Environmental and Exploration Geophysics I

1. Environmental and Exploration Geophysics I Magnetic Methods (III) 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. Magnetic field variations are generally of non-geologic origin Long term drift in magnetic declination and inclination Tom Wilson, Department of Geology and Geography

3. Magnetic Field Variations – annual drift of the magnetic pole Tom Wilson, Department of Geology and Geography

4. Diurnal variations in the Earth’s Magnetic field Tom Wilson, Department of Geology and Geography

5. Magnetic fields like gravitational fields are not constant. However, magnetic field variations are much more erratic and unpredictable Diurnal variations http://www.earthsci.unimelb.edu.au/ES304 /MODULES/ MAG/NOTES/tempcorrect.html Tom Wilson, Department of Geology and Geography

6. Solar activity and sunspot cycles Nov. 30th 2010 sunspot 1130 Tom Wilson, Department of Geology and Geography

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9. Micropulsations Today’s Space Weather http://www.swpc.noaa.gov/today.html Real Time Magnetic field data http://www.swpc.noaa.gov/ace/ace_rtsw_data.html Tom Wilson, Department of Geology and Geography

10. http://www.swpc.noaa.gov/ace/ace_rtsw_data.html From the Advanced Composition Explorer Satellite Tom Wilson, Department of Geology and Geography

11. Field Between Reversals Normal dipolar field http://www.es.ucsc.edu/~glatz/geodynamo.html Tom Wilson, Department of Geology and Geography

12. Corrections? In general there are few corrections to apply to magnetic data. The largest non-geological variations in the earth’s magnetic field are those associated with diurnal variations, micropulsations and magnetic storms. The vertical gradient of the vertical component of the earth’s magnetic field at this latitude is approximately 0.025nT/m. This translates into 1nT per 40 meters. The magnetometer we have been using in the field reads to a sensitivity of 1nT and the anomalies we observed at the Falls Run site are of the order of 200 nT or more. Hence, elevation corrections are generally not needed. Variations of total field intensity as a function of latitude are also relatively small (0.00578nT/m). The effect over 80 m of elevation would about 1/2 nT. International geomagnetic reference formula Tom Wilson, Department of Geology and Geography

13. Correcting for Diurnal Variations Reoccupy the base The single most important correction to make is one that compensates for diurnal variations, micropulsations and magnetic storms. This is usually done by reoccupying a base station periodically throughout the duration of a survey to determine how total field intensity varies with time and to eliminate these variations in much the same way that tidal and instrument drift effects were eliminated from gravity observations. Tom Wilson, Department of Geology and Geography

14. Anomalies - Total Field and Residual The regional field can be removed by surface fitting and line fitting procedures identical to those used in the analysis of gravity data. Tom Wilson, Department of Geology and Geography

15. Magnetic susceptibility is a key parameter, however, it is so highly variable for any given lithology that estimates of k obtained through inverse modeling do not necessarily indicate that an anomaly is due to any one specific rock type. Tom Wilson, Department of Geology and Geography

16. + - + - S N The induced magnetic field of a metallic drum N F E S The Earth’s main field Tom Wilson, Department of Geology and Geography

17. Vector Awareness N S Tom Wilson, Department of Geology and Geography

18. Cross sectional area A + n turns l - Magnetic fields are fundamentally associated with circulating electric currents; thus we can also formalize concepts like pole strength, dipole moment, etc. in terms of current flow relationships. pl = n iA pl is the dipole moment Tom Wilson, Department of Geology and Geography

19. I=kF Hysterisis Loops I is the intensity of magnetization and FE is the ambient (for example - Earth’s) magnetic field intensity. k is the magnetic susceptibility. Tom Wilson, Department of Geology and Geography

20. The intensity of magnetization is equivalent to the magnetic moment per unit volume or Magnetic dipole moment per unit volume where and also, . Thus yielding and The cgs unit for pole strength is the ups Tom Wilson, Department of Geology and Geography

21. Recall from our earlier discussions that magnetic field intensity so that Thus providing additional relationships that may prove useful in problem solving exercises. For example, Tom Wilson, Department of Geology and Geography

22. What does this tell us about units of these different quantities? Summary We refer to the magnetic field intensity as H (or as in Burger et al., F) Tom Wilson, Department of Geology and Geography

23. Potential versus Force The potential is the integral of the force (F) over a displacement path. From above, we obtain a basic definition of the potential (at right) for a unit positive test pole (mt). Note that we consider the 1/4 term =1 Tom Wilson, Department of Geology and Geography

24. The reciprocal relationship between potential and field intensity Thus - H (i.e. F/ptest, the field intensity) can be easily derived from the potential simply by taking the derivative of the potential Tom Wilson, Department of Geology and Geography

25. The Dipole Field Consider the case where the distance to the center of the dipole is much greater than the length of the dipole. This allows us to treat the problem of computing the potential of the dipole at an arbitrary point as one of scalar summation since the directions to each pole fall nearly along parallel lines. Tom Wilson, Department of Geology and Geography

26. If r is much much greater than l (distance between the poles) then the angle  between r+andr- approaches 0 and r, r+andr- can be considered parallel so that the differences in lengths r+andr- from r equal to plus or minus the projections of l/2 into r. Tom Wilson, Department of Geology and Geography

27. r- r r+ Determine r+ and r- Tom Wilson, Department of Geology and Geography

28. Working with the potentials of both poles .. Recognizing that pole strength of the negative pole is the negative of the positive pole and that both have the same absolute value, we rewrite the above as Tom Wilson, Department of Geology and Geography

29. Converting to common denominator yields where pl = M – the magnetic moment From the previous discussion , the field intensity H is just Tom Wilson, Department of Geology and Geography

30. Thus .. H - monopole = H - dipole This yields the field intensity in the radial direction - i.e. in the direction toward the center of the dipole (along r). However, we can also evaluate the horizontal and vertical components of the total field directly from the potential. Tom Wilson, Department of Geology and Geography

31. H Toward dipole center (i.e. center of Earth’s dipole field Vd represents the potential of the dipole. Tom Wilson, Department of Geology and Geography

32. arc - length relationship HE is represented by the negative derivative of the potential along the earth’s surface or in the S direction. Tom Wilson, Department of Geology and Geography

33. Evaluating the derivative along the surface Tom Wilson, Department of Geology and Geography

34. -dV/dS Tom Wilson, Department of Geology and Geography

35. Where M = pl and Let’s tie these results back into some observations made earlier in the semester with regard to terrain conductivity data. 32 Tom Wilson, Department of Geology and Geography

36. The field along the dipole equator Given What is HE at the equator? … first what’s ?  is the angle formed by the line connecting the observation point with the dipole axis. So , in this case, is a colatitude or 90o minus the latitude. Latitude at the equator is 0 so  is 90o and sin (90) is 1. Tom Wilson, Department of Geology and Geography

37.  is 90 The field at the pole At the poles,  is 0, so that What is ZE at the equator? Tom Wilson, Department of Geology and Geography

38. Field at pole is twice that at the equator ZE at the poles …. The variation of the field intensity at the poles and along the equator of the dipole may remind you of the different penetration depths obtained by the terrain conductivity meters when operated in the vertical and horizontal dipole modes. Tom Wilson, Department of Geology and Geography

39. Consider one of the Lab Questions …. compare the field of the magnetic dipole field to that of the gravitational monopole field Gravity:500, 1000, 2000m A more rapid decay Increase r by a factor of 4 reduces g by a factor of 16 Tom Wilson, Department of Geology and Geography

40. A 4 fold increase in distance For the dipole field, an increase in depth (r) from 4 meters to 16 meters produces a 64 fold decrease in anomaly magnitude Thus the 7.2 nT anomaly (below left) produced by an object at 4 meter depths disappears into the background noise at 16 meters. 0.113 nT 7.2 nT Tom Wilson, Department of Geology and Geography

41. Some in-class problems for the last week of class On Tuesday during the last week of class, we’ll work through some problems that will help you review materials we’ve covered on magnetic fields. Some of the problems are not too much different from those we worked for gravitational fields and so will help initiate some review of gravity methods. The first problem relates to our discussions of the dipole field and their derivatives. 7.1 What is the horizontal gradient in nT/m of the Earth’s vertical field (ZE) in an area where the horizontal field (HE) equals 20,000 nT and the Earth’s radius is 6.3 x 108 cm. Tom Wilson, Department of Geology and Geography

42. Problem 1 Recall that horizontal gradients refer to the derivative evaluated along the surface or horizontal direction and we use the form of the derivative discussed earlier. Tom Wilson, Department of Geology and Geography

43. To answer this problem we must evaluate the horizontal gradient of the vertical component - or Take a minute and give it a try. Tom Wilson, Department of Geology and Geography

44. Can you find it? 7.3 A buried stone wall constructed from volcanic rocks has a susceptibility contrast of 0.001cgs emu with its enclosing sediments. The main field intensity at the site is 55,000nT. Determine the wall's detectability with a typical proton precession magnetometer. Assume the magnetic field produced by the wall can be approximated by a vertically polarized horizontal cylinder. Refer to figure below, and see following formula for Zmax. Background noise at the site is roughly 5nT. Tom Wilson, Department of Geology and Geography

45. Magnetic effects of simple geometric shapes Read over pages 454 to 482 to get a general sense of how simple geometric objects can be used in the interpretation and modeling of magnetic fields. The following problems illustrate some uses of these ideas. Tom Wilson, Department of Geology and Geography

46. Problem 7.3 Vertically Polarized Horizontal Cylinder Maximum field strength Remember this kind of formulization used in gravity General form Normalized shape term Tom Wilson, Department of Geology and Geography

47. Detecting abandoned wells Non text question: In your survey area you encounter two magnetic anomalies, both of which form nearly circular patterns in map view. These anomalies could be produced by a variety of objects, but you decide to test two extremes: the anomalies are due to 1) a concentrated, roughly equidemensional shaped object (a sphere); or 2) to a long vertically oriented cylinder. Tom Wilson, Department of Geology and Geography

48. Non-text question Vertical Magnetic Anomaly Vertically Polarized Sphere As a function of x/z … The notation can be confusing at times. In the above, consider H = FE= intensity of earth’s magnetic field at the survey location. Tom Wilson, Department of Geology and Geography

49. Non-text question Vertically Polarized Vertical Cylinder Look familiar? Tom Wilson, Department of Geology and Geography

50. Non-text question Given that derive an expression for the radius, where I = kHE. Compute the depth to the top of the casing for the anomaly shown below, and then estimate the radius of the casing assuming k = 0.1 and HE=55000nT. Zmax (62.2nT from graph below) is the maximum vertical component of the anomalous field produced by the vertical casing. Tom Wilson, Department of Geology and Geography