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Gravity and Magnetic Mapping
- 1. Gravity and Magnetic Mapping
- 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 – 0.0000058sin2 2φ) • 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 m a = 0.03394 m/sec2 = 3394 mgal • v at equator = 466 m/sec, r = 6,371,000 m a = 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 ρ t • Note there is no elevation term • If ρ = 1000 kg/m3 and t = 1 m • 2 πG ρ t = 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
- 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
- 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
- 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
- 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
- 48. Overall Magnetic Field of Earth
- 51. MAGSAT Map of Earth
- 52. What Makes Rocks Magnetic? • Magnetic Minerals – Magnetite – Pyrrhotite – Ilmenite • Magnetite requires intermediate O activity – Too much O Hematite – Too little O Fe silicates • Complex: Al favors biotite over Fe oxides • No simple tie to lithology
- 53. Magnetic Mapping • Corrections are complex and time variable • No simple correlation with lithology • Can’t sense deep into crust because heat destroys magnetism • Magnetism is electromagnetic phenomenon • Instruments can be purely electronic • Can record continuously • Can be extremely detailed
- 54. Gravity and Magnetic Mapping Gravity maps Magnetic Maps Mechanical Instrument Instruments are purely electronic Discrete readings Continuous readings Less detail Great detail Can sense to great depths Can sense only a few kilometers deep Simple corrections for latitude and elevation Complex corrections in time and space Density correlates with rock type No simple correlation with rock type
- 56. Anomaly due to Induced Magnetism
- 57. Anomaly due to Remanent Magnetism
- 60. Magnetic Anomalies in the Atlantic