momentmagnitude

Moment magnitude, abbreviated Mw, is a scale used to describe the size of earthquakes. It is based on the seismic moment M0, a measure of the total amount of slip on the fault, the fault area that ruptured, and the rigidity of the rocks. The seismic moment is defined as M0 = μ A D, where μ is the shear modulus of the rocks, A is the rupture area, and D is the average slip.

Moment magnitude is related to M0 by the empirical formula Mw = (2/3) log10(M0) − 6.07, with M0 expressed in newton-meters. Because it is a logarithmic scale, a tenfold increase in M0 corresponds to about a 3-unit increase in Mw. Mw is designed to provide a consistent, non-saturating measure of earthquake size across a wide range of faulting styles and depths.

History and purpose: The moment magnitude scale was developed in the late 20th century as an improvement over older scales such as the Richter local magnitude. It uses the physical source parameter M0 and remains stable for large earthquakes, whereas earlier scales tended to saturate for big events.

Calculation and data: Seismic moments are estimated from seismic waves recorded by networks of seismometers, often through inversion for slip on fault patches. M0 depends on the fault's area, average slip, and rock rigidity, and can be inferred from far-field or near-field waveforms as well as geodetic data.

Interpretation and limitations: Mw correlates with the total energy released and with the size of the rupture, but is not a direct measure of radiated energy. Uncertainties arise from slip distribution, rupture geometry, and the chosen mantle properties. For small earthquakes, Mw converges toward values similar to other scales; for large events, Mw remains more reliable than older magnitudes.