【作者】 刘宁强；

【导师】 於崇文；

【作者基本信息】 中国地质大学（北京） ， 地球化学， 2010， 博士

【摘要】 Sornette和Ide(2003)提出了一种“自相似振荡有限时间奇点理论”。该理论指出:“一个二维的动力学系统,具有两个分别代表正反馈和负反馈的非线性项,二者相互竞争,通过自相似的对数周期振荡(离散标度不变性),继之以幂律式的加速增长(连续标度不变性)而在有限时间内达到奇点(临界点)”。该理论较准确地反映了复杂系统中过程或事件向临界点的时-空演化与发展趋势,并且在对于突发事件的预测中取得了良好的效果。作者从成矿系统复杂性的视角,将自相似振荡有限时间奇点理论与地质、地球化学相结合,对于大吉山钨矿地区成矿作用的发生与发展规律进行初步研究,探索非线性前沿科学在成矿系统中的应用与方法。作者以“地质作用与时-空结构是一切地质现象的本质与核心”的自然哲学理念为基本指导思想,以时-空对偶性为根本出发点,以化学波及其传播作为中心思想,以钨元素的含量M (r)作为成矿作用中正、负反馈的载体,运用地质统计学的理论与方法研究复杂成矿系统中成矿物质的时-空分布,选取“时-空剖面”;根据自相似振荡有限时间奇点理论,建立研究模型, ln(),选取研究变量Dr;运用“中间渐近”原则,在“宏观”和“中观”不同标度上,对成矿作用时-空剖面中成矿物质的M (r)和Dr进行观察和测度,绘制Dr ? lnr一维演化趋势图,运用成矿系统复杂性理论来研究复杂成矿系统中成矿作用的发生与发展规律。研究结果显示,钨元素的含量对数lnM(r)对于距离对数lnr的导数(dlnM(r)/dlnr),即“局部分数维”Dr由矿区外围向矿区中心的时-空演化过程中,具有通过“自相似对数周期振荡”过程转为幂律式增长而趋于成矿中心的明显规律性。这种规律性表明大吉山钨矿地区的复杂成矿系统中,钨元素在成矿过程中具有起着正、负反馈的作用,二者相互竞争,通过自相似的对数周期振荡,继之以幂律式的加速增长,而在有限时间内达到奇点(临界点),亦即成矿的发生。这一规律正确地反映了该矿区的成矿作用动力学过程与机制。由此作者认为,该理论可以进一步应用于成矿远景区的成矿预测。更多还原

【Abstract】 Sornette and Ide (2002, 2003) put forward a“theory of self-similar oscillatory finite-time singularities”. It states: a two-dimensional dynamic system with two nonlinear terms exerting respectively positive feedback and negative feedback, by competing with each other, reaches the singularities (critical point) in finite time by virtue of self-similar log-periodic oscillations (discrete-scale invariance) and succeeded by power-law accelerating growth (continuous-scale invariance). This theory reflects accurately the spatio-temporal evolution and trends of development of events and processes in complex systems approaching to the singularities (or critical point), and the effect of its prediction for catastrophic events has been tested to be satisfactory. In the light of the complexity of ore-forming systems, the author tries to apply this theory in combination with geology and geochemistry to studying and analyzing the onset and development of ore formation in Dajishan tungsten ore area, Jiangxi Province, China, and also tries to explore the theory and method of non-linear sciences applied in ore-forming systems.The author takes the natural philosophical ideology—“the geological processes and their spatio-temporal structures are the essence and crux of geological phenomena”proposed by Yu Chongwen as the basic guiding idea, takes the spatio-temporal duality as the basic starting point, takes chemical waves and its propagation as the central idea, and takes the contents of chemical element tungsten M(r) as the carrier of positive and negative feedbacks in the ore formation, try to apply the theory and method of Geostatistics to studying the spatio-temporal evolution of ore-forming material in complex ore-forming system. Then seven representative profiles AO, BO, CO, DO, EO, FO and GO are selected for researches. Basing on the Theory of Self-Similar Oscillatory Finite-Time Singularities, the author builds the modelthen takes Dr as the variable to be studied. In the two different scales of macroscopic and mesoscopic view, the author applies the principle of“Intermediate asymptotics”to observing and measuring M(r) and Dr of ore-forming materials in the spatio-temporal profiles of mineralization. In order to study and analyze the onset and development of ore formation in the studied ore area, the Dr versus lnr plots are used to illustrate the one-dimension trend of evolution of the ore-forming processes.The results of study show that during the spatio-temporal evolution from outside the ore area to its center, the derivatives of the logarithms of the contents of chemical element tungsten (lnM(r)) with respect to the logarithms of the distance (lnr) (local fractal dimension Dr) manifest an obvious regularity: by the way of the process of self-similar log-periodic oscillations and the transition to power-law accelerating growth, they eventually approach to the center of ore formation. The regularity makes clear that in the complex ore-forming system of the Dajishan tungsten ore deposit, the chemical element tungsten plays the role of the carrier of positive and negative feedbacks, and by competing with each other, approaches to the singularity (critical point) in finite time by virtue of self-similar log-periodic oscillations succeeded by power-law accelerating growth. In this way the onset of ore formation realizes. This regularity reflects correctly the dynamic process of ore formation of the studied ore deposit. The authors hold that the Sornette’s theory could be further applied to the prediction of perspective area.更多还原