  We prove a decomposition formula of logarithmic Gromov-Witten invariants in a
degeneration setting. A one-parameter log smooth family X->B with singular
fibre over b_0 \in B yields a family M(X/B,\beta) -> B of moduli stacks of
stable logarithmic maps. We give a virtual decomposition of the fibre of this
family over b_0 in terms of rigid tropical curves. This generalizes one aspect
of known results in the case that the fibre X_{b_0} is a normal crossings union
of two divisors. We exhibit our formulas in explicit examples.
