=http://scholar.ilib.cn/Abstract.aspx?A=dzyj200201016
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| | title=Study of Surface Wave Magnitude in China (中国面波震级研究)
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| | date=2002-01-01
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| | accessdate=2008-09-14
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| | language=Chinese
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| }}
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| </ref>
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| :<math> M_s = \log_{10}\left(\frac{A_{max}}{T}\right) + 1.54\cdot \log_{10}(\Delta) + 3.53 </math>
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| :<math> M_s = \log_{10}\left(\frac{A_{max}}{T}\right) + 1.73\cdot \log_{10}(\Delta) + 3.27 </math>
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| and | |
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| :<math> M_s = \log_{10}\left(\frac{A_{max}}{T}\right) - 6.2\cdot \log_{10}(\Delta) + 20.6 </math>
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| ==See also==
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| *[[Moment magnitude scale]]
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| *[[Seismic scale]]
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| ==Notes and references==
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| {{Reflist}}
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| ==External links==
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| *{{cite paper
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| | publisher=USGS
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| | author=Robert E. Wallace, ed.
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| | url=http://www.johnmartin.com/earthquakes/eqsafs/
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| | title=The San Andreas Fault System, California (Professional Paper 1515)
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| | year=1991
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| | accessdate=2008-09-14
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| }}
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| *[http://earthquake.usgs.gov/learning/glossary.php?termID=118 Visual Glossary - magnitude] - [[United States Geological Survey|USGS]]
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| *[http://eqseis.geosc.psu.edu/~cammon/HTML/Classes/IntroQuakes/Notes/earthquake_size.html Earthquake Size]
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| {{Seismic scales}}
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| {{DEFAULTSORT:Surface Wave Magnitude}}
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| [[Category:Seismic scales]]
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