# Surface wave magnitude scale

The surface wave magnitude (M S , of English surface wave magnitude ) is a method for measuring earthquakes - magnitude . It is based on the investigation of the movement of the surface by Rayleigh waves with a period T of 20 ± 2 seconds.

In 1945 Beno Gutenberg developed the following dimensionless number for teleseismic surface waves:

${\ displaystyle M _ {\ mathrm {S}} = \ log _ {10} A_ {H _ {\ max}} \ left (\ Delta \ right) + \ sigma \ left (\ Delta \ right)}$

The coefficients are:

• ${\ displaystyle A_ {H _ {\ max}} = {\ sqrt {A_ {N} ^ {2} + A_ {E} ^ {2}}}}$is the maximum horizontal movement of the surface measured on the seismogram in micrometers with a period T of 20 ± 2 seconds for the north-south or east-west components,${\ displaystyle A_ {N}}$${\ displaystyle A_ {E}}$
• ${\ displaystyle \ Delta}$ the distance of the place of measurement from the epicenter measured in degrees and
• ${\ displaystyle \ sigma \ left (\ Delta \ right)}$a calibration function as the inverse of a semiempirically determined relationship between and . In 1958 Charles Francis Richter established a table with values ​​for .${\ displaystyle A}$${\ displaystyle \ Delta}$${\ displaystyle 20 ^ {\ circ} <= \ Delta <= 180 ^ {\ circ}}$

Sergei Leonidowitsch Solowjow suggested in 1955 the use of the maximum soil particle velocity , which better reflects the seismic energy. ${\ displaystyle (A / T) _ {\ max}}$

Today 's scale , known as the Moscow-Prague formula, was formulated by Vít Kárník in 1962 as:

${\ displaystyle M _ {\ mathrm {S}} = \ log _ {10} \ left ({A \ over T} \ right) _ {\ max} + \ sigma \ left (\ Delta \ right) = \ log _ {10} \ left ({A \ over T} \ right) _ {\ max} +1 {,} 66 \ log _ {10} \ Delta +3 {,} 3}$

This formula only applies to and earthquakes with a focus depth of 50 km or less. ${\ displaystyle 2 ^ {\ circ} <= \ Delta <= 160 ^ {\ circ}}$

The surface wave magnitude scale has a saturation at M S = 8.5.

## source

• Peter Bormann: 3.2 Magnitude of seismic events . In: Peter Bormann (Ed.): New Manual of Seismological Observatory Practice NMSOP . revised edition. Deutsches GeoForschungsZentrum GFZ, Potsdam 2009, ISBN 3-9808780-0-7 , p. 30-31, 48 , doi : 10.2312 / GFZ.NMSOP_r1_ch3 .