In the elasticity theory, you can derive waves equation from the fundamental equation of motion for an elastic linear homogenues isotropic media:

$\rho \partial^2_t \overline{u} = \mu \nabla^2 \overline{u} + (\mu+\lambda) \nabla(\nabla \cdot \overline{u})$

But in seismology trattation, you introduce scalar and vector potentials for the P and S component of the displacements, derive waves equation for them and use them.

Now, in electrodynamics you can derive from Maxwell equations the waves equation for Fields and for Potentials; but there you use the potentials because they compose a quadrivector. In geophysics what's the convenience of it?

In the elasticity theory, you can derive a wave equation from the fundamental equation of motion for an elastic linear homogeneous isotropic medium:

$\rho \partial^2_t \overline{u} = \mu \nabla^2 \overline{u} + (\mu+\lambda) \nabla(\nabla \cdot \overline{u})$

But in the seismology tradition, you introduce scalar and vector potentials for the P and S components of the displacements, derive wave equations for them and use them.

Now, in electrodynamics you can derive from Maxwell's equations the wave equations for Fields and for Potentials; but there you use the potentials because they compose a quadrivector. In geophysics what's the convenience of it?