Site spectrum at the first quadrature order that agrees with the previous

Evaluates integrateSiteSpectrum() at the increasing Gauss-Legendre orders and returns the site spectrum of the first order whose ordinates agree with those of the previous order, together with the order and the agreement reached, so that the numerical error of the result is visible.

Usage

refineSiteSpectrum(spectrum, VS30, Vref, model, orders, tolerance)

Arguments

spectrum

The rock quantile spectrum, see integrateSiteSpectrum().

VS30

One target velocity in m/s.

Vref

One reference velocity in m/s.

model

Site factor model of evaluateSiteFactor(), "ST20" or "ST17".

orders

At least two increasing integers, each at least 4.

tolerance

One positive relative change.

Value

A list with spectrum (the site spectrum of the accepted order, as integrateSiteSpectrum() returns it), order (the accepted order) and change (\(\delta\) of that order).

Mathematics

With \(S_i\) the site ordinates (SaF, every period and level) at order \(n_i\) and the relative change \(\delta_i = \max |S_{i-1} - S_i| / \max(|S_i|, \epsilon)\) (\(\epsilon\) the smallest positive double), order \(n_i\), \(i \ge 2\), is accepted when \(\delta_i\) is finite and at most tolerance. No order accepted is an error.

Examples

P <- c("0.05", "0.10", "0.16", "0.50", "0.84", "0.90", "0.95", "mean")
Factor <- c(0.45, 0.60, 0.72, 0.95, 1.30, 1.48, 1.78, 1.00)
Spectrum <- data.table::data.table(Tn = rep(c(0, 0.2, 1), each = 8), p = rep(P, 3),
                                   Sa = rep(c(0.30, 0.45, 0.24), each = 8) * rep(Factor, 3))
refineSiteSpectrum(Spectrum, VS30 = 270, Vref = 760, model = "ST20",
                   orders = c(32, 64, 128), tolerance = 2e-3)[c("order", "change")]
#> $order
#> [1] 64
#> 
#> $change
#> [1] 0.0002114338
#>