  Travelling wave is identified as the mechanism of avalanche propagation in
the continuum SOC (self-organized critical) system. Recovering the hidden
causality based on a generalization of Fick's law, we lead the equivalent
continuum equation which has spatiotemporal nonlocality. Taking into account of
the hyperbolicity from the retarded response of the nonlocal kernel, it is
possible to capture the propagating avalanche in constant speed. Verifying the
computation, we analyze the evolution of instability as a nonlinear wave under
the control of the threshold dynamics, which imposes the "metastability" as the
survival condition of avalanche. Being consistent with the basic assumptions of
SOC theory, the result shows unified features of the existing models. This
provides a concept toward the SOC framework based on the physical principles of
transport process.
