# Geology and Quakes

..Firstly there was the richter scale...

---Local ("Richter") Magnitude (original defined by Richter - 1935)

ML = log A - log Ao

Because ML was not designed to to be applied to data with distances to the hypocenter of the earthquake greater than 600 km, its values become unreliable when the earthquake is larger than 7 and Richter's original method is no longer applied.

To overcome this shortcoming, Gutenberg and Richter later developed a magnitude scale based on surface waves, surface wave magnitude MS; and another based on body waves, body wave magnitude mb. MS and mb can still saturate when the earthquake is big enough.

---Surface Wave Magnitude

Ms = log (A/T) + 1.66 log D + 3.3

---Compressional Body Wave (P-wave) Magnitude

Mb = log (A/T) +Q(D,h)

...Then came Mw ...

The moment magnitude scale is used to measure the size of earthquakes in terms of the energy released. The magnitude is based on the seismic moment of the earthquake, which is equal to the rigidity of the Earth multiplied by the average amount of slip on the fault and the size of the area that slipped. The scale was developed in the 1970s to succeed the 1930s-era Richter magnitude scale (ML). Even though the formulæ are different, the new scale retains the familiar continuum of magnitude values defined by the older one. The MMS is now the scale used to estimate magnitudes for all modern large earthquakes by the United States Geological Survey.

---*Moment Magnitude

Mw = (2/3) log Mo - 10.7

USGS usually uses the Mw scale to report magnitudes - although i have seen them use the Mb sometimes too

...Then there's NZ - Geonet say...

The magnitudes assigned to local earthquakes are intended to be the values of ML as originally defined by C.F. Richter ..., but his procedure for performing the magnitude calculation at other than the standard distance of 100 km has been modified, to take account of the observed characteristics of energy propagation in New Zealand, including the effect of focal

And they use the following formulas instead

---For stations more than 100 km away from the epicentre

A = A0 R-N exp ( - a R )

---For stations closer than 100 km to the epicentre

MA = log10 A + 1.0 log10 R + 0.0029 R + K

which is why when you look here:

http://earthquake.usgs.gov/earthquakes/eqinthenews/2011/usb0001igm/

it says 6.1

but if you look here:

http://geonet.org.nz/earthquake/quakes/3468575g.html

it says 6.3

...So remember to add a couple of points to all the overseas shakes you see in order to compage them with the ones you feel in NZ :)

references...

http://www.geonet.org.nz/resources/earthquake/hypocentre-derivation.html

http://neic.usgs.gov/neis/phase_data/mag_formulas.html

all that maths make ya brain hurt? did mine :|