Apparent Resistivity

The resistivity value obtained using simplified geometry and physics is known as the apparent resistivity. It is useful in providing a ball-park estimate of the Earth’s electric properties. Various definitions for apparent resistivity will be provided when learning about direct current resistivity and magnetotelluric methods.

Here, we present the definition for apparent resistivity which is most relevant to magnetotellurics. According to our quasi-static approximation for the impedance, where resistivity is the reciprocal of the conductivity:

\[\rho_{app} = \frac{1}{\sigma_{app}} = \frac{| Z_{xy}|^2}{\omega \mu}\]

Therefore, if perpendicular components of the electric and magnetic fields are known within a homogeneous medium, it is possible to estimate the electrical resisitivity of that medium; assuming also that the Earth is approximately non-permeable (\(\mu = \mu_0\)). For a half-space model, the Earth’s true resistivity is equal to the apparent resistivity.