Environmental and Exploration Geophysics II

1. Environmental and Exploration Geophysics II Gravity Methods (VI) wrap up tom.h.wilson tom.wilson@mail.wvu.edu Department of Geology and Geography West Virginia University Morgantown, WV Tom Wilson, Department of Geology and Geography

2. X z r Sphere with radius R and density  Simple Geometrical Objects - the Sphere Review Tom Wilson, Department of Geology and Geography

3. X z r Sphere with radius R and density  Anomaly Shape gvert Tom Wilson, Department of Geology and Geography

4. The Shape Term This term defines the shape of the anomaly produced by any spherically shaped object. Where In this form, the relationship is normalized by the maximum value of g observed at a point directly over the center of the sphere. Tom Wilson, Department of Geology and Geography

5. The Diagnostic Position x½ is referred to as the diagnostic position, 1/x1/2 is referred to as the depth index multiplier Solve for x1/2/z We found that x1/2/z = 0.766 Tom Wilson, Department of Geology and Geography

6. That ratio can be solved for at any point on the curve to provide a diagnostic position. 3/4 1/2 1/4 Tom Wilson, Department of Geology and Geography

7. A table of diagnostic positions and depth index multipliers for the Sphere (see your handout). Note that regardless of which diagnostic position you use, you should get the same value of Z. Each depth index multiplier converts a specific reference X location distance to depth. Tom Wilson, Department of Geology and Geography

8. Once you figure out Z - Solve for R or  These constants (i.e. 0.02793 or 0.00852) assume that depths and radii are in the specified units (feet or meters), and that density is always in gm/cm3. Tom Wilson, Department of Geology and Geography

9. What is Z if you are given X1/3? … Z = 0.96X1/3 In practice we can get as many estimates of Z as we have diagnostic positions. This allows you to estimate Z as a statistical average of several values. Using the above table, we could make 5 separate estimates of Z. This allows the interpreter to evaluate how closely the object approximates the shape of a sphere. Tom Wilson, Department of Geology and Geography

10. 0.56 1.79 0.77 1.31 1.04 0.96 1.24 0.81 You could measure of 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. 0.46 2.17 Tom Wilson, Department of Geology and Geography

11. Test Review Look at your table for the sphere Using the depth index multiplier of 1.305, Z has to be 13.05 km Since X3/4=z/2.17, then X3/4 =6km Tom Wilson, Department of Geology and Geography

12. Another Test gmax=0.35 g1/2=0.175 g3/4=0.26 1000 m Based on the x1/2 distance and depth index multiplier of 1.305 what is z? Based on the value of x3/4 and the depth index multiplier of 2.17, What is z? ~2600m ~2700m Tom Wilson, Department of Geology and Geography

13. Refer to text for some background … The Horizontal Cylinder Tom Wilson, Department of Geology and Geography

14. Results for Horizontal Cylinder and Tom Wilson, Department of Geology and Geography

15. We can ask the same kinds of questions we asked regarding the sphere. For example, Where does This tells us that the anomaly falls to ½ its maximum value at a distance from the anomaly peak equal to the depth to the center of the horizontal cylinder Tom Wilson, Department of Geology and Geography

16. Horizontal Cylinder Just as was the case for the sphere, objects which have a cylindrical distribution of density contrast all produce variations in gravitational acceleration that are identical in shape and differ only in magnitude and spatial extent. When these curves are normalized and plotted as a function of X/Z they all have the same shape. It is that attribute of the cylinder and the sphere which allows us to determine their depth and speculate about the other parameters such as their density contrast and radius. Tom Wilson, Department of Geology and Geography

17. How would you determine the depth index multipliers from this graph? 1.72 1.41 1 0.7 0.57 Tom Wilson, Department of Geology and Geography

18. X2/3 X3/4 X1/2 X1/3 X1/4 0.57 Z=X1/2 0.7 0.57 0.7 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 at the diagnostic position. X times the depth index multiplier yields Z Tom Wilson, Department of Geology and Geography

19. Simple relationships and formula for the horizontal cylinder Again, note that these constants (i.e. 0.02793) assume that depths and radii are in the specified units (feet or meters), and that density is always in gm/cm3. Tom Wilson, Department of Geology and Geography

20. Non-uniqueness and the maximum depth That maximum depth is a depth beneath which an anomaly of given wavelength cannot have a physical origin. Maximum Depth Nettleton, 1971 Tom Wilson, Department of Geology and Geography

21. Which estimate of Z seems to be more reliable? Compute the range. You could also compare standard deviations. Which model - sphere or cylinder - yields the smaller range or standard deviation? Tom Wilson, Department of Geology and Geography

22. To determine the radius of this object, we can use the formulas we developed earlier. For example, if we found that the anomaly was best explained by a spherical distribution of density contrast, then we could use the following formulas which have been modified to yield answer’s in kilofeet, where - Z is in kilofeet, and  is in gm/cm3. Tom Wilson, Department of Geology and Geography

23. Vertical Cylinder ? A A' Tom Wilson, Department of Geology and Geography

24. What simple geometrical object could be used to make a rough evaluation of these anomalies? Horizontal cylinder Sphere or vertical cylinder Tom Wilson, Department of Geology and Geography

25. How about the anomaly below? Half plate or faulted plate Tom Wilson, Department of Geology and Geography

26. Non-Uniqueness Are alternative acceptable solutions possible? Tom Wilson, Department of Geology and Geography

27. At least two possibilities One large thrust sheet vs. two smaller ones - Tom Wilson, Department of Geology and Geography

28. The large scale geometry of these density contrasts does not vary significantly with the introduction of additional faults Tom Wilson, Department of Geology and Geography

29. The differences in calculated gravity are too small to distinguish between these two models Tom Wilson, Department of Geology and Geography

30. Estimate landfill thickness Shallow environmental applications Roberts, 1990 Tom Wilson, Department of Geology and Geography

31. Crustal Scale Tectonic Problems http://pubs.usgs.gov/imap/i-2364-h/right.pdf Tom Wilson, Department of Geology and Geography

32. The influence of near surface (upper 4 miles) does not explain the variations in gravitational field observed across WV c c’ The paleozoic sedimentary cover Morgan 1996 Tom Wilson, Department of Geology and Geography

33. The sedimentary cover plus variations in crustal thickness explain the major features we see in the terrain corrected Bouguer anomaly across WV Morgan 1996 Tom Wilson, Department of Geology and Geography

34. In this model we incorporate a crust consisting of two layers: a largely granitic upper crust and a heavier more basaltic crust overlying the mantle Morgan 1996 Tom Wilson, Department of Geology and Geography

35. Gravity model studies help us estimate the possible configuration of the continental crust across the region Derived from Gravity Model Studies Tom Wilson, Department of Geology and Geography

36. It could even help you find your swimming pool Ghatge, 1993 Tom Wilson, Department of Geology and Geography

37. From last time What is the radius of the smallest equidimensional void (such as a chamber in a cave - think of it more simply as an isolated spherical void) that can be detected by a gravity survey for which the Bouguer gravity values have an accuracy of 0.05 mG? Assume the voids are in limestone and are air-filled (i.e. density contrast, , = 2.7gm/cm3) and that the void centers are never closer to the surface than 100m. i.e. z ≥ 100m Tom Wilson, Department of Geology and Geography

38. Let gmax = 0.1 Recall the formula developed for the sphere. We reasoned that ganom shouldbe at least 0.1 mGal; that Z would be at least 100m, and  = 2.7 2.7gm/cm3 or 1.7gm/cm3 Tom Wilson, Department of Geology and Geography

39. A. C. B. In a problem similar to problem 6.9 (Burger et al.) you’re 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. Tom Wilson, Department of Geology and Geography

40. In this in-class/take home problem determine whether the anomaly below is produced by a sphere of a cylinder Tom Wilson, Department of Geology and Geography

41. Due Dates • Remember that paper summaries and gravity labs are due Thursday, November 15th • Problems 6.5 and 6.9 are due Tuesday Nov. 13th. • Begin reading Chapter 7 on Exploration using Magnetic Methods … • We will introduce magnetic methods during the week of November 13th. • No class next week Tom Wilson, Department of Geology and Geography