Isostatic Topography and Geoid
have been
recognized quite a long time ago: beginning of the last century? Then, scientists suggested that what we see on the
Earth surface is actually only "upper part of an iceberg" - the main structure is hidden below the sea level.
In another words: the crust is in an isostatic equilibrium. As an iceberg, the long-lived crustal formations are
mainly submerged into the upper mantle.
Since the ice is much heavier than air and lighter than water (the whole atmosphere above you weights
as much as 10 meters of water, or only 3 meters of rocks below your feet!), the height of what sticks out in the
air is much less of what is hidden below.
Only few years ago scientists managed to reconcile all the data and came up with more or less detailed crust
structure. This gave us an opportunity to analyze how much of the observed topography is "an iceberg cup" and how
far deep it continues. Of course, doing this we assume that the crust is preserved over long times and tends to
reach isostatic equilibrium, so we call this crust-related topography - static. In contrast, the topography
created by the mantle flow is often referred to as dynamic topography. But what we see at the surface is the total
topography, which brings up the question: how to distinguish between the static and the dynamic topographies?
Suppose you estimated the static part of the total topography, then you could assume that the rest of the
topography is due to the mantle dynamics. So, can we understand how does the mantle convection build up this
dynamic topography?
There are a few more tricky questions, of course, which we discuss and analyze in
the GJR paper. If you follow the next two links, you can download
spherical harmonic expansions (up to l,m=25) for our model of dynamic
topography and corresponding geoid.
Here I present pictures from the paper hoping that I can share the excitement of these new results with you!
Picture above shows four fields on a 5-by-5 degree grid: two for topography (a and b), and two for geoid (c and d).
The topography is the total isobaric surface topography calculated from ETOPO5 topography that was corrected for
the topography due to isostatically compensated crust, oceanic lithosphere (two models), and tectosphere. The
oceanic lithosphere is modeled as plate cooling (a) and as half-space cooling (b). The geoid fields are the total
geoid due to isostatically compensated crust, oceanic lithosphere (two models), and tectosphere; the oceanic
lithosphere is modeled as plate cooling (c) and as half-space cooling (d). White areas have no data coverage.
The dynamic topography fields displayed above show large variations over adjacent grid-cells, which are very
unlikely to be supported by the large-scale convective flow. Those short-wavelength variations are probably
due to the errors/uncertainties in the models we used. Each component of the total field (contributions from
crust, lithosphere, and tectosphere) has uncertainties associated with the data and assumptions used to build
each model. Some areas do not have data coverage at all (e.g., West Pacific plateaus and the Arctic do not
have reliable ocean floor age data). To gain robustness in our model, we estimate the errors in dynamic
topography at every grid point. In a similar way, we calculate the errors related to the residual (observed
minus isostatic) geoid anomaly, assuming that the horizontal scales of the dynamic topography and the geoid
anomaly are similar.
The picture below shows the uncertainties in the dynamic topography (e) and geoid (f), when the oceanic
lithosphere is modeled as plate cooling. The color bar for uncertainties in dynamic topography and geoid is
clipped at 1600 m and 40 m, correspondingly. White areas have no data coverage.