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Non-linear site amplification factor FST20

F_ST20.Rd

Final-generation NGA-East ergodic site-amplification model: linear component and F760 impedance/gradient weighting per Stewart et al. (2020), nonlinear component per Hashash et al. (2020), with the period-dependent nonlinear reference velocity (760 m/s for Tn < 0.4 s, 3000 m/s above) and the PGA-dependent nonlinear sigma \(\sigma_{F_{nl}} = \sigma_{f2}\,\ln((PGA_{3000}+f_3)/f_3)\). Coefficients are the USGS nshmp-lib table (see data-raw/SiteAmp2020.R for provenance); reference implementation cross-checked function-by-function against OpenQuake gsim/nga_east.py.

Usage

F_ST20(PGA, Tn, vs30, vref = 760)

Arguments

PGA

numeric vector - peak ground acceleration (g) at the vref condition.

Tn

numeric scalar - oscillator period (s).

vs30

numeric scalar - target Vs30 (m/s).

vref

numeric scalar - reference velocity, 760 or 3000 m/s.

Value

A data.table with columns muLnF, sdLnF, ID = "ST20".

Details

Conventions:

  • The published model is referenced to 3000 m/s. For vref = 760 the mean is the exact difference \(F(V_{s30}) - F(760)\) of the composite model (including the F760 weighting difference below 600 m/s and the small \(F_{nl}(760)\) term at Tn >= 0.4 s), and the input PGA (at 760 m/s) is converted to the 3000 m/s anchor via \(PGA_{3000} = PGA_{760}/2.275\) (PEER 2017/05 Eq. 2.4).

  • sdLnF is evaluated at the target vs30 only; for vref = 760 no reference-side sigma is added (the rock hazard carries its own dispersion). For vref = 3000 the weighted F760 sigma enters the SRSS.

  • vs30 == vref returns muLnF = 0, sdLnF = 0 (deterministic unit factor, same contract as F_ST17).

  • Coefficients interpolate linearly in \(\ln T_n\) (OpenQuake CoeffsTable rule); Tn = 0 uses the PGA row; Tn above the published 10 s limit is clamped to 10 s with a warning.

References

Stewart, J.P. et al. (2020) "Ergodic site amplification model for central and eastern North America." Earthquake Spectra 36(1). Hashash, Y.M.A. et al. (2020) "Nonlinear site amplification model for ergodic seismic hazard analysis in central and eastern North America." Earthquake Spectra 36(1).

Examples

# soft-soil amplification of the 0.2 s ordinate, hazard at 760 m/s
F_ST20(PGA = c(0.05, 0.2, 0.5), Tn = 0.2, vs30 = 300)
#>         muLnF     sdLnF     ID
#>         <num>     <num> <char>
#> 1: 0.37682363 0.2525448   ST20
#> 2: 0.24385574 0.2595137   ST20
#> 3: 0.06985233 0.2788971   ST20

# very-hard-rock reference (3000 m/s)
F_ST20(PGA = 0.1, Tn = 1.0, vs30 = 760, vref = 3000)
#>        muLnF     sdLnF     ID
#>        <num>     <num> <char>
#> 1: 0.1530131 0.2524343   ST20