Electrical propagation in a non uniform soil

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Dear All,

I would enjoy your help on electrical geophysics .

Suppose a soil divided into 3 layers, each of them having a different electrical resistivity (Rho1, Rho2 and Rho3, starting from the top to the bottom)

Now suppose a dc current injection from a point M located at the top surface of the soil. This injection is vertical, going from the top (surface of the soil) to the bottom. My purpose is to assess the electrical potential (with respect to far earth) of a point P (coordinates : x, y and z with respect to point M) depending on the injected dc current, the coordinates of P, and the 3 soil resistivities.

I've come to Bessel equations and functions, but there may be a more simple way to proceed.

Any light on my concern please ?

Thanks and Regards.

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This injection is vertical, going from the top (surface of the soil) to the bottom

Top to bottom of all three layers or just the top one?

Now suppose a dc current injection from a point M located at the top surface of the soil.

You need at least two electrodes to inject a current.

So you need the electrode spacing.

How about a sketch?

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The resistance of the separate layers depends on both the thickness of the layer and the resistance per mm. I just finished a project a couple of years ago that was somewhat similar. Aside from the resistance you have all sorts of leakages - how do you measure the resistance without a current? And then how do you generate a current that isn't grounded through several pathways?

It is extremely doubtful that soil has a resistance the is the same through every pathway that the current could travel and so you cannot guarantee the resistance pathway and hence a uniform resistance. Also water content drastically changes the resistance in some types of soil and not others.

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Good evening,

To Studiot : As fas as electrodes are concerned, my current is impressed by several voltage sources located at different places on a conductor that is laid down the soil. Currents leak from this conductor. Therefore, there are several electrodes. I'll put a sketch later on.

To RiceAway : thanks for your contribution. My purpose is not to measure the soil resistivity, but to assume several layers (with their respective resistivity's and thicknesses) of soil and from this assumption, calculate the potential of a point P in the soil depending on its relative location with respect to the injection, and of course depending on the characteristics of the soil layers that are mentioned above. With border conditions, I've come to Bessel equation and functions, but I'm not sure it is the best way to proceed...

Regards.

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I'll await the sketch before offering further comment then.

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• 2 weeks later...

Hello Studiot,

Please find attached a sketch, where 3 soil layers have been represented. A current is impressed in P and the goal is to determine the potential of points M1, M2 and M3 with respect to far earth.

If my purposes are not clear, please get back to me.

Kind Regards.

3 layers.pdf

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