Mathematical Methods in Geophysics

The course provides the physical-mathematical notions necessary for the modeling of the global dynamics of the Earth. The student will learn to represent vectorial and tensor fields in a generic coordinate system and to solve the moment and Poisson equations for a self-gravitating, compressible viscoelastic planet. These methodologies allow the student to understand several geological and geophysical processes in terms of topographical perturbations of the surface and of the internal interfaces of the Earth, as well as of gravitational anomalies associated with the mass redistribution within the mantle and the lithosphere.

Capability to understand the physical laws that govern the dynamics of the planet both at global and local spatial scales and the transition from elastic to fluid behavior.
Capability to model the deformations due to the Earth's rotation, to surface and internal loads (like a glacial shield and the density anomaly of a sinking slab) and to earthquakes.