Moment magnitude scale deal with significant earthquakes larger than . For these events, the official magnitude is the moment magnitude , not Richter's local magnitude . The symbol for the moment magnitude scale is , with the subscript "w" meaning mechanical work accomplished. The moment magnitude is a dimensionless value defined by Hiroo Kanamori as where is the seismic moment in dyne⋅cm (10 N⋅m). The constant values in the equation are chosen to achieve consistency with the magnitude values produced by earlier scales, such as the Local Magnitude and the Surface Wave magnitude. Seismic moment is not a direct measure of energy changes
Moment magnitude scale band. To simplify this calculation, he noted that the lowest frequency parts of the spectrum can often be used to estimate the rest of the spectrum. The lowest frequency asymptote of a seismic spectrum is characterized by the seismic moment, . Using an approximate relation between radiated energy and seismic moment (which assumes stress drop is complete and ignores fracture energy), (where E is in Joules and is in Nformula_4m), Kanamori approximated by The formula above made it much easier to estimate the energy-based magnitude , but it changed the fundamental nature of the scale into a moment magnitude scale.