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 (V)

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 Pancake solution

8. Tom Wilson, Department of Geology and Geography anomaly

9. Tom Wilson, Department of Geology and Geography How many drums? 4 square feet Area of one drum ~ What’s wrong with the format of this plot? The x and y scaling has to be 1:1!

10. Tom Wilson, Department of Geology and Geography …. compare the field of the magnetic dipole to that of the gravitational monopole 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 Specifically: Provide answers to the questions on the handout

13. You can structure your summary around the following three points (see handout) Tom Wilson, Department of Geology and Geography 3. Assume that the magnetic anomaly produced by a single drum located 10 feet beneath the surface is 10 nT: what anomaly will it produce if buried 20 feet beneath the surface? 1. Why are both gravity and magnetic surveys needed to accurately locate the buried drums in this area. 2. Using the triangular outline provided in the graph. Estimate the number of drums contained within the triangle.

14. The triangular area shown below shows the possible location and distribution of the drum cluster Tom Wilson, Department of Geology and Geography What is the base? What is the height?

15. Problems we’ve been working on … Tom Wilson, Department of Geology and Geography

16. 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.

17. Evaluate the horizontal gradient Tom Wilson, Department of Geology and Geography Since  is co-latitude, the direction of increasing  is southward (in the northern hemisphere). As we travel from pole to equator Z E decreases, thus the gradient is negative.

18. 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?

19. 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

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

21. Considerable difference in magnitude of Tom Wilson, Department of Geology and Geography For the dipole For the horizontal cylinder As discussed in class, it’s probably best to center the cylinder at 1.75 meters depth.

22. Tom Wilson, Department of Geology and Geography Just as an aside: The sample rate you use will depend on the minimum depth of the objects you wish to find. Your sample interval should 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 How often would you have to sample to detect this drum? X 1/2 =Z/2 Sampling

24. 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.

25. 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? Sampling issues – file for future reference! If the depth to the center of the drum is 3 meters then we’d want to have a minimum sample interval of 1.5 meters.Why?

26. Tom Wilson, Department of Geology and Geography You can usually make quick work of it an use only three diagnostic positions (red above)

27. Tom Wilson, Department of Geology and Geography Again, we can get by with only three diagnostic positions (red above)

28. Tom Wilson, Department of Geology and Geography Let’s go through it again: 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.

29. 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 2.86 3.1 3.35 1.95 2.03 2.00

30. 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 g max g 3/4 g 1/2 g 1/4 5.08 5 5.1 3.47 3.28 3.00

31. Tom Wilson, Department of Geology and Geography 5. 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

32. Tom Wilson, Department of Geology and Geography More review this coming Look over today’s sample questions, review your notes and come prepared to ask questions this Thursday. Answer questions on the magnetics lab and put in my mailbox by noon tomorrow (Wednesday, December 7 th ) Magnetics paper summaries are due this Thursday (December 8 th ) Exam, Tuesday December 13 th ; 3-5pm