Gutenberg–Richter law Gutenberg–Richter law In seismology, the Gutenberg–Richter law (GR law) expresses the relationship between the magnitude and total number of earthquakes in any given region and time period of "at least" that magnitude. or Where: The relationship between earthquake magnitude and frequency was first proposed by Charles Francis Richter and Beno Gutenberg in a paper published in 1956. This relationship between event magnitude and frequency of occurrence is remarkably common, although the values of a and b may vary significantly from region to region or over time. The parameter b (commonly referred to as the "b-value") is commonly close to 1.0
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.