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Calculation of safety index, β

@prec = 2
β(Rm, Em, Ve, Vr) = ln((Rm / Em) * (sqrt((1 + Ve^2) / (1 + Vr^2)))) / sqrt(ln((1 + Vr^2) * (1 + Ve^2)))

Gulf of Mexico:

βgom = 3.239 # for a target Pf = 3E-5

Rm(βgom, Em, Ve, Vr) = Em / (sqrt((1 + Ve^2) / (1 + Vr^2))) * exp(βgom * sqrt(ln((1 + Vr^2) * (1 + Ve^2))))

RSR_gom = Rm(βgom, 0.79, (sqrt(0.32^2 + 0.08^2)), 0.05) => 2.15
𝛾_gom = (1 / 1.37) * RSR_gom => 1.57

Australia (North West Shelf) by calibrating safety level of GoM to Australia:

RSR_aus = Rm(βgom, 0.78, (sqrt(0.33^2 + 0.08^2)), 0.05) => 2.18
𝛾_aus = (1 / 1.37) * RSR_aus => 1.59

Northern North Sea by calibrating safety level of GoM to NNS:

RSR_nns = Rm(βgom, 0.81, (sqrt(0.265^2 + 0.08^2)), 0.05) => 1.91
𝛾_nns = (1 / 1.37) * RSR_nns => 1.4

Central North Sea by calibrating safety level of GoM to CNS (also applicable to Southern North Sea):

RSR_cns = Rm(βgom, 0.84, (sqrt(0.212^2 + 0.08^2)), 0.05) => 1.72
𝛾_cns = (1 / 1.37) * RSR_cns => 1.26
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