Moment magnitude scale as (in Joules). Unfortunately, the duration of many very large earthquakes was longer than 20 seconds, the period of the surface waves used in the measurement of . This meant that giant earthquakes such as the 1960 Chilean earthquake (M 9.5) were only assigned an . Caltech seismologist Hiroo Kanamori recognized this deficiency and he took the simple but important step of defining a magnitude based on estimates of radiated energy, , where the "w" stood for work (energy): Kanamori recognized that measurement of radiated energy is technically difficult since it involves integration of wave energy over the entire frequency
Logarithmic scale the value of a logarithm function. Here, a given logarithmic unit will be denoted using the notation [log "n"], where "n" is a positive real number, and [log ] here denotes the indefinite logarithm function Log(). Examples of logarithmic units include common units of information and entropy, such as the "bit" [log 2] and the "byte" 8[log 2] = [log 256], also the "nat" [log e] and the "ban" [log 10]; units of relative signal strength magnitude such as the "decibel" 0.1[log 10] and "bel" [log 10], "neper" [log e], and other logarithmic-scale units such as the Richter magnitude scale