Magnitude and Energy
Magnitude and Energy
When an earthquake happens, the main quantity of interest is its magnitude. How big was the earthquake? Over the years, scientists have developed various ways to measure earthquake size and strength. Here's an overview of the most common magnitude measurements.
Mercalli Intensity Scale
This scale is a qualitative measure of the amount of felt shaking caused by an earthquake. This scale goes from I (not much of anything) to XII (total destruction). The amount of felt shaking is generally measured by interviewing witnesses to find out how much shaking they felt. Sometimes the interviews can be supplemented by observing any earthquake damage to buildings. For earthquakes in the historic record that happened before the advent of seismometers, Mercalli intensities are often assigned by checking out old newspaper reports and examining the foundations of old buildings. Mercalli intensities are generally depicted on maps by several concentric rings around the epicenter of the earthquake that give some idea of the severity of the felt shaking at various distances away from the earthquake. The Mercalli is not a very useful scale for science because it can't tell us much about big earthquakes that are not felt by people--earthquakes that occur at a great depth, or in the ocean, for example.
Isoseismal map showing reconstructed Mercalli intensities from the 1895 31 Oct earthquake at Charleston Missouri.
Source: Seismicity of the United States, 1568-1989 (Revised), by Carl W. Stover and Jerry L. Coffman, U.S. Geological Survey Professional Paper 1527, United States Government Printing Office, Washington: 1993. http://earthquake.usgs.gov/regional/states/events/1895_10_31_iso.php
Richter Scale
Charles Richter developed a magnitude scale in the 1930s because he wanted to be able to characterize the seismicity he had been measuring in California with some kind of numbering system that would encompass all the earthquakes, from ones that had hardly been felt at all, up to really big ones. The way he did this was to pick a reference earthquake and measure its maximum ground motion. Then all the other earthquakes he had recorded could be compared to the reference, after correcting for distance. Each integer increase represented a factor of 10 increase in ground motion amplitude. This scale worked because he always used the same type of seismometer and all his earthquakes were in southern California, so there didn't have to be any extra corrections for different depth or rock type.
Today, scientists don't use the Richter scale the way he did because not all earthquakes of interest happen in California, and also because the type of seismometer he used is out of date now.
Today, seismologists assign a magnitude number to quantify the energy released by an earthquake. The Richter scale is a base-10 logarithmic scale which means that as measured with a seismometer, an earthquake that registers 5.0 on the Richter scale has a shaking amplitude 10 times that of an earthquake that registered 4.0.
A Wood-Anderson torsion short-period seismometer. This is the type of seismometer used by Richter to measure earthquake amplitude and develop his magnitude scale.
Source: http://www.eas.slu.edu/Earthquake_Center/Instruments/wood_and.jpg
Moment Magnitude
The Richter Scale is not commonly used anymore, as it has been replaced by another scale called the moment magnitude scale which is a more accurate measure of the earthquake size.
Unfortunately, many scales, such as the Richter scale, do not provide accurate estimates for large magnitude earthquakes. Today the moment magnitude scale, abbreviated MW, is preferred because it works over a wider range of earthquake sizes and is applicable globally. The moment magnitude scale is based on the total moment release of the earthquake. Moment is a product of the distance a fault moved and the force required to move it. It is derived from modeling recordings of the earthquake at multiple stations. Moment magnitude estimates are about the same as Richter magnitudes for small to large earthquakes. But only the moment magnitude scale is capable of measuring M8 (read ‘magnitude 8’) and greater events accurately.
Energy
Another way to think about earthquake size is in terms of the energy released by an earthquake. It is actually not terribly easy to measure all the energy released by an earthquake because you have to integrate over time and space and include the broadest possible spectrum of frequencies to make sure you are recording all the energy. Therefore, direct measurements usually underestimate the energy. If they aren't trying to measure it instrumentally, most seismologists just use the following empirical formula, developed by Båth (1966) to relate magnitude to energy (in units of joules):
log E = 5.24 + 1.44M
This relationship was only meant to work for fairly big (M > 5) earthquakes. Plug magnitude values of 5.0, 6.0, and 7.0 into the equation above. The energy released by an M5 earthquake is about 2.8 x 1012 joules. An M6 earthquake releases 7.8 x 1013 joules, and an M7 radiates 2.1 x 1015 joules. If you don't have a sense for what these numbers mean, the bomb dropped on Hiroshima released about 7.4 x 1012 joules. Even though all of these are large numbers, what I want you to see here is that the difference between these values is huge. A magnitude 7 releases almost 30 times as much energy as a magnitude 6.
Okay, time for the big picture! A 60-watt incandescent light bulb uses 60 joules of energy per second. The rupture of the Sumatra-Andaman earthquake lasted about 500 seconds. By using the formula above, I can calculate that it radiated 1.6 x 1018 joules. Therefore, this earthquake released enough energy during its rupture to light up 5.3 x 1013 60-watt light bulbs. Wow, that's a lot of light bulbs!
Finding the Epicenter Virtual Simulation
Finding the Epicenter Virtual Lab 2017
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