# EARTHQUAKES

## The Richter Scale

On the Richter scale, the magnitude of an earthquake is related to the released energy E in joules (J) by the equation

log10 E = 4.4 + 1.5M

The 1906 San Francisco earthquake registered 8.2 on the Richter scale. Using the above equation, the released energy was

E = 5.011872336x1016 J

Or, using the British Engineering System, the released energy was

E = 3.698761784x1016 ft lb.

The Richter Scale is often misunderstood by individuals. In most cases, this is a result of having little or no understanding of the logarithmic nature of the scale. For example, what does a difference in magnitude of 1 make in the released energy? If we consider two earthquakes, one of magnitude M1 and another of magnitude M1 + 1, we get

log10 E1 = 4.4 + 1.5M1 and
log10 E2 = 4.4 + 1.5(M1 + 1) = 4.4 + 1.5M1 + 1.5

Thus, log10 E2 - log10 E1 = 1.5 and log10(E2/E1) = 1.5. We then have, E2/E1 = 101.5 = 31.623 and E2 = 31.623E1. We can therefore see that an increase in 1 of the magnitude of an earthquake results in an earthquake 31.623 times as strong.

An interesting web site on earthquakes is the USGS Earthquake Information site. In particular, this site has a map of the recent earthquakes in California.

The following table gives the released energies of earthquakes of magitudes 1 up to 9 in increments of 0.5. This table illustrates the exponential growth of the power of an earthquake.

 Magnitude Released Energy (to the nearest integer) 1 794,328 J 1.5 4,466,836 J 2 25,118,864 J 2.5 141,253,754 J 3 794,328,235 J 3.5 4,466,835,922 J 4 25,118,864,315 J 4.5 141,253,754,462 J 5 794,328,234,724 J 5.5 4,466,835,921,510 J 6 25,118,864,315,096 J 6.5 141,253,754,462,275 J 7 794,328,234,724,282 J 7.5 4,466,835,921,509,631 J 8 25,118,864,315,095,801 J 8.5 141,253,754,62,275,430 J 9 794,328,234,724,281,502 J