Calculates transversely isotropic electrical conductivity given the Watson distribution parameter κ, volume fraction φ, and conductivity of conductive phase σl. Select the pore geometry model (Crack or Tube).
Model:
σx = σy = σl φ ∫ f(θ) (1 − sin²θ cos²φ)3/2 dΩ
σz = σl φ ∫ f(θ) sin³θ dΩ
f(θ) = exp(κ cos²θ) / (4π 1F1(1/2, 3/2; κ))
σz = σl φ ∫ f(θ) sin³θ dΩ
f(θ) = exp(κ cos²θ) / (4π 1F1(1/2, 3/2; κ))
Given measured conductivities σx and σz, finds the Watson distribution parameter κ and volume fraction φ that best explain the observations. Select the model (Crack or Tube) to use for the inversion. Uses bisection search over κ ∈ [−100, 100] with convergence tolerance 0.001.
Model:
σx = σy = σl φ ∫ f(θ) (1 − sin²θ cos²φ)3/2 dΩ
σz = σl φ ∫ f(θ) sin³θ dΩ
f(θ) = exp(κ cos²θ) / (4π 1F1(1/2, 3/2; κ))
σz = σl φ ∫ f(θ) sin³θ dΩ
f(θ) = exp(κ cos²θ) / (4π 1F1(1/2, 3/2; κ))