基于栅格数据的局部奇异性分析迭代方法及其软件实现

近些年,弱缓化探异常识别已成为成矿预测和勘查评价中十分关键的问题。多重分形理论的局部奇异性分析因其崭新的思路、简便的方法、优良的效果而在弱缓异常识别中受到广泛关注。在深入剖析局部奇异性分析基本思想及计算方法的基础上,引入正规化尺度参数L,提出了迭代方法来改进局部奇异性指数的估值。给出了奇异性迭代算法并用C＋＋编程实现,软件功能强劲,操作灵活,不仅适用于各向同性情形,还适用于各向异性尺度的奇异性计算和方向性奇异性计算。软件的动态链接库版本已在Geo DAS矿产资源定量预测专业软件中应用。     

三维直流电场积分方程中奇异性的近似处理

直流电场积分方程的核函数是磁并矢格林函数,其数学表达式与电并矢格林函数的数学表达式完全不同。因此,在处理直流电场积分方程的奇异性时不能直接利用文献中针对电并矢格林函数所提出的奇异性消除公式。为了寻求处理磁并矢格林函数奇异性的有效途径,参考文献中针对电并矢格林函数的奇异性消除方法,提出了针对磁并矢格林函数的拟源并矢概念,并求出了当包围奇异点的小邻域为球体、立方体等不同形状时的拟源并矢。如果将这些拟源并矢代入到电场的积分方程中,可以得到只含有正常非奇异积分的数值计算方案。将这个计算方案用于实现关于直流电场的拟解析近似理论,则可以使三维直流电场的快速数值模拟成为可能。     

对称荷载正多边形孔洞弹性应力解析逼近方法

提出一种简单有效的计算方法,求解对称荷载作用下含正多边形孔洞无限平面体的弹性应力解。将孔洞内边界向两侧延伸至应力可忽略的远处,其外侧构成半无限平面体。相邻两个半无限平面体有一个公共域,其中一个半无限平面体顶边延伸至相邻两个半限平面体体内。孔洞内边界上面力是已知的,延伸至两相邻半无限平面体体内的顶边上面力可先假设,由弹性理论求出半无限平面体体内应力,再计算相邻半无限平面体顶边上面力,根据对称性得到本半无限平面体顶边上面力改进值,迭代求解直至收敛。该方法具有计算过程简单、精度高等优点。算例分析表明,该方法求解的工程尺度下孔洞周边应力场与复变函数方法、有限元方法计算结果吻合,拟合计算的孔边角点处应力奇异性次数与理论解基本一致。     

Singularity detection of the thin bed seismic signals with wavelet transform

IntroductionIn1977,Sheriff(1977)provedthedetectiftglimitthatwasdefinedasminimumthicknessofthereflectionthinbedtobel/30wavelength.Applyingthesingularitydetectionprinciplewithwavelettransforminthispaper,weanalyzethereflectionseismicsignalsofthethinbed...     

均匀介质中散射过程的奇性分析

本文比较详细地讨论和分析了均匀介质中零偏移距散射曲面拓扑奇性和相应回波解析奇性之间的关系和分类.其基础是衍射理论的Kirchhoff积分,原理是通过曲面几何函数的解析奇性和距离函数的拓扑奇性之间的联系.基本的数学工具是Morse理论和突变理论.     

Multifractal Characteristics of Intermittent Turbulence in the Urban Canopy Layer

The multifractality of energy and thermal dissipation of fully developed intermittent turbulence is investigated in the urban canopy layer under unstable conditions by the singularity spectrum for the fractal dimensions of sets of singularities characterizing multifractals. In order to obtain high-order moment properties of smallscale turbulent dissipation in the inertial range, an ultrasonic anemometer with a high sampling frequency of 100 Hz was used. The authors found that the turbulent signal could be singular everywhere. Moreover, the singular exponents of energy and thermal dissipation rates are most frequently encountered at around 0.2, which is significantly smaller than the singular exponents for a wind tunnel at a moderate Reynolds number. The evidence indicates a higher intermittency of turbulence in the urban canopy layer at a high Reynolds number, which is demonstrated by the data with high temporal resolution. Furthermore, the temperature field is more intermittent than the velocity field. In addition, a large amount of samples could be used for verification of the results.     

基于随机模拟技术和局部奇异性理论的地球化学异常不确定性分析

地球化学异常通常是直接按某个阈值将整个研究区划分为高异常区或低异常区,这可能导致一些重要异常信息的丢失或决策判断失误。从统计学角度分析,推断未采样点处可能取得结果的概率,或者刻画估计值大于或小于某一地球化学异常阈值的概率分布,更符合勘查地球化学找矿活动的实际需要。针对确定性地球化学场建模方法的局限性,本研究通过集成地统计随机模拟和局部奇异性理论实现地球化学异常识别及其不确定性度量。通过奇异性指数-分位数分析,刻画奇异性指数在频率域中的分布模式,实现地球化学异常阈值分割。采用局部不确定性和空间不确定性算法模拟地球化学异常不确定性传播过程,并以新疆西天山地区为研究区,开展铜异常识别及其不确定性评价应用研究。     

Geochemical Anomalies Identified by Multifractal Modeling: Implications for Mineral Exploration in the Ziyoutun Cu-Au District, Jilin Province, China

The Ziyoutun Cu-Au district is located in the Jizhong–Yanbian Metallogenic Belt and possesses excellent prospects. However, the thick regolith and complex tectonic settings present challenges in terms of detecting and decomposition of weak geochemical anomalies. To address this challenge, we initially conducted a comprehensive analysis of 1:10,000-scale soil geochemical data. This analysis included multivariate statistical techniques, such as correlation analysis, R-mode cluster analysis, Q–Q plots and factor analysis. Subsequently, we decomposed the geochemical anomalies, identifying weak anomalies using spectrum-area modeling and local singularity analysis. The results indicate that the assemblage of Au-Cu-Bi-As-Sb represents the mineralization at Ziyoutun. In comparison to conventional methods, spectrum-area modeling and local singularity analysis outperform in terms of identification of anomalies. Ultimately, we considered four specific target areas (AP01, AP02, AP03 and AP04) for future exploration, based on geochemical anomalies and favorable geological factors. Within AP01 and AP02, the geochemical anomalies suggest potential mineralization at depth, whereas in AP03 and AP04 the surface anomalies require additional geological investigation. Consequently, we recommend conducting drilling, following more extensive surface fieldwork, at the first two targets and verifying surface anomalies in the last two targets. We anticipate these findings will significantly enhance future exploration in Ziyoutun.     

Quantum fluctuations in radiation dominated anisotropic cosmology

Using the metric conformal transformation and simple path integral, Feynman propagator method, for computing its quantum fluctuations, we analyse the radiation dominated anisotropic Bianchi Type I cosmology. We proceed to show that the quantum conformal fluctuations diverge at the classical spacetime singularity, suggesting that a singularity free solution can exist in anisotropic cosmology in the quantum regime. Since the December 1998 issue of this journal was delayed, we were able to include this paper in this issue.     

A Geometrical Interpretation of the Deflection of Almost Rectilinear Orbits in a Central Field

We give a geometrical interpretation for the deflection at the origin of rectilinear orbits in a central field. This interpretation is based on the correspondence between the plane orbits of a conservative force field and the geodesics of a certain surface. If the field is hard near the origin, the surface is tangent to a cone. By considering the development of this cone, we obtain the deflection. We study also almost rectilinear orbits.This revised version was published online in October 2005 with corrections to the Cover Date.