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The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of amplitude (see below), which are all functions of the magnitude of the differences between the variable's extreme values. In older texts, the phase of a periodic function is sometimes called the amplitude. [1]
First, the scale is logarithmic, so that each unit represents a ten-fold increase in the amplitude of the seismic waves. [12] As the energy of a wave is proportional to A 1.5, where A denotes the amplitude, each unit of magnitude represents a 10 1.5 ≈ 32-fold increase in the seismic energy (strength) of an earthquake. [13]
The Richter scale [1] (/ ˈ r ɪ k t ər /), also called the Richter magnitude scale, Richter's magnitude scale, and the Gutenberg–Richter scale, [2] is a measure of the strength of earthquakes, developed by Charles Richter in collaboration with Beno Gutenberg, and presented in Richter's landmark 1935 paper, where he called it the "magnitude scale". [3]
A is the amplitude of the wave (the peak magnitude of the oscillation), φ is a phase offset , ω is the (temporal) angular frequency of the wave, describing how many radians it traverses per unit of time, and related to the period T by the equation ω = 2 π T , {\displaystyle \omega ={\tfrac {2\pi }{T}},}
A complex valued frequency-domain representation consists of both the magnitude and the phase of a set of sinusoids (or other basis waveforms) at the frequency components of the signal. Although it is common to refer to the magnitude portion (the real valued frequency-domain) as the frequency response of a signal, the phase portion is required ...
These include the length of the fault, magnitude, the depth of the quake, the distance from the epicentre, the duration (length of the shake cycle), and the geology of the ground (subsurface). Shallow-focused earthquakes generate stronger shaking (acceleration) than intermediate and deep quakes, since the energy is released closer to the surface.
The amplitude of different harmonic components of same long-held note on the flute come into dominance at different points in the phase cycle. The phase difference between the different harmonics can be observed on a spectrogram of the sound of a warbling flute. [4]
According to this definition, if the amplitude of the seismic wave measured by the Wood Anderson torsion seismometer at the epicentral distance of 100 km is 1 mm, then the magnitude is 3.