Surface-wave magnitude

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

${\displaystyle M=\lg \left({\frac {A}{T}}\right)_{\text{max}}+\sigma (\Delta )\,,}$

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

${\displaystyle \sigma (\Delta )=1.66\cdot \log _{10}(\Delta )+3.5\,.}$

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:

${\displaystyle T={\frac {T_{N}A_{N}+T_{E}A_{E}}{A_{N}+A_{E}}}\,,}$

where A_N is the north–south displacement in μm,　A_E is the east–west 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[3]

${\displaystyle M_{s}=-3.2+1.45M_{L}}$

Other formulas include three revised formulae proposed by CHEN Junjie et al.:[4]

${\displaystyle M_{s}=\log _{10}\left({\frac {A_{max}}{T}}\right)+1.54\cdot \log _{10}(\Delta )+3.53}$

${\displaystyle M_{s}=\log _{10}\left({\frac {A_{max}}{T}}\right)+1.73\cdot \log _{10}(\Delta )+3.27}$

and

${\displaystyle M_{s}=\log _{10}\left({\frac {A_{max}}{T}}\right)-6.2\cdot \log _{10}(\Delta )+20.6}$

• Seismic magnitude scales

• Robert E. Wallace, ed. (1991). "The San Andreas Fault System, California (Professional Paper 1515)". USGS. Retrieved 2008-09-14. Cite journal requires |journal= (help)CS1 maint: extra text: authors list (link)