gravity correction excludes the effect of the polar flattening about shtools HOT 3 CLOSED

I made the following changes to the jupyter notebook

It is immediately obvious that the Bouguer anomaly plot has a large component associated with the flattening of the planet: This is because the Bouguer correction was computed for relief with respect to a sphere, and not with respect to a flattened ellipsoid. To compute the Bouguer anomaly with respect to a flattened ellipsoid, it is only necessary to add the gravity coefficients of the flattened ellipsoid to the bouguer coefficients. Here, for simplicity, we assume that the reference flattened ellipsoid has a constant density:

b = constants.Mars.b.value

ellipsoid = pysh.SHGrid.from_ellipsoid(lmax=bc.lmax,
                                       a=a,
                                       b=b)
clm_ellipsoid = pysh.SHGravCoeffs.from_shape(ellipsoid,
                                      rho=2800.,
                                      gm=clm.gm)

clm_ellipsoid = clm_ellipsoid.change_ref(r0=clm.r0)
bouguer_ellipsoid = bouguer + clm_ellipsoid
bouguer_ellipsoid_grid = bouguer_ellipsoid.expand(lmax=95, a=a, f=f)
fig8, ax8 = bouguer_ellipsoid_grid.plot_total(cmap='RdBu_r', show=False)

What do you think?

The problem is that we really should have a routine that computes the spherical harmonic coefficients of the reference sphere using something like the Somigliana formula. We would either need to write this from scratch, or perhaps use the Boule project to do this. My goal is to use Boule at some point, but I just haven't had the time to work on this.

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Thanks Mark, adding the gravity coefficients of the flattened ellipsoid to the bouguer coefficients seems correct and does work. But the result still seems to contain a large component (associated with the hemispheric dichotomy?) since it doesn't have any small-scale features as those are represented in the free air anomaly / topography.

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The shape of Mars (when referenced to a flattened ellipsoid) has a large degree-1 component, so the Bouguer anomaly will also have a large degree-1 signal. This degree-1 Bouguer anomaly is most likely a result of hemispheric variations in crustal thickness.

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