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Site Scaling

Site response is defined in terms of site amplification, or impedance effects, as well as damping – via a kappa filter.

The overall site model is therefore written as: $S(f; \bm{\theta}_S) = S_I(f) \times S_K(f)$ with $S_I(f)$ representing the impedance effects, and $S_K(f)$ being the kappa filter.

Impedance functions

Impedance effects are represented using custom types that define an amplification function. These functions take a frequency as an argument and return the corresponding amplification level. Each of these custom types is a subtype of the abstract type SiteAmplification

Currently, the following impedance functions (custom types) are implemented:

  • SiteAmpBoore2016_760: is the Boore (2016) impedance function for a Western US generic rock profile with $V_{S,30}=760$ m/s
  • SiteAmpAlAtikAbrahamson2021_ask14_620: is the Al Atik & Abrahamson (2021) impedance function obtained by inverting the Abrahamson et al. (2014) GMM. The reference profile has a $V_{S,30}=620$ m/s
  • SiteAmpAlAtikAbrahamson2021_ask14_760: is the Al Atik & Abrahamson (2021) impedance function obtained by inverting the Abrahamson et al. (2014) GMM. The reference profile has a $V_{S,30}=760$ m/s
  • SiteAmpAlAtikAbrahamson2021_ask14_1100: is the Al Atik & Abrahamson (2021) impedance function obtained by inverting the Abrahamson et al. (2014) GMM. The reference profile has a $V_{S,30}=1100$ m/s
  • SiteAmpAlAtikAbrahamson2021_bssa14_620: is the Al Atik & Abrahamson (2021) impedance function obtained by inverting the Boore et al. (2014) GMM. The reference profile has a $V_{S,30}=620$ m/s
  • SiteAmpAlAtikAbrahamson2021_bssa14_760: is the Al Atik & Abrahamson (2021) impedance function obtained by inverting the Boore et al. (2014) GMM. The reference profile has a $V_{S,30}=760$ m/s
  • SiteAmpAlAtikAbrahamson2021_bssa14_1100: is the Al Atik & Abrahamson (2021) impedance function obtained by inverting the Boore et al. (2014) GMM. The reference profile has a $V_{S,30}=1100$ m/s
  • SiteAmpAlAtikAbrahamson2021_cb14_620: is the Al Atik & Abrahamson (2021) impedance function obtained by inverting the Campbell & Bozorgnia (2014) GMM. The reference profile has a $V_{S,30}=620$ m/s
  • SiteAmpAlAtikAbrahamson2021_cb14_760: is the Al Atik & Abrahamson (2021) impedance function obtained by inverting the Campbell & Bozorgnia (2014) GMM. The reference profile has a $V_{S,30}=760$ m/s
  • SiteAmpAlAtikAbrahamson2021_cb14_1100: is the Al Atik & Abrahamson (2021) impedance function obtained by inverting the Campbell & Bozorgnia (2014) GMM. The reference profile has a $V_{S,30}=1100$ m/s
  • SiteAmpAlAtikAbrahamson2021_cy14_620: is the Al Atik & Abrahamson (2021) impedance function obtained by inverting the Chiou & Youngs (2014) GMM. The reference profile has a $V_{S,30}=620$ m/s
  • SiteAmpAlAtikAbrahamson2021_cy14_760: is the Al Atik & Abrahamson (2021) impedance function obtained by inverting the Chiou & Youngs (2014) GMM. The reference profile has a $V_{S,30}=760$ m/s
  • SiteAmpAlAtikAbrahamson2021_cy14_1100: is the Al Atik & Abrahamson (2021) impedance function obtained by inverting the Chiou & Youngs (2014) GMM. The reference profile has a $V_{S,30}=1100$ m/s
  • SiteAmpUnit: simply provides a unit impedance for all frequencies, i.e., $S_I(f)=1.0$
  • SiteAmpConstant: provides a constant, c, impedance for all frequencies, i.e., $S_I(f)=c$
StochasticGroundMotionSimulation.site_amplification — Function
site_amplification(f::T, amp_model::S; fmin=1e-3, fmax=999.99) where {T<:Real,S<:SiteAmplification}

Computes the site amplification (impedance) for a given frequency f. The argument amp_model is a subtype of the abstract type SiteAmplification.

# Examples

	f = 5.0
	# returns the amplification from AlAtik (2021) in both cases
	Af = site_amplification(f)
    Af = site_amplification(f, SiteAmpAlAtikAbrahamson2021_cy14_760())
    # returns the Boore (2016) amplification
	Af = site_amplification(f, SiteAmpBoore2016_760())
	# returns 1.0
	Af = site_amplification(f, SiteAmpUnit())
source
site_amplification(f::Vector{T}, amp_model::S; fmin=1e-3, fmax=999.99) where {T<:Real,S<:SiteAmplification}

Computes the site amplification (impedance) for a given frequency f. The argument amp_model is a subtype of the abstract type SiteAmplification.

# Examples

	f = 5.0
	# returns the amplification from AlAtik (2021) in both cases
	Af = site_amplification(f)
    Af = site_amplification(f, SiteAmpAlAtikAbrahamson2021_cy14_760())
    # returns the Boore (2016) amplification
	Af = site_amplification(f, SiteAmpBoore2016_760())
	# returns 1.0
	Af = site_amplification(f, SiteAmpUnit())
source
site_amplification(f, site::SiteParameters)

Computes the site amplification (impedance) for a given frequency f.

source
site_amplification(f, fas::FourierParameters)

Computes the site amplification (impedance) for a given frequency f.

source

Kappa filter

In addition to the impedance effects, the near surface damping is represented by a generic kappa filter:

\[S_K(f) = \exp\left( -\pi \kappa_0 f \right)\]