Working with partial data for surface and volume processing in geosciences

Proposes several methods to get a regular surface from partial data (Lagrange or Hermite data, tangential planes, data along curves, or surface patches). The originality of these approaches is that one always takes into account the characteristics of the data in the energy functional minimized. The authors address the problem from a mathematical point of view, and show applications to geophysical data coming from ship-track bathymetry measurements (from the Kermadec and Tonga trenches), from surface patches (obtained after geophysical processing such as migration of time-maps or depth-maps) and from Digital Elevation Models (DEM) of the Pyre´ne´es mountains at the border between France and Spain