Gravity and Magnetic Mapping

Gravity Map of

Wisconsin

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.

Gravimeter

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

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

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

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

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

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

Raw Gravity, Canada

Colorado Bouguer Map

Colorado Isostatic Map

Chicxulub Impact Basin Gravity Map

Venus Gravity Maps

Gravity Map of Mars

Sea Floor Seen from Space

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

The Geoid

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

Inherent Ambiguity

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

The Gaussian Myth

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

Magnetic Map of

Wisconsin

Gravity Map of

Wisconsin

Magnetic Field (Dipole)

Why Lines of Force?

Magnetic Poles

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

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

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

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

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).

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

Geodynamo

World Magnetic Declination

Overall Magnetic Field of Earth

Magnetic Field 1900-2000

MAGSAT Map of Earth

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

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

Gravity and Magnetic MappingGravity 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

Magnetic Anomalies

Anomaly due to Induced Magnetism

Anomaly due to Remanent Magnetism

Magnetic Anomalies in the Atlantic