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
Richter magnitude scale used by astronomers. Second, he wanted a magnitude of zero to be around the limit of human perceptibility. Third, he specified the Wood-Anderson seismograph as the standard instrument for producing seismograms. Magnitude was then defined as "the logarithm of the maximum trace amplitude, expressed in microns", measured at a distance of 100 km. The scale was calibrated by defining a magnitude 3 shock as one that produces (at a distance of 100 km) a maximum amplitude of 1 micron (1 µm, or 0.001 millimeters) on a seismogram recorded by a Wood-Anderson torsion seismograph. Finally, Richter calculated a table of distance