The Moment Magnitude scale and the Richter scale are both measures of the magnitude of earthquakes, where magnitude is the seismic energy released by the earthquake. The Richter scale is the older of the two but is now being gradually superseded by the Moment Magnitude scale.
The Richter scale was developed in the 1930s by American seismologist Charles Richter who devised a way of calculating the location of the epicentre of an earthquake and its magnitude relative to other earthquakes. It gave scientists an objective measurement of the size of earthquakes, and served us well for many decades.
The scale is logarithmic, so that for example, an earthquake measuring 6 on the Richter scale is ten times greater in magnitude than one measuring 5. An earthquake measuring 7 on the scale is ten times greater again.
The main problem with the Richter scale is that is a comparison of one earthquake to another rather than an absolute measurement. Another problem was that it was developed in Southern California and conditions elsewhere in the world are not exactly comparable.
Moment Magnitude Scale
A newer measurement of the magnitude of earthquakes is the Moment Magnitude scale, which is designed to overcome the problems of the Richter scale. This means that the Moment Magnitude is not comparative, and it is applicable equally everywhere in the world. It is also completely independent of the type of equipment used to measure the earthquake. This new way of measuring the magnitude of earthquakes has become possible through the development of more sophisticated seismology devices than were available to Richter.
Seismologists can now directly measure where the rupture in the fault line occurs, and to calculate the energy that is released in the earthquake. This energy is called the seismic moment, the total energy of an earthquake. Moment Magnitude is a calculation based (in part) on the area of the ruptured section of the fault and the distance the earth moved along the fault during the rupture.
In order to make a scale comparable to the well-known Richter scale, seismologists invented the (Seismic) Moment Magnitude Scale, which gives magnitudes roughly equivalent to the Richter magnitudes.
Both scales are still used, but the Moment Magnitude scale is gradually replacing the Richter scale and is preferred now by most seismologists. The numbers generated by the two scales are usually very similar. For example, the earthquake in Northridge California in 1994 measured 6.4 on the Richter and 6.7 on the Moment Magnitude scale.
When reporting the magnitude of an earthquake, many news organisations simply report the earthquake has having a magnitude of [number], without stating whether the Richter or Moment Magnitude scale is being used. For most people, the difference is unimportant. The bigger the number, the worse the earthquake.