Richter magnitude scale from it empirically as a quantity without units, just a number designed to conform to the formula_3 scale. A spectral analysis is required to obtain formula_12, whereas the other magnitudes are derived from a simple measurement of the amplitude of a specifically defined wave. All scales, except formula_5, saturate for large earthquakes, meaning they are based on the amplitudes of waves which have a wavelength shorter than the rupture length of the earthquakes. These short waves (high frequency waves) are too short a yardstick to measure the extent of the event. The resulting effective upper limit of measurement for formula_17
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