  In this paper we study the phase diagram of a disordered, spin-orbit coupled
superconductor with $s$-wave or $d+id$-wave pairing symmetry in symmetry class
$D$. We analyze the topological phase transitions by applying three different
methods which include a disorder averaged entanglement entropy, a disorder
averaged real-space Chern number, and an evaluation of the momentum space Chern
number in a disorder averaged effective model. We find evidence for a
disorder-induced topological state. While in the clean limit there is a single
phase transition from a trivial phase with a Chern number $C=4$ to a
topological phase with $C=1$, in the disordered system there is an intermediate
phase with $C=3$. The phase transition from the trivial $C=4$ phase into the
intermediate phase with $C=3$ is seen in the real-space calculation of the
Chern number. In spite of this, this phase transition is not detectable in the
entanglement entropy. A second phase transition from the disorder induced $C=3$
into the $C=1$ phase is seen in all three quantities.
