1. Tom Wilson, Department of Geology and Geography Environmental and Exploration Geophysics I tom.h.wilson tom.wilson@mail.wvu.edu Department of Geology and Geography West Virginia University Morgantown, WV Magnetic Methods (III)

2. The vector components of the Earth’s magnetic field Tom Wilson, Department of Geology and Geography http://en.wikipedia.org/wiki/File:XYZ-DIS_magnetic_field_coordinates.svg

3. Tom Wilson, Department of Geology and Geography Long term drift in magnetic declination and inclination Magnetic field variations are generally of non-geologic origin

4. Declination - 2010 Tom Wilson, Department of Geology and Geography http://en.wikipedia.org/wiki/File:World_Magnetic_Declination_2010.pdf

5. Variations in declination through time Tom Wilson, Department of Geology and Geography http://en.wikipedia.org/wiki/File:Earth_Magnetic_Field_Declination_from_1590_to_1990.gif

6. Variations in the Earth’s Magnetic field Tom Wilson, Department of Geology and Geography http://en.wikipedia.org/wiki/File:Magnetic_North_Pole_Positions.svg

7. Magnetic reversals Tom Wilson, Department of Geology and Geography Reversals are quite infrequent occuring on average about once every 250,000 yrs. http://www.pbs.org/wgbh/nova/magnetic/timeline.html

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

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

10. Short term fluctuations Tom Wilson, Department of Geology and Geography http://en.wikipedia.org/wiki/File:Animati3.gif

11. Tom Wilson, Department of Geology and Geography Solar activity and sunspot cycles Nov. 30 th 2010 Nov. 28 th 2011

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

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

14. Tom Wilson, Department of Geology and Geography 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 may be on 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 NS distance would about 1/2 nT, and over a kilometer, about 5.8 nT (increase to the north. International geomagnetic reference formula http://www.ngdc.noaa.gov/IAGA/vmod/igrf.html

15. Tom Wilson, Department of Geology and Geography 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. Reoccupy a base station at frequent intervals

16. Tom Wilson, Department of Geology and Geography Other corrections? Total Field versus Residual The regional field can be removed by surface fitting and line fitting procedures identical to those used in the analysis of gravity data. The efforts that Stewart undertook to eliminate the regional field from his data may be very appropriate to magnetic field data analysis and modeling

17. Tom Wilson, Department of Geology and Geography 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.

18. Variable vector fields Tom Wilson, Department of Geology and Geography The Earth’s main field S N The induced magnetic field of a metallic drum

19. Tom Wilson, Department of Geology and Geography SN

20. 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 + - l n turns Cross sectional area A pl is the dipole moment

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

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

23. Tom Wilson, Department of Geology and Geography 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,

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

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

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

27. Tom Wilson, Department of Geology and Geography 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.

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

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

30. Tom Wilson, Department of Geology and Geography 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 Working with the potentials of both poles..

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

32. Tom Wilson, Department of Geology and Geography 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.

33. Get started with the magnetics lab Tom Wilson, Department of Geology and Geography In this lab we will be looking for buried metallic drums. We suspect that drums of radioactive material have been secretly buried to avoid being found. Simple excavation (back-hoeing) of the area is ruled out since accidental rupture of the drums would release radioactive materials into the local groundwater system and atmosphere. Clean up would be extremely hazardous, difficult, and expensive. We’ll come back to the following slides on Thursday

34. Tom Wilson, Department of Geology and Geography Next week will be spent in review Problems handed out in class today will be discussed Thursday and be due next Tuesday. We will be going over them as in-class problems, but you will receive take-home grade credit for them. Magnetics paper summaries are due next Thursday December 6 th Lab summary due Thursday, December 6 th Exam, Friday, December 14 th ; 3-5pm