There are many mathematical problems in geosciences and many geoscientific problems require mathematics to improve their solutions. One of the important problems in geodesy is to estimate the geopotential. It is crucial for both civial and millitary uses to know as accurate as possible the geopotential near the surface of the earth. For example, from the geopotential, we can obtain the gravity vector field and the geoid. Thus, we obtain the surface of the oceans or lakes. The changes of geopotential are related to the landslides and glaciers and the movement of earth plates undernearth of the earth. It is indispensible to calculate the geopotential accurately. One of the ultimate goals of geoscientists is to predict major earthquakes from changes of the geopotential. As satellites orbit around the earth every day, the geopotential measurements are obtained daily. The volume of these data is huge and the data locations are scattered arround the earth as shown below in 3D and 2D versions.

The mathematical tools we are using are spherical splines and spherical wavelets. Spherical spline functions are smooth piecewise spherical harmonic polynomials over spherical triangulations. They are originally defined in [Alfed, Neamtu, Schumaker'96]. We devise a computational scheme which allows us to use these splines for interpolation and fitting of scattered data without constructing locally supported basis functions. See our paper [Baramidze, Lai, and Shum'05] in publication section. The following figures show the data values after a normalization (left) and a spherical spline interpolation (right). We continue working on the computation of the geopotential near the earth surface.

This section is under construction.