  A characteristic action $\Delta S$ is defined whose magnitude determines some
properties of the expectation value of a general quantum displacement operator.
These properties are related to the capability of a given environmental
`monitoring' system to induce decoherence in quantum systems coupled to it. We
show that the scale for effective decoherence is given by $\Delta
S\approx\hbar$. We relate this characteristic action with a complementary
quantity, $\Delta Z$, and analyse their connection with the main features of
the pattern of structures developed by the environmental state in different
phase space representations. The relevance of the $\Delta S$-action scale is
illustrated using both a model quantum system solved numerically and a set of
model quantum systems for which analytical expressions for the time-averaged
expectation value of the displacement operator are obtained explicitly.
