What is the moment magnitude scale and how does it work?

Answer 1

The Moment Magnitude Scale (Mw) was developed by the seismologists Hanks and Kanamori during the 70's and their work was published in the Journal of Geophysical Research in 1979 (see the related link).

It was developed to enable seismologists to better estimate the magnitude of large earthquakes (those greater than 7) as the Local Magnitude (ML) or Richter scale originally developed in 1935 is not accurate at estimating earthquake magnitudes where the epicentre was greater than 600 km from the seismometer station or where the earthquake magnitude was greater than 7.0.

As such, the moment magnitude scale (MW) provides an estimate of the total energy released in an earthquake and is currently the preferred magnitude scale in use by seismologists in large earthquakes.

It is calculated from the seismic moment (M0 - which has the unit of dynes/cm =where 1 dyne/cm = 1x10-7 N/m) which is a measure of the total energy released during an earthquake and is derived based on the elastic moduli of the crust where the earthquake occurred, the length of the slip surface and the cross sectional area of the slip surface as follows:

M0 =G x AFx DF

Where:

G = Shear modulus of the rock mass

AF = Area of the rupture along the fault

DF = average displacement on AF

Seismic moment can also be estimated from the amplitude spectra of seismic waves as recorded by a seismometer.

In order to make the moment magnitude scale (Mw) consistent with older magnitude scales such as the Local Moment (or "Richter") scale the seismic moment (M0) is converted into a logarithmic scale using the following equation:

Mw = 2/3 x log10 x (M0) - 10.7

This ultimately yields a dimensionless number and as such, Moment Magnitude has no units.

Please see the related links.

Answer 2

The moment magnitude scale is a measure of the size of an earthquake based on the seismic moment released during the event. It provides a more accurate representation of an earthquake's size compared to the Richter scale, as it takes into account the total energy released by the quake. Moment magnitude is calculated using factors such as the amount of displacement along the fault and the area of the fault surface that slipped.