Displacement events of nearest neighbor spring coupled mass points, embedded in a semi-infinite, periodic 1D lattice, which is driven at constant velocity at one end, are studied. The displacements of the mass points are due to small amplitude, linear oscillations, and large amplitude, low frequency translations due to nonlinear waves, or solitons, propagating on the lattice. The translational symmetry of the underlying rigid periodic lattice is broken by defect sites whose positions and amplitudes are random. Because of intermittent reflections and transmissions of the solitons at the impurity defect sites, there results stick- slip motions of the mass points of varying magnitudes and durations. The joint distribution for these events, of magnitude (delta) x and duration (delta) t, is approximated by way of the zero crossings of the wavelet transform of the displacement time series of a tracer atom in the complex flow. There follows estimates of the scaling laws of statistical quantities characterizing the motion.