We study roughening interfaces with a constant slope that become self-
organized critical by a rule that is similar to that of invasion perco
lation. The transient and critical dynamical exponents show Galilean i
nvariance. The activity along the interface exhibits non-trivial power
law correlations in both space and time. The probability distribution
of the activity pattern follows an algebraic relation. (C) 1998 Publi
shed by Elsevier Science B.V.