Moment Magnitude Mw Calculator

Seismic moment is the physical measure of an earthquake, defined as the product of the shear modulus of the faulted rock, the area that ruptured, and the average slip across it. It has units of newton meters and describes the strength of the equivalent double-couple force system that radiates the seismic waves. Because it is built from fault geometry rather than from the peak swing of a needle, it does not saturate for large events. Moment magnitude converts that number onto the familiar scale as two thirds of the base-ten logarithm of moment minus 9.1, a constant that applies when moment is in newton meters; the older dyne centimeter convention uses 10.7. The two-thirds factor preserves continuity with earlier scales, and it means one magnitude unit corresponds to a factor of 10 to the 1.5 power, about 31.6, in seismic moment. Shear modulus is normally taken as about 30 GPa for crustal rock and 40 to 70 GPa in the mantle. Sensible inputs matter. Rupture areas run from a few square kilometers for a magnitude 5 to well over 100,000 square kilometers for the largest subduction events, with average slip from centimeters to tens of meters. Several caveats apply to the derived figures. The radiated energy expression assumes a roughly constant apparent stress, which real earthquakes violate by an order of magnitude either way, so energy and TNT equivalents are order-of-magnitude guides rather than measurements; the energy magnitude Me is a separate quantity. Published Mw values for the same event commonly differ by 0.1 to 0.2 between agencies depending on whether a W-phase, body-wave or full moment tensor inversion was used, and early automatic estimates for great earthquakes are often revised upward within hours.

Charles Richter introduced the original local magnitude scale in 1935 for southern California, calibrated to the maximum trace amplitude on Wood-Anderson torsion seismographs at a reference distance. Beno Gutenberg, working with Richter, extended the idea to teleseismic distances with body-wave and surface-wave magnitudes. A structural flaw emerged as the global network grew: these amplitude-based scales saturate, with body-wave magnitude flattening near 6.5 and surface-wave magnitude near 8.3, because the finite bandwidth of the measurement cannot capture the very long periods that dominate great earthquakes. Events of visibly different size were being assigned indistinguishable magnitudes. The fix required a quantity tied to the rupture itself. Building on elastic dislocation theory, Keiiti Aki estimated seismic moment directly from long-period seismograms of the 1964 Niigata earthquake in 1966, establishing moment as a measurable physical parameter. Hiroo Kanamori proposed in 1977 that magnitude be defined through the strain energy implied by moment, and in 1979 Thomas Hanks and Kanamori published the moment magnitude scale in the Journal of Geophysical Research, choosing constants so the new scale would agree with existing ones in the range where those still worked. Routine determination became possible through the Centroid Moment Tensor project begun by Adam Dziewonski and colleagues in 1981. Reassessment on this basis confirmed the 1960 Chile earthquake as the largest instrumentally recorded event at magnitude 9.5.