Abstract: Combining the probability theory method with the Logistic equation, we explored methods trying to describe the swarm-equanimity phenomenon quantitatively and judge the system in equilibrium state or not by some statistical parameters of variant (X) distribution, i.e. the variation coefficient C_v, skewness coefficient γ₁ , kurtosis coefficient γ₂, the information entropy H(X) and h^* quantity value and fractal dimension D^*₀, D^*₁. It is believed that the substance of the earthquake activity anomaly is actually the statistical distribution of X transforming from single-peak distribution (equanimity state) to two-or more-peak distribution (non-equanimity state) which can be distinguished by integratedly analyzing the above described statistical parameters, especially the γ₂ and h^*. The transformation for fore earthquake sequence and ex-sequence of strong aftershock can be explained by “time branch behavior”. We propose a simple method to estimate fore earthquake sequence type by the ratio of time period with earthquake (X≥1) to that without earthquake(X=0). The two-peak distribution characteristics of yearly frequency for M≥7.0 earthquake in Mainland China may show that M≥7.0 earthquakes activity in the area is far from equanimity state. In the period of a strong earthquake evolvement, the seismic activity and precursor phenomenon undergo from disordered state at elastic strain accumulation step(shows single-peak Poison procedure) to ordered state at mid-term of non-elastic strain accumulation step( self-organize structure order, shows two or more peak distribution), and then to disordered state at imminent step. At this step, the chaos appears which is characterized by that synchronal anomalies are being disrupted obviously, and the system is inevitable falling into unstable state. Trigger factor is very important at this time and would cause strong earthquake occurrence, which makes the system release strain energy largely and long term attenuation. After that, it begins a new run for seismogenic period. The phenomenon of earthquake activity and its precursor seems impossible to study based on pure mechanics theory, it should be thought as a compositional part of non-linear geodynamics system that is far away from equilibrium state. The effort to deepen this cognition maybe is a breakthrough in earthquake prediction realm.

Key words: “Swarm—Equanimity”, Quantitative change of the probability distribution, Single-peak type, Multi-peak type, Chaos, Judging method