Gravity

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Gravity

• (or, lies my physics class told me about physical
  contants)

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Couple of things

• Problem sets are due today.
• Lectures on web.
• AWOL papers.
• February 12 (and maybe part 19) Gravity
• February 19 Magnetics (problem set)
• February 26 Examples (combined data sets).
• February 26 Maps to 2-credit people.
• April 1 Papers due, 2-credit people.

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What physics 101 says
All objects falling toward the Earth have the
same acceleration (free-fall) (neglecting air
resistance). Weight (w) mass x gravity. Physics
says g 9.81 N/kg 9.81 m/s2 (a constant).
A good approximation and O.K. for physics
problems, but NOOOOOOOO!
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What geologists say

• Gravity varies from location to location on the
  Earth!
• Varies inversely with the square of distance
  from the center of the Earth (objects weigh
  slightly less at high altitudes than at sea
  level) (goes as r2)
• Varies with latitude (Earth is not precisely
  spherical is flattened at the poles)
• Varies with subsurface geology

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How does gravity help in geology?

• Bathymetry, sidescan surface observations.
• Gravity subsurface.
• Density mass/volume.
• Look at relative density contrasts between
  subsurface geological bodies .

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Density of Earth materials
Material Density (g/cm3)
Air 0
Water 1
Sediment 1.7-2.3
Sandstone 2.0-2.6
Shale 2.0-2.7
Limestone 2.5-2.8
Granite 2.7-3.1
Basalt 2.6-3.0
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Caveat Emptor

• Note that theres a lot of overlap in densities
  of Earth materials.
• Cannot use gravity to uniquely identify rock
  formations (dont know absolute magnitudes,
  either -- just relative densities).
• Must use other geological information
  (identification, geological context, etc.).

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Caveat Emptor

• But -- the measured gravity profile can be used
  to model the shape of the subsurface density
  anomaly.
• Buried sphere, buried cylinder, infinitely long
  sheet, infinitely long line.

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Gravimeter
Gravimeter gravity meter Two kinds Land and
air/sea Air/sea built on gyroscope to keep
instrument stable Measures SMALL, relative
variations in the Earths gravity field.
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Gravimeter
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Gravimeter measurements
Hang a mass on a spring --gt force of gravity will
stretch spring a distance x that is proportional
to the gravitational force. Gravitational
acceleration g (Gm)/r2 x (mg)/k, where h is
spring constant (describes stiffness of spring)
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Gravity units
Land gravimeter precision 1 part in 100
million 1 milligal 1 x 10-5 m/s2 Land
gravimeter precision 0.01 mgal Marine
gravimeter precision few mgal Marine seafloor
features tens to hundreds of milligals
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Correcting gravity
Terrestrial
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Correcting gravity

• Instrument drift (systematic changes in absolute
  value of measurements over time). Fit straight
  line.
• Latitude effects (Earth is an oblate spheroid.)
  Reference acceleration of gravity
• go 978.03185 (1.0 0.005278895
  sin2(lat) - 0.000023462 sin4(lat)),
  cm/s2

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Correcting gravity

• Elevation. Correction for taking measurements at
  different altitudes
• gh (2hgo)/ro, where go reference
  (latitude-corrected gravity), and ro Earths
  radius.
• Elevation correction at 1 km 3.08 mm/s2
  (0.308 mgal per meter of elevation change).
• Free-air correction.
• Corrected gravity free-air anomaly (gfa).
• gfa gmeasured - go - gh.

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Correcting gravity

• Bouguer correction
• Corrects for excess mass underlying
  observation points that were higher than the
  observation datum (or conversely).
• gb 2 pi G pc h, where G
  gravitational constant, pc density of
  underlying rocks (2.67 g/cm3), and h
  observation height.
• Bouguer gravity gobserved - go - gh - gb

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Correcting gravity

• Terrain correction
• Accounts for variations in local gravitational
  field caused by topography. Usually used only in
  areas of steep terrain, or where defined regional
  gradient exists.
• Terrain correction (gtc) ad hoc function
  defined by researcher
• Residual gravity gobserved - go - gh - gb -
  gtc

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Example from Sebago pluton, ME
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Correcting gravity
Marine
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Marine gravity
To first order, marine gravity looks like
bathymetry. Marine gravity is poor mans
bathymetry. Ship --gt marine gravity measured at
sea surface. Sea surface equipotential surface
(elevation datum everywhere equals 0). No height
corrections necessary. Gravity measured on ship
free-air gravity. Do correct for known or
calculable subsurface effects.
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AtlanticBathymetry
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Bathymetry
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Gravity
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Satellite gravity
ERS-1
Geosat
Geosat data was classified by the military until
1995, when the European ERS-1 data (of comparable
quality) was released.
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Ship vs satellite
Test accuracy of satellite-derived gravity by
comparing to shiptrack measurements. RMS
(root-mean-square, a way of quantifying error) is
about 3 mgal when shiptrack is along altimeter
profile. Away from altimeter profile, 4-7
mgal. Satellite gravity is less accurate near
shelf areas and near coasts (because of tidal
effects). Shiptrack and satellite data are
coherent down to wavelengths of 25-30 km.
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Global satellite-derived gravity
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Marine gravity corrections
Great, got free-air everywhere. What do you do
with it?
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Marine gravity corrections
Free-air (FAA) measured gravity at sea
surface. Want to know whats going on in
subsurface. Subtract from FAA the gravitational
signal of a model oceanic crust (6 km thick, with
assumed density, whose shape follows seafloor
topography). Result Mantle Bouguer anomaly
(MBA) MBA reflects subsurface density variations
due to (1) crustal thickness variations, (2)
mantle temperature variations, and (3)
lithospheric cooling. Lithospheric cooling
Plates diverge away from ridge axis, cooling as
they go. Cooling --gt lower density --gt lower
gravity. Cooling is a function of lithospheric
age. Know lithospheric age --gt can calculate
lithospheric cooling --gt can calculate
gravitational signal of lithospheric
cooling. Subtract gravitational signal of
lithospheric cooling from MBA. Result Residual
mantle Bouguer anomaly (RMBA)
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Marine gravity corrections
Example Southwest Indian Ridge (SWIR) Will mail
out PDF of Georgen et al. (gravity variations
near hotspots along the SWIR). Another reading
Turcotte and Schubert, chapter 5 (outside office
tonight).