Seismic Moment and Moment Magnitude

Seismic moment is a quantity that combines the area of the rupture and the amount of fault offset with a measure of the strength of the rocks - the shear modulus m.
Seismic Moment = m x (Rupture Area) x (Fault Offset)Usually we measure the moment directly from seismograms, since the size of the very long-period waves generated by an earthquake is proportional to the seismic moment. The physical units of seismic moment are force x distance, or dyne-cm.
For scientific studies, the moment is the measure we use since it has fewer limitations than the magnitudes, which often reach a maximum value (we call that magnitude saturation).
To compare seismic moment with magnitude, M_w , we use a formula constructed by Hiroo Kanamori of the California Institute of Seismology:
M_w = 2 / 3 * log(Seismic Moment) - 10.73where the units of the moment are in dyne-cm.

Richter's Magnitude Scale

 In 1935 Charles Richter constructed a similar diagram of peak ground motion versus distance and used it to create the first earthquake magnitude scale (a logarithmic relationship between earthquake size and observed peak ground motion). He based his scale on an analogy with the stellar brightness scale commonly used in astronomy which is also similar to the pH scale used to measure acidity (pH is a logarithmic measure of the Hydrogen ion concentration in a solution).

 To complete the construction of the magnitude scale, Richter had to establish a reference value and identify the rate at which the peak amplitudes decrease with distance from an earthquake. He established a reference value for earthquake magnitude when he defined the magnitude as the base-ten logarithm of the maximum ground motion (in micrometers) recorded on a Wood-Anderson short-period seismometer one hundred kilometers from the earthquake. Richter was pragmatic in his definition, and chose a value for a magnitude zero that insured that most of the earthquakes routinely recorded would have positive magnitudes. Also, the Wood-Anderson short-period instrument that Richter chose for his reference records seismic waves with a period of about 0.8 seconds, roughly the vibration periods that we feel and that damage our buildings and other structures.

Puente_Hills_Earthquake

Richter magnitudes

The Richter magnitude of an earthquake is determined from the logarithm of the amplitude of waves recorded by seismographs (adjustments are included to compensate for the variation in the distance between the various seismographs and the epicenter of the earthquake). The original formula is:

where A is the maximum excursion of the Wood-Anderson seismograph, the empirical function A₀ depends only on the epicentral distance of the station, δ. In practice, readings from all observing stations are averaged after adjustment with station-specific corrections to obtain the M_L value.
Because of the logarithmic basis of the scale, each whole number increase in magnitude represents a tenfold increase in measured amplitude; in terms of energy, each whole number increase corresponds to an increase of about 31.6 times the amount of energy released, and each increase of 0.2 corresponds to a doubling of the energy released.
Events with magnitudes greater than about 4.6 are strong enough to be recorded by a seismograph anywhere in the world, so long as its sensors are not located in the earthquake's Shadow.
The following describes the typical effects of earthquakes of various magnitudes near the epicenter. The values are typical only and should be taken with extreme caution, since intensity and thus ground effects depend not only on the magnitude, but also on the distance to the epicenter, the depth of the earthquake's focus beneath the epicenter, and geological conditions (certain terrains can amplify seismic signals).