Fourier Amplitude Spectrum

The Fourier amplitude spectrum (FAS) can be represented as the product of source, path and site contributions.

Specifically, the Fourier amplitude spectrum $|A(f)|$ of acceleration (in units of m/s) is defined as:

\[|A(f; \bm{\theta})| = E(f; \bm{\theta}_E)\times P(f; \bm{\theta}_P) \times S(f; \bm{\theta}_S)\]

where $f$ is a frequency in Hz, and $\bm{\theta}$ holds all of the relevant model parameters and predictor variables. The Fourier Source Spectrum, $E(f; \bm{\theta}_E)$ is a function of the earthquake magnitude $m$, as well as other properties of the source. The Path Scaling, $P(f; \bm{\theta}_P)$ accounts for the effects of both geometric spreading and anelastic attenuation. The Site Scaling, $S(f; \bm{\theta}_S)$ includes the effects of near-surface impedance as well as damping ($\kappa_0$) effects.