Earthquake duration magnitude (Md) for earthquakes recorded on short-period vertical seismographs. Numerous studies determined the relation between coda duration and magnitude for different regions of the World. According to a recent study by Mandal et al. (2004), previous studies showed that duration magnitude estimation is quite stable for local earthquakes ranging from magnitude Md 0.0 to 5.0. In two most recent investigations using statistically stable samples for Italian earthquakes [approximately 100,000 events over the period 1981-2002 in the Richter local [ML] magnitude range of 3.5-5.8] and for Indian earthquakes exemplified by an aftershock sequence of 121 events with (surface wave magnitude) > 4.0
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.