Environmental and Exploration Geophysics I

1. Environmental and Exploration Geophysics I Magnetic Methods (IV) tom.h.wilson tom.wilson@mail.wvu.edu Department of Geology and Geography West Virginia University Morgantown, WV Tom Wilson, Department of Geology and Geography

2. Relative Response functions vertical polarization Vertically polarized sphere or dipole Vertically polarized vertical cylinder Vertically polarized horizontal cylinder Tom Wilson, Department of Geology and Geography

3. Zmax vertical polarization Vertically polarized sphere or dipole Vertically polarized vertical cylinder Vertically polarized horizontal cylinder Tom Wilson, Department of Geology and Geography

4. We measure the distances (x) to the various diagnostic positions and then convert those x’s to z’s using the depth index multipliers which are just the reciprocal of the x/z values at which the anomaly drops to various fractions of the total anomaly magnitude. Tom Wilson, Department of Geology and Geography

5. is a function of the unit-less variable x/z Dipole/sphere Vertical cylinder Horizontal cylinder The vertical field is often used to make a quick estimate of the magnitude of an object. This is fairly accurate as long as i is 60 or greater Tom Wilson, Department of Geology and Geography

6. For these three magnetic objects, the anomalies associated with the sphere and horizontal cylinder both drop off to1/2 their maximum value at X = ½ the depth Z The vertical cylinder behaves like a magnetic monopole. Tom Wilson, Department of Geology and Geography

7. The map view clearly indicates that consideration of two possible origins may be appropriate - sphere or vertical cylinder. Tom Wilson, Department of Geology and Geography

8. Half max relationships In general one will not make such extensive comparisons. You may use only one of the diagnostic positions, for example, the half-max (X1/2) distance for an anomaly to quickly estimate depth if the object were a sphere or buried vertical cylinder…. Burger limits his discussion to half-maximum relationships. X1/2 = Z/2 X1/2 = 0.77Z X1/2 = Z X1/2 = Z/2 Breiner, 1973 Tom Wilson, Department of Geology and Geography

9. The total field and total field anomaly Remember how the proton precession magnetometer works. Protons precess about the earth’s total field with a frequency directly proportional to the earth’s field strength The proton precession magnetometer measures the scalar magnitude of the earth’s main field. Tom Wilson, Department of Geology and Geography

10. Gradients The gradient is just the rate of change in some direction - i.e. it’s just a derivative. How would you evaluate the vertical gradient of the vertical component of the earth’s magnetic field? vertical component horizontal component Tom Wilson, Department of Geology and Geography

11. The vertical gradient is just the variation of ZE with change in radius or distance from the center of the dipole. Tom Wilson, Department of Geology and Geography

12. Vertical Gradient Tom Wilson, Department of Geology and Geography

13. Total Field Vertical Gradient http://rubble.phys.ualberta.ca/~doug/G221/MagLecs/magrem.html Tom Wilson, Department of Geology and Geography

14. Visit http://www.gemsys.ca/papers/site_characterization_using_gsm-19gw.htm Tom Wilson, Department of Geology and Geography

15. Representing the earth’s horizontal field in dipole form as The vertical gradient is just the variation with change of radius or Can you evaluate the vertical gradient of the horizontal component of the earth’s magnetic field? Tom Wilson, Department of Geology and Geography

16. Sampling You are asked to run a magnetic survey to detect a buried drum. What spacing do you use between observation points? $$ Reliability Tom Wilson, Department of Geology and Geography

17. X1/2=Z/2 How often would you have to sample to detect this drum? Tom Wilson, Department of Geology and Geography

18. oops! …. how about this one? The anomaly of the drum drops to ½ at a distance = ½ the depth. Tom Wilson, Department of Geology and Geography

19. Sampling does depend on available equipment! As with the GEM2, newer generation magnetometers can sample at a walking pace. Tom Wilson, Department of Geology and Geography

20. Remember, the field of a buried drum can be approximated by the field of a dipole or buried sphere. X1/2 for the sphere (the dipole) equals one-half the depth z to the center of the dipole. The half-width of the anomaly over any given drum will be approximately equal to its depth Or X1/2 =Z/2 Tom Wilson, Department of Geology and Geography

21. Resolution issues Tom Wilson, Department of Geology and Geography

22. The sample rate you use will depend on the minimum depth of the objects you wish to find. Your sample interval should probably be no greater than X1/2. But don’t forget that equivalent solutions with shallower origins do exist! Tom Wilson, Department of Geology and Geography

23. Carefully read over the Magnetics lab manual Follow the recommended reporting format. Specifically address points mentioned in the results section, above. Tom Wilson, Department of Geology and Geography

24. Specifically address points mentioned in the results section. Tom Wilson, Department of Geology and Geography

25. Magnetics Lab Questions?? Review from lab manual Where are the drums? Tom Wilson, Department of Geology and Geography

26. We just happen to have some gravity data from lab manual Tom Wilson, Department of Geology and Geography

27. Now we know what the bedrock configuration is from lab manual Tom Wilson, Department of Geology and Geography

28. & the bedrock contribution to the magnetic field from lab manual Tom Wilson, Department of Geology and Geography

29. Where are the drums? From the bedrock from lab manual Tom Wilson, Department of Geology and Geography

30. anomaly non-uniqueness and the drum cluster Tom Wilson, Department of Geology and Geography

31. A range of possibilities exist Tom Wilson, Department of Geology and Geography

32. 4. How many drums? Area of one drum ~ 4 square feet What’s wrong with the format of this plot? Tom Wilson, Department of Geology and Geography

33. Consider one of the Lab Questions (5) …. compare the field of the magnetic dipole field to that of the gravitational monopole field Gravity:500, 1000, 2000m A more rapid decay Increase r by a factor of 4 reduces g by a factor of 16 Tom Wilson, Department of Geology and Geography

34. A 4 fold increase in distance For the dipole field, an increase in depth (r) from 4 meters to 16 meters produces a 64 fold decrease in anomaly magnitude Thus the 7.2 nT anomaly (below left) produced by an object at 4 meter depths disappears into the background noise at 16 meters. 0.113 nT 7.2 nT Tom Wilson, Department of Geology and Geography

35. Questions about the Magnetics lab Again - follow the recommended reporting format. Specifically address listed points. Tom Wilson, Department of Geology and Geography

36. Back to the Homework Problems The first problem relates to our discussions of the dipole field and their derivatives. 7.1. What is the horizontal gradient in nT/m of the Earth’s vertical field (ZE) in an area where the horizontal field (HE) equals 20,000 nT and the Earth’s radius is 6.3 x 108 cm. Tom Wilson, Department of Geology and Geography

37. Problem 7.1 Recall that horizontal gradients refer to the derivative evaluated along the surface or horizontal direction and we use the form of the derivative discussed earlier Tom Wilson, Department of Geology and Geography

38. To answer this problem we must evaluate the horizontal gradient of the vertical component - or Take a minute and give it a try. Hint: See Equation 7.20 Tom Wilson, Department of Geology and Geography

39. Can you find it? 4. A buried stone wall constructed from volcanic rocks has a susceptibility contrast of 0.001cgs emu with its enclosing sediments. The main field intensity at the site is 55,000nT. Determine the wall's detectability with a typical proton precession magnetometer. Assume the magnetic field produced by the wall can be approximated by a vertically polarized horizontal cylinder. Refer to figure below, and see following formula for Zmax. What is z? What is I? Background noise at the site is roughly 5nT. Tom Wilson, Department of Geology and Geography

40. Problem 4 Vertically Polarized Horizontal Cylinder General form Normalized shape term How do you estimate the effective radius of the cylinder? Tom Wilson, Department of Geology and Geography

41. Detecting abandoned wells 5. In your survey area you encounter two magnetic anomalies, both of which form nearly circular patterns in map view. These anomalies could be produced by a variety of objects, but you decide to test two extremes: the anomalies are due to 1) a concentrated, roughly equidemensional shaped object (a sphere); or 2) to a long vertically oriented cylinder. Tom Wilson, Department of Geology and Geography

42. Question 5 Is the anomaly associated with a sphere? Tom Wilson, Department of Geology and Geography

43. Question 5 or vertical cylinder? Tom Wilson, Department of Geology and Geography

44. Determine depths (z) assuming a sphere or a cylinder and see which assumption yields consistent estimates. It’s all about using diagnostic positions and the depth index multipliers for each geometry. Tom Wilson, Department of Geology and Geography

45. X3/4 X1/2 X1/4 0.9 1.55 2.45 diagnostic distance Sphere vs. Vertical Cylinder; z = __________ The depth 2.17 1.31 0.81 1.95 2.03 2.00 3.18 2 1.37 2.86 3.1 3.35 Tom Wilson, Department of Geology and Geography

46. gmax g3/4 g1/2 g1/4 5.01 5.0 5.07 Sphere or cylinder? 3.47 3.28 2.99 Tom Wilson, Department of Geology and Geography

47. What is R? Algebraic manipulation 6. Given that derive an expression for the radius, where I = kHE. Compute the depth to the top of the casing for the anomaly shown below, and then estimate the radius of the casing assuming k = 0.1 and HE=55000nT. Zmax (62.2nT from graph below) is the maximum vertical component of the anomalous field produced by the vertical casing. Tom Wilson, Department of Geology and Geography

48. Feel free to discuss these problems in groups, but realize that you will have to work through problems independently on the final. Tom Wilson, Department of Geology and Geography

49. The end of the tunnel - onward ... Problems 1 & 2 are due today, December 3rd Next week will be spent in review Problems 3-6 are due next Tuesday, Dec 8th Magnetics lab, Magnetics paper summaries are due Thursday December 10th Exam, Thursday December 17th; 3-5pm Questions? Tom Wilson, Department of Geology and Geography