Moment Magnitude (Mw)

Moment magnitude Mw is a logarithmic measure of earthquake size that is tied directly to the physics of fault rupture, not just to how strongly a seismograph shakes. It is computed from the seismic moment M₀, which depends on how much rock slipped, how large the fault area was, and how rigid the rocks are; that is why it tracks the actual energy release better than older magnitude scales for very large quakes. The logarithm makes the scale compact: each 10× increase in seismic moment increases Mw by about 2/3 of a unit.

Use this formula when converting a known seismic moment into an earthquake magnitude, especially in seismology, geophysics, and hazard analysis. It is most useful for comparing large earthquakes, where traditional magnitude scales can saturate or become less reliable.

• Using the natural logarithm instead of log base 10
• Forgetting that M₀ must be in dyn·cm for this constant to apply
• Treating Mw as a direct linear scale instead of a logarithmic one