Voids cause polarity inversions in GPR data….

The first time I read this sentence in a peer reviewed paper I thought that it was a useful tip to aid the interpretation and easy to apply practically. I didn’t think much at the time.

I then read similar sentences on other papers, on commercial websites, PhD thesis etc sometimes even less precise definitions (voids start with black reflections), but after a lot of surveys where cavities showed different responses despite similar conditions, I went deeper and looked for the cause of a polarity inversion. That sits in the reflection coefficient definition. A simplified definition is the following:

where ε1 is the dielectric of the material where the wave travels from (top material) and ε2 is the dielectric of the material the wave is travelling to (bottom material).

The reflection coefficient is a simple function of the dielectric contrast and it is negative (polarity inversion) when the numerator is negative, so when the wave travels from lower dielectric material to higher dielectric material. Air dielectric is 1 so always less than everything else. A polarity inversion can therefore occur when the wave travel from air to something and not from something to air. This is opposite to what I mentioned above and read many times.

But where does this statement come from then?

I gave myself a few answers:

• The first one is that statement is a simple mention in papers that focused on other topics, likely copied nad pasted from somewhere else.
• The second one is that the formula has been reported in the wrong way with the numerator inverted as below because 2-1 is more intuitive than 1-2

• The third one is lack of careful looks at what the radargrams show and generalisation of specific occurrence in that context (i.e. voids start with black) to any context.
• The fourth one requires more considerations that can be explained with simple radargrams.

If we have a material with dielectric of 8 over a multi-dielectric material, we see what we expect from the formula (the right one): inversions occur when the wave travels from lower to higher dielectric (right-hand side on the radargram). What if we make the situation more realistic? It is much more difficult to visualise and assess the polarity and at first sight it looks that the inversion occurs on the left-hand side of the radargram where it shouldn’t as we have a prominent white band (instead of black one).

Looking at the A-Scans indicated by the dashed red and blue lines, we see that what happened is that all the three bands of the wavelets are still there, but the first has been attenuated so much that its amplitude is very close to zero and it now looks that the second one is the first.

Looking now at a real radargram collected on the side of a concrete beam, we see three layers of reinforcement (there is a fourth one, but it is in the shadow zone of the others) and the beam backface.

Reinforcing bar cause polarity inversions: the dielectric of metal is generally assumed to be infinite, so very large compared to everything else, although it actually has a strong dependence on the frequency and could be even negative as far as I know. For sure the dielectric of something conductive is an oxymoron.

The backface of the beam, which is an interface high to low dielectric, shouldn’t produce a polarity inversion, but it looks it does as the prominent first reflection looks negative (black).

The A-scan reveals that the first band is still there, just very attenuated, and the second one is more prominent: from there the statement that voids start with negative (or worse with black; the color scale means nothing if we don't specify what is negative and what is positive).

Each GPR antenna can be different: one can have a wavelet made of two bands, one of three, one of four, one can start with a negative pulse, one with positive, one may not record a direct wave because of the antenna structure….. Personally I think that interpretation of signal polarity (at least from visual inspection) is not so reliable unless you have crystal clear data. I saw this crystal-clear data from time to time but not as a rule. To note that the wavelength of the signal and the shape of the target can make the polarity a much more complex matter where the rule dictated by the formula above wouldn’t work so easily.

I’ve been asked the question “so if polarity is not so reliable for voids surveys what should we do?” Man, you should do what you always do when you applied a geophysical method: contextualise it.