$\nabla ^2 \mathbf{E} + k^2 \mathbf{E} = 0$

$\nabla ^2 \mathbf{H} + k^2 \mathbf{H} = 0$

$ k = \sqrt{\omega ^2 \mu \varepsilon - i \omega \mu \sigma } $

$k_{ground} \simeq (1-i) \sqrt{ \frac{\omega \mu \sigma}{2} }$

$k_{air} \simeq \omega \sqrt{ \mu_0 \varepsilon_0}$

$\begin{split}\left(\begin{matrix} E_{x} \\ E_{y} \end{matrix} \right) = \left(\begin{matrix} \hat{Z}_{xx} & \hat{Z}_{xy} \\ \hat{Z}_{yx} & \hat{Z}_{yy} \end{matrix} \right) \left(\begin{matrix} H_x \\ H_y \end{matrix} \right)\end{split}$

$\begin{split} H_z = \left(\begin{matrix} T_{zx} & T_{zy} \end{matrix} \right) \left(\begin{matrix} H_x \\ H_y \end{matrix} \right)\end{split}$

$\delta = \sqrt{ \frac{2}{\omega \mu \sigma}} \simeq \frac{500}{\sqrt{\sigma f}}$

$ \phi_d = \sum \left(\frac{d^{obs}_i-d^{pred}_i}{\varepsilon} \right) ^2 $

$\phi = \phi_d +\beta \phi_m$