Magnitude

The earthquake magnitude measures the intensity of the seismic event, based on an appropriate processing of the seismic signal.

Two magnitude definitions are considered in ITACA: the local magnitude and the moment magnitude.

The local magnitude M_L, or Richter magnitude, is defined as follows:

where:

A = peak amplitude, in mm, of the track recorded by a Wood-Anderson (WA) seismograph at a given distance;

A0 = amplitude corresponding to the reference earthquake (“zero”) at the same distance.

The Richter magnitude scale is logarithmic, so an increase of a unit of M_L implies an increase of 10 times in the motion amplitude.

Therefore, in moving from M_L = 4 (low intensity earthquake) to M_L = 7 (strong intensity earthquake), there is an increase in amplitude of 1000 times.

One limitation of the magnitude scale ML is the tendency to saturation for magnitude around 7.0-7.5; this depends on the bandwidth limitations of the WA seismograph, which do not make it suitable for recording the long period oscillations generated by large earthquakes.

The moment magnitude is instead defined from the seismic moment, which is defined as:

where G is the shear modulus of the crustal material where the seismic rupture occurs, A the area of the rupture surface in the seismogenic fault, and Δu;

the average coseismic slip on the rupture surface.

The seismic moment contains the most important physical parameters associated with the energy released during an earthquake.

The moment magnitude M_W is calculated based on the seismic moment as follows:

where cost = 10.7 if M0 is measured in dyne⋅cm and cost = 6.0 if M0 is measured in N⋅m.

M is a quantity that can increase indefinitely as the source and dislocation dimensions increase, so M_W does not saturate.

This concept is illustrated in the following by the relationship between M_W and the other commonly used magnitude scales.

This shows that, in practice, M_W = M_L for MW ≤ 6.2 can be assumed.

The relationship between moment magnitude M_W and other magnitude scales, in particular, the local magnitude M_L.