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Impedance of earth return in ground

Definition according to Cigré guide 531 chapter 4.2.1, 4.2.2.8

Refer to 'Electromagnetic Transients in Power Cables', F.F. da Silva, C.L. Bak (2013)

Symbol
$\mathscr{z}_g$
Unit
$\Omega$/m
Formulae
$\frac{j \omega \mu_E}{2\pi} \left(\ln\left(\frac{D_E}{r_{z4}}\right)-\frac{4}{3} m_{z,e} L_{cm}\right)$Cigre 531, 4.2.1
$\frac{\omega \mu_E}{8}+j \frac{\omega \mu_E}{2\pi} \ln\left(\frac{D_E}{r_{z4}}\right)$Cigre 531, 4.2.2.8
$\frac{\rho_E {m_{z,e}}^2}{2\pi} \left(\operatorname{kv}\left(0, m_{z,e} r_{z4}\right)+\frac{2}{4+{m_{z,e}}^2 {r_{z4}}^2} e^{-2L_{cm} m_{z,e}}\right)$da Silva
Related
$D_E$
Equivalent depth of earth return path [m]
$L_{cm}$
Depth of laying [m]
$m_{z,e}$
Parameter m of earth
$\mu_E$
Magnetic permeability of earth [H/m]
$\omega$
Angular frequency [rad/s]
$\pi$
Archimedes' constant $\pi$
$r_{z4}$
Radius of armour (inner) [m]
$\rho_E$
Specific electrical resistivity of soil [$\Omega$.m]
Used in
$\mathscr{z}_{ss}$
Impedance external of cable [$\Omega$/m]