Gravity Anomalies

In January 2005 the USS San Francisco encountered a seamount south of Guam, causing substantial damage and killing one crew member.  In the southern ocean, shipping lanes are far apart and detailed mapping very sparse, and our best knowledge of the bathymetry generally comes from satellites measuring variation in the the earth's gravity field and the resulting changes in the sea surface.  The earth's gravity field is normally given by the equation

F=GMm/rē

which works well when we can consider M to be the mass of the earth, and m the object being attracted, and view both as point masses.  If we want to consider the small differences in gravity that will result from variations in the distribution of mass within the earth, we might have to use calculus:

 

M, instead of simply being the mass of the earth, will be the mass distribution in three dimensional space, and we have to consider both the density of anomalous material, and the distance away from our gravity meter.  In Figure 1, we have three ways of covering the ocean with the gravimeter to measure the value of gravity: towing it in mid-ocean depths (A1 to A3), putting it on a ship near the surface (B1 to B3), and flying it on a plane or satellite (C1 to C3).  The seamount will have a specific gravity ρ=3.0, and the seawater will have ρ=1.0.  Near the seamount, we will have rock replacing water, so we have more mass, and because it is close, the inverse square fall-off will be much less and we will see a substantially larger value of gravity.  The difference will be greatest for the deep towed instrument, because as we go from A1 to A3, the relative distances change significantly.  At the sea surface, B1 to B3, the differences in relative distance to the mass anomaly will be less drastic, and we will have a harder time picking out the actual size and shape of the seamount.  If we have to fly the sensor (C1 to C3), our resolution becomes even less, and a satellite will be hundreds of kilometers up.  We will still see a slightly higher value for gravity at C1 compared to C3, but in nothing like the detail for the deep towed instrument.

  Figure 1.  Seamount, with nine locations at which we might measure the earth's gravity field.

If there are different values of gravity at B1 to B3, the sea surface will respond.  Sea level is a gravitational equipotential surface, with the water at no place having a tendency to flow downhill as it would at B3 if the sea surface were truly flat.  B1 will have a higher sea surface than B3, by about 1/1000th of the height of the seamount above the ocean floor.  The seamount thus might have sea level a few meters above normal, but spread over a few tens of kilometers horizontally, so the slope will be very small (tangent about 3/30,000, so angle essentially 0, since for a small angle, the tangent equals the angle).  Nevertheless, we can measure these changes in the sea surface from space, and the "best" maps of the entire ocean floor have been measured using radar altimeters from space, and then work back to likely mass distributions on the ocean floor that can translate into ocean depths.  The resolution is not great, and while we have detected a large number of seamounts, we had not previously detected the seamount encountered by the San Francisco.

Interpreting the results can be complicated, because in addition to the ρ=3.0 seamount, we might have ρ=3.3 upper mantle involved, the shape of the seamount might not be a cone, and there is likely to be a "moat" around the seamount where the crust subsided due to the weight.  Despite the shortcomings, measuring anomalies (changes for the expected values) in gravity and the sea surface are powerful tools for geologists, but we must always consider that there could be multiple ways to get the observed patterns we see.

Gravity has been used to search for seamounts, and was in fact the first use of scientific geophysics used to look for oil.  Many oil fields in the Gulf Coast region are associated with salt domes (ρ=2.2) which will be substantially less dense than the rocks around them (ρ=2.7), and the use of gravimeters led to the discovery of many oil fields and convinced the oil company managers that employing scientists made sense. 

Gravity anomalies can map the geoid, and provide an estimate of water depth.


Last revision 2/7/2015