Moment magnitude scale magnitude corresponds to a 10 ≈ 32 times increase in the amount of energy released, and an increase of two steps corresponds to a 10 = 1000 times increase in energy. Thus, an earthquake of of 7.0 contains 1000 times as much energy as one of 5.0 and about 32 times that of 6.0. The moment magnitude (>) scale was introduced to address the shortcomings of the Richter scale (detailed above) while maintaining consistency. Thus, for medium-sized earthquakes, the moment magnitude values should be similar to Richter values. That is, a magnitude 5.0 earthquake will be about a 5.0 on
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.