关键词: 最大熵原理, 无序, 分布, 地震频度-震级关系

Abstract: Entropy is a state function. Entropy increasing principle shows that under isolated or adiabatic condition the process of a system developed spontaneously from non equilibrium state to equilibrium state is a process of entropy increasing. The equilibrium state corresponds to the maximum entropy. In equilibrium state, the state of the system is most chaotic and disorder. Earthquake is a random event, the occurrence of which possesses extremely great uncertainty, and hence can be expressed by entropy. Earthquake occurs disorderly in different areas, implying that the seismic entropy has reached a maximum value. Therefore, magnitude distribution of earthquakes in one region for a certain time period can be expressed by the principle of maximum entropy. Assuming that M₀ is starting magnitude and AM-U is average magnitude, through the deduction we can get lgn= lgN/AM-U-M₀+M₀/AM-U-M₀-1/AM-U-M₀M, where n is differential frequency, N is total number of earthquakes, and M is magnitude. The magnitude frequency relation proposed by Gutenberg and Richter according to seismic data and experience is expressed as: lg n=a-bM. Comparing the two equations gives a= lgN/AM-U-M₀+M₀/AM-U-M₀, b=1/AM-U-M₀. Obviously, the Gutenberg-Richter magnitude-frequency relation is essentially a negative exponent distribution obtained by taking the maximum value of seismic entropy under a given constrained conditions. In this way the cause of magnitude-frequency relation is theoretically explained.

Key words: maximum entropy principle, disorder, distribution, magnitude-frequency relation