  We use an exact analytical technique [Phys. Rev. B \textbf{101}, 115405
(2020), Phys. Rev. B \textbf{102}, 165117 (2020)] to recover the surface
Green's functions for Bernal (ABA) and rhombohedral (ABC) graphite. For
rhombohedral graphite we recover the predicted surface flat bands. For Bernal
graphite we find that the surface state spectral function is similar to the
bilayer one, but the trigonal warping effects are enhanced, and the surface
quasiparticles have a much shorter lifetime. We subsequently use the T-matrix
formalism to study the quasiparticle interference patterns generated on the
surface of semi-infinite ABA and ABC graphite in the presence of impurity
scattering. We compare our predictions to experimental STM data of
impurity-localized states on the surface of Bernal graphite which appear to be
in a good agreement with our calculations.
