Environmental and Exploration Geophysics II

1. Environmental and Exploration Geophysics II Gravity Methods (V) t.h. wilson wilson@geo.wvu.edu Department of Geology and Geography West Virginia University Morgantown, WV

7. Simple Geometrical Objects The Sphere

8. The Sphere You could measure the values of the depth index multipliers yourself from this plot of the normalized curve that describes the shape of the gravity anomaly associated with a sphere.

9. Geometrical factor Horizontal Cylinder

10. Locate the points along the X/z Axis where the normalized curve falls to diagnostic values - 1/4, 1/2, etc. The depth index multiplier is just the reciprocal of the value at X/Z. X times the depth index multiplier yields Z X2/3 X3/4 X1/2 X1/3 X1/4 Z=X1/2 0.58 0.71 Depth Index Multipliers 1.72 1.41 1 0.7 0.57

11. Sphere:__?_ or Cylinder _?__ Sphere:__?_ or Cylinder _?__ What is the depth Z? What is the depth Z? If  = 0.1 what is R ____? If  = 0.1 what is R ____? We left you with questions about these two anomalies last Thursday. Which anomaly is associated with a buried sphere and which with the horizontal cylinder?

12. The standard deviation in the estimates of Z assuming that you have a sphere is 0.027kilofeet. The range is 0.06 kilofeet. When you assume that the anomaly is generated by a cylinder, the range in the estimate is 0.2 kilofeet and the standard deviation is 0.093 kilofeet. Assuming that the anomaly is generated by a sphere yields more consistent estimates of Z.

13. The standard deviation in the estimates of Z assuming that you have a sphere is 0.14 kilofeet. The range is 0.37kilofeet. When you assume that the anomaly is generated by a cylinder, the range in the estimate is 0.09 kilofeet and the standard deviation is 0.03 kilofeet. Assuming that the anomaly is generated by a cylinder, in this case, yields more consistent estimates of Z.

14. Left If we take the average value of Zsphere as our estimate we obtain Z=2.05kilofeet which we can round off to 2kilofeet right If we take the average value of Zcyl as our estimate we obtain Z=2 kilofeet.

15. We left you with questions about these two anomalies last Thursday. Which anomaly is associated with a buried sphere and which with the horizontal cylinder? Sphere: _X_ or Cylinder __ Sphere:___ or Cylinder _X__ Depth Z = 2kf Depth Z = 2kf If  = 0.1 what is R ____? If  = 0.1 what is R ____?

16. Sphere If  = 0.1gm/cm3 For the sphere, we find that R = 1 kilofoot Cylinder For the cylinder, we find that R is also = 1 kilofoot

17. Horizontal Cylinder Vertical Cylinder or or Vertical Dike Sphere Offset Half Plates Half Plate or

18. Vertical Cylinder Ztop Zbottom 2R Note that the table of relationships is valid when Zbottom is at least 10 times the depth to the top Ztop, and when the radius of the cylinder is less than 1/2 the depth to the top.

19. Vertical Sheet Z1  W Z2 Assumes Z2 is very large compared to W  The above relationships were computed for Z2=10Z1 and W is small with respect to Z1

20. Non-Uniqueness Do you believe it?

21. At least two possibilities One large thrust sheet vs. two smaller ones -

22. The large scale geometry of these density contrasts does not vary significantly with the introduction of additional faults

23. The differences in calculated gravity are too small to distinguish between these two models

24. Estimate landfill thickness Roberts, 1990

25. Crustal Scale Modeling http://pubs.usgs.gov/imap/i-2364-h/right.pdf

26. Morgan 1996

27. Morgan 1996

28. Morgan 1996

29. Derived from Gravity Model Studies

30. It could even help you find your swimming pool Ghatge, 1993

31. Questions about Problem 3 (part 2) 3. What is the radius of the smallest equidimensional void (e.g. chamber in a cave) that can be detected by a gravity survey for which the Bouguer gravity values have an accuracy of 0.05 mGals? Assume the voids are formed in limestone (density 2.7 gm/cm3) and that void centers are never closer to the surface than 100m. (Problem 6.5 from Burger et al.)

32. Questions about Problem 3 (part 2) 3. What is the radius …..? What simple geometrical object could be used to help you answer this questions? What size anomaly are you trying to detect? What equation should you use?

33. problem 3 Begin by recalling the list of formula we developed for the sphere. What are your givens?

34. Pb. 4: The curve in the following diagram represents a traverse across the center of a roughly equidimensional ore body. The anomaly due to the ore body is obscured by a strong regional anomaly. Remove the regional anomaly and then evaluate the anomaly due to the ore body (i.e. estimate it’s depth and approximate radius) given that the object has a relative density contrast of 0.75g/cm3 with surrounding strata.

35. You could plot the data on a sheet of graph paper. Draw a line through the end points (regional trend) and measure the difference between the actual observation and the regional (the residual). You could use EXCEL or PSIPlot to fit a line to the two end points and compute the difference between the fitted line (regional) and the observations. residual Regional

36. In problem 5 your given three anomalies. These anomalies are assumed to be associated with three buried spheres. Determine their depths using the diagnostic positions and depth index multipliers we’ve been discussing in class. Carefully consider where the anomaly drops to one-half of its maximum value. Assume a minimum value of 0. A. B. C.

37. What can you find out about this anomaly? Given  = 1 gm/cm3

38. Due Dates • Problems 6.1 through 6.3 are due today Tuesday, Nov. 6th. • Hand in gravity lab this Thursday, Nov. 8th . • Turn in Part 1 (problems 1 & 2) of gravity problem set 3, Thursday, November 8th. Remember to show detailed computations for Sector 5 in the F-Ring for Pb. 2. • Turn in Part 2 (problems 3-5) of gravity problem set 3, Tuesday, November 13th. • Gravity paper summaries, Thursday, November 15th.