  We propose an approach of Mellin type for the approximation of integration
currents or the effective realization of normalized Green currents associated
with a cycle $ \bigwedge_1^m[{\rm div} (s_j)] $, where $s_j $ is a meromorphic
section of a line bundle $ \mathscr{L}_j \rightarrow U$ over an open $U$ in a
good Berkovich space when each $ \mathscr{L}_j$ has a smooth metric and $ {\rm
codim}_{U}\big (\bigcap_{j \in J} {\rm Supp} [{\rm div (s_j)}] \big)\geq \# J$
for every set $ J \subset \{1, ..., p \} $. We also study the transposition to
the non archimedean context of Crofton and King formulas, particularly the
approximate realization of Vogel and Segre currents.
