Gravity Field Data
Let us assume that Earth expands globally at a rate of 4 cm/year. The acceleration due gravity on Earth’s surface can be calculated as follows:
We know the Earth’s mass and its radius. The value of acceleration for radius 6,378,000 m is:
If we change the value of radius to 6,378,000.04 m, we get:
The ESA’s GOCE Probe (2009-2013) was able to detect the variations of gravity at levels of 1 mgal, which is quite high accuracy, but not for the purpose of expansion measurement.
Let us take the first value and mark the levels of GOCE’s accuracy:
The red color marks GOCE’s accuracy, the green color marks the field of changing gravity due to expansion.
The next problem is that the gravity field has many temporal variations (atmosphere, water redistribution, sand, soils), which is another negative (noisy) effect. Thus the accuracy with respect to expansion would be even worse.
Another technique is a GPS measurement via vertical changes. Have a look at the DTRF2014 image made by the Technical University of Munich:
We see there no data from the oceanic floor. The data from Canada or Greenland (the same with Norway) indicate a clear expansion.
The problem of such data is that the Earth’s surface is in a constant motion (centimeters to meters). Another problem is the number of stations – one cannot cover the whole surface. One would also expect that the expansion would be noticeable primarily on the oceanic floor.
I also recommend a paper from Wen-Bin Shen et al. (2011):
Although we don’t have suitable vertical data today, we have a lot of other tools like VGG maps or ocean floor ages that indicate the most probable scenario for Earth’s global dynamics – expansion.