地下水位的混沌和多重分形特征演化及其中短期预报意义

EVOLUTION OF CHAOTIC AND MULTIFRACTAL CHARACTERISTICS FOR WATER LEVEL AND ITS APPLICATION IN EARTHQUAKE PREDICTION

采用苏 ２０ 井记录到的 １９９５ 年７ 月１ 日至１９９７ 年６ 月３０ 日地下水位观测数据作为研究的原始资料，计算并研究了 １９９６ 年 １１ 月 ９ 日南黄海 Ｍ Ｓ ６．１ 地震前后地下水位系统混沌吸引子的关联维数 Ｄ２ 、二阶熵 Ｋ２ 和最大 Ｌｙａｐｕｎｏｖ 指数 λ１ ，并用推广 Ｇ Ｐ法研究了地震前后系统多重分形的广义维数谱 Ｄｑ。研究结果表明：地下水位系统为混沌系统，系统的自由度在 ３ ～ １６ 之间；地震过程中系统有降维减熵现象，震前广义维数谱 Ｄｑ 左半边曲线变陡，因而可被看作为强震前的前兆信息。此结果对今后在预报工作中认识地震前兆观测的非线性动力学特征和利用这些特征进行地震预报具有重要的实用意义。

Using the observed water level data recorded from 1 July 1995 to 30 June 1997 at Su20 well, the correlation dimension D 2 and order 2 Renyi entropy K 2 as well as the largest Lyapunov exponent λ 1 of the chaotic attractors of the water level system before and after South Yellow Sea earthquake ( M S 6.1) in 9 November 1996 are calculated and studied with the time delay phase space reconstruction algorithm. Besides, the generalized fractal dimension spectrum D q before and after the earthquake is also calculated and studied with the generalized Grassberger Procaccia algorithm. The research result indicates that the water level system is a chaotic system, the freedom degree of which is within the range of 3～16, and the dimension and entropy of the system declined before the earthquake. It also indicates that the left half of the generalized fractal dimension spectrum D q curve became steep before the earthquake. The conclusion of this research can be of great applicable significance in recognizing the nonlinear dynamic features of the earthquake precursor observation and in earthquake prediction.