Lab 7 EOSC 350

Lab 7: GPR Part II

TA: Seogi Kange-mail: sgkang09@gmail.comoffice: ESB 4021

DUE: November 3 & November 6, 2014

Overview

Due to high relative permittivity of water compared to earth materials, GPR can bea useful geophysical method to characterize hydrological systems. In addition, somehydrological units can have high conductivity values, which makes significant attenua-tion of EM wave in the earth. This lab will lead you to recognize practical usage ofGPR to characterize hydrological systems, and identify conductivity effects in EM wavepropagation.

Instructions

• There are 9 questions labeled Q, some with multiple parts. Provide solutions forall of them.

Running the iPython Notebook

For this lab, you do not have to write any code, you will only be running it.

• Shift + Enter runs the code within the cell (so does the forward arrow button nearthe top of the document)

• You can alter variables and re-run cells by changing the values and doing Shift +Enter

• If you want to start with a clean slate, restart the Kernel either by going to thetop, clicking on Kernel: Restart, or by esc + 00

Resources

• GPG Geophysical Surveys: GPR

• Zip File containing the notebook

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Lab 7 EOSC 350

• GPR Article: “Georadar for hydrogeology” (Overmeeren, 1994)

Refer to Lab 5 for more details on how to use the notebook. To install it on yourpersonal computer, refer to the instructions in the Appendix of the lab.

Effect of electrical conductivity in GPR

To simplify the GPR problem, we previously assumed that there was no conductivity effect.However, in practice, this is not true. Some earth materials can have quite high conductivityvalues. In this case, assuming that we do not have a conductivity effect does not makesense. In addition, this conductivity effect can be advantageous in certain circumstances.For example, we can differentiate fresh and saline water boundaries, which is useful to mapsea water intrusion, because saline water is much more conductive than fresh water. In thissection, we investigate the effect of conductivity in GPR.

EM wave velocity

Q1. Background checks for EM wave velocity:

a. What is the EM wave velocity as a function of relative permittivity (εr) andvelocity of light (c).

b. What are we assuming in the above equation?

c. There are two other physical properties which impact the EM wave velocity.What are they?

Q2. Next we use the SigmaEffectWidget to explore EM wave velocity.

a. Run this widget, then see the left plot, which shows the velocity of the EMwave. Here the x and y axes are frequency (Hz) and velocity (m/s), respectively.Observe how the EM wave velocity changes as a function of frequency, and providea description of the frequency effect. Record the frequency range where EM wavevelocity is independent of frequency.

b. Fix conductivity (sigma in the widget) to 10−4, then change relative permittivity(epsr in the widget) from 1 − 80. Record your observations.

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Lab 7 EOSC 350

c. Fix relative permittivity (epsr in the widget) to 1, then change conductivity(sigma in the widget) from 10−8-100 S/m. Write down your observations.

Attenuation of EM waves

Q3. Background checks for EM wave attenuation:

a. What affects the attenuation of EM waves? Provide two factors.

b. What is the definition of skin depth?

c. Based on the definition of skin depth, let us assume that we have three GPRinstruments, which use 25, 50 and 100 MHz frequencies. Which one provides you thelargest depth of investigation?

Q4. Now we will use SigmaEffectWidget to explore EM wave attenuation

a. Run this widget, then see the right plot, which shows the skin depth of an EMwave. Here the x and y axes are frequency (Hz) and skin depth (m), respectively.Observe how skin depth changes as a function of frequency, provide a description ofthis relationship. Record the frequency range where skin depth is independent offrequency.

b. Fix conductivity (sigma in the widget) as 10−4, then change relative permittivity(epsr in the widget) from 1 − 80. Write down your observations.

c. Fix relative permittivity (epsr in the widget) as 1, then change conductivity(sigma in the widget) from 10−8-100 S/m. Write down your observations.

Hydrological application of GPR

Due to high relative permittivity of water compared to earth materials, GPR can be a usefulgeophysical method to characterize hydrological systems. For this section, you first need toread an article: “Georadar for hydrogeology” (Overmeeren, 1994). With following questionswe will lead you to identify how GPR can be used to characterize hydrological systems inthe subsurface.

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Lab 7 EOSC 350

Resolution of GPR

Q5. Consider the GPR sections at different frequencies shown in Figure 1

Figure 1: Georadar sections illustrating the influence of radar frequency on exploration depthand resolution (Overmeeren, 1994).

a. The vertical axis is labeled in depth and time. What is the velocity used to makethis conversion? What is the average value of ε for the upper region?

b. The obvious difference between the images is the resolution. Using the velocitythey used above, compute wave lengths for the following frequencies: 25, 50, 100,and 200 MHz. Then compute vertical resolution for each frequency.

c. In a single figure, sketch an ideal GPR signal as a time series that corresponds tothe frequencies of 25, 50, 100, and 200 MHz with appropriate time scales. Here, usethe same velocity that you used above question.

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Lab 7 EOSC 350

d. Although the features in the images are small, attempt to use the reflectionfrom the water table to quantify how the time width of the wavelet changes withfrequency. Give the wavelet width you have measured on the images. Is this inaccordance with your result in above question?

Conductivity effects in EM wave

Q6. In the section: “Hydrogeology and physical properties-Attenuation and resolutionof radar waves”, the author said: “In practice, georadar is unfit for use in areas wherethe soil resistivity is less than 100 Ω-m; this is the case in clayey and silty formations andin brackish and saline ground water environments”. In addition, they provide a table,which shows EM wave velocity and attenuation in various materials, as shown in Figure2. Answer following questions:

Figure 2: Characteristic values of physical properties of media important for georadar(CITE).

a. Use the SigmaEffectWidget; set your relative permittivity to 4, which is similarto dry sand, then record the skin depth of a medium with a conductivity of 10−2

S/m at 100 MHz. Record the EM wave velocity as well.

b. Now we decrease the conductivity value to 10−3 S/m. Leave the other parametersfixed. Record the skin depth and EM wave velocity, and compare them with theprevious case where the conductivity value was 10−2 S/m.

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Lab 7 EOSC 350

c. In Figure 2, the author states that the EM wave velocities of fresh and saline waterare the same (3.4 cm/ns). Evaluate this statement using the SigmaEffectWidget.Use 10−2 and 100.5 S/m for the conductivity values of fresh and saline waters,respectively, and 100 MHz frequency.

Q7. In Figure 1, we can observe a different depth of investigation for each frequency.Explain this phenomenon based on the skin depth.

Evaluation of Case study

Q8. Consider the GPR sections at different frequencies shown in Figure 3

Figure 3: Georadar sections illustrating the influence of radar frequency on exploration depthand resolution (Overmeeren, 1994).

a. What reason is given for the lack of radar signal beneath the water table?

b. Why is a step seen as a flat reflector plus a half of a hyperbola?

c. What is the vertical resolution expected from a 25 MHz system? (Use v = 14.5cm/ns). The authors estimate the size of the step in the water table to be about 2meters. Based on your vertical resolution calculation, do you expect to be able toresolve a step of this size?

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Lab 7 EOSC 350

Q9. Consider the GPR sections at the different frequencies shown in Figure 4.

Figure 4

a. What reason is given for the lack of radar signal beneath the water table?

b. What is the velocity and associated ε used to convert time to depth?

c. How large, in time and depth, is the step in Profile 3 near station 285? Whatis the vertical resolution for the 100 MHz system? Should we be able to resolve thestep with this system?

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Lab 7 EOSC 350

d. Consider the statement:

“To exclude the possibility that the observed offset is caused by a suddenchange in wave propagation velocity rather than by a groundwater step, CMPmeasurements were performed on both sides of the feature.”

Suppose there was no physical step in profile 3 but rather that the water ta-ble was flat-lying. What is the distribution of the dielectric constant that could giverise to the same step structure?

Appendix

How to get the iPython Notebook

If you want to run ipython notebook in your home, first you need to download whateverpython package mananger, for instance Canopy or Ananconda. We provide you the instruc-tions for Canopy.

1.) Download Canopy. The basic version is free.

2.) Open up the download and install. Follow the instructions. It will install the requiredpackages and set the necessary paths on your computer.

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