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Lecture 4 January 24, 2008

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... anomalies are more prominent in the FAA map than they are in the geoid. ... gathering references about gravity in Hawaii, and maps and other images of the ... – PowerPoint PPT presentation

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Title: Lecture 4 January 24, 2008


1
Lecture 4 January 24, 2008
  • Geoid, Global gravity, isostacy, potential, field
    methods

2
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3
Integrator
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4
The world map on the next slide shows the FAA
anomaly for the world. Notice several things
the short wavelength anomalies are more prominent
in the FAA map than they are in the geoid. The
short wavelengths are well correlated with
tectonic boundaries.  continental boundaries
that are not bounded by subduction zones are
subdued. The GEOID is referenced to the center of
the earth. The FAA is referenced to SEA LEVEL.
What does this imply about the values of the FAA?
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7
Homing in on some areas
8
Iceland gravity contains considerable information
about the tectonics of the mid-Atlantic ridge.
9
Lunar Gravity
10
Mars Gravity
11
Isostacy
Much like ice bergs in the ocean, the earth's
crust "floats" on the mantle. While not a liquid,
the viscosity of the mantle is low enough to
allow the crust to push mantle material away to
equalize pressure. This is the theory of
ISOSTACY. In more modern terms, the lithosphere
floats on the asthenosphere, and the lithosphere
has a much lower viscosity than the upper mantle
below the crust.
12
Physics of isostacy The pressure at the base of
a column of earth depends on the height of the
column and its density. Pressureforce/area
Mg/area height(x-sectional area)
?????????????/area height?
13
If a column has more than one density, the masses
add linearly to give pressure?1h1?2h2
14
In a fluid, the pressure at any depth is a
CONSTANT given by the pressure of the column
above. Ice berg ?ice????? gm/cm3 ?sea
water?????? gm/cm3 An iceberg goes to a depth of
50m in sea water. What is it's height above sea
level?
15
Two models of isostacy Pratt Density of each
column above the "compensation depth" varies to
keep the base of the crust flat
Airy Densities of each column is constant,
higher columns also extend deeper
16
Which theory is correct Can we tell from
gravity? Remember PrattFLAT
  • Homework for Tuesday
  • You take a boat out into a small lake and pick up
    a large rock from the bottom of the lake and put
    it in the boat. Does the level of the lake
    change? Explain your answer.
  • An huge iceberg floating in the ocean melts. Does
    sea level change? Explain your answer in terms of
    isostacy.

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18
Field Methods
  • Before the field work
  • collect background information
  • maps, (roads, topographic)
  • references, previous data
  • geologic background
  • check instruments
  • gravimeters, GPS, cell phone contacts, vehicles
  •  plan station locations
  • choose site easily identified on maps

19
in the field
  • Set up the GPS and start averaging data.
  • Pick a safe, stable site for the meter reading,
    and begin reading.
  • locate yourself on a map or air photo. Label the
    map with the station number.
  • Take pictures of the area to aid in re- location.
  • Record all information - including REDUNDANT
    information.

20
Your first big lab begins next week. Begin
gathering references about gravity in Hawaii, and
maps and other images of the Kawainui Swamp
region of Oahu. No restrictions. Get anything you
can to improve your results.
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22
Gravity over a sphere
We can calculate the gravity at a distance x from
a buried sphere of density ?, depth zz, and
radius RR using the gravity formula or by
calculating the potential.
23
Using the gravity formula, remember that we only
want the vertical component recall
where r is the distance to the center of the
sphere, and M is the mass of the sphere.
We only want the vertical component of g, so we
need to multiply by the sin (Atan(zz/x))
24
To get the same result using the gravity
potential, we calculate the potential from the
sphere at two nearby points, one directly above
or below the surface. Recall
We calculate the potential at two points at each
x with zzazz.1, and zzbzz-.1. The value of g
is then
Calculating g in both ways yields identical
results.
25
simple profile models
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