Magnitudes and Fault Rupture Lengths


The original calculations for this came from a site called ES&S which appears to have vanished off the web.

I reproduce here such information as I have from the site and if the site owners are still around and wish me to remove it on the grounds of copyright please let me know.

Earthquake Size

The Size of Earthquakes

Earthquakes vary enormously in the amount of energy released, over a range exceeding a million million. It is not possible to measure the energy release directly, so it must be computed from measurements of the amplitude of the ground vibrations.

Earthquake Magnitude

The most common method of describing the size of an earthquake is the Richter magnitude scale, ML. This takes the logarithm of the ground displacement as measured by a seismograph, and applies a correction which varies with the distance from the earthquake to the seismograph.

This means that for each unit of magnitude there is a tenfold increase in ground displacement. Because larger earthquakes last longer than small earthquakes, there is about a thirty-fold increase in seismic energy release for each unit increase in magnitude. An ML 1.0 earthquake releases a similar amount of seismic energy as a typical quarry blast. An ML 5.0 earthquake releases about the same seismic energy as a 10,000 tonne equivalent nuclear blast, such as that used at Hiroshima.The Richter magnitude scale can only be used when seismographs are within 600 km of the earthquake. For greater distances, other magnitude scales have been defined. While not exactly the same as the original Richter magnitude, they give values that can range from less than 0.0 to over 9.0. For example, the surface wave magnitude, MS, is often used for large distant earthquakes. Most of these scales saturate at some magnitude and do not properly represent earthquake size for larger events. For example, the ML scale saturates over ML 6.0, while the MS scale can be used to about MS 8.0.

The most modern scale is the moment magnitude scale MW, which can be used for a wide range of magnitudes and distances. This has been defined so that the numerical value is close to ML for earthquakes up to magnitude 6.0, and close to MS for magnitudes 6.0 to 8.0. The very largest earthquakes, such as experienced in Chile in 1960 or Alaska in 1964, can reach magnitudes larger than MW 9.0.

Fault Dimensions

The area of a fault that ruptures in a particular earthquake correlates with the magnitude of the earthquake. Typical fault rupture dimensions are as follows:

(I have expanded and adapted the original table)
RuptureDimensions
(Click the Image for a slightly larger/clearer version)

The rupture displacement in an earthquake is typically about 1/20,000 of the rupture length. For example, a 1 km long rupture from an Mw 4.0 event has a displacement of about 1km/20,000, or 0.05 metres. A magnitude Mw 8.0 earthquake with a rupture length of 100 km may give a displacement of a few metres.

The rupture velocity is about 3 km/s, so the rupture duration in seconds is given by fault length in kilometres divided by 3. For example, a 1 km long rupture from an Mw 4.0 event will occur in 1km/3, or one third of a second. A magnitude Mw 8.0 earthquake with a rupture length of 100 km may take 100/3 or over thirty seconds to rupture.

THESE FIGURES ARE ALL APPROXIMATE AND WILL VARY FROM EARTHQUAKE TO EARTHQUAKE, DEPENDING ON THE FOCAL MECHANISM AND STRESS DROP.

The very small spreadsheet RuptureCalcs.xlsx is here if anyone would like to expand it.

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About PuterMan

A retired programmer.
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