Richter magnitude scale Richter correlation tables based on Richter standard seismic event (formula_26, formula_27, formula_28). Below, formula_29 is the epicentral distance (in kilometers unless otherwise specified). The Lillie empirical formula: Where formula_31 is the amplitude (maximum ground displacement) of the P-wave, in micrometers, measured at 0.8 Hz. For distances formula_32 less than 200 km, and for distances between 200 km and 600 km, where formula_31 is seismograph signal amplitude in mm and formula_32 is in km. The Bisztricsany (1958) empirical formula for epicentral distances between 4˚ to 160˚: Where formula_38 is the duration of the surface wave in seconds, and formula_39 is in
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.