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

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

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

4. Tom Wilson, Department of Geology and Geography 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.

5. Tom Wilson, Department of Geology and Geography is a function of the unit-less variable x/z 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 Dipole/sphere Horizontal cylinder Vertical cylinder

6. Tom Wilson, Department of Geology and Geography X/Z Vertical Cylinder SphereHorizontal Cylinder X 3/4 0.460.3150.31 X 1/2 0.7660.50.495 X 1/4 1.230.730.68 Depth Index Multipliers Vertical Cylinder SphereHorizontal Cylinder X 3/4 2.173.183.23 X 1/2 1.30522.02 X 1/4 0.811.371.47 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.

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

8. Tom Wilson, Department of Geology and Geography In general one will not make such extensive comparisons. You may use only one of the diagnostic positions, for example, the half-max (X 1/2 ) 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. Breiner, 1973 X 1/2 = Z/2 X 1/2 = 0.77Z X 1/2 = Z X 1/2 = Z/2

9. Tom Wilson, Department of Geology and Geography 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.

10. Tom Wilson, Department of Geology and Geography 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?

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

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

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

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

15. Tom Wilson, Department of Geology and Geography 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?

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

17. Tom Wilson, Department of Geology and Geography How often would you have to sample to detect this drum? X 1/2 =Z/2

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

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

20. Tom Wilson, Department of Geology and Geography Remember, the field of a buried drum can be approximated by the field of a dipole or buried sphere. X 1/2 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 X 1/2 =Z/2

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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 X 1/2. But don’t forget that equivalent solutions with shallower origins do exist!

23. Tom Wilson, Department of Geology and Geography Follow the recommended reporting format. Specifically address points mentioned in the results section, above.

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25. Where are the drums?

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29. From the bedrock

30. Tom Wilson, Department of Geology and Geography anomaly

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32. 4. How many drums? 4 square feet Area of one drum ~ What’s wrong with the format of this plot?

33. Tom Wilson, Department of Geology and Geography …. compare the field of the magnetic dipole field to that of the gravitational monopole field Gravity:500, 1000, 2000m Increase r by a factor of 4 reduces g by a factor of 16

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

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

36. Tom Wilson, Department of Geology and Geography 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 (Z E ) in an area where the horizontal field (H E ) equals 20,000 nT and the Earth’s radius is 6.3 x 10 8 cm.

37. Tom Wilson, Department of Geology and Geography 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

38. Tom Wilson, Department of Geology and Geography 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

39. Tom Wilson, Department of Geology and Geography 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. Background noise at the site is roughly  5nT. What is z? What is I?

40. Tom Wilson, Department of Geology and Geography Vertically Polarized Horizontal Cylinder General form Normalized shape term

41. Tom Wilson, Department of Geology and Geography 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.

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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.

45. Tom Wilson, Department of Geology and Geography Sphere vs. Vertical Cylinder; z = __________ Diagnostic positions Multipliers Sphere Z Sphere Multipliers Cylinder Z Cylinder X 3/4 = X 1/2 = X 1/4 = The depth 2.86 3.1 3.35 1.95 2.03 2.00 2.17 1.31 0.81 3.18 2 1.37 diagnostic distance 0.9 X 3/4 1.55 X 1/2 2.45 X 1/4

46. Tom Wilson, Department of Geology and Geography Diagnostic positionsMultipliers Sphere Z Sphere Multipliers Cylinder Z Cylinder X 3/4 = 1.6 meters3.182.17 X 1/2 = 2.5 meters21.31 X 1/4 = 3.7 meters1.370.81 Sphere or cylinder? 5.01 5.0 5.07 3.47 2.99 3.28 g max g 3/4 g 1/2 g 1/4

47. Tom Wilson, Department of Geology and Geography 6. Given that derive an expression for the radius, where I = kH E. 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 H E =55000nT. Z max (62.2nT from graph below) is the maximum vertical component of the anomalous field produced by the vertical casing. Algebraic manipulation

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

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