Abstract: The spatial distribution of unbalanced seismic system is studied according to non-linear theory, method of probability and statistics. It is concluded that spatial variation coefficient δ_V can be used to judge the types of seismic activity; i.e. coherence, gathering, Poisson, uniform-lattice distribution. Self-organization structure of seismic colony and statistical characteristics of critical state are further discussed, using such statistical value as co-variance μ₁₁, non-negative value I (x, y), information entropy, scattering degree σ and δ_V. Seismic events with M≥43/4 in Capital Circle Area and events with M_L≥3.0 in different areas of North China are statistically analyzed. We think that μ₁₁ ≈ 0, I(x, y)>0, high H(x, y) value, low and δ_V are the basic characteristics and essential condition of self-organization and critical state of strong and large earthquakes. A new viewpoint and statistic interpretation is supposed for the causes of seismic gap, seismic stripe, precursory swarm and foreshock. Conclusion is drawn that only when a seismic system far from balance state has enough randomness and non-Poisson fluctuation, then sudden change of the system, i.e. large earthquake occurrence will be irreversible.

Key words: Fluctuation, Spatial variation coefficient, Self-origination, Critical state, Statistical characteristics