This PR adds functional support of boule Ellipsoid classes in many pyshtools routines. To use this PR, you must first install boule version 0.5 or greater.

Create a grid of an ellipsoid using one of the boule predefined ellipsoids:

grid = pysh.SHGrid.from_ellipsoid(ellipsoid=boule.Mars2009, lmax=100)
grid.plot()

Create an area-weighted histogram of spherical elevations with respect to an ellipsoid:

grid = pysh.datasets.Mars.MOLA_shape().expand()
hist, bin_edges = grid.histogram(ellipsoid=boule.Mars2009)
fig, ax = grid.plot_histogram(ellipsoid=boule.Mars2009, bins=100)

Plot spherical heights with respect to an ellipsoid

fig, ax = grid.plot(ellipsoid=boule.Mars2009, colorbar='bottom')
figure = grid.plotgmt(ellipsoid=boule.Mars2009, colorbar='right')
figure.show()

Create grids of the spherical gravity vector components, gravity disturbance, and gravity potential on a rotating ellipsoid

clm = pysh.datasets.Mars.MRO120F()
grids = clm.expand(ellipsoid=boule.Mars2009)
grids.plot()

Create grids of the gravity gradient tensor on a flattened ellipsoid

grids = clm.tensor(ellipsoid=boule.Mars2009, degree0=True)
grids.plot()

Create a grid of the geoid height with respect to an ellipsoid

geoid = clm.geoid(boule.Mars2009)
geoid.plot()

Create grids of the magnetic field tensor on a flattened ellipsoid

glm = pysh.datasets.Mars.Langlais2019()
grids = glm.tensor(ellipsoid=boule.Mars2009)
grids.plot()

Notes

• Almost all of the real calculations are performed using pre-existing pyshtools routines (fortran or python). The boule ellipsoids are used only to obtain ellipsoid parameters such as a, b, c, f, omega, GM, reference_normal_gravity_potential.
• Neither boule nor pyshtools compute the normal gravity of a triaxial ellipsoid (yet).
• The vector components of the gravity and magnetic field are for spherical components, r-hat, theta-hat, and phi-hat. r-hat and theta-hat are not normal and tangent to the ellipsoid. The transformation from spherical components to geodetic components will be implemented in a future release or PR.
• All heights above the ellipsoid are spherical heights, and not geodetic (ellipsoidal) heights that are measured normal to the ellipsoid.