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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 177401999) for categorising earthquakes.^{[1]}
Surface wave magnitude was initially developed in 1950s by the same researchers who developed the local magnitude scale M_{L} in order to improve resolution on larger earthquakes:^{[2]}
The successful development of the localmagnitude scale encouraged Gutenberg and Richter to develop magnitude scales based on teleseismic observations of earthquakes. Two scales were developed, one based on surface waves, , and one on body waves, mb.
Surface waves with a period near 20 s generally produce the largest amplitudes on a standard longperiod seismograph, and so the amplitude of these waves is used to determine , using an equation similar to that used for .
— William L. Ellsworth , The San Andreas Fault System, California (USGS Professional Paper 1515), 19901991
Recorded magnitudes of earthquakes during that time, commonly attributed to Richter, could be either or .
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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 177401999, 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 A_{N} is the northsouth displacement in μm, A_{E} is the eastwest displacement in μm, T_{N} is the period corresponding to A_{N} in s, and T_{E} is the period corresponding to A_{E} in s.
Vladimír Tobyáš and Reinhard Mittag proposed to relate surface wave magnitude to local magnitude scale M_{L}, using^{[4]}
Other formulas include three revised formulae proposed by CHEN Junjie et al.:^{[5]}
and
