A Ground Penetrating Radar formula

AI Thread Summary
The discussion centers on the physics of ground penetrating radar (GPR) and the importance of the dielectric constant (K) in determining reflected energy. Participants seek a derivation of the formula related to energy reflection and an intuitive explanation of K's significance, particularly regarding the motion of free electrons. It is noted that the reflection coefficient is expressed in terms of fields rather than power, and that changes in permittivity and conductance when entering different media affect the electric field strength. The role of water's high permittivity due to its molecular structure is also highlighted. Understanding these principles is crucial for interpreting GPR data effectively.
PeterPeter
Messages
23
Reaction score
0
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.
Thanks in advance
Jerry

Source of jpg:

Interpreting GPR Data: The Basics Part 1 by Greg Johnston
Ground Penetrating Radar formula for reflection.jpg
 
Physics news on Phys.org
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?
 
Thread 'Question about pressure of a liquid'
I am looking at pressure in liquids and I am testing my idea. The vertical tube is 100m, the contraption is filled with water. The vertical tube is very thin(maybe 1mm^2 cross section). The area of the base is ~100m^2. Will he top half be launched in the air if suddenly it cracked?- assuming its light enough. I want to test my idea that if I had a thin long ruber tube that I lifted up, then the pressure at "red lines" will be high and that the $force = pressure * area$ would be massive...
I feel it should be solvable we just need to find a perfect pattern, and there will be a general pattern since the forces acting are based on a single function, so..... you can't actually say it is unsolvable right? Cause imaging 3 bodies actually existed somwhere in this universe then nature isn't gonna wait till we predict it! And yea I have checked in many places that tiny changes cause large changes so it becomes chaos........ but still I just can't accept that it is impossible to solve...
Back
Top