Prospects for the Representation of Geophysical Fields from MESSENGER Observations of Mercury Using Harmonic Radial Bases

At present, the most common representation of global planetary geophysical data is a spherical harmonic expansion. While this representation is suitable for data that are well distributed globally, it does not adequately represent datasets with highly variable resolution. Many geophysical datasets are acquired in a fashion that produces a very unevenly resolved distribution of observations. For example, the gravity and magnetic field data to be acquired during the orbital phase of the MESSENGER mission to Mercury will have highly variable spatial resolution at the surface because of the spacecraft's strongly elliptical orbit. Due to the nature of potential field continuation, data acquired from higher altitudes will be biased towards longer wavelengths and poorer spatial resolution than data acquired at lower altitudes. Representations of data that can faithfully accommodate variations in resolving power and allow for such data processing operations as interpolation, continuation, differentiation, and integration are necessary make to full use of observations with large variations in resolution. A harmonic radial basis is well suited to these tasks. Further, incorporation of this basis into the spherical spline approach can accurately represent the data, regardless of distribution. Accuracy tests of several reproducing kernels (e.g. Green's functions, Abel-Poisson, logarithmic) demonstrate the advantages and disadvantages of this class of representations relative to spherical harmonics for datasets that are non-uniform over the sphere in either distribution or resolution. We discuss the results of modeling aimed at quantifying how well this approach, relative to spherical harmonics, could recover the gravity field at Mercury based upon the expected orbit of MESSENGER during the orbital phase of the mission.