1. Environmental and Exploration Geophysics I tom.h.wilson wilson@geo.wvu.edu Department of Geology and Geography West Virginia University Morgantown, WV Magnetic Methods (IV) Problem Discussions and Final Review

2. Vertically polarized sphere or dipole Vertically polarized vertical cylinder Vertically polarized horizontal cylinder

3. Vertically polarized sphere or dipole Vertically polarized vertical cylinder Vertically polarized horizontal cylinder

4. Is a function of the unitless 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

5. For any relative response function, for example, the buried vertical cylinder - Z A /Z max provides a quantitative description of the shape of the anomaly associated with the vertical cylinder, and that shape or the relative variations of anomaly magnitude as a function of the variable x/z (where z is the depth to the top of the buried cylinder in this case) will be the same for any buried vertical cylinder regardless of its size or depth. Thus, since the shape of the relative response does not vary, we have a means of estimating the depth to the top of the cylinder from measurements of distances (x) from the peak anomaly to points where the anomaly falls off to a certain fraction of its peak value.

6. These distances are referred to as diagnostic positions. Thus in the plot below the points along the x axis where the anomaly falls off to 3/4 ths, 2/3 rds, 1/2, 1/3 rd and 1/4 th of the maximum value of the anomaly are referred to as X 3/4, X 2/3, X 1/2, X 1/3 and X 1/4, respectively. X 2/3 X 1/2 X 1/3 X 1/4

7. Those measurements provide us with the above table. In this case we have distances in multiples of x/z.

8. In working with an actual anomaly, we can measure the actual distances to points where a given anomaly drops to various fractions of the maximum anomaly value and then compute the depth z.

9. 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.

10. We get multiple estimates of z this way, from which we can compute the average depth. In this example, we obtain a depth z~3.46km to the top of the buried vertical cylinder.

11. For the in-class problem you not only had to determine the depth to the object, but you also had to determine what shape object produced the anomaly - Buried sphere or vertical cylinder

12. The anomaly above left Cylinder - Z=2km *note DIM = depth index multiplier

13. Sphere, z=4km Anomaly - above right

14. The comparisons at right indicate that it would be very difficult to discriminate between the sphere and horizontal cylinder, however, if 2D coverage were available, this would be an easy distinction.

15. The map view clearly indicates that consideration of two possible origins may be appropriate - sphere or vertical cylinder.

16. 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

17. Determine the depth z to the center of the basalt flow. Also indicate whether you think the flow is faulted (two offset semi- infinite sheets) or just terminates (a semi- infinite sheet). What evidence do you have to support your answer? Refer to illustration on page 433 and associated discussion. This problem relies primarily on a qualitative understanding of equation 7-47.

18. Field of the semi-infinite plate X = 0 at the surface point directly over the edge of the plate. The field at a point X is derived from the two angles shown below -  1 and  2 - used in the text. 11 22

19. The angle subtended by the top of the sheet at x is The angle subtended by the bottom of the sheet at x is

22. Half-plate (the Slab, semi infinite plate, the half-sheet …) - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + z t

23. In your comments about the subsurface geology inferred from the anomaly profile consider the overall shape of the anomaly and how it may allow you to discriminate between the faulted versus terminated flow interpretations.

24. In the lab exercise you are working on, you were given the magnetic susceptibility of the drums a 0.55cgs units. The magnetization of drums, pipes and other hollow metallic objects is proportional to wall thickness and not to cross sectional area of the object. In the modeling phase the susceptibility assigned to an object s its effective susceptibility. Take a look at the examples of the pipe and 55 gallon drum in today’s handout.

25. The dimensions given for the pipe are an outer diameter of 15cm and inner diameter of 14cm (inferred from wall thickness of 0.5 cm).

26. A typical value of k for the iron comprising the pipe is 25cgs units. The ratio of solid cross sectional area to total cross sectional area is 0.129. If the susceptibility of the solid wall is averaged over the cross section of the pipe, then the effective susceptibility of the pipe is 0.129 x 25cgs ~ 3.2cgs units.

29. You are asked to run a magnetic survey to detect a buried drum. What spacing do you use between observation points?

30. How often would you have to sample to detect this drum?

31. …. how about this one?

32. 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 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

33. The sample rate you use will depend on the minimum depth of the objects you wish to find.

35. A 50 foot long drum? Drums in the bedrock?

36. Sign Conventions Vectors that point down are positive. Vectors that point south are negative.

37. Anomaly asymmetries

38. Anomaly Magnitude

40. The final exam will concentrate on resistivity, gravity and magnetic methods.