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FIGURE E.1 A plot of measured earthquake amplitude versus magnitude. The more sensitive the seismic instruments, the smaller the measureable magnitude, reaching into the negative magnitude range.

tied to other direct measures of the size of an earthquake. The seismic moment is a routine measurement describing the strength of an earthquake and is defined as

Mo = μSd

where μ is the shear modulus, S is the surface area of the fault, and d is the average displacement along the fault. The moment magnitude, Mw, is related to seismic moment by the Hanks and Kanamori (1979) equation

Mw = img LogMo – 6

where Mo is in Newton meters, valid for earthquakes ranging from magnitude 3 to 7 (Shemeta, 2010). There are a variety of methods used to calculate a seismic moment from microseismic waveforms.


Small earthquakes occur much more often than large earthquakes. The number of earthquakes with respect to magnitude follows a power law distribution and is described by

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