  Splice type surface singularities were introduced by Neumann and Wahl as a
generalization of the class of Pham-Brieskorn-Hamm complete intersections of
dimension two. Their construction depends on a weighted tree called a splice
diagram. In this paper, we study these singularities from the tropical
viewpoint. We characterize their local tropicalizations as the cones over the
appropriately embedded associated splice diagrams. As a corollary, we reprove
some of Neumann and Wahl's earlier results on these singularities by purely
tropical methods, and show that splice type surface singularities are Newton
non-degenerate complete intersections in the sense of Khovanskii. We also
confirm that under suitable coprimality conditions on its weights, the diagram
can be uniquely recovered from the local tropicalization.
  As a corollary of the Newton non-degeneracy property, we obtain an
alternative proof of a recent theorem of de Felipe, Gonz\'alez P\'erez and
Mourtada, stating that embedded resolutions of any plane curve singularity can
be achieved by a single toric morphism, after re-embedding the ambient smooth
surface germ in a higher-dimensional smooth space. The paper ends with an
appendix by Jonathan Wahl, proving a criterion of regularity of a sequence in a
ring of convergent power series, given the regularity of an associated sequence
of initial forms.
