Non-Linear Theory and Power-Law Models for Information Integration and Mineral Resources Quantitative Assessments

Singular physical or chemical processes may result in anomalous amounts of energy release or mass accumulation that, generally, are confined to narrow intervals in space or time. Singularity is a property of different types of non-linear natural processes including cloud formation, rainfall, hurricanes, flooding, landslides, earthquakes, wildfires, and mineralization. The end products of these non-linear processes can be modeled as fractals or multifractals. Hydrothermal processes in the Earth’s crust can result in ore deposits characterized by high concentrations of metals with fractal or multifractal properties. Here we show that the non-linear properties of the end products of singular mineralization processes can be applied for prediction of undiscovered mineral deposits and for quantitative mineral resource assessment, whether for mineral exploration or for regional, national and global planning for mineral resource utilization. In addition to the general theory and framework for the non-linear mineral resources assessment, this paper focuses on several power-law models proposed for characterizing non-linear properties of mineralization and for geoinformation extraction and integration. The theories, methods, and computer system discussed in this paper were validated using a case study dealing with hydrothermal Au mineral potential in southern Nova Scotia, Canada.     

小震空间分在奇异性谱f（α）研究

本文用数盒子法计算了１９７９年３月２日固镇５．０级、１９７４年４月２２日溧阳５．５级和１９７９年７月９日溧阳６．０级地震前后小震空间分布分形集合的奇异性谱ｆ（α），详细讨论了ｆ（α）谱所揭示的主震前后各阶段小震空间分布从稀疏到密集的各种密度分布不均匀性的定量特征。经分析可以看出，奇异性谱ｆ（α）较多重分形谱Ｄｑ的概念更直观、清晰，它包含了空间分布的全部信息，且计算量明显减少。     

亮点周围的衍射模式

将衍射问题研究中的回波解析奇性归结为探讨含参量的振荡积分的渐近性态问题，并利用广义函数的算子理论，以十分简捷的方式给出了上述振荡积分的稳定位相公式，以及结合Ｔｈｏｍ理论逐一地算出非退化奇点、岐点和脐点周围的衍射模式．     

一维波动方程的奇性反演与小波

利用线性化的技巧及Ｇ．Ｂｅｙｌｋｉｎ引进的奇性反演的概念，使波动方程非均匀背景场的反演问题有了实质性的进展，但在进行线性化简时，往往会将数值小但奇性高的项略去，因而使反演结果失真，本文利用小波变换这一工具，在化简时保留了奇性的主要部分，从而使反演所得的结果从奇性分析的观点看来更为。     

A compact model for the planar rhomboidal 4-body problem

We obtain a compact model for the global study of the planar rhomboidal 4-body problem in a level of constant negative energy. This model is a variation of the non compact model obtained through a McGehee blow up transformation. but compactness permits to obtain results which are not clear in the other case.     

一维有耗散波动方程的奇性分析与小波

对系数有强奇性（间断）的波动方程,用通常的线性化简的方法时往往会将数值小但奇性强的项略去,导致结果严重失真。利用小波变换这一工具,可以在化简时保留奇性的主要部分,使所得的结果从奇性分析的观点看来更为精确。此方法曾被用来处理系数有间断的一维波动方程,得到了与精确解的奇性主部完全一致的解．在本文中,我们改进了用小波变换作奇性化简的方法,对系数有间断的一维有耗散波动方程求得了与精确解奇性主部完全一致的解。这说明利用小波分析作奇性化简的方法对高频近似及奇性分析问题是普遍适用的．     

地震反应谱初探

在计算地震荷载时,计算的依据是常规反应谱理论,然而,当质点间出现刚体移动时,用常规反应谱理论计算会出现奇异点.如利用相对加速度进行计算,将常规反应谱理论进行修正,所得结论将更加安全,又弥补了常规反应谱的不足.     

Identifying gravity anomalies caused by granitic intrusions in Nanling mineral district,China: a multifractal perspective

Several power‐law relationships of geophysical potential fields have been discussed recently with renewed interests, including field value–distance () and power spectrum–wavenumber () models. The singularity mapping technique based on the density/concentration–area (C–A) power‐law model is applied to act as a high‐pass filter for extracting gravity and magnetic anomalies regardless of the background value and to detect the edges of gravity or magnetic sources with the advantage of scale invariance. This is demonstrated on a synthetic example and a case study from the Nanling mineral district, Southern China. Compared with the analytic signal amplitude and total horizontal gradient methods, the singularity mapping technique provides more distinct and less noisy boundaries of granites than traditional methods. Additionally, it is efficient for enhancing and outlining weak anomalies caused by concealed granitic intrusions, indicating that the singularity method based on multifractal analysis is a potential tool to process gravity and magnetic data.     

基于小波多尺度分析的奇性指数：一种新地震属性

传统的地震解释主要是观测地震振幅及相位的变化，但是地震振幅也会掩盖地下介质中真实的地质情况.在许多情况下，重要的地质信息可能是通过与振幅特征无关的奇异性参数来传递的.本文提出奇异性指数，即Hlder指数α（又被称为Lipschitz指数），可以作为一种新的地震属性，它能够准确反映数据中的奇点的位置和奇异性强度.Hlder指数α是对某一点上或某一点周围很小的范围内的奇异性强度的度量，大的α值表示低的奇异性（或高的正则性）.研究表明α可以作为一种自然的能够精确刻画地层边界的地震属性.本文根据这一思想，对合成和实测的地震数据进行了小波基础上的多尺度分析研究，结果表明由本文的算法得到的α提高了对地层边界划分的能力，而这些地层界面在传统的地震振幅显示则不明显.     

Singularity. A manifesto for incomparable geographies

This paper is a methodological response to the challenge of decolonizing geographical knowledge. It mobilizes post‐ and de‐colonial critiques of geographical knowledge production and conceptual work, suggesting how such work unwittingly disfigures the precise contours of the places and socio‐spatial formations on which geographers work, drawing them into implicit and reductive forms of comparison. Drawing on research and sources from South Asia, the paper moves instead toward more uncertain engagements with, and dispositions to, the production of geographical knowledge; ones attuned to the poetics of planetary difference. The paper speculates on five intellectual and methodological resources, or tactics, aimed toward producing geographical scholarship attuned to the tableaux of heterogeneous and incomparable singularities at large across the world: theory and reading; friction and fragments; translation/untranslatability; abiding by; and poetics.