Geodetic measurement of Earth growth

[Florian]

A recent attempt is to measure the global growth rate using geodetic means.
This is collaborative work between the JPL, 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-authors from IGN.

We discussed details on the model and data they used, and I identified two critical flaws.

First, they deliberately selected stations outside 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 every station affected by critical geodynamic processes from their database. This simplification is a rather unfortunate choice, given that these geodynamic processes are part of the expression of 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 best measure of the ball's volume increase 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, mainly focusing on the area where clay was extruded.

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

Second, they used a plate model to account for horizontal displacement and added a unique global vertical component 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 following 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 global growth with spherical symmetry independent of horizontal lithosphere motion. Interpreting horizontal velocities in terms of plate motion is a big flaw.

In the auxotectonics model, the lithosphere moves relatively to a fixed referential frame in response to the inner growth, including horizontal velocities. We also know from the seafloor spreading rates at mid-ocean ridges that the growth is asymmetrical (much more prominent in the southern hemisphere). Let's illustrate it using a simple scheme:

GPS-horizontal.jpg (30.83 KiB) Viewed 4431 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 4432 times

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

However, the Wu et al. paper excluded the horizontal velocities from the growth measurement and instead used it in an additional component, a plate model.
This does not make any sense. They must use a plate or an expanding earth model for all the vector components, but not a mix! They should not 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 the earth to verify if this global deformation corresponds to a worldwide increase in volume.

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

Unfortunately, this paper is biased by premises and simplifications from the plate tectonic model, which is a good example of circular reasoning.
The background issue is that the growth is much more challenging to model than the relatively simple rotations of plates around the 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 calculate the growth of Earth.