momentmagnitudes

Moment magnitudes, abbreviated Mw, are a scale used to quantify the size of earthquakes based on the seismic moment of the event. Mw provides a consistent measure across a wide range of earthquake sizes and rupture styles, addressing limitations of earlier scales when dealing with large events.

Seismic moment M0 is a physical quantity describing the total slip on a fault during an earthquake. It is calculated as M0 = μ A D, where μ is the shear modulus of the rocks (roughly 3×10^10 pascals), A is the area of the fault that slipped, and D is the average displacement (slip) on that area. The moment magnitude is then defined in terms of M0 by the formula Mw = (2/3) log10(M0) − 9.1, with M0 measured in newton-meters. This logarithmic relationship means each whole-number increase in Mw corresponds to about a factor of 10^1.5 (roughly 31.6) increase in seismic moment.

Moment magnitude tends to correlate with the total energy released by an earthquake and does not saturate as quickly as older local magnitude scales, especially for large events. It is widely used in global and regional catalogs and is complemented by other measures that describe rupture duration, slip distribution, and depth.

Limitations remain: Mw depends on the geometry and distribution of slip, and rapid estimates early after an event can carry substantial uncertainty. Nonetheless, Mw is the standard benchmark for comparing earthquake sizes across different tectonic settings.