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 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
Magnetic Anomalies
Anomaly due to Induced Magnetism
Anomaly due to Remanent
Magnetism
Magnetic Anomalies in the
Atlantic