The surface wave magnitude (M_s) 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]}
Recorded magnitudes of earthquakes during that time, commonly attributed to Richter, could be either M_s or M_L.
Contents

Definition 1

Other studies 2

See also 3

Notes and references 4

External links 5
Definition
The formula to calculate surface wave magnitude is:^{[1]}^{[3]}
M = \log_{10}\left(\frac{A}{T}\right)_{\text{max}} + \sigma(\Delta)
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
\sigma(\Delta) = 1.66\cdot\log_{10}(\Delta) + 3.5
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:
T = \frac{T_{N}A_{N} + T_{E}A_{E}}{A_{N} + A_{E}}
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.
Other studies
Vladimír Tobyáš and Reinhard Mittag proposed to relate surface wave magnitude to local magnitude scale M_{L}, using^{[4]}

M_s = 3.2 + 1.45 M_{L}
Other formulas include three revised formulae proposed by CHEN Junjie et al.:^{[5]}

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

M_s = \log_{10}\left(\frac{A_{max}}{T}\right) + 1.73\cdot \log_{10}(\Delta) + 3.27
and

M_s = \log_{10}\left(\frac{A_{max}}{T}\right)  6.2\cdot \log_{10}(\Delta) + 20.6
See also
Notes and references

^ ^{a} ^{b}

^

^ It is obvious that the entire formula cannot stand dimensional analysis without additional qualifications. References here provide no such qualification.

^

^
External links


Visual Glossary  magnitude  USGS

Earthquake Size

Surface wave magnitude calculator


Modern scales

Intensity scales



Magnitude scales




Historical scales



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