1. Tom Wilson, Department of Geology and Geography Environmental and Exploration Geophysics II tom.h.wilson tom.wilson@mail.wvu.edu Department of Geology and Geography West Virginia University Morgantown, WV Tie up Gravity methods & begin Magnetic methods

2. Tom Wilson, Department of Geology and Geography We make simplifying assumptions about the geometry of 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. to estimate the scale of an anomaly we might be looking for or to estimate maximum depth, density contrast, fault offset, etc. without the aid of a computer. Burger gets into a lot of the details in Section 6.5 of the text

3. Tom Wilson, Department of Geology and Geography Recall our earlier discussions of the gravity anomaly produced by a roughly spherical or equidimensional distribution of density contrast - Go to 31

4. Two term solution with one of the terms describing the shape of the anomaly Tom Wilson, Department of Geology and Geography z g directly over the center of the sphere is g max

5. Shape term and maximum g directly over the sphere Tom Wilson, Department of Geology and Geography g max

6. We recognize the shape term as this ratio Tom Wilson, Department of Geology and Geography Divide through by g max g max contains information about volume, density and radius

7. Diagnostic position and depth index multiplier Tom Wilson, Department of Geology and Geography In the above, the “diagnostic position” is X 1/2, 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 X 1/2 by to obtain an estimate of the depth Z. X 1/2 ½ ½

8. Recall the in-class worksheet Tom Wilson, Department of Geology and Geography

9. 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 0.56 0.77 1.04 1.24 2.17 1.79 1.31 0.96 0.81

10. Tom Wilson, Department of Geology and Geography 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 – to Z. Note that these constants (e.g. 0.02793) assume that depths and radii are in the specified units (feet or meters), and that density is always in gm/cm 3.

11. Tom Wilson, Department of Geology and Geography We can undertake similar development for the Horizontal Cylinder (see section 6.5.3 in our text) and

12. Tom Wilson, Department of Geology and Geography Locate the points along the X/Z Axis where the normalized curve falls to diagnostic values - 1/4, 1/2, of the maximum. 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. X 3/4 X 2/3 X 1/2 X 1/3 X 1/4 Z=X 1/2 0.71 0.58 0.71 1.0 1.42 1.74 0.58

13. Tom Wilson, Department of Geology and Geography How would you determine the depth index multipliers from this graph? 1 0.7 1.41 0.57 1.72 0.58 0.71 1.0 1.42 1.74

14. Diagnostic positions and multipliers for the horizontal cylinder Tom Wilson, Department of Geology and Geography Again, note that these constants (i.e. 0.01277) assume that depths and radii are in the specified units (feet or meters), and that density is always in gm/cm 3.

15. Consider the two near-surface gravity anomalies below and determine whether they are associated with roughly equidimensional or cylindrically shaped density contrast Tom Wilson, Department of Geology and Geography

16. What simple geometrical object could be used to make a rough evaluation of these anomalies? Sphere or vertical cylinder Horizontal cylinder

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

18. Tom Wilson, Department of Geology and Geography Are alternative acceptable solutions possible?

19. Tom Wilson, Department of Geology and Geography

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

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

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

23. Tom Wilson, Department of Geology and Geography http://pubs.usgs.gov/imap/i-2364-h/right.pdf

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

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

26. Tom Wilson, Department of Geology and Geography Morgan 1996 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

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

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

29. Tom Wilson, Department of Geology and Geography We’ll pick up with Magnetic Methods on Thursday

30. Looking ahead Tom Wilson, Department of Geology and Geography Gravity lab and paper summaries due this Thursday We’ll get into the magnetics lab this Thursday.

31. Follow the standard reporting format. Include the following or similar subdivisions: Tom Wilson, Department of Geology and Geography Abstract: a brief description of what you did and the results you obtained (~200 words). Background: Provide some background on the data we’re analyzing. All of this would come from Stewart’s paper. Explain his approach and answer question 1 below in this section to illustrate his approach. Results: Describe how you tested the model proposed by Stewart along XX’. Include answers to questions 2 through 4 below in this discussion. Conclusions: Summarize the highlights of results obtained in the forgoing modeling process.

32. In your write-up answer the following questions and refer to them by number for identification. Tom Wilson, Department of Geology and Geography 1.The residual gravity plotted in Figure 5 of Stewart's paper (also see illustrations in this lab exercise) has both positive and negative values. Assume that an anomaly extends from +2milligals to -2 milligals. Use the plate approximation (i.e. Stewart’s formula) and estimate the depth to bedrock? What do you need to do to get a useful result? Residuals of any kind usually fluctuate about zero mean value. What would you guess Stewart must have done to the residual values before he computed bedrock depth using the formula t=130g?

33. In your write-up answer the following questions and refer to them by number for identification Tom Wilson, Department of Geology and Geography 2. At the beginning of the lab you made a copy of GMSYS window showing some disagreement between the observations (dots) and calculations (solid line) across Stewart's model (section XX' Figure 7). As we did in class and in the lab manual, note a couple areas along the profile where this disagreement is most pronounced, label these areas in your figure for reference. In your lab report discussion offer an explanation for the cause(s) of these differences? Assume that the differences are of geological origin and not related to errors in the data. See lab manual

34. In your write-up answer the following questions and refer to them by number for identification. Tom Wilson, Department of Geology and Geography 3. With a combination of inversion and manual adjustments of points defining the till/bedrock interface, you were able to eliminate the significant differences between observed and calculated gravity. Your model is incorrect though since the valleys do not extend to infinity in and out of the cross section. Use the 2 ¾ modeling option to reduce the extents of the valleys in and out of the section to  800 feet. Make the changes to the Y+ and Y- blocks and then apply. Take a screen capture to illustrate the reduction in g associated with the glacial valleys. Make a screen capture of this display showing the new calculation line and the dashed gray values associated with the infinite valleys. Include this figure in your report and discuss your results.

35. In your write-up answer the following questions and refer to them by number for identification. Tom Wilson, Department of Geology and Geography 4. Use Stewart's formula t = 130g and estimate the depth to bedrock at the x location of 7920 feet along the profile located in the deepest glacial valley. Does it provide a reliable estimate of bedrock depth in this area? Explain in your discussion. 5. Lastly, describe the model you obtained and comment on how it varies from the starting model taken from Stewart (the model we started with).

36. Use questions to guide your discussion Tom Wilson, Department of Geology and Geography These questions provide discussion points in your lab report. Use figures you've generated in GMSYS to illustrate your point. All figures should be numbered, labeled and captioned.

37. Once again …. Tom Wilson, Department of Geology and Geography Gravity lab and paper summaries due this Thursday We’ll get into the magnetics lab this Thursday.

38. To be continued …. Magnetic polarity reversals on the sea floor provide Tom Wilson, Department of Geology and Geography

39. Charged particles from the sun stream into the earth’s magnetic field and crash into the gasses of the atmosphere

40. Tom Wilson, Department of Geology and Geography Protons and electrons in the solar wind crash into earth’s magnetosphere.

41. Tom Wilson, Department of Geology and Geography Gochioco and Ruev, 2006 We are also interested in local induced magnetic fields

42. Tom Wilson, Department of Geology and Geography Data Acquisition

43. Tom Wilson, Department of Geology and Geography Steve Sheriff’s Environmental Geophysics CourseEnvironmental Geophysics Proton Precession Magnetometers Tom Boyd’s Introduction to Geophysical Exploration CourseIntroduction to Geophysical Exploration Measuring the Earth’s magnetic field water kerosene & alcohol

44. Tom Wilson, Department of Geology and Geography Source of Protons and DC current source Proton precession generates an alternating current in the surrounding coil Magnetic Fields – Basic Relationships

45. Tom Wilson, Department of Geology and Geography Proton precession frequency (f) is directly proportional to the main magnetic field intensity F and magnetic dipole moment of the proton (M). L is the angular momentum of the proton and G is the gyromagnetic ratio which is a constant for all protons (G = M/L = 0.267513/  sec). Hence -

46. Tom Wilson, Department of Geology and Geography Locating Trench Boundaries Theoretical model Examination of trench for internal magnetic anomalies. actual field data Gilkeson et al., 1986

47. Tom Wilson, Department of Geology and Geography Trench boundaries - field data Trench Boundaries - model data Gilkeson et al., 1986

48. Tom Wilson, Department of Geology and Geography From Martinek Abandoned Wells

49. Tom Wilson, Department of Geology and Geography Locating abandoned wells

50. Tom Wilson, Department of Geology and Geography From Martinek Abandoned Well - raised relief plot of measured magnetic field intensities

51. Tom Wilson, Department of Geology and Geography Magnetic monopoles p1p1 p2p2 r 12 F m12 Magnetic Force  Magnetic Permeability p 1 and p 2 pole strengths Coulomb’s Law Magnetic Fields – Basic Relationships

52. Tom Wilson, Department of Geology and Geography Force Magnetic Field Intensity often written as H p t is an isolated test pole The text uses F instead of H to represent magnetic field intensity, especially when referring to that of the Earth (F E ). Magnetic Fields – Basic Relationships

53. Tom Wilson, Department of Geology and Geography The fundamental magnetic element is a dipole or combination of one positive and one negative magnetic monopole. The characteristics of the magnetic field are derived from the combined effects of non-existent monopoles. Dipole Field Magnetic Fields – Basic Relationships

54. Tom Wilson, Department of Geology and Geography monopole vs. dipole Toxic Waste Magnetic Fields – Basic Relationships

55. Tom Wilson, Department of Geology and Geography The earth’s main magnetic field

56. Tom Wilson, Department of Geology and Geography Magnetic Elements

57. Location of north magnetic pole Tom Wilson, Department of Geology and Geography http://www.compassdude.com/compass-declination.shtml

58. Tom Wilson, Department of Geology and Geography Magnetic Elements

59. Tom Wilson, Department of Geology and Geography Magnetic Elements

60. Tom Wilson, Department of Geology and Geography Magnetic Elements

61. Tom Wilson, Department of Geology and Geography Magnetic north pole: point where field lines point vertically downward Geomagnetic north pole: pole associated with the dipole approximation of the earth’s magnetic field. The compass needle points to the magnetic north pole.

62. Tom Wilson, Department of Geology and Geography Magnetic Intensity

63. Tom Wilson, Department of Geology and Geography Magnetic Inclination

64. Tom Wilson, Department of Geology and Geography Magnetic Inclination

65. Tom Wilson, Department of Geology and Geography Magnetic Declination

66. Tom Wilson, Department of Geology and Geography W Magnetic Declination

67. Tom Wilson, Department of Geology and Geography Magnetic Elements for your location http://www.ngdc.noaa.gov/geomagmodels/struts/calcPointIGRF

68. Tom Wilson, Department of Geology and Geography Today’s Space Weather http://www.swpc.noaa.gov/today.html Magnetic Elements http://www.ngdc.noaa.gov/geomag/magfield.shtml

69. Tom Wilson, Department of Geology and Geography Anomaly associated with buried metallic materials Bedrock configuration determined from gravity survey Results obtained from inverse modeling Computed magnetic field produced by bedrock Introduction to the magnetics computer lab

70. Tom Wilson, Department of Geology and Geography Where are the drums and how many are there?

71. Looking ahead Tom Wilson, Department of Geology and Geography Gravity lab and paper summaries due this Thursday We’ll get into the magnetics lab this Thursday.