Lecture 2 GRAVITY CLASS WEBSITES Lectures Labs http://moho.ess.ucla.edu/~pdavis/ESS135_2013/ Labs http://crust.ess.ucla.edu/~igor/ESS135/2013/

New Class Time Thurs 8-9:30 Fri 8-9:30

UCLA Student taking gravity reading

As a first approximation the Earth has an ellipsoidal shape, wider at the equator. A better approximation is the geoid (height) which measures the variation of shape relative to the ellipsoid. This variation is caused by mass heterogeneities

Geoid The geoid is the potential due to gravity. Potential is proportional to mass but decreases with distance away. The geoid is the shape of the ocean surface, i.e. defines sea level. On land the geoid is the height the water in a canal would have if it were connected to the ocean (this can be calculated using surveying methods, gravity, GPS) A (+) mass heterogeneity has more mass so the geoid rises above it.

A liquid surface is an equipotential (same potential) Surface Ocean equipotential seamount Ocean floor Ocean floor rise over a seamount (or drops above a trench) because to keep the absolute value of potential the same the increase due to the seamount is compensated by a decrease as you move away from the rest of the earth (Note potential is negative).

The Global Geoid: A ship sailing from s. India to s. Africa rises

Seamounts, trenches, and pull-apart basin as detected by the Geoid measured from satellites. Note underwater seamounts are eroded flat. Smith and Sandwell

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Gravityis the negative gradient of potential Since from Given a gravity survey you can sum the normal gravity field Times area to obtain the anomalous mass.

Calculate excess mass: Sum area times g divide answer by 2πG

Gravity measures the force of attraction of the Earth which Depends on the mass distribution through Newton’s law of Gravity Force= G m1m2/r2=m1g

Gravity from an Infinite Slab gz R h gz

Gravity changes at different elevations in mines tunnels or buildings g2=gE2+gb gb g1-g2= gE1 -gE2 -2gb g1=gE1-gb gE

Gravity Cylinder z dy x R z

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