Drucker–Prager yield criterion: Difference between revisions

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{{Earthquakes}}
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
| 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
| accessdate=2008-09-14
| language=Chinese
}}
</ref>
 
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
| 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
}} {{Dead link|date=October 2010|bot=H3llBot}}
</ref>
{{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.
 
<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}}
 
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" /><ref>It is obvious that the entire formula cannot stand [[dimensional analysis]] without additional qualifications. References here provide no such qualification.</ref>
 
<math>M = \log_{10}\left(\frac{A}{T}\right)_{\text{max}} + \sigma(\Delta)</math>
 
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)|&deg;]], 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&nbsp;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=Vladim&iacute;r&nbsp;Toby&aacute;&scaron; 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
}}
</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==
*[[Moment magnitude scale]]
*[[Seismic scale]]
 
==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
}}
*[http://earthquake.usgs.gov/learning/glossary.php?termID=118 Visual Glossary - magnitude] - [[United States Geological Survey|USGS]]
*[http://eqseis.geosc.psu.edu/~cammon/HTML/Classes/IntroQuakes/Notes/earthquake_size.html Earthquake Size]
 
{{Seismic scales}}
 
{{DEFAULTSORT:Surface Wave Magnitude}}
[[Category:Seismic scales]]

Revision as of 18:03, 19 September 2013

Template:Earthquakes The surface wave magnitude () scale is one of the magnitude scales used in seismology to describe the size of an earthquake. It is based on measurements in 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.[1]

Surface wave magnitude was initially developed in 1950s by the same researchers who developed the local magnitude scale ML in order to improve resolution on larger earthquakes:[2] 36 year-old Diving Instructor (Open water ) Vancamp from Kuujjuaq, spends time with pursuits for instance gardening, public listed property developers in singapore developers in singapore and cigar smoking. Of late took some time to go China Danxia.

Recorded magnitudes of earthquakes during that time, commonly attributed to Richter, could be either or .

Definition

The formula to calculate surface wave magnitude is:[1][3]

where A is the maximum particle displacement in surface waves (vector sum of the two horizontal displacements) in μm, T is the corresponding period in s, Δ is the epicentral distance in °, and

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:

where AN is the north-south displacement in μm,　AE is the east-west displacement in μm,　TN is the period corresponding to AN in s, and TE is the period corresponding to AE in s.

Other studies

Vladimír Tobyáš and Reinhard Mittag proposed to relate surface wave magnitude to local magnitude scale ML, using[4]

Other formulas include three revised formulae proposed by CHEN Junjie et al.:[5]

and

See also

Notes and references

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

External links

Template:Seismic scales

  1. ↑ 1.0 1.1 Template:Cite web
  2. ↑ Template:Cite paper Template:Dead link
  3. ↑ It is obvious that the entire formula cannot stand dimensional analysis without additional qualifications. References here provide no such qualification.
  4. ↑ Template:Cite paper
  5. ↑ Template:Cite paper
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