<p>As described in the question there are two similar coils, one radiates the AC magnetic field ("transmitter") and the other picks up the weak radiated AC magnetic field produced by subsurface electrical currents induced by the primary field.</p>

<h2>Sensitivity vs. Depth</h2>

<p>There are two modes of operation. The following two figures are from Section 4.1 of <a href="http://www.geonics.com/pdfs/technicalnotes/tn6.pdf" rel="nofollow noreferrer">GEONICS Technical note #6; Electromagnetic Terrain Conductivity Measurement at Low Induction Numbers</a>. (more technical notes <a href="http://www.geonics.com/html/technicalnotes.html" rel="nofollow noreferrer">here</a>) In both figures the two coils are separated by a horizontal distance <span class="math-container">$s$</span> which is typically a few meters.</p>

<p>In <strong>Horizontal mode</strong> the axes of the two coils point in the horizontal plane. In this orientation the sensitivity always peaks near the surface, and falls off to about 30% at a depth of <span class="math-container">$0.4 s$</span>. </p>

<p><img src="https://i.sstatic.net/c2BmX.png" alt="Electromagnetic Terrain Conductivity Measurement"></p>

<p>In <strong>Vertical mode</strong> the axes of the two coils point "up" or vertically. In this orientation the sensitivity is low near the surface <em>and peaks</em> at depth of <span class="math-container">$0.4 s$</span>. </p>

<p><img src="https://i.sstatic.net/fMU1S.png" alt="Electromagnetic Terrain Conductivity Measurement"></p>

<p>In either case, if <span class="math-container">$s$</span> is twice as big (the coils are twice as far apart) these two shapes will be stretched by the same amount. If <span class="math-container">$s$</span> is 2 meters, the vertical method will have peak sensitivity at 0.8 meters. If <span class="math-container">$s$</span> is 5 meters, vertical sensitivity peaks at 2.0 meters.</p>

<p>The two plots can be seen on the right side of Figure 1. in <a href="https://www.mdpi.com/1424-8220/17/11/2540/htm" rel="nofollow noreferrer">The Application of EM38: Determination of Soil Parameters, Selection of Soil Sampling Points and Use in Agriculture and Archaeology</a> Kurt Heil and Urs Schmidhalter, Sensors 2017, 17(11), 2540; <a href="https://doi.org/10.3390/s17112540" rel="nofollow noreferrer">https://doi.org/10.3390/s17112540</a></p>

<p>That article also links to <a href="https://www.sciencedirect.com/science/article/pii/S0168169914002968" rel="nofollow noreferrer">Comparison of the EM38 and EM38-MK2 electromagnetic induction-based sensors for spatial soil analysis at field scale</a> which may cite further references but it's paywalled.</p>

<p><img src="https://i.sstatic.net/Sm8Ld.png" alt="Electromagnetic Terrain Conductivity Measurement"></p>

<blockquote>
  <p>Figure 1. (Left) Relative cumulative contribution vs depth for vertically (RV(z)) and horizontally (RH(z)) orientated dipoles; (Right) Comparison of the relative responses for vertically (FV(z)) and horizontally (FH(z)) oriented dipoles.</p>
</blockquote>

<h2>Yes, that's all fine and dandy... But Why?</h2>

<p>I can't come up with a simple model for why this is true, so I'll have to read further. It's possible someone else will be able to provide a better answer. I think it's related to how the phase of the signals are process, but I'm not sure about that yet.</p>

<p>However, the Computers and Electronics in Agriculture paper <a href="https://www.sciencedirect.com/science/article/pii/S016816990000185X" rel="nofollow noreferrer">Accuracy issues in electromagnetic induction sensing of soil electrical conductivity for precision agriculture</a> (also available <a href="http://extension.missouri.edu/sare/documents/EMImethods2002.pdf" rel="nofollow noreferrer">here</a>) K.A.Sudduth, S.T.Drummond and N.R.Kitchen, Volume 31, Issue 3, May 2001, Pages 239-264 <a href="https://doi.org/10.1016/S0168-1699(00)00185-X" rel="nofollow noreferrer">https://doi.org/10.1016/S0168-1699(00)00185-X</a> happens to give equations for these shape, and a clue to where these are from.</p>

<p><img src="https://i.sstatic.net/8nONU.png" alt="enter image description here"></p>

<p>Those equations are close but <span class="math-container">$\color{red}{wrong!!}$</span> they are missing a division "/" sign.</p>

<blockquote>
  <p>Fig. 2. Relative response of EM38 sensor as a function of distance (adapted from McNeill, 1992).</p>
</blockquote>

<p>The equations in the figure have obviously been typed incorrectly, but if I make some simple adjustments they work nicely</p>

<p><span class="math-container">$$\phi_V(z) = \frac{4z}{(4z^2+1)^{3/2}} $$</span></p>

<p><span class="math-container">$$\phi_H(z) = 2 - \frac{4z}{(4z^2+1)^{1/2}} $$</span></p>

<p>where z has to be unitless, so is almost certainly given by:</p>

<p><span class="math-container">$$z \equiv \frac{\text{depth}}{s}$$</span></p>

<p>where <span class="math-container">$s$</span> is the separation between the two coils as before.</p>

<p><img src="https://i.sstatic.net/C0qlv.png" alt="plot of equations"></p>

<h2>Possibly helpful links:</h2>

<ul>
<li><a href="https://www.sciencedirect.com/science/article/pii/S0016706114000548" rel="nofollow noreferrer">The use of electromagnetic induction techniques in soils studies</a> (also available <a href="https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=2462&amp;context=usdaarsfacpub" rel="nofollow noreferrer">here</a>)</li>
<li><a href="https://pdfs.semanticscholar.org/7896/794afd56a72e5eb6525182fef383c2420031.pdf" rel="nofollow noreferrer">Comparison of Electromagnetic Induction and Direct Sensing of Soil
Electrical Conductivity</a></li>
</ul>

CC BY-SA 4.0
2019-07-29T18:02:00.850Z
Note that the simple linear model presented here becomes very inaccurate in the presence of higher conductivity soils.  More complicated nonlinear models are available.
Brian Borchers
CC BY-SA 4.0
2019-07-29T22:34:15.043Z
@BrianBorchers I'd love to know more! While I was able to *find a source* for these equations, I don't understand them yet. Any further reading/references are welcome.  Your point is well taken; as soon as the soil starts interacting significantly with the field all bets are off.
uhoh
CC BY-SA 4.0
2019-07-30T19:28:47.623Z
THis is explained in great detail in Wait's Geoelectromagnetism book.
Brian Borchers
CC BY-SA 4.0
2019-07-30T21:31:57.733Z
@BrianBorchers do you mean this one? https://www.elsevier.com/books/geo-electromagnetism/wait/978-0-12-730880-7
uhoh
CC BY-SA 4.0
2019-07-30T23:04:20.787Z
Yes, that's the book.  See my implementation in MATLAB and a reference to a paper about the model at http://euler.nmt.edu/~brian/nonlinem38.html
Brian Borchers
CC BY-SA 4.0
2019-07-30T23:26:58.630Z
@BrianBorchers I'll definitely have a look, *thanks!*
uhoh
CC BY-SA 4.0
2019-07-13T09:40:55.400Z
2019-07-26T00:00:00.680Z
2019-07-26T00:00:00.680Z
uhoh
<p>Why increasing transmitter-receiver coil separation in EM survey (<a href="http://www.geonics.com/html/em31-mk2.html" rel="nofollow noreferrer">EM31</a>, also <a href="https://www.reynolds-international.co.uk/uploads/files/04tssem31.pdf" rel="nofollow noreferrer">here</a>) increases depth of penetration? </p>

<p>Suppose there is a horizontal flat conductive layer underneath a flat resistive layer. Why receiver coil records stronger signals at 4 m transmitter-receiver coil spacing compared to 2 m transmitter-receiver coil spacing? What us the physical explanation of this?</p>

<geophysics><measurements><electromagnetism><field-measurements>
Transmitter receiver coil separation for Electromagnetic Terrain Conductivity Measurement
David
# Transmitter receiver coil separation for Electromagnetic Terrain Conductivity Measurement

(Asked by: username_0 on 2019-07-12)

Why increasing transmitter-receiver coil separation in EM survey ([EM31](http://www.geonics.com/html/em31-mk2.html), also [here](https://www.reynolds-international.co.uk/uploads/files/04tssem31.pdf)) increases depth of penetration?

Suppose there is a horizontal flat conductive layer underneath a flat resistive layer. Why receiver coil records stronger signals at 4 m transmitter-receiver coil spacing compared to 2 m transmitter-receiver coil spacing? What us the physical explanation of this?

**Tags:** geophysics, measurements, electromagnetism, field-measurements


---

## 1 answers

### Answer by username_1 on 2019-07-13. Score: 2

As described in the question there are two similar coils, one radiates the AC magnetic field ("transmitter") and the other picks up the weak radiated AC magnetic field produced by subsurface electrical currents induced by the primary field.

## Sensitivity vs. Depth

There are two modes of operation. The following two figures are from Section 4.1 of [GEONICS Technical note #6; Electromagnetic Terrain Conductivity Measurement at Low Induction Numbers](http://www.geonics.com/pdfs/technicalnotes/tn6.pdf). (more technical notes [here](http://www.geonics.com/html/technicalnotes.html)) In both figures the two coils are separated by a horizontal distance $s$ which is typically a few meters.

In **Horizontal mode** the axes of the two coils point in the horizontal plane. In this orientation the sensitivity always peaks near the surface, and falls off to about 30% at a depth of $0.4 s$.

![Electromagnetic Terrain Conductivity Measurement](https://i.sstatic.net/c2BmX.png)

In **Vertical mode** the axes of the two coils point "up" or vertically. In this orientation the sensitivity is low near the surface *and peaks* at depth of $0.4 s$.

![Electromagnetic Terrain Conductivity Measurement](https://i.sstatic.net/fMU1S.png)

In either case, if $s$ is twice as big (the coils are twice as far apart) these two shapes will be stretched by the same amount. If $s$ is 2 meters, the vertical method will have peak sensitivity at 0.8 meters. If $s$ is 5 meters, vertical sensitivity peaks at 2.0 meters.

The two plots can be seen on the right side of Figure 1. in [The Application of EM38: Determination of Soil Parameters, Selection of Soil Sampling Points and Use in Agriculture and Archaeology](https://www.mdpi.com/1424-8220/17/11/2540/htm) Kurt Heil and Urs Schmidhalter, Sensors 2017, 17(11), 2540; <https://doi.org/10.3390/s17112540>

That article also links to [Comparison of the EM38 and EM38-MK2 electromagnetic induction-based sensors for spatial soil analysis at field scale](https://www.sciencedirect.com/science/article/pii/S0168169914002968) which may cite further references but it's paywalled.

![Electromagnetic Terrain Conductivity Measurement](https://i.sstatic.net/Sm8Ld.png)

> Figure 1. (Left) Relative cumulative contribution vs depth for vertically (RV(z)) and horizontally (RH(z)) orientated dipoles; (Right) Comparison of the relative responses for vertically (FV(z)) and horizontally (FH(z)) oriented dipoles.

## Yes, that's all fine and dandy... But Why?

I can't come up with a simple model for why this is true, so I'll have to read further. It's possible someone else will be able to provide a better answer. I think it's related to how the phase of the signals are process, but I'm not sure about that yet.

However, the Computers and Electronics in Agriculture paper [Accuracy issues in electromagnetic induction sensing of soil electrical conductivity for precision agriculture](https://www.sciencedirect.com/science/article/pii/S016816990000185X) (also available [here](http://extension.missouri.edu/sare/documents/EMImethods2002.pdf)) K.A.Sudduth, S.T.Drummond and N.R.Kitchen, Volume 31, Issue 3, May 2001, Pages 239-264 <https://doi.org/10.1016/S0168-1699(00)00185-X> happens to give equations for these shape, and a clue to where these are from.

![enter image description here](https://i.sstatic.net/8nONU.png)

Those equations are close but $\color{red}{wrong!!}$ they are missing a division "/" sign.

> Fig. 2. Relative response of EM38 sensor as a function of distance (adapted from McNeill, 1992).

The equations in the figure have obviously been typed incorrectly, but if I make some simple adjustments they work nicely

$$\phi\_V(z) = \frac{4z}{(4z^2+1)^{3/2}} $$

$$\phi\_H(z) = 2 - \frac{4z}{(4z^2+1)^{1/2}} $$

where z has to be unitless, so is almost certainly given by:

$$z \equiv \frac{\text{depth}}{s}$$

where $s$ is the separation between the two coils as before.

![plot of equations](https://i.sstatic.net/C0qlv.png)

## Possibly helpful links:

* [The use of electromagnetic induction techniques in soils studies](https://www.sciencedirect.com/science/article/pii/S0016706114000548) (also available [here](https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=2462&context=usdaarsfacpub))
* [Comparison of Electromagnetic Induction and Direct Sensing of Soil
  Electrical Conductivity](https://pdfs.semanticscholar.org/7896/794afd56a72e5eb6525182fef383c2420031.pdf)

> **Comments:**
> **username_2**: Note that the simple linear model presented here becomes very inaccurate in the presence of higher conductivity soils.  More complicated nonlinear models are available.  
> **username_1**: @username_2 I'd love to know more! While I was able to *find a source* for these equations, I don't understand them yet. Any further reading/references are welcome.  Your point is well taken; as soon as the soil starts interacting significantly with the field all bets are off.  
> **username_2**: THis is explained in great detail in Wait's Geoelectromagnetism book.  
> **username_1**: @username_2 do you mean this one? https://www.elsevier.com/books/geo-electromagnetism/wait/978-0-12-730880-7  
> **username_2**: Yes, that's the book.  See my implementation in MATLAB and a reference to a paper about the model at http://euler.nmt.edu/~username_2/nonlinem38.html  
> **username_1**: @username_2 I'll definitely have a look, *thanks!*  

---

