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

3. Sphere

4. 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.

5. Horizontal Cylinder

6. X 3/4 X 2/3 X 1/2 X 1/3 X 1/4 Z=X 1/2 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 0.58 0.71 0.58 1 1.42 1.74

7. Below are two symmetrical gravity anomalies. Which anomaly is associated with a buried sphere and which with the horizontal cylinder?

8. 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 generate 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.

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

10. If we take the average value of Z sphere as our estimate we obtain Z=2.05kilofeet which we can round off to 2kilofeet If we take the average value of Z cyl as our estimate we obtain Z=2 kilofeet.

11. Sphere Cylinder For the sphere, we find that R = 1 kilofoot For the cylinder, we find that R is also = 1 kilofoot If  = 0.1gm/cm 3

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

13. Z1Z1 Z2Z2 W   The above relationships were computed for Z 2 =10Z 1 and W is small with respect to Z 1

20. Yuhr, 1993

22. Ghatge, 1993

24. Roberts, 1990

28. Morgan 1996

29. Gurshaw, 1996

30. Morgan 1996

33. Derived from Model Studies

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

35. 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 deptj and approximate radius) given that the object has a relative density contrast of 0.75g/cm 3

36. residual Regional 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.

37. 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 discussed in class today. Carefully consider where the anomaly drops to one-half of its maximum value. Assume a minimum value of 0. A. C. B.

38. Nov. 10th Problems 1 & 2. Gravity lab Nov. 17th Problems 4, 5, & 6 - & The take home simple geometrical object problem Nov. 17th Gravity paper summaries