The energy and magnitude of earthquakes

About 100 joules of energy is released from each cubic metre of rock at the time of an earthquake. This may not seem very much. However, a large earthquake associated with a fault 1000 km long, extending 100 km downwards, and distorting the ground as far as 50 km on either side of the fault amounts to a strained volume of 1016 cubic metres which gives a total of 1018 joules.

This is equivalent to about a thousand nuclear explosions, each with a strength of 1 megaton of TNT. Although the energy released gives a measure of the size of an earthquake it is not easy to determine the fault dimensions, slip and other factors needed to compute it. Seismologists have therefore adopted the Richter magnitude scale which relates the local magnitude to the logarithm of the maximum amplitude recorded by seismographs (an empirical factor takes into account the attenuation of seismic waves as they spread out from the focus).

Because magnitudes are based on a logarithmic scale, an increase in magnitude of one unit corresponds to an increase in the amount of energy released by a factor of about thirty. The actual range of magnitudes is enormous, the largest events representing motions a hundred million times (9 magnitudes) as large as those of small events. The scale is open at both ends. It does not have a maximum value often, as is often reported. Two or three earthquakes this century have had Richter magnitudes of 8.9. The 1906 San Francisco earthquake had a Richter magnitude of 8.25, and the great Chilean earthquake of 22 May 1960. one of 8.5.

At the other extreme earthquakes with a magnitude of less than —2 are routinely observed by seismologists studying micro-earthquakes. Most earthquakes are small, and each year about 800000 small tremors recorded by instruments are not felt by human beings. Generally speaking shallow earthquakes have to reach a Richter magnitude of more than 5.5 before significant damage occurs near the source. Great earthquakes with magnitudes exceeding 8 occur about once every five to ten years.

The current practice at seismic observatories is to use two magnitude scales both of which are different from the original Richter scale. The reason for using two scales is that earth quakes having deep focuses give very different seismic records from those having shallow focuses, even though the amount of energy released in each event might be the same. In particular deep-focus earthquakes produce only small or insignificant trains of surface waves.

A new measure of earthquake strength called seismic moment (defined as the product of the rigidity of the rock, the area of faulting and the amount of slip) has recently been suggested. This measure of earthquake size has indicated the need for some revision of previous estimates of the relative magnitudes of great earthquakes. Another scale—the intensity—has been used to describe the 'bigness' of an earthquake. The intensity scale is a measure of the observed effects of earthquake damage at a particular place and is not based on actual measurements of any kind.

At some distance (more than about 150 km) from an earthquake the shorter-period vibrations tend to be damped out, resulting in ground periods of more than a second. Tall buildings often have periods of this order, and resonant vibrations may be set up, such as the 'pounding' of adjacent tall buildings in Los Angeles at the time of the Kern County earthquake. This effect has been particularly pronounced in Mexico City.

3.6: Earthquake damage in Los Angeles, California. Originating in the San Andreas fault system, the earthquake took place on 9 February 1971

The business section of this city is built on very soft soil, which shows a predominant period of vibration in earthquakes of about 2.5 seconds. Many tall buildings have been constructed in this district, and their periods of vibration are very nearly the same. When, in 1957. an earthquake of magnitude 7.5 occurred off the coast. 350 km from the city, many of these tall buildings were thrown violently into their natural periods of vibration and suffered major damage. Smaller buildings, on the other hand, many of them old, came through the earthquake unharmed.