Geodetic measurement of Earth growth

[Florian]

There is a recent attempt to measure the global rate of growth using geodetic means.
This is a collaborative work between the JPL and the IGN (France) and some Dutch people.
This work was published in Geophysical Research Letters under the title "Accuracy of the International Terrestrial Reference Frame origin and Earth expansion" and there was a new article on the JPL news website:NASA Research Confirms it's a Small World, After All.

I had the opportunity to discuss this GRL paper with one of the co-author from IGN.

We discussed details on the model and data they used and I identified 2 important flaws.

First they deliberately selected stations outside of regions that actively deform (orogens, active margins, post glacial rebound).

ITRF2008 geocentric velocities from a global network of 233 SLR, VLBI and GPS sites distributed as evenly as possible are selected and supplemented by the published and transformed (to ITRF2008) continuous and episodic GPS velocities at 448 sites in North America, Fennoscandia, Alaska, Antarctica and Greenland [Wu et al., 2010 and references therein] (see Figure 1 for site distribution). They are not located in orogenic or local tectonic areas and are at least 200 km away from plate boundaries. Sites with suspected sediment loading or man‐made ground water extractions are also excluded.

So they eliminate from their database every station that would be affected by important geodynamic processes. This simplification is a rather unfortunate choice knowing that these geodynamic processes are part of the expression of the growth.

Let's use a practical simplified example to illustrate why.
Let's say we have a ball of clay. This ball of clay is injected at its core with fresh clay using a syringe. The injected fresh clay did not stay inside the ball, but found its way toward the ball surface and extruded. What is the most appropriate method to measure the increase in volume of the ball due to the clay injection?
1: a method excluding the area where the fresh clay extruded and focusing the measurement on the undisturbed surface?
2: a method measuring the whole deformation of the ball and especially focusing on the area were clay got extruded?

By analogy, Wu et al used method 1. Excluding the active regions is equivalent to discard a lot of data accounting for the growth.

Second, they used a plate model to account for horizontal displacement and simply add a unique global vertical component to account for vertical displacement (radius growth).

ITRF2008 origin drift components and a mean solid Earth expansion rate are estimated and resolved simultaneously with rigid plate motions.
[...]
The sum of the next three terms is the site velocity in the CE frame r_i caused by radial expansion, plate motion, PDMT loading and GIA. R_ is the constant mean radial expansion rate of the solid Earth.

Thus they assume a global growth with spherical symmetry independent on lithosphere horizontal motion. Interpreting horizontal velocities in term of plate motion is big flaw.

In the auxotectonics model, the lithosphere does move relatively to a fixed referential frame in response to the inner growth, and this includes horizontal velocities. We also know from the age of seafloor a spreading rates at Mid Ocean ridges that the growth is asymetrical (much larger in the southern hemisphere). Let's illustrate it using a simple scheme:

GPS-horizontal.jpg (30.83 KiB) Viewed 4089 times

The outflow of mantle material induces horizontal shear and tension at the surface. The rigid shell breaks apart, thus forming a spreading ridge. The two opposite sides of the ridge diverge, so we measure a relative horizontal displacement.
Over a time span of millions of years, the relative displacement can be very important as illustrated by this simplified scheme illustrating the relative northward drift of India:

india-N-drift.jpg (52.25 KiB) Viewed 4090 times

The horizontal velocity contains information about the global growth rate and must evidently be used to calculate the rate.

But in the Wu et al paper, they excluded the horizontal velocities from the measurement of the growth and instead, use it in an additional component, a plate model.
This does not make any sense. Either they must use a plate model or an expanding earth model for all the components of the vector, but not a mix of them! Actually they should not even separate the vertical and horizontal components of the vectors, since what we truly want to measure at our timescale is a global deformation of the surface of earth, to verify if this global deformation corresponds to a global increase in volume.

Obviously, this combination of data and model choices can't measure a growth as we know it : asymetrical (much larger in the southern hemisphere), occurs locally by bulging (orogens) and concurrent or subsequent isostatic adjustment, including gravity gliding.

This paper is unfortunately biased by premises and simplifications which arise from the plate tectonic model. A good example of circular reasoning.
The background issue is that the growth is much more difficult to modelize than the relatively simple rotations of plates around euler poles of the kinematic plate model. Hopefully, geodesists will be able to build the necessary tools and models to measure the complete deformation of Earth's surface, including that under the ocean, and thus measure the growth of Earth.