Have you ever wondered why there were two or three different magnitudes for the same earthquake?

Earthquakes are measured in a number of different ways. One of those ways is to identify the size (energy released) of an earthquake in units of magnitude. There are different methods for getting a magnitude. There is a magnitude that is based on the body waves that travel deep within the earth’s interior. There is a method to calculate a earthquake’s magnitude from the seismic surface waves that travel along the surface layers of the earth. There is even a method that defines a magnitude based on how much of the earth “broke” during the earthquake. The most commonly used magnitudes are the Ml, Mb, MS and Mw types.

The Ml or Local (“Richter”) Magnitude is based on the maximum amplitude (A) in micrometers recorded on standard short period (1 sec) seismometer.

Ml = logA – logA0,

Where A0 is a standard value as a function of distance. This magnitude is good for earthquakes less than 1000 kilometers from the instrument measuring the earthquake. It is valid for earthquakes less than 6 units of magnitude.

The Mb or Body Wave Magnitude is based on the amplitude of the P body waves generated by the earthquake. This earthquake measurement scale is most appropriate for earthquakes that occur at distances greater than 12 degrees (about 1300 kilometers since 1 degree = 111 kilometers) from a seismometer. This scale is valid for magnitudes less than 6.5 units.

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

Where T is the period of the wave being measured, A is its amplitude and Q(D,h) is a correction function of distance from the recording station and depth of the earthquake.

The MS or Surface Wave Magnitude is used to measure the magnitude for shallow earthquakes up to about magnitude 8 and between 5 and 180 degrees from the recording seismometer. The MS magnitude method measures the greatest amplitude of 20-second period surface radiation.

MS = log(A/t) + 1.66*log(D) + 3.3

The correction factor is not always 3.3. Various corrections have been proposed for distances less than 20 degrees.

For deep (greater than 75 km), large earthquakes, the MS scale underestimates the earthquake’s size.

Mw or Moment Magnitude is different from the other magnitude scales in that this scale is based on the actual physical area of the moving fault. This area (S) is multiplied by the average amount of slip (d) times a constant that depends on the rigidity properties of the rocks that slip (u). This value is known as the seismic moment, Mo.

Mo = u*S*<d>.

The moment magnitude is then defined as

Mw = (2/3)*log(Mo) - 10.7.

This magnitude is valid for any size earthquake. It should be noted that there are many techniques for determining the moment magnitude, some directly from seismographs, and each has its own limitations.

So, the next time you see a magnitude for an earthquake, you can ask yourself if it is a Ml or Mb or MS or Mw magnitude.