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from geoscilabs.em.ResponseFct import interactive_responseFct
from IPython.display import display
%matplotlib inline

Computing Apparent Resistivity

In this app, we compute apparent resistivity using the response curves for a two-loop Frequency domain system for a two-layer earth. Below figure shows horizontal coplanar (HCP) configuration.

Assuming the coil spacing $s \ll \delta$, where $\delta$ is the skin depth, the apparent conductivity is given by

$$ \sigma_a = \int_0^\infty \phi(z) \sigma(z) dz $$

Where

$\sigma_a$ is the apparent conductivity
$\phi$ is the response function
$\sigma$ is the conductivity structure

Note that in the following plots, the y-axis is a normalized depth: $z/s$ where $s$ is the source-receiver separation.

Two different configurations of source-receiver configurations are considered:

HCP: Horizontal coplanar system. The associated dipoles are perpendicular to the plane of the loops and are therefore in the vertical direction. The response function associated with this is .
VCP: Vertical coplanar system. The associated dipoles are perpendicular to the plane of the loops and are therefore in the horizontal direction. The response function associated with this is .

For more, see the GPG section on dual loop systems

Parameters:

h$_{boom}$: height of the source-receiver boom from the surface [m]
h$_{1}$: thickness of the first layer [m]
$\sigma_{1}$: conductivity of the first layer [S/m]
$\sigma_{2}$: conductivity of the second layer [S/m]
configuration: configuration of the source-receiver



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app = interactive_responseFct()
display(app)



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