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Paired intensity measures of a displacement scenario

sampleIntensities.Rd

Draws NS joint realizations of the intensity measures that the six displacement models read for a sliding mass of initial fundamental period Ts: peak ground acceleration, the spectral accelerations at the degraded periods \(1.3 T_s\) and \(1.5 T_s\), and the peak ground velocity and Arias intensity derived from each sampled PGA. One row is one realization; every column of a row belongs to the same draw.

Usage

sampleIntensities(spectrum, Ts, NS, zTrunc)

Arguments

spectrum

The spectrum of the scenario as sampleSpectra() accepts it: a quantile table (Tn, p, Sa in g) or an analytic mixture of \(\ln S_a\) (Tn, k, muLn, sigmaLn, w).

Ts

One finite positive initial fundamental period of the sliding mass in seconds.

NS

Number of realizations, one positive integer.

zTrunc

Truncation of the copula marginals in standard deviations for an analytic mixture, or NA, see sampleSpectra().

Value

A data.table with one row per realization: realization, PGA (g), Sa13 and Sa15 (spectral accelerations at \(1.3 T_s\) and \(1.5 T_s\), g), PGV (cm/s) and AI (m/s).

Mathematics

The periods \((0,\ 1.3 T_s,\ 1.5 T_s)\) are sampled jointly with sampleSpectra() under the correlation matrix \(C_{jk} = \rho(T_j, T_k)\) of correlateResiduals(), with \(C_{jj} = 1\) and the zero period evaluated at 0.01 s. A quantile spectrum that lacks \(1.3 T_s\) or \(1.5 T_s\) is first interpolated there with interpolateSpectrum(); an analytic mixture is interpolated by sampleSpectra() itself. Then \(PGV\) = estimatePGV() and \(I_a\) = estimateAI() of each sampled PGA. The draws consume NS trivariate normal deviates of the caller's random stream.

Examples

Sigma <- c(0.2, 0.45, 0.75)
Spectrum <- data.frame(Tn = c(0, 0.4, 1), k = "oq", muLn = log(c(0.8, 0.55, 0.42)) - Sigma^2 / 2,
                       sigmaLn = Sigma, w = 1)
set.seed(46)
sampleIntensities(Spectrum, Ts = 0.4, NS = 5, zTrunc = NA)
#>    realization       PGA      Sa13      Sa15       PGV        AI
#>          <int>     <num>     <num>     <num>     <num>     <num>
#> 1:           1 0.6252963 0.2379672 0.1768348  69.05494  5.518402
#> 2:           2 0.9840209 0.5198845 0.3563937 111.30898 13.196180
#> 3:           3 0.9398400 0.7513831 0.7848981 106.05336 12.080574
#> 4:           4 0.9358673 0.8527261 0.9651064 105.58141 11.982578
#> 5:           5 0.5149754 0.1836924 0.1574377  56.29061  3.799466