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

a  t+v 0 v  t+d 0 Integrator

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 mid- Atlantic 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=  1 h 1 +  2 h 2 +…

In a fluid, the pressure at any depth is a CONSTANT given by the pressure of the column above. Ice berg:  ice  gm/cm 3  sea water  gm/cm 3 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 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: 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))

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 zz a =zz+.1, and zz b =zz-.1. The value of g is then: Calculating g in both ways yields identical results.

simple profile models