# [aspect-devel] Fwd: geoid

Wolfgang Bangerth bangerth at tamu.edu
Mon Apr 20 12:31:23 PDT 2015

```[Forwarding this on Scott's behalf.]

-------- Original Message --------
Subject: geoid
Date: Mon, 20 Apr 2015 13:13:45 -0400
From: Scott King <sdk at vt.edu>
To: Wolfgang Bangerth <bangerth at math.tamu.edu>

Hi;

Your point about the gravity vector not being vertical but relative to the
geoid is an interesting one.  I think we have always considered that second
order, but it would be interesting to know.  Actually most of my career I
thought of the earth as a 2D box!!!    This image is from an older paper of
mine, but others have produced much the same.    The red line in the middle is
dynamic topography, blue is the gravitational contribution from a internal
density anomaly.   One  of the things Brad (Hager) is famous for, is
recognizing that the geoid from tomography would not be like the figure on the
left (what seismologists originally thought) but would have a contribution of
dynamic topography.  Further if you assumed a uniform (with depth) mantle,
this you got the middle picture (geoid lows over subduction) but what we
observe is geoid highs over subduction (originally why seismologists were
pleased with the static earth calculation).   This became the origin of the
argument for a jump in viscosity in the lower mantle (figure on the right).
This was all done with propagator matrices and semi-analytic 3D techniques in
the late 70's and early 80's.

So this is all ancient history and somewhat esoteric geodynamics, but it is
part of why I'm interested not only in the dynamic topography but also the
geoid anomalies as output.  It seems like Ian and Rene are working on this.
I'm glad to know that.  I will make sure Shangxin hooks up with them.   He has
been looking at dynamic topography as a function of element type.   I've
always wondered, since the usually computation of dynamic topography depends
on stress and stress is less accurate than velocity, just how does the low
order that we use affect the result.   As you can see from the plot, since
dynamic topography and internal mass anomalies are of opposite sign, a
smallish error in one can lead to a big error in the total geoid anomaly.

Indeed it would be a very interesting study to include the shape and geoid
relative to the local geoid and compare with a spherical Earth.  My gut
reaction is that this will not be a significant effect, but I don't know that
anyone has ever looked at this.  Just too much going on to sit down and try.

Best,

Scott

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