Time-averaged shear-wave velocity of the upper 30 m

Usage

estimateVS30(hs, VSm, Vref)

Arguments

hs: Positive layer thicknesses in metres, from the surface down.
VSm: Positive layer shear-wave velocities in m/s, aligned with hs.
Vref: One positive velocity in m/s of the material below the column, used only when the column is shallower than 30 m.

Value

One velocity in m/s, unrounded.

Mathematics

With layer thicknesses $h_k$ from the surface and velocities $V_k$, the travel time through the part of each layer inside the upper 30 m is accumulated and $$V_{S30} = \frac{30}{\sum_k h_k^{(30)} / V_k + \max(30 - \sum_k h_k, 0)/V_{ref}},$$ where the second term completes a column shallower than 30 m with the reference velocity Vref and vanishes otherwise. The result is the harmonic average of the velocities weighted by thickness (ASCE/SEI 7-22 Eq. 20.4-1), evaluated at the supplied profile; it carries no dispersion.

Examples

estimateVS30(hs = c(10, 20), VSm = c(200, 400), Vref = 760)   # 300
#> [1] 300
estimateVS30(hs = 10, VSm = 200, Vref = 760)                  # padded
#> [1] 393.1034