The British Caving Association

CREG journal 88 includes an article by myself, entitled How Earth-Current Antennas Really Work, which hypotheses on a
mathematical model of earth current antennas, which I first spoke about four years ago at Hidden Earth. Whenever I have mentioned this it has generated some interesting debate, because the points I am making are rather subtle. Rob Gill and I thought it could be helpful for people to discuss the article on the CREG forum rather than by the much slower method of writing a letter to the editor. So, after reading the article, if anyone has any questions, or any point they wish to raise, please post to this thread.

The article is accessible at http://doi.bcra.org.uk/j088013 but you will need a valid BCRA login to download it.

Abstract: With cave radio equipment, there has been a trend away from the use of induction loop antennas to the use of so-called earth-current antennas, i.e. long wires grounded at both ends. Both the HeyPhone and Nicola system use this type of antenna. However, the popular explanation for how this antenna works is fallacious. The antenna does not operate by allowing the current to flow in a 'big loop' in the ground, nor is it a 'conduction mode' of operation. In fact, it does not depend, fundamentally, on current flow in the ground at all. The fact that the popular explanation is wrong is important because, if we do not understand how the antenna works, it is difficult to know the best way to use it, nor how to design a better one. In this short note, David Gibson outlines a more useful model - that of the Grounded Horizontal Electric Dipole - but without the mathematical justification, which will be given in a future article.

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Thanks for a really useful article and I look forward to the promised article describing the G-HED model in more detail...

I guess my thoughts revolve around what one might expect a developed G-HED model to be able to shed light on.

Many years ago, we trialled very large surface electrode spacings (well over 200m, compared with the ‘normal’ HeyPhone 20m, or so). The results clearly showed a progressive increase in underground received signal strength with increase spacing until, just before we ran out of wire, the increase tailed off. It seemed that we could potentially cover a very large area from a given surface location and that this would have practical benefits, for example, if either the exact underground position was unknown or the overhead location was inaccessible. Or we could simply improve range by adjusting the spacing of the earth electrodes.

Is it reasonable to believe that we could use the developed G-HED model to optimise the length of G-HED to maximise vertical range or area coverage?

Rob Gill wrote:Many years ago, we trialled very large surface electrode spacings (well over 200m, compared with the ‘normal’ HeyPhone 20m, or so). The results clearly showed a progressive increase in underground received signal strength with increase spacing until, just before we ran out of wire, the increase tailed off.

Hi Rob, the tail-off is to be expected. If the antenna was effectively a point source then lengthening the wire would (in uniform ground, constant antenna current) result in a proportional increase in signal strength. However, given that your receiver was likely very close to the antenna, this is not the case, i.e. the antenna cannot be modelled as a point source. The longer you make the wire, the "less" it looks like a point source, until you reach a situation where, to the receiver, the transmitter looks essentially, infinitely long. In that situation the signal strength would not depend on the length of the wire. If you like, the signal strength is more dependent on the field in the vicinity and that clearly does not change if you simply make the wire longer.

Interestingly, if the ground resistance is much greater than the wire resistance then making the wire longer does not result in any wasted power because (in uniform ground) the resistance between electrodes does not depend on distance. But you have to carry more wire, and there will eventually come a point when the wire resistance becomes significant.

It seemed that we could potentially cover a very large area from a given surface location and that this would have practical benefits, for example, if either the exact underground position was unknown or the overhead location was inaccessible. Or we could simply improve range by adjusting the spacing of the earth electrodes. Is it reasonable to believe that we could use the developed G-HED model to optimise the length of G-HED to maximise vertical range or area coverage?

Yes. Although if you are going to make the wire "very long" you might as well make a very large loop instead as it is likely to perform better.

Consider the factors that limit you - one is the amount of wire you can carry; another is the size of your transmitter battery.

To get maximum range, you want to run as much current into the wire as possible, whilst limiting the amount of power it draws, because, for the same battery energy this will give you the maximum transmission time. This means that you want the circuit resistance to be as low as possible. In almost all situations, the resistance is minimised by using a wire as the return path for the transmitter current rather than the earth (unless you are going to invest in extremely large electrodes).

However, because the amount of wire you can carry is also limited, this limits the size of the loop you can make (i.e. the diameter of the loop will be less than the length of the wire when deployed linearly). Additionally, the current returning through the far side of the loop will generate a field that partially cancels the field from the other side. This leads to an inverse cube law of magnetic field v. distance instead of the inverse square law, which you get from a linear wire. Thus you have to balance the increased moment (due to the lower resistance of the loop v. the ground) with the fact that its size is smaller and youre dealing with an inverse cube law.

So, to answer your question... "yes". You can use the G-HED model, alongside the similar model of loop antenna in order to determine which would be better. The assertion, in my article, was that in some situations a large loop is better than a long wire. But it depends on the volume you wish to cover, as well as the range of distances. It is, as we say, "a subject for further investigation (on paper)". (Incidentally, assuming that it is correct to use the G-HED model to describe an earth-current antenna, this analysis is a good demonstration of why this particular model is better than, say, the "big loop in the ground" model, because the BL model does not come with any helpful equations relating antenna parameters to signal strength).

I mentioned, above, that the magnetic field from a wire had an inverse square law relationship with distance instead of the inverse cube law you get from a loop. Both those statements assume point-source antennas. If you are closer to the antenna than such a model tolerates then the field relationships are different. Also, its worth pointing out that the electric field from an electric dipole follows an inverse cube law, which is one reason why I say that the correct receiver to use with an earth-current transmitter is a loop antenna, not another earth-current antenna. But this is, as Chris T would remind us, is "for some value of 'correct' ".

Your article is thought-provoking and I look forward to the mathematical justification which, I understand, you intend to write in due course. However, you make one claim that seems so counter-intuitive that I think some clarification would be helpful. Except in the realm of quantum effects, where common sense is turned on its head and the apparently impossible becomes possible, I’d like to think that most physical systems can be understood, albeit at a lower level of appreciation, without having to understand the underlying maths. However, if something appears to behave in a way that is contrary to common sense, it’s also too easy to dismiss it.

The claim, which is at the very centre of the argument, is that the Big Loop model is fallacious. Here, I can imagine, just as you indicate how the penny dropped and you became aware that G-HED model was obviously correct, that others are equally sure that the Big Loop model is obviously correct. Indeed, I have some sympathy with this view, one that is bolstered in part, no doubt, by the familiar textbook image that invariably appears alongside discussion of earth resistance tomography, and which shows multiple loops of current in the ground resulting from the injection of a signal through a pair of electrodes.

Saying that the Big Loop model is incorrect could mean several things, including, but certainly not limited to:

1. That a current does not flow in the ground.

2. That a current does flow in the ground but these ground currents are not responsible for the generation of a magnetic field.

3. That the BL model is not particularly useful because analysing earth currents through multiple loops would be difficult and when, as is usually the case, the structure of the underlying geology is unknown, it becomes impossible.

I acknowledge, of course, that you do shed some light on these issues in the article but I did find myself re-reading it several times to appreciate what you were saying. If you are able, concisely, to clarify the basic premise of your claim with respect to the BL model, I think it will go a long way to reassuring those who have, no doubt, come to the conclusion that your suggestion is so counter-intuitive that they don’t stand a chance of understanding it. Indeed I too would appreciate having a better understanding of the fundamental claim.

Mike Bedford wrote:Your article is thought-provoking and I look forward to the mathematical justification which, I understand, you intend to write in due course.

Well... probably. The reason I have not yet done it is that it is not, in fact, necessary, because it is "obvious". It is certainly not novel. All I have done is to study the right parts of the right textbooks to pull it all together. I realise that refusing to explain it because it is "obvious" is, on the face of it, a ridiculous position, but what I mean is this: because the underlying theory is not novel, nor original, there is, in fact, no need for me, specifically, to explain it. It is not my theory! Explaining it would amount solely to my re-writing chunks of other people's text books. But... perhaps I will get around to it sometime, although Im more interested in explaining the applications of the result.

Mike Bedford wrote:The claim, which is at the very centre of the argument, is that the Big Loop model is fallacious.

I certainly used that word; and the BL concept is based on a fallacy, but its not really the central part of my argument. I made the point in the article that there is more than one way of looking at things and that different explanations, if they all have validity, will converge on the same reality. To that extent, I am willing to accept that a BL-type concept might have some validity but only provided its proponents can demonstrate that it converges on reality. So its over to you, really, Mike: what testable predictions on field strength and field orientation does your BL model make? And - importantly - are they the same predictions that the G-HED model makes? (If they arent - we have a problem).

Saying that the Big Loop model is incorrect could mean several things, including, but certainly not limited to:

1. That a current does not flow in the ground.

2. That a current does flow in the ground but these ground currents are not responsible for the generation of a magnetic field.

3. That the BL model is not particularly useful because analysing earth currents through multiple loops would be difficult and when, as is usually the case, the structure of the underlying geology is unknown, it becomes impossible.

Im not saying 1 or 2 (was that not clear from my article?). Im not really saying saying (3) either, but that's a good-enough approximation. Some of what Im saying - certainly in "sound bites" like in the abstract of my article - was designed to grab your attention. It might be fairer to say "the BL model serves no purpose", which is certainly true, unless anyone can demonstrate how it leads to testable predictions of e.g. field strength and orientation.

I acknowledge, of course, that you do shed some light on these issues in the article but I did find myself re-reading it several times to appreciate what you were saying. If you are able, concisely, to clarify the basic premise of your claim with respect to the BL model, I think it will go a long way to reassuring those who have, no doubt, come to the conclusion that your suggestion is so counter-intuitive that they don’t stand a chance of understanding it.

The "basic premise of my claim w.r.t. the BL model" is that it is , fundamentally, not a "model" (i.e. a hypothesis) because it makes no testable predictions. It is just "hand-waving". If anyone wants to confer on it the status of a model/hypothesis we would be in a position to discuss it further. Until then, it is not really possible to have a meaningful discussion about it.

The HeyPhone is traditionally used with earth current antennas at both ends so, surely, the "Conduction Mode" model makes more sense than the BL model in any case? CM is more testable than BL - it is straightforward to write down the shape of the field lines and the (d.c.) electric field strength from the CM model and to confirm that they agree with the G-HED model. This would allow a prediction of HeyPhone signal strength to be made, although unfortunately, the CM model does not account for skin depth, so the prediction would not be entirely accurate. The CM model allows the magnetic field to be calculated too. This makes it rather surprising that apparently radio amateurs have been claiming that the CM model implies that no radio interference is generated because it is all "conduction". This is clearly not the case since the CM model actually implies a "full strength" magnetic field if you do the analysis properly!

Going back to my comment about "sound bites", I have said that that the current in the ground does not contribute "materially" to the operation of the antenna. This was designed to catch the attention of the reader but I think this the statement has been misinterpreted. So, to recap/rephrase what I said in the article...

• The current in the antenna, together with all the current loops in the ground contribute to producing the observed fields.
• The fields are the same as would be generated by the same antenna current flowing in an isolated electric dipole, i.e. disconnected from the ground.
• Such an antenna (isolated dipole, uniform line current) is easy to model, so it provides an easy way to describe what is going on.

So, because the earth-current description can be equated to a situation where there is no earth current, it is as if the earth currents did not "materially" affect the field. (That is the central point of my argument - not the thing about the BL model). The salient point is that the isolated antenna I have described is a theoretical one, it could not physically exist. This is where a lot of people have misunderstood: they assume that Im saying that you can disconnect the antenna and it makes no difference to the fields. That is nonsense, of course, because if you disconnect the antenna no current will flow. It doesnt matter at all that the antenna is a theoretical one because we are only using it as a model - we are not intending to build it!

Correct me if Im wrong, Mike, but I think part of the problem is that we are discussing this at two different levels. I am interested in a scientific hypothesis, which is testable, which is why I call the BL concept merely "hand-waving". Whereas you, coming from your journalistic background, are interested in conveying the concept to lay people, to explain how it works. From your point of view the BL concept seems adequate ... and perhaps it is ... but it doesnt actually get us anywhere useful. Suppose we have a caver attempting to detect an earth current signal using a small portable induction loop or ferrite rod receiver? Clearly it helps if he knows the likely orientation of the field lines. The G-HED (and CM) model provides this (and we can test the hypothesis); the BL model does not - or at least, I have never heard a proponent of the BL concept ever describe the orientation of the magnetic field lines from this mysterious "big loop" in the ground - nor even where this big loop is actually situated!

I think it is possible to provide a good explanation for the lay person without either a) getting caught up in the question of the "material" nature of the earth currents or b) creating a fallacious (as I assert) "big loop" in the ground. It is something we ought to try to work towards. In fact... Im pretty sure I already gave a lay explanation "in passing", in a CREG article many years ago. Perhaps I just didnt emphasise it enough at the time?

Anyway... I hope this reply helps.

Thanks for your interesting response, David. Please don’t think I’m trying to flog a dead horse in returning to the BL theory, that’s not my intention because, at this point, I really haven’t come to any conclusion regarding the comparative merits of the BL and G-HED theories. However, the following comment caused me to think about the BL theory in a bit more depth.

Suppose we have a caver attempting to detect an earth current signal using a small portable induction loop or ferrite rod receiver? Clearly it helps if he knows the likely orientation of the field lines. The G-HED (and CM) model provides this (and we can test the hypothesis); the BL model does not - or at least, I have never heard a proponent of the BL concept ever describe the orientation of the magnetic field lines from this mysterious "big loop" in the ground - nor even where this big loop is actually situated!

My initial thought is that here was a means of carrying out some measurements that would go some way to differentiating between the BL and the G-HED theories.

If we consider the G-HED theory, the current in the wire would give rise to a magnetic field that forms concentric circles around the wire. As a result, in order to provide maximum coupling, a loop antenna would have to be oriented with the plane of the loop parallel to the wire. So, for example, in the case of a wire antenna on the surface, a loop antenna in a cave directly underneath would need to be oriented vertically with the plane of the antenna parallel to the surface wire, while a loop on the surface, broadside to the wire, would need to be oriented horizontally.

If we now turn our attention to the BL theory, I’d always envisaged the supposed large loop in the ground as a vertical loop (or, more accurately, an infinite number of vertical loops of different diameters) with their plane parallel to the wire antenna. This would, indeed, give rise to magnetic fields that have different orientations from those predicted by the G-HED theory. However, while these current paths would surely exist, so would current paths with different orientations. We can also envisage a horizontal loop (or multiple loops) skimming the surface, and an infinite number of other sets of loops at orientations intermediate between the vertical and the horizontal. Now, if we assume that all these loops of differing sizes and orientations exist, the orientations of the loops required for maximum coupling of the magnetic field would be the same as predicted for the G-GED model.

I guess this really isn’t too surprising in view of your comment...

I made the point in the article that there is more than one way of looking at things and that different explanations, if they all have validity, will converge on the same reality. To that extent, I am willing to accept that a BL-type concept might have some validity but only provided its proponents can demonstrate that it converges on reality. So its over to you, really, Mike: what testable predictions on field strength and field orientation does your BL model make? And - importantly - are they the same predictions that the G-HED model makes? (If they arent - we have a problem).

Mike Bedford wrote:If we consider the G-HED theory, the current in the wire would give rise to a magnetic field that forms concentric circles around the wire. As a result, in order to provide maximum coupling, a loop antenna would have to be oriented with the plane of the loop parallel to the wire.

Not "parallel", as such, but passing through the wire.

So, for example, in the case of a wire antenna on the surface, a loop antenna in a cave directly underneath would need to be oriented vertically with the plane of the antenna parallel to the surface wire, while a loop on the surface, broadside to the wire, would need to be oriented horizontally.

Yes. Although with the caveat that you would have to be operating at a sufficiently low frequency for there to be no secondary field effects. But that is true whatever type of antenna arrangement you are trying to examine - i.e. even loop antenna transmitters will give peculiar results if youre not careful.

If we now turn our attention to the BL theory, I’d always envisaged the supposed large loop in the ground as a vertical loop (or, more accurately, an infinite number of vertical loops of different diameters) with their plane parallel to the wire antenna. This would, indeed, give rise to magnetic fields that have different orientations from those predicted by the G-HED theory. However, while these current paths would surely exist, so would current paths with different orientations. We can also envisage a horizontal loop (or multiple loops) skimming the surface, and an infinite number of other sets of loops at orientations intermediate between the vertical and the horizontal.

OK so far

Now, if we assume that all these loops of differing sizes and orientations exist, the orientations of the loops required for maximum coupling of the magnetic field would be the same as predicted for the G-GED model.

You havent explained (to our readers) how you arrived at the "would be" but, in fact, you are right and, from a consideration of of symmetry, one can see that the resultant magnetic field must be horizontal and at right angles to the antenna. If you like, the vertical field component of all the loops on one side cancels the vertical field from all the loops on the other side - that was how Chris Trayner used to explain it. However, it gets a bit more difficult when the field point is elsewhere in space and, of course, the crucial point is that this description of the situation does not tell us the field strength - only its orientation. That is really why I say the the BL concept is not really a 'model' - you cannot put any numbers in.

I guess this really isn’t too surprising in view of your comment...

I made the point in the article that there is more than one way of looking at things and that different explanations, if they all have validity, will converge on the same reality. To that extent, I am willing to accept that a BL-type concept might have some validity but only provided its proponents can demonstrate that it converges on reality. So its over to you, really, Mike: what testable predictions on field strength and field orientation does your BL model make? And - importantly - are they the same predictions that the G-HED model makes? (If they arent - we have a problem).

Yes. The salient point is that if one were to try to put the BL model on a sound footing by, for example, actually working out the magnetic field strength, one would have the utterly impossible task of trying to sum together the effects of an infinite number of loops. The situation is not dissimilar to that in "ordinary" radio. How do you work out the magnetic field strength at some point in space, due to a conventional electric dipole transmitter? You either treat it as a dipole and do some straightforward maths, or you look at the infinite number of current loops (ok, its displacement current, not conduction current, but that doesnt really make a difference) and sum together the effect of each... which one assumes would give the same answer, but would be impossible to do. (Well, not impossible - you could iterate it on a computer - but it would be "pointless" when there is a much simpler answer).