Lab 6 EOSC 350. There are 15 questions labeled Q, some with multiple parts. Provide solutions for all of them.

Transcription

1 Lab 6: GPR Part I TA: Seogi Kang sgkang09@gmail.com office: ESB 4021 DUE: October 27 & October 29, 2014 Overview Ground Penetrating Radar (GPR) uses electromagnetic energy to excite a response in the earth. Using a source antenna, an EM signal can be emitted. This signal propagates as a wave through the earth, and the radar signals can be measured using a receiver antenna (similar to how you receive signal to your cell phone). As in seismology, reflection and refraction events can occur when there are physical property contrasts in the subsurface. For GPR, the primary diagnostic physical property is dielectric permittivity. GPR data are generally collected with a single source antenna and receiver antenna. We move along a line with fixed separation between source and receiver antenna so that we can obtain a line profile data, which is analogous to vertical section of the earth. In this lab, you will be working with GPR data collected near UBC. To do so, you will begin by examining how these EM waves propagate through the earth. You will then explore GPR responses for several geologic models. Finally, you will interpret field GPR data obtained near University of British Columbia. Instructions There are 15 questions labeled Q, some with multiple parts. Provide solutions for all 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 near the 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 the top, clicking on Kernel: Restart, or by esc

2 Resources GPG Geophysical Surveys: GPR GPR Movie Zip File containing the notebook Refer to Lab 5 for more details on how to use the notebook. To install it on your personal computer, refer to the instructions in the Appendix of the lab. Identification of EM waves Ray approach We will start by considering the model shown in Figure 1. The source and receiver antennas are oriented in y-direction. Separation between them is x. The earth model is composed of three layers: air, layer 1, and layer 2, with relative permittivities ɛ r,air, ɛ r,1 and ɛ r,2. Figure 1: Conceptual diagram of GPR source antenna and receivers. 2

3 Q1. For this model, consider the case where ɛ r,air = 1, ɛ r,1 = 2 and ɛ r,2 = 5, and that for the air and both layers, µ = µ 0 and the electrical conductivity is small (σ 0). For such a model, there are a suite of waves we expect to see in the data. For the survey we will consider a. There will be two direct waves. Where do each of these waves propagate? On Figure 1 or on your own diagram, sketch these two rays. b. Which of the two direct rays will arrive first? Justify your answer by considering physical properties. c. If the transmitter and receiver are separated by a distance x, when will each of the direct rays arrive? d. Assuming ɛ r,air = 1, ɛ r,1 = 2 and ɛ r,2 = 5, add the arrivals for these direct rays to the t-x plot in Figure 2 (or to your own T-X plot on a seperate piece of paper). Here separation between the source and receiver (x) is variable. 3

4 Figure 2: T-X plot e. Energy also propagates downward into the earth. When the GPR signal reaches the interface between layers 1 and 2, some of the energy is reflected and some is refracted. Add a reflected ray path to your diagram. When will this signal arrive at a receiver that is a distance x from the transmitter? f. Using the model, ɛ r,air = 1, ɛ r,1 = 2 and ɛ r,2 = 5, add the reflected arrivals to the diagram in Figure 2 g. For the geologic model we are considering, will a critically refracted wave, which travels along the interface between layer 1 and 2 be generated? Explain. 4

5 h. There is a critically refracted ray that will be measured by receivers at the surface. Sketch this ray on your diagram in Figure 1. What is the critical angle for this ray? What is the velocity with which this ray travels? Is there another possible ray path that could give rise to the same arrival time? i. At what offset x c will this ray first be detected by receivers at the surface? j. Add this critically refracted arrival to your t-x plot (Figure 2). Wave approach Although the ray approach provides us with some insight, when a GPR signal travels through the earth, it travels not as a ray, but as a wave. Figure 3: Conceptual diagram of wavefront and ray. In this section, we recall the case study: Glacier girl. As shown in the left panel of Figure 4, we have a three layered-earth structure composed of air, snow, and ice layer. Based on that we consider a similar model shown in the right panel of Figure 4. However, the thickness of the first layer (h), and relative permittivity of the first and second layers (ɛ r,1 and ɛ r,2, respectively) are unknown. The survey is a common shot gather that consists of 100 receiver antennas deployed along a 40 m line. The following questions will lead you to estimate those unknown parameters by interpreting measured responses. 5

6 Lab 6 EOSC 350 Figure 4: Conceptual diagram of GPR source antenna and receivers. Q2. Watch the GPR Movie and look for the waves that correspond to the ray-paths you drew in 1. In the GPR movie, Tx indicates the source location, and Rx with red dots indicate receiver locations. a. Take a screen grab (or several) and label the wavefronts you recognize that correspond to the ray-paths you drew in question 1. b. Do you only observe those four waves? Put two observations about other events visible as the wave-field propagates through the earth. It may be helpful to include screen grabs. Q3. Using the GPR widget (contained in the Zip File ), we will estimate the unknown earth parameters: r,1, r,2, h from the given data (which corresponds to the movie). For each of the following questions, record the value(s) you find and save the image showing how you found it. Before executing any of the codes be sure you have run Step 0: Import necessary packages. a. Identify the direct air wave in the data and fit t with a straight line (blue) by adjusting epsrl and tinterpl. Record these values and include an image showing your fit. 6

7 b. Identify the direct ground wave and fit it with a straight line (blue) by adjusting epsrl on the bar and tinterpl. Record these values and include an image. c. Identify the reflected wave from the interface between the first and second layer and fit it with a hyperbola (red) by adjusting tinterph and epsrh. Since the reflected wave travels through the first layer, you may use the relative permittivity you found for the direct ground wave for epsrh. Record the estimated tinterph value and include an image. d. What is the EM wave velocity of the first layer? e. What is the thickness of the first layer, h? f. Estimate the relative permittivity of the second layer, ɛ r,2 using given tools and information. Sketch ray paths on a profile line Rays are defined as the normal to the wavefronts as shown in Figure 3. In this section, we sketch ray paths for the provided GPR survey configuration and models. To make the problem simpler, we consider a zero-offset profile line. We mark a source and receiver antenna pair as solid dots in Figure 5. Q4. First, we consider a pipe model. a. Sketch the reflected ray paths for the pipe model given below. 7

8 Figure 5: Ray paths for the pipe model for a zero-offset transmitter and receiver b. Based on ray paths you drew, sketch the arrival time of those rays at receiver locations. Figure 6: Arrival times for the pipe model Q5. Next, we consider a thick slab model, where the slab extends to depth. 8

9 a. Sketch the reflected ray paths for the slab model given below. Figure 7: Ray paths for the slab model. b. If the slab was very thin, would the ray paths change? c. Based on ray paths you drew, sketch the arrival time of those rays at receiver locations. 9

10 Figure 8: Arrival times for the slab model Q6. The last model we will consider is an anticline. a. Sketch the reflected ray paths for an anticline model given below. Figure 9: Ray paths for the anticline model 10

11 b. Based on zero-offset ray paths you drew, sketch the arrival time of those rays at the receiver locations. Figure 10: Arrival times for the anticline model Interpretation of Field data In this section, we will interpret two field GPR data sets obtained at University of British Columbia. Applications in the GPRWidget will help you answer following questions. Q7. The data shown in Figure 11 were collected using the common midpoint survey method. In the following questions, use Step 4a of the GPR widget. 11

12 Figure 11: Common Midpoint data collected by UBC. a. Pick out the air wave and estimate its velocity. Include an image of your result to justify your answer. b. Identify the direct ground wave and estimate its velocity. Include an image of your result to justify your answer. Q8. We consider the line profile data shown in Figure 12. Let us assume that we know that there are three different types of objects are embedded: 12

13 Layer Buried pipes Concrete utilities casing Figure 12: Common offset profile collected by UBC a. On Figure 12, draw a line where you observe a layer boundary. Estimate the depth of this layer using the velocity of the ground that you estimated from Q7b b. On Figure 12, identify responses due to the pipes (there are two), and fit those responses with GPRWidget by adjusting provided parameters. Record the best parameters for both pipes. There are four parameters that you need to estimate: epsr (relative permittivity), h (distance of the pipe center from the surface), xc (the pipe center location), r (radius of the pipe). 13

14 c. Choose one of the hyperbolic response you attributed to a pipe (because you can find couple of them). Fix the radius of the pipe as 0.5 m and 1.5 m, respectively. Then find fit the hyperbolic responses so that you can find two different sets of parameters for r = 0.5 and 1.5 m, respectively. If you were in charge of interpreting these data, how would you characterize the pipe? d. Compute the velocity of GPR signal using the estimated relative permittivity. Compare this velocity with one that you computed at Q7b (based on the CMP gather shown in Figure 11. The CMP gather data were acquired near the location of the profile line data). How do the velocities compare? Can you suggest any reason for the discrepancy or could you reconsider any of your analysis to find relative permittivity for the top layer that was satisfactory for both data sets. e. Identify responses due to a concrete casing (similar to a slab), and fit those with GPRWidget adjusting provided parameters. Record parameters that you find. Appendix How to get the ipython Notebook If you want to run ipython notebook in your home, first you need to download whatever python package mananger, for instance Canopy or Ananconda. We provide you the instructions for Canopy. 1.) Download Canopy. The basic version is free. 2.) Open up the download and install. Follow the instructions. It will install the required packages and set the necessary paths on your computer. 14