Measuring the geoid. What is the geoid?

During my weekly fitness session with one of my friends, we started discussing gravity (yes, also my friends are geeks (in the good way)). We discussed the measurements done by Vening Meinesz in the K18. He used I pendulum device, that directly measures the downward gravity attraction in the location of the device, plus all the motions of the device itself. On land, these motion are negligible, but on sea the device swings a lot due the ocean waves. Therefore, Vening Meinesz used a submarine to reduce the motions of the measurement device (waves are dampened underwater). Furthermore, he used three pendulums instead of one, which he ingeniously used to separate the motions of the device and the gravity attraction. Explaining this all to my friend, he remarked that it sounded very complicated and asked me if this could be done more easy. "Yes, this is possible", I replied, "with a GPS receiver". "How is it possible to measure Earth's gravity field with a GPS receiver?", my friend replied. You do not measure the gravity directly like Vening Meinesz, but with some cool mathematics, you can get a pretty good idea.

In order to explain what the geoid is, I have to first introduce a different concept. The Earth is not flat (you know this, some just don't accept this), but it is also not a sphere (really?!?). It is more like a flattened sphere, or ellipsoid if you use the proper term. As if the poles of the sphere are pressed inward. Actually, pulled inward. This is because of the rotation of the Earth and the Earth's viscoelastic behavior (in less scientific terms, this means that the Earth is slightly mushy). The ellipsoidal shape is even not true, because the Earth has bumps on its surface. However, we can approximate this shape with a mathematical ellipsoid. The differences from this shape, we call undulations.

The geoid, roughly follows an ellipsoid like this, but has the humps and bumps discussed earlier (undulations). Those undulations, or deviations from the ellipsoid are very interesting and can give us information about processes beneath the surface. So it is worth measuring this shape.

The figure represents the 3D view of the geoid, where we exaggerate the radial variations. The blue colors represent areas where the geoid is below the mathematical ellipsoid and the red areas are above the ellipsoid.

The cool thing about the geoid is that the sea level follows this surface, when there would not be any winds or currents, perturbing the ocean surface (Ok, and you neglect tidal forcing, solid Earth movements and hydrology. But who is not doing this!). So in a sense, when you sail the oceans, you actually follow the curved gravity field of the Earth, called the geoid. Lets make use of this.

My friend (introduced in the beginning) is currently on his way to New Zealand, where he will board the sail boat, "Oosterschelde". This large, three mast, sailing ship will set sail to the Falkland islands (the hard way). They will cross the Indian Ocean, around Cape Horn, and across the South Atlantic Ocean, without stopping at a harbor. During this 50 day trip, my friend will place a GPS device (for the electronic geeks: GARMIN GPS 60CSx. In good conditions, this device can have an accuracy of 2m) and track the location and altitude of the ship.

You would think, "The altitude must be zero (plus the offset on the boat), because the boat is at sea level". However, the GPS receiver will measure its 3D position with respect to the mathematical ellipsoid (WGS84). So it should differ, because it will follow the geoid not the ellipsoid :)

By how much? Well, the Indian Ocean has the largest negative geoid anomaly (the big blue dent in the figure), of more than 100 meter !!! This would be visible, with my 2m accurate, so let the observations begin. In three weeks, he will set sail across some off the most dangerous oceans, but he will manage! On christmas eve, he will be back in Holland. I will let you know, what he observed.