View source for Earth:Surface wave magnitude

{{Earthquakes}}

The '''surface wave magnitude''' ('''<math>M_s</math>''') scale is one of the magnitude scales used in [[Earth:Seismology|seismology]] to describe the size of an [[Earth:Earthquake|earthquake]]. It is based on measurements in [[Physics: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
 | publisher=General Administration of Quality Supervision, Inspection, and Quarantine of P.R.C.
 | 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)
 | url=http://www.dccdnc.ac.cn/html/zcfg/gfxwj1.jsp
 | title=Specifications on Seismic Magnitudes (地震震级的规定)
 | date=1999-04-26
 | access-date=2008-09-14
 | language=Chinese
 | archive-url=https://web.archive.org/web/20090424211418/http://www.dccdnc.ac.cn/html/zcfg/gfxwj1.jsp
 | archive-date=2009-04-24
 | url-status=dead
 | df=
 }}
</ref>

Surface wave magnitude was initially developed in the 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
 | publisher=USGS
 | author=William L. Ellsworth
 | url=http://www.johnmartin.com/earthquakes/eqsafs/safs_694.htm
 | title=SURFACE-WAVE MAGNITUDE (M<sub>S</sub>) AND BODY-WAVE MAGNITUDE (mb)
 | year=1991
 | accessdate=2008-09-14
}}
</ref>

{{Quotation|The successful development of the local-magnitude scale encouraged Gutenberg and 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, <math>M_b</math>.

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}}

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>.

==Definition==
The formula to calculate surface wave magnitude is:<ref name="GB 1740-1999" />

:<math>M = \lg\left(\frac{A}{T}\right)_{\text{max}} + \sigma(\Delta)\,,</math>

where A is the maximum [[Physics:Particle displacement|particle displacement]] in surface waves (vector sum of the two horizontal displacements) in [[Micrometre|μm]], T is the corresponding period in [[Second|s]], Δ is the [[Epicentral distance|epicentral distance]] in [[Degree (angle)|°]], and

:<math>\sigma(\Delta) = 1.66\cdot\log_{10}(\Delta) + 3.5\,.</math>

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:

:<math> T = \frac{T_{N}A_{N} + T_{E}A_{E}}{A_{N} + A_{E}}\,,</math>

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.

==Other studies==
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
 | publisher=Studia Geophysica et Geodaetica
 | author=Vladimír Tobyáš and Reinhard Mittag
 | url=http://www.springerlink.com/content/lv140444x5m01362/
 | title=Local magnitude, surface wave magnitude and seismic energy
 | date=1991-02-06
 | accessdate=2008-09-14
}}
</ref>

:<math> M_s = -3.2 + 1.45 M_{L} </math>

Other formulas include three revised formulae proposed by CHEN Junjie et al.:<ref>{{cite paper | 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) | url=http://scholar.ilib.cn/Abstract.aspx?A=dzyj200201016 | title=Study of Surface Wave Magnitude in China (中国面波震级研究) | date=2002-01-01 | accessdate=2008-09-14 | language=Chinese }}{{Dead link|date=June 2018 |bot=InternetArchiveBot |fix-attempted=no }}
</ref>

:<math> M_s = \log_{10}\left(\frac{A_{max}}{T}\right) + 1.54\cdot \log_{10}(\Delta) + 3.53 </math>

:<math> M_s = \log_{10}\left(\frac{A_{max}}{T}\right) + 1.73\cdot \log_{10}(\Delta) + 3.27 </math>

and

:<math> M_s = \log_{10}\left(\frac{A_{max}}{T}\right) - 6.2\cdot \log_{10}(\Delta) + 20.6 </math>

==See also==
*[[Earth:Seismic magnitude scales|Seismic magnitude scales]]

==Notes and references==
{{Reflist}}

==External links==
*{{cite paper
 | publisher=USGS
 | author=Robert E. Wallace, ed.
 | url=http://www.johnmartin.com/earthquakes/eqsafs/
 | title=The San Andreas Fault System, California (Professional Paper 1515)
 | year=1991
 | accessdate=2008-09-14
}}

{{DEFAULTSORT:Surface Wave Magnitude}}
[[Category:Seismic magnitude scales]]

{{Sourceattribution|Surface wave magnitude|1}}