Fourier amplitude spectra

A Fourier amplitude spectrum model predicts the amplitude of the Fourier transform of the acceleration. The models expose freqs and fourier_amps (and ln_std where the model has a standard deviation).

Model

Input

BaylessAbrahamson2019

Scenario

SourceTheoryModel

magnitude, distance and region, with optional stress drop and depth

StaffordEtAl2022

magnitude, rupture or Joyner-Boore distance and mechanism (point-source model for \(V_{s30}\) = 760 m/s)

 
from pygmm import fourier_spectrum

fas = fourier_spectrum.SourceTheoryModel(magnitude=6.5, distance=20.0, region="wna")
fas.freqs, fas.fourier_amps, fas.duration

Site amplification is included by default and disable_site_amp=True removes it, so that the spectrum can be used as input at a different reference condition.

Site attenuation

pygmm.kappa has the relationships between \(V_{s30}\) and the site attenuation parameter \(\kappa_0\): calc_site_atten_vhea11() and calc_site_atten_xr21().

Correlation models

BaylessAbrahamson2018 and Stafford2017 are registered as correlation models, which take no scenario (input="stateless").

Use in pyRVT and pyStrata

A source-theory model has the Fourier amplitudes and the duration that pyRVT needs, so it is passed to RvtMotion.from_fas (pyRVT or pyStrata) to compute the peak response with random vibration theory.

Examples