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• PeterPeter
In summary, the reflection coefficient, K, is a measure of how much power is reflected from a wave travelling through a medium. The dialectic constant is important in determining the energy reflected.
PeterPeter
TL;DR Summary
Derivation of reflection coefficient?
I am interested in the physics of ground penetrating radar.
1) Does anyone know where I can find a derivation of the formula in the attached jpg for the energy reflected? K=the dialectic constant.
2) An intuitive explanation of why the dialectic constant is important in determining the energy reflected. Obviously it must have something to do with the motion of the free elections.
Jerry

Source of jpg:

Interpreting GPR Data: The Basics Part 1 by Greg Johnston

In this formula, notice that the SQRT sign could be placed ahead of the whole expression. Then we can see that K1-K2 is the portion of incident power reflected and K1+K2 is the total incident power, so the formula is trivial and not very enlightening. Reflection Coefficient is specified in terms of the fields (or voltages) rather than the power, so we take a square root.
When a wave is traveling in free space, the electric and magnetic fields have a fixed ratio of 377. When the wave enters another medium, such as moist soil, the main things that happen are that the permittivity and conductance increase. Permittivity is associated with capacitance. This causes the electric field to be weaker than in free space, and the ratio of electric to magnetic fields is altered. This is equivalent to the case of a transmission line where there is a change in characteristic impedance. The wave entering the ground cannot suddenly adjust to the new impedance, and part of it is reflected back.
Water has a very high permittivity which is caused by the asymmetrical shape of the molecule, making it polar.

tech99 said:
In this formula, notice that the SQRT sign could be placed ahead of the whole expression. Then we can see that K1-K2 is the portion of incident power reflected and K1+K2 is the total incident power, so the formula is trivial and not very enlightening. Reflection Coefficient is specified in terms of the fields (or voltages) rather than the power, so we take a square root...

Are you saying that the energy is proportional to the SQRT of the dialectic constant, K?

## 1. What is the formula for calculating depth using Ground Penetrating Radar?

The formula for calculating depth using Ground Penetrating Radar is: Depth = (velocity of electromagnetic waves * time delay) / 2. This formula takes into account the speed of the electromagnetic waves in the ground and the time it takes for the waves to travel to and from the target.

## 2. How accurate is the Ground Penetrating Radar formula?

The accuracy of the Ground Penetrating Radar formula depends on various factors such as the type of soil, the depth of the target, and the equipment used. Generally, the formula can provide accurate depth measurements within a range of 10-20% of the actual depth.

## 3. Can the Ground Penetrating Radar formula be used for any type of material?

The Ground Penetrating Radar formula is most effective for materials with relatively low electrical conductivity, such as soil, concrete, and rock. It may not be as effective for highly conductive materials like metals or highly resistive materials like clay.

## 4. How does the Ground Penetrating Radar formula differ from other geophysical methods?

The Ground Penetrating Radar formula uses electromagnetic waves to detect and measure subsurface features, while other geophysical methods such as seismic surveys use sound waves or electrical resistivity surveys use electrical currents. Each method has its own advantages and limitations, and the choice of method depends on the specific needs of the project.

## 5. Are there any limitations to using the Ground Penetrating Radar formula?

Yes, there are some limitations to using the Ground Penetrating Radar formula. It may not be as effective in areas with high levels of interference or in areas with highly variable soil conditions. Additionally, the accuracy of the formula may decrease with increasing depth, and it may not be able to detect small or shallow targets.

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