THEORY & CONCEPTS

GEOSCANNERS  AB

GPR Antenna Resolution

By Reinaldo Alvarez Cabrera

 

How many antennas should I have?

We have all heard that question, especially coming from the newcomers to the Ground

Penetrating Radar (GPR) technology. The people starting to master this technology are

amazed that one has to have so many different antennas for what appears to be the

same thing, scrutinizing the earth.

What antenna(s) should I choose?

To get a suitable data set is of the paramount importance, so selecting the proper radar

antenna in each case is a must.

There are countless tables scattered all over the

literature and the Internet, putting out controversial information and leaving the unwary

in total confusion and with a feeling of despair

.

To make things worse, manufacturers are

not very kind on giving out emission parameters, radiation lobes, transmission loses or

any other important data for the antennas they sell. In this paper I'll try to approach one

of the many important factors contributing to a successful ground penetrating radar

survey, the resolution of the antenna.

A little bit of theory first

What's all this resolution stuff after all? -

Bob Pease would say if he dealt with

the GPR and I would only say, Amen! In ground penetrating radar there are two types of

resolutions: the vertical, which is the one looking straight down into the earth and the

horizontal, which is the one parallel to the surface plane of the survey line. In other

words, we should be able to calculate, or at least to estimate, the minimum distance

the objects we are trying to survey should be apart, vertically and horizontally. So let's

get acquainted with each of these terms separately and see if we can make some sense

out of it.

The

vertical resolution

is nothing else than the smallest difference in time

between two objects the ground penetrating radar can resolve before starting to “see”

both as one. A little bit cryptic, right? Well, no, not really. The ground penetrating radar

measures time only, the translation into depth comes later from the knowledge of the

dielectric constant of the media. But if we consider, for the clarity sake, that the radar

measures distance, then we can say that vertical resolution is the smallest distance in

the direction perpendicular to the surface that two targets can be apart for us to see

them and distinguish them as separate objects. See Figure 1. to get a better idea, it is

marked with “Vr” for vertical resolution.

The

horizontal resolution

is a bit more clear because distance is measured in the

length units and not in the time units. So, the horizontal resolution is the minimum

distance between two objects in the same horizontal plane parallel to the surface that

the radar “sees” both object as separate ones. To put it simply, it is the minimum

horizontal distance between two targets at the same depth before the radar smears

them out into one single event. See Figure 1. to understand a little bit better the

 

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GEOSCANNERS AB

concept, it is marked with “Hr” for horizontal resolution.

Fig. 1 Vertical and Horizontal resolution diagram, the golden dots are the targets.

How do we calculate them

Now that we know what the vertical and horizontal resolution are, we should be

able to get them out from the antenna datasheet the manufacturer supplies, right?

Sorry, but no. The antenna manufacturers will be more than happy to give you a lots of

commercials, brochures, and almost “out of the geophysics text books” data samples,

but nothing else. There is one thing though that we can get from almost every antenna

manufacturer on the market, the center frequency of the antenna. Be aware though

that different manufacturers specify this parameter differently. A much better approach

would be to ask, what is the transmitted pulse width? That would allow you to make

your own conclusions on the center frequency in the way you are familiar with.

The reciprocity theorem states that a receiving antenna is as good at receiving as it is at

transmitting if all physical and fabrication parameters are kept identical. So, anything

that gets transmitted can theoretically get received back by a similar device. Taking into

account that the earth works like a low pass filter, then we can surely state that what

was not transmitted has absolutely no chance of being received if it has higher

frequency than the existing ones in the frequency spectrum of the original signal. The

only exception of that rule is if you are using an unshielded antenna and the source of

the signal is an external transmitter. This concept is important because I have personally

read about antennas marvelously receiving microwaves frequencies with pulse width of 3

to 4 ns. How that happened was unfortunately never explained to me, but I'll publish it

out as soon as I know all the facts.

Copyright 2007-2011 © Geoscanners AB AN002112109ENrev2.0

GEOSCANNERS AB

Why is the transmitted pulse or the center frequency so important? It is because the

vertical resolution is nothing else than half of the duration of the transmitted pulse in

time. If we translate that into depth information then we can say that the vertical

resolution is half the width of the transmitted pulse times the velocity in the media:

Vr = Tpulse⋅c2⋅

(1)

where: Vr is the vertical resolution Tpulse is the transmitted pulse duration, this can be calculated by taking the

inversion of the fundamental or center frequency.

c is the speed of light in vacuum

RDP

is the relative dielectric permittivity of the media.

Please keep in mind that this is an approximate formula that works most of the time,

but not always. The reason for that is that the transmitted pulse will suffer from low

pass filtering in the media it is traveling through. Spreading losses of the signal also

affect the above explained formula. This means that objects that are far away from the

surface will most likely have a different vertical resolution than those closer to the

source of the sounding pulse.

Another important factor to consider when trying to estimate the vertical resolution is

the type of materials of the two close targets. Materials that produce strong reflections

are more likely to mask the objects that are close to them, while materials that produce

weak reflections will be easier to detect due to a more local signature. This last

conclusion is, of course, true only if the weak reflections are strong enough to be

detected reliably otherwise you might loose them entirely.

The bottom line about vertical resolution is that promising too high a resolution is not a

good practice. A more conservative approach of taking twice as much as the calculated

value will put the survey in a better perspective. The level of expertise of the person

interpreting the survey data will also, without any doubt, play an important roll in this

matter. GPR surveys, more often that not, don't fail. They just don't live up to the

promises made and the expectations from the customer ordering them. Using all the

knowledge the theory provides us and exercising common sense is a key to success.

Now, the second type of resolution, the horizontal resolution. This is a topic of

much debate and many people have their own opinion on what should be the right way

of calculating the horizontal resolution. Basically, one could summarize that the

horizontal resolution depends on the following parameters:

1.

The amount of traces per unit of distance. If you have 10 traces per meter there

is no chance of discriminating objects that are 50 mm apart from one another.

Actually I'd be very surprise if you can actually discriminate objects that are

100mm apart from one another.

2.

The beam width of your antenna. This parameter is almost never specified in the

antennas datasheet and many people use approximations for the real value. It is

Copyright 2007-2011 © Geoscanners AB AN002112109ENrev2.0