  The trajectory of energy is modeled by the solution of the Eikonal equation,
which can be solved by solving a Hamiltonian system. This system is amenable of
treatment from the point view of the theory of Differential Algebra. In
particular, by Morales-Ramis theory it is possible to analyze integrable
Hamiltonian systems through the abelian structure of their variational
equations. In this paper we obtain the abelian differential Galois groups and
the representation of the quiver, that allow us to obtain such abelian
differential Galois groups, for some seismic models with constant Hessian of
square of slowness, proposed in Cerveny 2001, which are equivalent to linear
Hamiltonian systems with three uncoupled harmonic oscillators.
