Transcript Field, Isostacy

Lecture 4
January 24, 2008
Geoid, Global gravity, isostacy,
potential, field methods
a
area=
velocity
time
b
slope=a
area=
displacement
b=a(t1-t0)
time
slope=b
c=(1/2)a(t1-t 0)2
c
t0
t1
time
Integrator
at+v0
vt+d0
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?
Homing in on some areas:
Iceland gravity contains
considerable
information about the
tectonics of the midAtlantic ridge.
Lunar Gravity
Mars Gravity
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.
Physics of isostacy:
The pressure at the base of a
column of earth depends on
the height of the column and
its density.
Pressure=force/area
=Mg/area
=height*(x-sectional area)*
/area
=height*
If a column has more
than one density, the
masses add linearly to
give:
pressure=1h1+2h2+…
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?
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:
Which theory is correct: Can we tell from gravity?
Remember: Pratt=FLAT
Homework for Tuesday:
1) 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.
2) An huge iceberg floating in the ocean melts.
Does sea level change? Explain your answer in
terms of isostacy.
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
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.
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.
Gravity over a sphere
x
zz
.
RR
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.
Using the gravity formula, remember that we only want the
vertical component: recall:
g  GM /r
2
where r is the distance to the center of the sphere, and M is
the mass of the sphere.

4
r  x  zz , M   (RR)3 
3
2
2
We only want the vertical component of g, so we need to
x
multiply by the sin (Atan(zz/x))

zz
1
g  G  mass sin(tan (zz / x)) / x  zz
2
2
gz
g
.
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:
U  GM/r
We calculate the potential at two points at each x with
zza=zz+.1, and zzb=zz-.1.
The value of g is then:
gz  Ub U a  / z
Calculating g in both ways yields identical results.
simple profile models