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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.

Fourier spectral ordinates, or complete Fourier spectra are obtained via the functions:

StochasticGroundMotionSimulation.fourier_spectrum — Function
fourier_spectrum(f::Vector{U}, m::S, r_ps::T, fas::FourierParameters) where {S<:Real,T<:Real,U<:Float64}

Fourier acceleration spectrum (m/s) based upon an equivalent point source distance r_ps

  • f is Vector of frequencies (Hz)
  • m is magnitude
  • r_ps is the equivalent point source distance including saturation effects (km)
  • fas are the Fourier spectral parameters FourierParameters

See also: fourier_spectral_ordinate

source
StochasticGroundMotionSimulation.fourier_spectrum! — Function
fourier_spectrum!(Af::Vector{U}, f::Vector{V}, m::S, r_ps::T, fas::FourierParameters) where {S<:Real,T<:Real,U<:Real,V<:Float64}

Fourier acceleration spectrum (m/s) based upon an equivalent point source distance r_ps

  • Af is the vector of fas amplitudes to be filled (m/s)
  • f is Vector of frequencies (Hz)
  • m is magnitude
  • r_ps is the equivalent point source distance including saturation effects (km)
  • fas are the Fourier spectral parameters FourierParameters

See also: fourier_spectrum

source
StochasticGroundMotionSimulation.fourier_spectral_ordinate — Function
fourier_spectral_ordinate(f::S, m::S, r_ps::T, src::SourceParameters, geo::GeometricSpreadingParameters, ane::AnelasticAttenuationParameters, site::SiteParameters) where {S<:Float64,T<:Real}

Fourier acceleration spectral ordinate (m/s) based upon an equivalent point source distance r_ps

  • f is frequency (Hz)
  • m is magnitude
  • r_ps is the equivalent point source distance including saturation effects (km)
  • src are the source parameters SourceParameters
  • geo are the geometric spreading parameters GeometricSpreadingParameters
  • sat are the near source saturation parameters NearSourceSaturationParameters
  • ane are the anelastic attenuation parameters AnelasticAttenuationParameters
  • site are the site parameters SiteParameters

See also: fourier_spectrum, fourier_spectrum!

source
fourier_spectral_ordinate(f::U, m::S, r_ps::T, src::SourceParameters, path::PathParameters, site::SiteParameters) where {S<:Real,T<:Real,U<:Float64}

Fourier acceleration spectral ordinate (m/s) based upon an equivalent point source distance r_ps

  • f is frequency (Hz)
  • m is magnitude
  • r_ps is the equivalent point source distance including saturation effects (km)
  • src are the source parameters SourceParameters
  • path are the path parameters PathParameters
  • site are the site parameters SiteParameters
source
fourier_spectral_ordinate(f::U, m::S, r_ps::T, fas::FourierParameters) where {S<:Real,T<:Real,U<:Float64}

Fourier acceleration spectral ordinate (m/s) based upon an equivalent point source distance r_ps

  • f is frequency (Hz)
  • m is magnitude
  • r_ps is the equivalent point source distance including saturation effects (km)
  • fas are the Fourier spectral parameters FourierParameters
source

Individual contributions to the Fourier spectrum are also available, for example: