# Gravity anomalies : geoid v reference ellipsoid

1. Sep 22, 2008

### JP O'Donnell

Hi.

When reducing the value of measured gravity to produce gravity anomalies, the measured gravity is reduced to it's value on the geoid (conventional interpretation). This is then compared to the value generated by the reference ellipsoid at the ellipsoid surface.

I would have thought that measured gravity should be reduced to it's value at the reference ellipsoid rather than the geoid for comparison.

But I've read (without explanation!) that the value of reduced gravity at the geoid is exactly comparable to that on the reference ellipsoid.

This result is somehow tied up in the consideration of the respective potential fields...but I don't understand how...

Any explanations welcome (except those stating that the geoid undulation can be neglected!)

Thanks.

2. Sep 22, 2008

### billiards

Hi, correct me if I'm wrong but I am relying on memory here...

Isn't correcting to the reference ellipsoid to do with latitudinal variations of gravity? Because g varies with latitude (where at the equator it is at minimum and at the poles maximum) to normalize the global field you need to correct for latitude.

And correcting to the geoid would be to correct for height, where the geoid is the datum (roughly at mean sea level), i.e. you would want to correct your data from the top of the mountain so it is comparable with data at sea level, this would be achieved via the free air correction and the Bouguer correction.

I could be wrong, but that seeems to make sense to me.

3. Sep 22, 2008

### D H

Staff Emeritus
First off, what "conventional interpretation"? I suggest you read this paper,
D.A.Smith, There is no such thing as "The" EGM96 geoid: Subtle points on the use of a global geopotential model, IGeS Bulletin No. 8, International Geoid Service, Milan, Italy, p. 17-28, 1998

Six of one, half dozen of the other. One can compute the gravitational acceleration at any point given a set of spherical harmonics coefficients. (The computed value for points below the surface of the Earth will of course be incorrect.) The intent of these reductions is visualization, not computation of gravitational potential or force. It is much, much better to directly use the spherical harmonic coefficients (and some tidal model) if you want to compute the potential (or acceleration, or gravity gradient) at some point. The graphical reduction is better if you want to use graphical techniques to search for oil, for example, and to do that you need to get rid of the gross deviations such as those resulting from J2.

4. Sep 23, 2008

### JP O'Donnell

Billiards - removal of the gravity effect of the reference ellipsoid is indeed referred to as a latitude correction. Removal of this latitude dependent term results in a gravity anomaly which, upon further reduction, may be used for geological interpretation.

The further (main) reductions are the Free-Air reductions, simple/complete Bouguer reductions like you mention...

My gripe was that, in the Free-Air correction for example, measured gravity is reduced to the geoid from which normal gravity (at appropriate latitude) at the reference ellipsoid surface is subtracted. I thought that measured gravity should be reduced to the same eillipsoid level for comparison, rather than a comparison based on different points.

D H - By the conventional interpretation, again taking the Free-Air anomaly as an example, I mean the reduction of measured gravity to the geoid for comparison with normal gravity. This would involve knowing the vertical gradient of real gravity and an assumption that no mass exists between station level and the geoid. The vertical gradient of real gravity is frequently unknown and the second assumption is just not correct. A modern interpretation is the raising of normal gravity to the station level using the vertical gradient of normal gravity (known). The assumption that of no mass between between station level and ellipsoidal surface is now obviously satisfied also.

I should say that I am ultimately interested in the location of causative density anomlies by inversion of gravity anomalies.

My confusion over measured gravity at the geoid versus theoretical gravity at the ellipsoid may be due to the fact that they have to be compared at these levels. These surfaces have the same potential implying the same contained mass. I am trying to isolate mass anomalies. Measured gravity reduced to the geoid (conventional interpretation) relates to the total mass of the earth, while theoretical gravity at the reference ellipsoid relates to the same total mass. So unless they are compared at these levels we are dealing with different overall masses and therefore anomaly interpretation is messed up.

No doubt a spherical harmonic expansion of the potential with accurate coeffients is the way forward. But I believe the above problem remains - for isolation of the anomaly causative source you need to compare measured and calculated potentials (converted to gravitational attraction), and they will have to be compared on equipotential surfaces, to ensure you are dealing with the same overall mass in each case. However these surfaces will in general not coincide spatially.

This is my own interpretation as it stands, and I could well be wrong! So any corrections welcome...