Magnitude and intensity of earthquake

Difference

How strength is measured

1. Richter local magnitude (1935):

$$M_L = \log_{10} A + 3\log_{10}(8\Delta t) - 2.92$$

where $A$ is the maximum amplitude on the Wood-Anderson seismograph in mm and $\Delta t$ is the S-P time lag in s. Each unit increase in magnitude means a 10 times larger amplitude and about 32 times more energy.

2. Moment magnitude ($M_w$), preferred for large earthquakes:

$$M_w = \frac{2}{3}\log_{10} M_0 - 6.07$$

($M_0$ = seismic moment in N m = rigidity $\times$ fault area $\times$ slip.)

3. Energy relation: $\log_{10} E = 1.5 M + 4.8$ ($E$ in joules), so the energy ratio per unit of magnitude is $10^{1.5}\approx 31.6$.

4. Intensity is assigned on the Modified Mercalli scale from field observation (I: not felt; V: felt by nearly everyone; VII: damage to poorly built buildings; X: most masonry structures destroyed; XII: total destruction).