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Article 2. GPR and plane layers.

Let's consider plane-layered underground structures with endless bounds.

We take three parameters for each layer:
- relative dielectric constant or permittivity (epsilon);
- electric conductivity (sigma);
- the physical thickness in meters.

We create various sets of layers and define different center frequencies of antennas.
In result we gain some understanding how reflected signal of the ground penetrating radar looks for various combinations of layers.

For this investigation we use the program created by Geoscanners AB.
The first layer is always air. The thickness of the last layer is taken to be infinite.

We define three layers:
1. concrete (epsilon = 6; sigma = 0.01; thickness = 0.3 meters)
2. limestone (epsilon = 7; sigma = 0.01; thickness = 0.5 meters)
3. dry sand (epsilon = 3.3; sigma = 0.0001; thickness = infinite)

We set the operating frequency of the antenna to 750 megahertz.
The simulation gives image with three reflections.
Layers 1
The first reflection in the plot is the interface air - concrete.
The second reflection is the interface concrete - limestone.
The third reflection is the interface limestone - dry sand.

The second reflection has the same sign of amplitude as the first one because the GPR signal goes to the higher value of permittivity ( 6 -> 7 ).
The third reflection changes the sign of amplitude because the GPR signal goes to the lower value of permittivity ( 7 -> 3.3 ).
Amplitude of the third reflection is bigger due to the bigger differences of the permittivities.

If we change epsilon of the second layer from 7 to 3 we have the following plot:
Layers 2
The second reflection changes sign of amplitude (now signal goes to the lower permittivity) and the value (due to the bigger differences of the permittivities).
The third reflection changes sign of amplitude (now signal goes to the higher permittivity) and the value (due to the smaller differences of the permittivities).

Now we go to the first example and set the operating frequency of the antenna to 250 megahertz.
Layers 3
We see wide reflections, it can two close reflections look like single one.

Let's simulate plane layers with GprMax 2D.
We created the same three layers but in two dimensions world.
plane layers
We move transmitter an receiver in the opposite directions starting from some initial distance. It is so called "common depth point" method.
common depth point method
We get the following result:
radargram: common depth point
We see three lines. The top line has complicated structure because it contains combination of reflection from the interface air - concrete and direct wave between transmitter and receiver.
The second and the third lines are reflections between bounds of other media.

The program GprProfile contains tools to calculate depths and permittivities of plane layers if GPR radargram was created by the method "common depth point".
Often in new place of a survey you do not know exact properties of underground soils. You need to have calibration parameters to transform time scaled depths into meter depths. The method "common depth point" helps in solving of this problem.

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