Seismic moment, abbreviated as \(M_o\), is used to measure the size of an earthquake. It represents the physical scale of the fault rupture, specifically the total mechanical work or torque associated with the sudden displacement along a fault plane. Unlike earlier magnitude scales that rely primarily on the amplitude of seismic waves recorded at distant stations, the seismic moment is derived from the actual source parameters of the earthquake.
Seismic Moment Formula |
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\( M_o \;=\; \mu \cdot A \cdot D \) (Seismic Moment) \( \mu \;=\; \dfrac{ M_o }{ A \cdot D } \) \( A \;=\; \dfrac{ M_o }{ \mu \cdot D } \) \( D \;=\; \dfrac{ M_o }{ \mu \cdot A } \) |
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| Symbol | English | Metric |
| \( M_o \) = Seismic Moment | \( ft \cdot lbf\) | \(N \cdot m\) |
| \( \mu \) = Shear Modulus of Rock | \(lbf \;/\; in^2\) | \(Pa\) |
| \( A \) = Fault Rupture Area | \(ft^2\) | \(m^2\) |
| \( D \) = Average Fault Displacement | \(ft\) | \(m\) |
Seismologists determine the seismic moment through analysis of seismic waveforms recorded by instruments, often by methods such as moment tensor inversion. This approach allows for a more accurate representation of the earthquake source, including the geometry of the fault and the nature of the forces involved. Seismic moment tensor is a mathematical representation (a 3 × 3 symmetric matrix) that describes the forces driving a seismic event and how the ground deforms at the source location. The scalar moment is the magnitude of this tensor for the dominant double-couple mechanism typical of tectonic earthquakes
