地震活动信息熵在地震危险区判定中的研究

震例和实验指出，大震的孕育准备过程中，总是要出现小震活动时空分布随机性减少及有序性增大的过程。本文从现代统计物理学熵的概念出发，系统定义了反映地震活动分析有序性大小的信息熵，并通过分析新疆乌恰、西克尔、乌什及北天山玛纳斯地区的地震资料，探讨信息熵的动态变化与强震发生时间的关系及信息熵值的空间分布与强震发生地点的关系。     

地震活动的分形特征及其对地震预测的意义

岩石破裂是一个自相似过程,地震作为地壳岩石破裂的结果,它在时间和空间上的分布具有分形结构。基于系统科学和分形几何学的观点,本文采用标度变换法和嵌入空间法,分别研究了唐山7.8级、海城7.3级和松潘7.2级地震前后地震活动时、空分布的分维数,同时分析了宁夏灵武5.5级震群和澜沧5.0级前震序列的时间分维随时间的变化特征。初步结果表明:大震后余震的分维数明显增大,无标度区范围减小,展示了震后地震活动随机干扰背景增强！前兆性地震序列的时间分维数相对偏低,有序性增加。此外,文中还研究了单轴压缩下岩石破裂声发射序列的分形特征,结果表明,声发射序列亦具有自相似性,在岩石破坏过程中,声发射序列的分线数随时间的变化不是单调的。最后,籍助于“耗散结构理论”的基本概念,简要地探讨了地震时间、空间分维与地震活动熵的关系。提出了地震时、空分维作为表征地震孕育系统演化过程的序参量之一,应用于地震预测的可能途径及需要进一步研究的若干问题。     

地震活动性的多重分维特征

本文根据多重分维的定义,研究了华北和西北地区地震的空间和时间分布的多重分维特征。结果表明,地震时空分布的多重分维特征能较好地描述地震时空分布的有序性。一般在地震活动性较强的阶段,多重分维D_q,尤其是高阶的D_q有明显的异常变化,其D_q—q曲线较陡;而D_q—q曲线变化较平缓的阶段,统计区内一般无大震发生。     

澜沧—耿马7.6级地震前中小地震活动信息熵和分维的研究

从信息论原理和分形几何学的观点出发,采用多种方法,分析研究1988年澜沧—耿马7.6级地震前地震活动的信息、信息熵和分维的变化特征表明,地震前1—2年内,中、小地震活动的信息熵、缺信量和容量维、信息维出现明显的低值变化过程,反映了地震前兆的减熵、降维特点,从一个侧面反映了大震前,一定区域内中、小地震活动的时空变化从无序向有序的演化过程。     

6.6级地震前小金地区地震活动性

小金6.6级地震发生在鲜水河断裂带与龙门山断裂带之间一个地震活动水平较低的地区.根据该地区近10多年来中小地震活动的频度～震级统计关系,计算得到这一地区7级地震复发周期为435～523年;6级为58～69年;5级为10.1～11.7年.对该区及附近地震活动分析表明,小金地震前6年左右震中附近出现4级背景性地震空区;1989年3月1日小金5.0级地震为空区内逼近地震。小金地震前1年多四川西部曾出现背景性地震条带;震中附近曾出现弱震空区。b 值的时空扫描显示这次地震前2年多附近地区 b 值存在一个由高值到低值的变化过程.对周围4°×4°范围2.5级以上地震活动归一化熵计算结果,断层面总面积熵有下降异常,反映地震时间间隔及单位面积地震频度的熵无变化.     

地震前兆模糊分维特征的研究

本文利用模糊分维公式计算了大同6.1级和5.8级地震前震中及附近地区前兆观测资料的模糊维数。结果表明,震前前兆观测资料的模糊维数明显下降,且震中位于降维最大的地区附近。唐山7.8级地震前,短水准观测资料也有类似的情况。     

地震分形与地震预报

本文认为,分维及无标度区是地震分形自组织两个重要特征参数。讨论了两个层次关联维特征及关联维 D_2计算的基本限制。初步探索了强震序列生长结构与分形原理间关系。提出地震分维函数与地震时序分布律新的研究方法及课题。分析了分维随时间变化特征及其在地震预报上的应用。     

初探地震活动的时间分维特征

本文运用分维的概念和方法,对我国部分强震前地震活动时间分维,前震震群活动时间分维,7级以上大地震的余震活动时间分维和小震群活动时间分维进行了计算。初步结果表明,同一类型的地震活动(如强震前较大时空范围内地震活动、强震的余震、前震震群、小震群等类型)的时间分维十分相近,而不同类型地震活动的时间分维存在着差异,一般说来,强震前的地震活动比较普遍地存在降维现象,表现出临近强震时,震源及附近地区地震活动时间结构的有序性增强。这为地震预报开辟了一个新的途径。     

海城地震前后地震活动的广义分维变化

应用广义分维的概念于地震活动时间分形的研究可避免确定无标度区的困难。海城地震前后地震活动的广义分维D_o(ε)的变化表明,时间标度区间为2—16天时,D_o(ε)的变化可以反映大震酝育过程中地震时间分布的不均匀性,并表现出震前降维的前兆变化特征。     

中强地震前山东地下流体地震前兆模糊分维特征研究

采用模糊集理论与分形理论相结合的模糊分维方法，计算山东地下流体在１９８３年菏泽５．９级地震和１９９５年苍山５．２级地震前的变化。分析结果认为，模糊分维值反映了地震前兆时序观测资料的结构变化特征，具有一定的物理意义，为从复杂的地下流体前兆观测值中提取地震异常信息提供了新的方法，但对某些台、测项而言、必须具体分析其模糊分维变化特征及其震前异常变化特征。     

熵的原理与地震活动研究

熵是多种学科的一个重要交叉点。熵的原理广泛适用于物理、化学、生物、医学、气象乃至社会经济等科学领域,并已取得了令人注目的成果。本文以熵的基本含意出发,简要地阐述了熵概念的扩展,包括热温熵、信息熵以及条件熵等。将地震孕育过程作为一个复杂的开放系统,基于耗散结构理论的基本思想,为定量描述地震活动时、空、强分布的有序度,引入地震活动熵作为序参量,并将其应用于大地震前后地震活动演变特征的研究。初步结果表明,随着临近大地震的发生,在一定范围内地震活动熵值减小,即地震活动分布状态从无序趋向有序。可以预期,把熵的原理引入地震研究领域必将加深人们对地震发生物理过程本质的认识。同时也将为探索地震预测提供新的思路和新的途径。     

闽,赣地区小震群性质探讨

本文运用地震频度衰减系数h值,震群能量释放均匀度u值、震群归一化熵值K等地震活动参数的统计分析,研究了长汀震群以及闽赣地区其它小震群的殊征,认为长汀震群是一次无前兆性质的正常地震活动,而龙南震群是一次前兆性震群。     

现代谱估计的进展

本文首先详细评述了最大熵谱估计的进展,然后介绍了近年来发展起来的最小交叉熵谱方法、自回归滑动平均谱方法。作为比较,还简述了最大似然谱估计方法。最后讨论了时谱和多谱。     

大同－阳高2次地震前的震级熵异常

利用最大熵原理推导了连续型随机变量震级熵的表达式，计算了大同－阳高地震前后Ｍ≥２．０地震的震级熵，计算结果表明，从１９８８年４月开始，震级熵开始出现低值异常，１９８９年３月震级熵开始回升，在回升途中发生了１９８９年１０月１８日的大同－阳高６．１级地震。１９９０年４月份后震级熵再次出现低值异常，９月份后震级熵再次回升，在回升途中发生了１９９１年３月２６日的５．８级地震。     

The Entropy Score and its Uses in Earthquake Forecasting

Suppose a forecasting scheme associates a probability p^* with some observed outcome. The entropy score given to this forecast is then –logp^*. This article provides a review of the background to this scoring method, its main properties, and its relationships to concepts such as likelihood, probability gain, and Molchans - diagram. It is shown that, in terms of this score, an intrinsic characterization can be given for the predictability of a given statistical forecasting model. Uses of the score are illustrated by applications to the stress release and ETAS models, electrical signals, and M8.     

地震前兆吸引子及可预报性问题研究

利用溧阳台和徐州台体应变前兆观测资料,计算并研究了地震前兆吸引子的关联维数Ｄ２和二阶Ｒｅｎｙｉ料Ｋ２,提出了在一定异常判据下估算前兆吸引子可预报时间长度的方法。     

Research on Earthquake Precursor Attractor and Its Predictability

Based on the body strain observation data at Liyang and Xuzhou stations, the Correlation Dimension D2 and the second-order Renyi entropy K2 of the attractor are calculated and studied. In addition, a new method of evaluating the longest predictable time of precursor attractor is advanced under the condition of a certain anomalous criterion rule. The conclusion indicates that the body strain precursor attractor is one of the chaotic attractors and it has some determinate change rules such as the dimension declines before an earthquake and the number of the independent factors on which the variation of the system depends is within the range of 5 - 12. The conclusion also indicates that the longest evaluated predictable time of the body strain attractor is 213 days at the Liyang station and 342 days at the Xuzhou station. It is clear that this research can be of great reference value for recognizing the nonlinear behavior of precursor attractors and for evaluating the predictability of different precursor     

A univariate model for long-term streamflow forecasting

This paper, the first in a series of two, employs the principle of maximum entropy (POME) via maximum entropy spectral analysis (MESA) to develop a univariate model for long-term streamflow forecasting. Three cases of streamflow forecasting are investigated: forward forecasting, backward forecasting (or reconstruction) and intermittent forecasting (or filling in missing records). Application of the model is discussed in the second paper.     

Precipitation,dynamical intermittency,and sporadic randomness

While rainfall intermittency is a dynamical phenomenon, little progress has been made in the literature on the link between rainfall intermittency and atmospheric dynamics. We present the basic dynamical models of intermittency that are phenomenologically most similar to rainfall: Pomeau–Manneville Type-III and On–Off. We then illustrate each type with both a 1-D iterative map and a corresponding stochastic process stressing the appearance of these dynamics in high-dimensional (stochastic) systems as opposed to low-dimensional chaotic systems. We show that the pdf of rainfall intensities, the pdf of “laminar phases” (periods of zero rainfall intensity), and the spectrum of the rainfall series all have power-law behavior that is broadly consistent with intermittency in the classic types. Using a seasonal analysis, we find that summer convective rainfall at daily and sub-daily scales seems consistent with features of Type-III intermittency. The correspondence with Type-III intermittency and a preliminary entropic analysis further suggest that rainfall may be an example of sporadic randomness, blending deterministic and stochastic components.     

Two-dimensional equilibrium morphological modelling of a tidal inlet: an entropy based approach

The management of tidal inlets requires the accurate prediction of equilibrium morphologies. In areas where the flow from rivers is highly regulated, it is important to give decision makers the ability to determine optimal flow management schemes, in order to allow tidal inlets to function as naturally as possible, and minimise the risk of inlet closure. The River Murray Mouth in South Australia is one such problem area. Drought and the retention of water for irrigation and urban water consumption have limited the amount of water entering the estuary. As a result, sediment from the coastal environment is being deposited in the mouth of the estuary, reducing the effect of further coastal interactions. Currently, situations such as this are modelled using traditional process-based methods, where wave, current, sediment transport and sediment balance modules are linked together in a time-stepping process. The modules are reapplied and assessed until a stable morphology is formed. In this paper, new options for modelling equilibrium morphologies of tidal inlets are detailed, which alleviate some of the shortfalls of traditional process-based models, such as the amplification of small errors and reliance on initial conditions. The modelling problem is approached in this paper from a different angle and involves the use of entropy based objective functions, which are optimised in order to find equilibrium morphologies. In this way, characteristics of a system at equilibrium can be recognised and a stable system predicted without having to step through time. This paper also details the use of self-organisation based modelling methods, another non-traditional model application, where local laws and feedback result in the formation of a global stable equilibrium morphology. These methods represent a different approach to traditional models, without some of the characteristics that may add to their limitations. Responsible Editor: Alejandro Souza