Mathematical physics in stratified media

 

In stratified media there are many common mathematical aspects in phenomena so physically diverse as acoustics, electromagnetic waves, magnetostatics, gravitational-elastic spherical resonance, heat flow, gas diffusion, electric current in a resistive material, seismic waves, water waves, and atmospheric gravity waves, among many others. We will present the general theory and work out some of the details for the case of simple acoustics.

By a stratified medium we mean one in which material properties, compressibility, conductivity, density, etc., are functions of one spatial coordinate only. The usual situation is cartesian coordinates, but when geophysics is done on a global scale spherical coordinates may be used.