Environmental and Exploration Geophysics II

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

2. Terrain Correction Problem Reviewed

3. What’s the station elevation? What’s the average elevation in Sector 1? What’s the relative difference between the station elevation and the average elevation of sector 1? 200 520 2840 520 280

4. 2640 200 3 (0.03mG) 0.028mG What did you get? Determine the average elevation, relative elevation and T for all 8 sectors in the ring. Add these contributions to determine the total contribution of the F-ring to the terrain correction at this location. We will also consider the F-ring contribution if the replacement density of 2.67 gm/cm3 is used instead of 2 gm/cm3 and the result obtained using equation 6-30

5. Equation 6-30

6. If you tried to use formula 6-30 to calculate the sector effects explicitly - did you remember to convert from feet to meters? Remember that these corrections were made assuming a replacement density of 2 gm/cm3. If you wish to estimate the effect of topography assuming another replacement density then you must adjust the total sum by a factor equal to the ratio of the desired density contrast to 2.0 gm/cm3. Hence, in the present example, use of a 2.67 gm/cm3 replacement density requires that the sum (0.6065 milligals) be factored by the ratio 2.67/2.00 = 1.33. Thus the total f-ring adjustment for 2.67gm/cm3 replacement density is 0.81 milligals. You don’t have to hand this in but make sure you understand how to do it. Aspects of this procedure could appear on the final exam.

7. Graphical Separation of Residual Examine the map at right. Note the regional and residual (or local) variations in the gravity field through the area. The graphical separation method involves drawing lines through the data that follow the regional trend. The green lines at right extend through the residual feature and reveal what would be the gradual drop in the anomaly across the area if the local feature were not present.

8. The residual anomaly is identified by marking the intersections of the extended regional field with the actual anomaly and labeling them with the value of the actual anomaly relative to the extended regional field. 0 -1 -0.5 -0.5 After labeling all intersections with the relative (or residual ) values, you can contour these values to obtain a map of the residual feature. Turn in next time for extra credit

9. Zero Max = 0 Min ~-1.8 negative

10. Stewart makes his estimates of valley depth from the residuals. You shouldn’t be concerned too much if you don’t understand the details of the method he used to separate out the residual, however, you should appreciate in a general way, what has been achieved. There are larger scale structural features that lie beneath the drift valleys and variations of density within these deeper intervals superimpose long wavelength trends on the gravity variations across the area. These trends are not associated with the drift layer. The potential influence of these deeper layers is hinted at in one of Stewart’s cross sections.

11. Bouguer anomaly Regional anomaly - Residual anomaly =

12. If one were to attempt to model the Bouguer anomaly without first separating out the residual, the interpreter would obtain results suggesting the existence of an extremely deep glacial valley that dropped off to great depths to the west. However, this drop in the Bouguer anomaly is associated with the deeper distribution of density contrasts.

13. More on “Stewart’s law” - Stewart assumes that the residual anomaly can be directly related to drift thickness using the Bouguer plate equation. Stewart assumes a density contrast of -  = 0.6 gm/cm3 and combines the terms 1/2G to yield the constant 130 which incorporates density units of grams/cm3 and thickness or depth (t) in units of feet

14. Stewart obtains the general relationships - or Where Z, is the drift thickness at station , and R is the value of the gravity residual at station 

15. From Tuesday's Lab What would be the maximum value of the residual anomaly over this model? Convert t=500 meters to feet. 500 meters = 1640 feet. 9 = -1640/130 milligals or -12.6 milligals

16. If we are only 700 meters from the edge - what would the computed depth be using the plate approximation? g = 9.5 milliGals. t = 130 g = 1245 feet or 380 meters. Note how the reference point becomes super critical here. In order to get total depth rather than depth relative to the top of the valley wall, all these anomaly values need to be shifted down 11.3 milligals

17. It is important to realize that 1) that there is the underlying assumption that the drift valleys are much wider than they are deep, 2) that the expression t = 130g specifically uses the residual gravity to estimate drift thickness, 3) and in order to do that effectively, the reference value will have to be chosen carefully. If bedrock rises to the surface at some point, that would be a good point to assign a value of 0 to the residual.

18. Last Chance for Questions on - Edge Effects Gravity Lab Due Wednesday, Nov. 6th by 5pm

19. Simple Geometrical Objects

20. Simple Geometrical Objects We can often estimate the gravitational acceleration associated with complex objects such as dikes, sills, faulted layers, mine shafts, cavities, caves, culminations and anticline/syncline structures by approximating their shape using simple geometrical objects - such as horizontal and vertical cylinders, the infinite sheet, the sphere, etc. Estimates of maximum depth, density contrast, fault offset, etc. can often be made quickly and without the aid of a computer using simple relationships derived for simple geometrical forms.

21. Let’s start with one of the simplest of geometrical objects - the sphere

28. gmax

29. Divide through by gmax

35. Highlight the fact that X measures distance from the anomaly peak, and is NOT an absolute reference along the profile line.

36. The “diagnostic position” is a reference location. It refers to the X location of points where the anomaly has fallen to a certain fraction of its maximum value, for example, 3/4 or 1/2.

37. In the above, the “diagnostic position” is X1/2, or the X location where the anomaly falls to 1/2 of its maximum value. The value 1.31 is referred to as the “depth index multiplier.” This is the value that you multiply the reference distance X1/2 by to obtain an estimate of the depth Z.

38. 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. 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.

39. What is Z if you are given X1/3? … Z = 0.96X1/3 In general you will get as many estimates of Z as you have diagnostic positions. This allows you to estimate Z as a statistical average of several values. We can make 5 separate estimates of Z given the diagnostic position in the above table.

40. 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.

47. Now compute variation of g across the cylinder and consider only the vertical component. take vertical component