What is Fourier amplitude spectrum?
The Fourier amplitude spectrum FS(ω) is defined as the square root of the sum of the squares of the real and imaginary parts of F(ω). Thus:  Since a(t) has units of acceleration, FS(ω) has units of velocity. The Fourier amplitude spectrum is of interest to seismologists in characterizing ground motion.
What is the point of an amplitude spectrum?
Understanding Seismic Wave Propagation The amplitude spectrum simply gives amplitude at each frequency. The phase spectrum simply gives the phase at each frequency (Figure 2.20).
What is the amplitude of the Fourier transform?
The Fourier Transform amplitude simply tells you how much of each Logo black are in any contraption. The magnitude of each bin is the magnitude of that frequency component for that waveform in the time-domain, specifically when the time domain waveform is expressed as a sum of complex exponential frequencies.
What is the Fourier spectrum in earthquake?
Therefore in the ω-2 model, the Fourier amplitude spectrum of the seismic wave radiating from the source is proportional to the seismic moment on the long period side, and is proportional to the seismic moment to the power of 1/3 on the short period side.
What is power spectrum in Fourier Transform?
The power spectrum of a time series. describes the distribution of power into frequency components composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discrete frequencies, or a spectrum of frequencies over a continuous range.
How do Fourier transforms work?
The Fourier Transform is a tool that breaks a waveform (a function or signal) into an alternate representation, characterized by sine and cosines. The Fourier Transform shows that any waveform can be re-written as the sum of sinusoidal functions.
What is a Fourier transform and how is it used in seismic processing?
A set of mathematical formulas used to convert a time function, such as a seismic trace, to a function in the frequency domain (Fourier analysis) and back (Fourier synthesis). The Fourier transform is used extensively in signal processing to design filters and remove coherent noise.