  In this work we study the evolution of the free boundary between two
different fluids in a porous medium where the permeability is a two dimensional
step function. The medium can fill the whole plane $\mathbb{R}^2$ or a bounded
strip $S=\mathbb{R}\times(-\pi/2,\pi/2)$. The system is in the stable regime if
the denser fluid is below the lighter one. First, we show local existence in
Sobolev spaces by means of energy method when the system is in the stable
regime. Then we prove the existence of curves such that they start in the
stable regime and in finite time they reach the unstable one. This change of
regime (turning) was first proven in \cite{ccfgl} for the homogeneus Muskat
problem with infinite depth.
