1. Environmental and Exploration Geophysics I tom.h.wilson tom.wilson@geo.wvu.edu Department of Geology and Geography West Virginia University Morgantown, WV Terrain Conductivity Phone - 293-6431

2. Geol454-## (i.e. ## =01, 02, 12, 13, …) Password is just geol454 Check out contents of the H: (common) drive And the G: Drive (your personal drive on the network) Your G drive and the common drive are accessible on any machine hooked into our network. Copy the Burger files from the H: drive to your G: drive Store your classwork and models on the G:Drive. That way if you move to another machine those files will still be accessible to you. This also avoide the possibility that someone might inadvertently delete your files from the local C:\Drive.

3. In this picture an ammeter is connected in the circuit of a conducting loop. When the bar magnet is moved closer to, or farther from, the loop, an electromotive force (emf) is induced in the loop. The ammeter indicates currents in different directions depending on the relative motion of magnet and loop. Notice that, when the magnet stops moving, the current returns to zero as indicated by the ammeter. http://ww2.slcc.edu/schools/hum_sci/physics/tutor/2220/em_induction/index.html

4. What would happen if you cut the ring? What would happen if you put a can of coke inside the coil? http://ww2.slcc.edu/schools/hum_sci/physics/tutor/2220/em_induction/experiments.html

5. “Dynamic” Tables 8.1 and 8.2 ~15 km (about 9 miles) < 30 m (about 100 feet) ~1.5 m (about 5 feet)

7. Clay particles are a source of loosely held cations

8. Cation clouds provide a source of electrolytes, they can also form a partial barrier to current flow through small pores. In this case their effect is similar to that of a capacitor.

9. Archie’s Law The general form of Archie’s law is  b is the conductivity of the mixture (bulk conductivity) and  l the conductivity of the liquid which we assume is water. F is the formation factor, and porosity is related to F as follows Note also that Empirical conductivity porosity relationships

10. Terrain Conductivity Survey EM31 EM34 Geonics Limited has specially designed these terrain conductivity meters to take advantage of simple relationships between secondary and primary magnetic fields. The instrument was designed to operate in areas where the induction number is low.

12. tiltmeters Tracer and soil gas monitors EM Survey VSP Source Point CO2 injection well

13. Marshall Co. WV, coal sequestration pilot

14. Hunting for Abandoned Wells

15. Hunting for abandoned Wells

16. The induction number? B induction number s intercoil spacing  skin depth depth at which amplitude of the em field drops to 1/e of the source or primary amplitude e natural base - equals 2.71828.. 1/e ~0.37 In general for a plane wave, the peak amplitude (A r ) of an oscillating em field at a distance r from the source will drop off as -

17.  is an attenuation coefficient. r =1/  is the skin depth . The distance r=  is referred to as the skin depth

18. The attenuation factor  varies in proportion to the frequency of the electromagnetic wave. Higher frequencies are attenuated more than lower frequencies over the same distance. Hence if you want to have greater depth of penetration/investigation, lower frequencies are needed. As a rough estimate,  (the skin depth) can be approximated by the following relationship We can think of the skin depth as a “depth of penetration”

19. Low Induction Number When that assumption is met, there is a simple linear relationship between the primary and secondary fields when subsurface conductivity and the operating frequency of the terrain conductivity meter are confined to certain limits. Under low induction number conditions the ratio of the secondary to the primary magnetic field is linearly proportional to the terrain-conductivity. Since the secondary and primary fields are measured directly, their ratio is known. Hence, the net ground conductivity is also known.

20. HpHp Surface Contamination Plume HsHs TransmitterReceiver s  Is what we are after

21. HpHp Surface Contamination Plume HsHs H S secondary magnetic field at receiver coil H P primary magnetic field  = 2  f – angular frequency f = frequency  o = magnetic permeability of free space  = ground conductivity s = intercoil spacing (m) i = imaginary number

22. HpHp Surface Contamination Plume HsHs s f refers to the frequency of the alternating current in the transmitter coil The operating frequency is adjusted depending on the intercoil spacing Together, the EM31 and EM34 provide 4 different intercoil spacings and two different coil orientations. The coils can be oriented to produce either the vertical or horizontal dipole field. EM31 EM34

23. The operating frequencies for the different intercoil spacings are We could also write this as  is the skin depth f is the frequency of the em wave  is the conductivity (in mhos/meter)  is the resistivity Remember EM31 EM34

24. In the following table we examine the effect of operating frequency, intercoil spacing and ground conductivity on the induction number. Since - As the frequency and conductivity increase, the depth of penetration decreases These instruments are designed to work when the induction number is relatively low

25. In general, for the EM31, operation under the assumption of low induction number is valid for ground conductivity of about 100 mmhos/meter and less.

26. The text isn’t very specific, but a little calculation suggests that induction numbers of 0.2 or less can be considered “low” induction numbers for the EM31. Perhaps as much as 0.5 or less for the EM34. Generally high ground conductivity is considered 100mmhos/m or greater. Fortunately, ground conductivity in general tends to be much less than 100 mmhos/meter

27. For example, on the Greer site, terrain conductivities in the darker areas are 22 mmhos/meter and greater. The terrain conductivities in the lighter areas are less than 6 mmhos/meter. Fahringer (1999)

28. Vertical Dipole Horizontal Dipole Changing the dipole orientation changes the depth of penetration and thus the instrument response will provide information about apparent ground conductivity at different depths. McNeill refers to these “depths of investigation” as exploration depths. The orientation of the dipole is easily controlled by changing the orientation of the coil. As suggested by the drawing, the vertical dipole will have a greater depth of penetration than the horizontal dipole.

29. Vertical dipole mode of operation Exploration Depths “Rule of Thumb”

30. Those are easy to remember and useful relationships. However, the apparent conductivity measured at the surface is a composite response - a superposition of responses or contributions from the entire subsurface medium. The contribution from arbitrary depths is defined by the relative response function  (z), where z is the depth divided by the intercoil spacing.

31. Continue reading Chapter 8 – pages 499 to 510 (top). Look over the problem I handed out today and ask yourself how you would solve this problem using methods described in pages 514 – 519. We’ve jumped ahead into some of the technical issues associated with terrain conductivity methods. Next Tuesday we will back up a bit and review some more fundamentals.

32. Note that the relative response function for the horizontal dipole  h is much more sensitive to near-surface conductivity variations and that its response or sensitivity drops off rapidly with depth Vertical dipole interaction has no sensitivity to surface conductivity, reaches peak sensitivity at z ~0.5, and is more sensitive to conductivity at greater depths than is the horizontal dipole.

33. The contribution of this thin layer to the overall ground conductivity is proportional to the value of the relative response function at that depth. Constant conductivity 

34. The contribution of a layer to the overall ground conductivity is proportional to the area under the relative response function over the range of depths (Z 2 -Z 1 ) spanned by that layer. Z1Z1 Z2Z2

35. As you might expect, the contribution to ground conductivity of a layer of constant conductivity that extends significant distances beneath the surface (i.e. homogenous half-space) is proportional to the total area under the relative response function.

36. So in general the contribution of several layers to the overall ground conductivity will be in proportion to the areas under the relative response function spanned by each layer.

37. You all will recognize these area diagrams as integrals. The contribution of a given layer to the overall ground conductivity at the surface above it is proportional to the integral of the relative response function over the range of depths spanned by the layer.

38. McNeill introduces another function, R(z) - the cumulative response function - which he uses to compute the ground conductivity from a given distribution of conductivity layers beneath the surface. For next time continue your reading of McNeill and develop a general appreciation of the relative and cumulative response functions.

39. Each point on the R V (z) curve represents the area under the  V (z) curve from z to . The following diagrams are intended to help you visualize the relationship between R(z) and  (z).

40. Z2Z2

43. Consider one additional integral - How would you express this integral as a difference of cumulative response functions?

45. Note that R(0) = 1, hence

46. According to our earlier reasoning - the contribution of a single conductivity layer to the measured ground (or terrain) conductivity is proportional to the area under the relative response function. The apparent conductivity measured by the terrain conductivity meter at the surface is the sum total of the contributions from all layers. We know that each of the areas under the relative response curve can be expressed as a difference between cumulative response functions

47. Let’s consider the following problem, which is taken directly from McNeill’s technical report (TN6). See also Box 11.2 and Figure 11.7 (p 594 & 596 of Reynolds)

50. Visually, the solution looks like this..

51. Compare this result to that of McNeill’s (see page 8 TN6). Mathematical formulation -

52. In this relationship  a is the apparent conductivity measured by the conductivity meter. The dependence of the apparent conductivity on intercoil spacing is imbedded in the values of z. Z for a 10 meter intercoil spacing will be different from z for the 20 meter intercoil spacing. The above equation is written in general form and applies to either the horizontal or vertical dipole configuration.

53. In the appendix of McNeill (today’s handout), he notes that the assumption of low induction number yields simple algebraic expressions for the relative and cumulative response functions. We can use these relationships to compute specific values of R for given zs.

54. The simple algebraic expressions for R V (z) and R H (z) make it easy for us to compute the terms in the problem McNeill gives us. In that problem z 1 is given as 0.5 and z 2 as 1 and 1.5 Assuming a vertical dipole orientation R V (z=0.5) ~ 0.71 R V (z=1.0) ~ 0.45 R V (z=1.5) ~ 0.32

55.  1 =20 mmhos/m  2 =2 mmhos/m  3 =20 mmhos/m Z 1 = 0.5 Z 2 = 1 and 1.5 Substituting in the following for the case where Z 2 =1.

56. Problems 8.5, 8.6, and 8.7 and AMD problem will be due next Thursday Bring questions for discussion to class on Tuesday. Papers on the Terrain Conductivity reading list are available in the 3 rd floor mail room.

58. Here’s a problem for you to work through before our next class. A terrain conductivity survey is planned using the EM31 meter (3.66 m (or 12 foot) intercoil spacing). Our hypothetical survey was conducted over a mine spoil to locate migration pathways within the spoil through which acidic mine drainage as well as neutralizing treatment are being transported. Scattered borehole data across the spoil suggest that these paths are approximately 10 feet thick and several meters in width. Borehole resistivity logs indicate that areas of the spoil surrounding these conduits have low conductivity averaging about 4mmhos/m. The bedrock or pavement at the base of the spoil also has a conductivity of approximately 4mmhos/m. Depth to the pavement in the area of the proposed survey is approximately 60 feet. Conductivity of the AMD transport channels is estimated to be approximately 100mmhos/m. Mine spoil surface AMD contamination zone Pit Floor ~10ft ~60ft

59. A. Evaluate the possibility that the EM31 will be able to detect high conductivity transport zones with depth-to-top of 30feet. Evaluate only for the vertical dipole mode. It may help to draw a cross section.

60. How many different conductivity layers will you actually have to consider? Does it matter whether d (depth) and s (intercoil spacing) are in feet or meters? Set up your equation following the example presented by McNeill and reviewed in class, and solve for the apparent conductivity recorded by the EM31 over this area of the spoil. Bring your work in and be prepared to discuss it at the beginning of the next class. Note - a table of R values are presented on the following page.

61. Z R V R H.000 1.000000 1.000000.200.9284767.6770329.400.7808688.4806249.600.6401844.3620499.800.5299989.2867962 1.000.4472136.2360680 1.200.3846154.2000000 1.400.3363364.1732137 1.600.2982750.1526108 1.800.2676438.1363084 2.000.2425356.1231055 2.200.2216211.1122055 2.400.2039542.1030602 2.600.1888474.0952811 2.800.1757906.0885849 3.000.1643990.0827627 3.200.1543768.0776539 3.400.1454940.0731363 3.600.1375683.0691128 3.800.1304545.0655074 4.000.1240347.0622578 4.200.1182129.0593147 4.400.1129097.0566359 4.600.1080592.0541887 4.800.1036061.0519428 5.000.0995037.0498762 5.200.0957124.0479660 5.400.0921982.0461979 5.600.0889320.0445547 5.800.0858884.0430231