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
Rating scale at the ordinal level. Numbers indicate the relative position of items, but not the magnitude of difference. Attitude and opinion scales are usually ordinal; one example is a Likert response scale: Some data are measured at the interval level. Numbers indicate the magnitude of difference between items, but there is no absolute zero point. A good example is a Fahrenheit/Celsius temperature scale where the differences between numbers matter, but placement of zero does not. Some data are measured at the ratio level. Numbers indicate magnitude of difference and there is a fixed zero point. Ratios can be calculated. Examples include