# Earthquake: Magnitude's scales

_{L}) was then extended to the observations of earthquakes of any distance and focal depths between 0 and 700 kilometers. Since earthquakes produce two types of waves, body waves (P and S), traveling inside the Earth, and surface waves (L and R), who are forced to follow the natural waveguide of the Earth's uppermost layers, have evolved two new magnitude's scales: the m

_{b}(body waves) and M

_{S}(surface waves).

**m _{b} = log_{10} (A / T) + Q (D, h)**

**M _{S} = log_{10} (A / T) + 1,66 log_{10} (D) + 3,30**

**seismic moment and radiated energy.**

## Fault's geometry and Seismic Moment M_{O}

**M _{O} = μ S <d>**

**M _{w} = 2/3 log_{10} (M_{O}) - 10.7 **

^{30}dyn · cm for the Chile earthquake of 1960 (M

_{S}8.5, M

_{w}= 9.6) and 7.5 X 1029 dyn · cm for the Alaska earthquake of 1964 (M

_{S}8.3, M

_{w}9.2).

**Energy - E**

The amount of energy radiated by an earthquake is a measure of the potential for damage to man-made structures. Theoretically, its calculation requires to add energy's flow to a wide range of frequencies generated by an earthquake during the process of faulting. Due to instrumental limitations, historically most of the estimates of energy have always relied on the empirical relationship developed by Beno Gutenberg and Charles Richter:

**Log _{10}E = 11,8 + 1,5 M_{S}**

where the energy, E, is expressed in ergs. The disadvantage of this method is that the MS is calculated by a bandwidth between about 18 to 22 s. It is now known that the energy radiated by an earthquake is focused on a different band and higher frequencies. With the worldwide spread of modern digital recording seismographs that have responses with large bandwidths, the calculation methods are now able to make accurate and explicit estimates of energy on the basis of the calculation routines for all large earthquakes. A magnitude based on energy radiated by an earthquake, Me, can now be defined:

**M _{e} = 2/3 Log_{10}E - 2.9**

**M**and

_{w}**M**are both magnitudes, they describe different physical properties of the earthquake. Mw, calculated from seismic data at low frequency, is a measure of the fractured area of an earthquake;

_{e}**M**, calculated from seismic data at high frequency, is a measure of potential seismic damage. Consequently,

_{e}**M**and

_{w}**M**often do not have the same numerical value.

_{e}

It may be interesting and instructive to analyze the relationship between two seismic events, 1 and 2, as well as between the corresponding energies involved, E_{1} and E_{2}, related with their magnitude, M_{1} and M_{2}. In fact:

log E_{2}= 11.8 + 1.5 M_{2 }

log E_{1} = 11.8 + 1.5 M_{1}

making a difference:

log E_{1} - log E_{2} = 1.5 (M_{1} - M_{2}), ovvero log E_{1}/E_{2} = 1.5 (M_{1} - M_{2})

and then, placing M_{1} - M_{2} = Δ M

E_{1}/E_{2} = 10^{1.5} ^{ΔM}

that is to say that, for example:

se ΔM = 1, E_{1}/E_{2} = 10^{1.5} = 31.6

se ΔM = 2, E_{1}/E_{2} = 10^{3} = 1000

se ΔM = 3, E1/E2 = 10^{4.5} = 31600

se ΔM = 4, E_{1}/E_{2} = 10^{6} = 1000000 ecc.

In other words, an earthquake of magnitude 5 compared to an earthquake of magnitude 4 (ΔM = 1) has a displacement of ground 10 times, but energy that is released and then create potential damage of about 30 times (31.6) higher . An earthquake of M = 5 with respect to a magnitude of M = 3 (ΔM = 2) has a displacement amplitude of 100 times higher but energy liberated 1000 times higher and so on ....

At DiSTAR a research group coordinated by Prof. Tina Nunziata is currently involved in "Seismics and Seismology Applied to Vs definition", and "Seismic zonation and microzonation".

** **

**Dr. Raffaele Viola**