Gravity and Magnetic Mapping

1. Gravity and Magnetic Mapping

2. Gravity Map of Wisconsin

3. Gravity • Mean value about 9.8 m/sec2 = 1 g • About 0.5% smaller at equator than poles • Map unit = gal (for Galileo) = 1 cm/sec2 • Mean gravity = 980 gal • Maps contoured in mgal = 10-6 g • Modern gravimeters can detect .001 mgal variations (= 1 ppb) • A gravimeter is essentially a spring balance.

4. Gravimeter

5. Gravity and Latitude • Centrifugal force (3400 mgal at equator) • Variation of Earth’s radius • g(φ) = 9.78(1 + 0.0053sin2 φ – 0.0000058sin22φ) • 0.5% less at equator than pole = 5000 mgal • At 45⁰ = 58 mgal/degree

6. Gravity and Motion • Earth is a sphere (sort of) • Moving on the earth results in centrifugal force • Centripetal acceleration = v2/r • v at equator = 465 m/sec, r = 6,371,000 ma = 0.03394 m/sec2 = 3394 mgal • v at equator = 466 m/sec, r = 6,371,000 ma = 0.03409 m/sec2 = 3409 mgal • Moving 1 m/sec = 15 mgal at equator

7. Gravity Corrections • Raw Gravity • Latitude Corrections • Altitude • Mass between observer and sea level • Thickness of Crust and Regional Variations • Purpose is to identify features of geologic interest, not cancel everything out

8. Gravity and Altitude • Gravity decreases 0.31 mgal/m • A correction for altitude only is a free-air correction • However, there is also mass between the observer and sea level • A correction for excess mass is a Bouguer correction

9. Gravitational Attraction of a Plate • Attraction of a plate = 2 πG ρt • Note there is no elevation term • If ρ = 1000 kg/m3 and t = 1 m • 2 πG ρt = 41.93 × 10-8 m/s2 = 0.042 mgal • For ρ = 2700 kg/m3, correction = 0.11 mgal/m • Combined with altitude correction, total correction = 0.19 mgal/m

10. Gravity Maps • Gravity varies by latitude due to earth’s equatorial bulge and centrifugal force • Need altitude correction = 0.3 mgal/m = 3 x 10-7 g/m • Altitude only correction = Free-Air Anomaly Map • Correct for mass between you and sea level = Bouguer Anomaly Map • May also need terrain corrections • Correct for variations in thickness of crust = Isostatic Anomaly Map

11. Raw Gravity, Canada

14. Colorado Bouguer Map

15. Colorado Isostatic Map

16. Chicxulub Impact Basin Gravity Map

18. Venus Gravity Maps

19. Gravity Map of Mars

21. Sea Floor Seen from Space

22. Shape of the World • Earth with topography • Geoid: Ideal sea-level shape of the earth • Eliminate topography but keep the gravity • Gravity is what determines orbits and leveling of survey instruments • How do we know where the sea would be at some point inland? • Datum: Ellipsoid that best fits the geoid • Sphere: Globes and simple projections

23. The Geoid

24. Gravity Mapping • Simple corrections for latitude and altitude • Density = Lithology • Can sense deep into crust • Gravimeters are basically sensitive spring balances • Fragile • Prone to drift • Discrete data points • Labor intensive, low detail

25. Inherent Ambiguity

26. The Gaussian Myth • Gravity and Magnetic data are inherently ambiguous • There are an infinite number of possible interpretations • Therefore we can’t conclude anything useful from gravity or magnetic maps

27. The Gaussian Myth

28. The Gaussian Myth Debunked • Locations of anomaly sources are constrained • Shapes of anomaly sources are constrained • Sources cannot have geologically absurd properties • Maximum depths are constrained • Total masses constrained

29. Magnetic Map of Wisconsin

30. Gravity Map of Wisconsin

32. Magnetic Field (Dipole)

33. Why Lines of Force?

34. Magnetic Poles

35. Geomagnetism • Magnetic field of Earth = 40 microtesla = 40,000 nt (= 40,000 gamma) • Varies from 25 to 70 microtesla • Non-axial • Not centered on the earth • Varies over a human lifetime

36. Magnetism • Diamagnetism: weak repulsion from electron orbital motion, all materials • Paramagnetism: moderate attraction due to unpaired electrons • Ferromagnetism: strong attraction due to parallel alignment of electrons

37. Curie Point • Ferromagnetism is due to parallel electron magnetic moments • Organization breaks down under heating • Most materials lose magnetism around 500 C • Can’t pick up red hot iron with a magnet • Responsible for most paleomagnetism • Magnetic anomalies must be shallow • Geomagnetic field has some other origin

38. Source of Geomagnetic Field • Global and Approximately a Dipole • Must be in center of earth • Changes rapidly on a scale of years • Rules out a Permanent Magnet • Most Likely a Geodynamo

39. Dynamo Effect • Generator: Wire coil spinning in magnetic field to generate current • Uses own current to power electromagnets • Not perpetual motion: needs a starter and continuing source of energy (wind, steam, etc).

40. Geodynamo • Core is electrically conducting fluid • Electric currents in core create magnetic field • Motion of conducting fluid creates electric currents • Currents generate magnetic field…. • Probable driver: convection • Rotation affects flow and field orientation

41. Geodynamo

42. World Magnetic Declination

48. Overall Magnetic Field of Earth

50. Magnetic Field 1900-2000