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 Where are the drums?

3. Tom Wilson, Department of Geology and Geography

6. From the bedrock

7. Tom Wilson, Department of Geology and Geography anomaly

8. Tom Wilson, Department of Geology and Geography

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

10. 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

11. 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.

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

13. Tom Wilson, Department of Geology and Geography

14. 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.

15. 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

16. 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

17. 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?

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

19. 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.

20. Tom Wilson, Department of Geology and Geography

22. 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.

23. 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

24. 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

25. 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

26. 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.

27. 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