# Why an M6.0 Earthquake Is More than Twice as Big as an M3.0

August 06, 2018

Six tons is twice as heavy as three tons, and 60 mph is twice as fast as 30 mph—so why do M6.0 earthquakes release so much more than twice the destructive energy of M3.0 temblors? The answer lies in the way that earthquake magnitude is expressed.

Earthquakes range enormously in scale, from tiny temblors far too small to be felt to massive quakes that can actually move mountains. Since the 1780s various scales have been devised in an effort to convey the power of earthquakes and several systems remain in use around the world today. The first widely adopted intensity scale—the Italian Rossi–Forel scale—was used for about two decades until the 1902 introduction of the Mercalli intensity scale, which describes the intensity of earthquakes based on observed effects. The more objective Richter scale was developed in the U.S. in the 1930s, and quantified the size of earthquakes by assigning them magnitude numbers. Since the 1970s the moment magnitude scale has been preferred in the United States.

The Richter and moment magnitude scales share one major feature in common—the scales do not linearly increase with their corresponding seismic parameters but follow logarithmic formulations. To convey the huge range of earthquake ground motions and energy experienced, the Richter magnitude is defined as a base-10 logarithmic scale of the amplitude of the peak ground displacement recorded on a particular seismic recording instrument (the Wood Anderson seismogram) and scaled by an arbitrary reference displacement for magnitude zero earthquakes.

What this means in plain English is that each point on the scale marks shaking with an amplitude 10 times bigger than the point below it. The shaking from an M4.0 quake is 10 times bigger than that from an M3.0, 100 times bigger than an M2.0, and 1,000 times bigger than an M1.0. An M6.0 is 1,000 times bigger than an M3.0, not twice its size, and at the top end of the scale, an M9.0 is a staggering 100,000,000 times bigger than an M1.0!

The Richter scale was designed for measuring earthquakes in Southern California; the moment magnitude scale was developed to overcome the issue of magnitude saturation. Ground motion amplitudes do not increase linearly with the true size of earthquakes, defined by their moment or energy release. Depending on the frequency of the peak ground motion used to define the magnitude, the magnitude scales tend to saturate (to flatten with increasing magnitudes).

Moment is a physical quantity proportional to the slip on the fault multiplied by the area of the fault surface that slips; it is related to the total energy released in the earthquake. The moment magnitude scale uses different formulas than the Richter scale, but it is similarly a base-10 logarithmic scale and expresses earthquake magnitudes in a very similar range of values.

The scales we have been discussing express the size (amplitude) of earthquake shaking as recorded by seismographs, and as we have seen, the difference between one magnitude and the next gets progressively bigger. But when looking at the energy released by earthquakes—which is what drives the ground shaking that destroys buildings—the differences are significantly greater still.

The energy released by a quake of a given magnitude is not 10 times but almost 32 times that released by a temblor of the magnitude below it on the scale! If the energy released by an M2.0 quake is 32 times that of an M1.0, an M3.0. is 1,024 times greater than an M1.0. At the top end of the scale, the energy released by an M9.0 is a mind-boggling 1,099,511,627,776 times that released by an M1.0!

In general, magnitude numbers are used in communications because, as the USGS puts it so succinctly, they “are neater and a little easier to explain.” The USGS has a great online tool for calculating how much bigger one earthquake is than another, and how much stronger the energy release is. Enjoy!

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