Direction of maximum horizontal stress from the stress tensor

Calculates the direction of maximum horizontal stress using only the directions of the principal stress and \(R = \frac{S1 - S2}{S1 - S3}\). This function Equations 11 and 10 from Lund and Townend (2007).

Usage

SH(S1, S2, S3, R, tol = .Machine$double.eps^0.5, ortho.tol = 1e-04)

Arguments

S1, S2, S3

numeric three-column vectors. The principal stress orientations. The variables hold the coordinates in the North, East and Down geographical coordinate system, e.g. S1 = c(s1N,s1E,s1D)

R

numeric. Relative magnitude of S2 with respect to S1 and S3: \(R = \frac{S1 - S2}{S1 - S3}\). Values ranging from 0 to 1, with 0 being S1==S2 and 1 being S2==S3.

tol

Tolerance of comparison.

ortho.tol

tolerance angle (in radians) for orthogonality check of the three principal stress vectors.

Value

numeric angle in degrees. The direction of SH from North.

References

Lund and Townend, (2007). Calculating horizontal stress orientations with full or partial knowledge of the tectonic stress tensor, Geophys. J. Int., doi:doi:10.1111/j.1365-246X.2007.03468.x .

Examples

# first example from https://www.snsn.se/SH/SHcode/benchmark.out
S1 <- Line(250.89, 70.07)
S3 <- Line(103.01, 17.07)
S2 <- vcross(S3, S1)
SH(S1, S2, S3, R = 1) #  70.89
#> [1] 70.89

R <- seq(0, 1, .05)
cbind(R, SH = sapply(R, function(x) {
  SH(S1, S2, S3, R = x)
}))
#>          R       SH
#>  [1,] 0.00 13.01021
#>  [2,] 0.05 13.18337
#>  [3,] 0.10 13.37695
#>  [4,] 0.15 13.59476
#>  [5,] 0.20 13.84162
#>  [6,] 0.25 14.12371
#>  [7,] 0.30 14.44908
#>  [8,] 0.35 14.82843
#>  [9,] 0.40 15.27621
#> [10,] 0.45 15.81249
#> [11,] 0.50 16.46586
#> [12,] 0.55 17.27842
#> [13,] 0.60 18.31445
#> [14,] 0.65 19.67656
#> [15,] 0.70 21.53704
#> [16,] 0.75 24.20154
#> [17,] 0.80 28.23884
#> [18,] 0.85 34.69668
#> [19,] 0.90 45.01043
#> [20,] 0.95 58.66746
#> [21,] 1.00 70.89000