Inversion for ocean depth and core-mnatle boundary depth

For any possible combination of thermal structure and composition, we find the depth of the ocean and of the core-mantle boundary which best fits the mass and moment of inertia of Europa. For any physical structure, the uncertainties on those two depths are quite small and are mainly due to the uncertainty of the gravitational constant (fig. 1).

We choose to not invert for the gravity acceleration (g) profile, which requires tedious iterations because of the feedback with the density profile. Instead, we approximate the gravity profile by pre-computing the values at the core-mantle boundary (assuming an average density of the core, based on the composition used), at the ocean bottom (assuming an average density of the water-ice layer combined with information about Europa's total mass) and by taking the known values at the surface (circa 1.31 m/s$^2$) and at the center (0) and by interpolating linearly between these points. The resulting gravity profile is sufficiently accurate, and does not noticeably affect our results.

Figure 13.54: Example of determination of the ocean depths and core-mantle boundary for one physical structure. Yello-reddish contours are for mass value, blue for moment on inertia values. The green ellipse is the field of possible combination of the two depths to fit mass and moment of inertia
\epsfig{file=cammarano05_2_1.eps, width=8cm}\end{center}\end{figure}

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