长江干流日径流序列的多重分形特征

基于长江干流寸滩、宜昌和大通三个主要控制水文站多年的日径流资料,运用多重分形消除趋势波动分析 (MF-DFA)等方法,识别长江流域不同空间尺度上径流序列的多重分形特征,并采用推广的乘积阶次模型,对多重分形谱进行拟合。结果表明: (1)长江干流的日径流序列具有自相似的多重分形特征,该多重分形特征是由序列内在的长程相关性引起的;(2)长江干流日径流序列的多重分形谱可用推广的乘积阶次模型进行描述,模型拟合的参数a、b可作为该水文站点的特征参数,能够对降雨径流模型有效地进行检测;(3)长江干流日径流变化的复杂程度具有空间差异性。下游大通水文站径流序列的奇异性大于上游两站点,其径流变化过程更为复杂,而上游两站奇异性相差不大。造成三个站点径流过程变化复杂程度差异的主要原因,包括集水面积、来水组成、降水特点和下垫面状况等。     

Scaling properties of the spatio–temporal distribution of earthquakes: a multifractal approach applied to a Californian catalogue

We study the spatio–temporal scaling properties of the NCSN California catalogue for the period 1975–1995 (about 137 000 events) using a multifractal approach. The study is based on a new method of declustering earthquake catalogues based on looking for independent events. This technique makes use of the properties of the multifractal distribution of the inter-event times. A comparison test between our method and the Gardner and Knopoff (GK hereafter) approach reveals that our method produces a catalogue of independent events (monofractal Poissonian catalogue), while the GK declustered catalogue remains multifractal. The main difference lies in the assumption that the events can be considered to be correlated at large distances. The spatial properties of the declustered catalogue reveal a distribution of epicentres that is more complex than the distribution for the complete catalogue. We suggest that such results are very similar to the scaling properties of fully developed turbulence.     

城市地理研究中的单分形、多分形和自仿射分形

分形几何学在城市地理研究中具有广泛的应用,然而很多基本概念却让初学者感到迷惑。如何区分单分形、自仿射分形与多分形,是一个基本而重要的问题。简单分形容易理解,而真实的地理现象很少是单分形的。城市生长过程具有自仿射特征,而城市空间格局却具有多分形性质。作者发现,各种分形的共性在于三个方面：标度律、分数维和熵守恒。论文基于标度、分维和熵守恒公式,借助隐喻城市生长的规则分形来区分单分形、多分形和自仿射分形,讨论分形系统演化的机理、分形与空间自相关和空间异质性的联系,同时澄清一些在地理分形研究中的常见错误概念。最后以城市位序-规模分布为例,说明并对比单分形和多分形在城市地理研究中的建模与应用思路。     

Fractal structure of the time distribution of microfracturing in rocks

Using acoustic emission data obtained from laboratory double torsion tests, we have analysed the fractal nature of a series of 29 granite microfracturing processes in time. The data represent a wide variety of timescales, stress environments (increasing load with a constant displacement rate, relaxation, creep), soaking conditions [air, water, dodecyl trimethyl ammonium bromide (DTAB), polyethelene oxide (PEO) ], and material anisotropy. We find that the time distribution of rock microfracturing displays fractal and multifractal properties. In some cases, it has a single fractal or a multifractal structure. In other cases, it changes from a single fractal structure into a multifractal structure as the system evolves dynamically. We suggest that the heterogeneity of the rock, the distribution of joints or weak planes, the stress level, and the nature of the microfracturing mechanism lead to these multifractal properties. Whatever the fractal structure of the system, a lower fractal dimension is generally produced at near-failure of the rock due to an increased clustering. This result concerning the fractal-dimension decrease is consistent with the conclusion drawn from the spatial distribution of rock microfracturing. Therefore, from the vantage point of observation of the time distribution of rock microfracturing, the decrease of the fractal dimension has a potential use as a rock failure predictor.     

基于多维分形模型与指示克里格方法的地球化学异常识别研究

指示克里格方法是一种不依赖于分布假设条件的非参数估值方法,对于异常值和偏态分布都具有良好的稳健能力,因此可以作为地球化学异常研究的理想工具。阈值作为指示克里格方法最重要的参数,对于插值结果具有很大影响。该文从多维分形理论出发,利用浓度-面积(C-A)模型计算地球化学异常下限值,并将其作为阈值参与指示克里格法插值计算。为了解决多维分形测度时的不确定性,利用Voronoi图的唯一性对C-A模型进行了改进,并通过安徽省某铜矿区大比例尺化探Cu元素地球化学数据对上述方法进行了实例研究。结果显示,较之反距离加权插值法、普通克里格插值法,指示克里格法获取的最高累计概率范围与已知矿体的空间吻合程度更高,具有更好的地球化学异常识别能力。对于地球化学数据空间变异性强烈的地区,指示克里格方法在稳定变异函数形状和高值信息重建能力方面具有很大的优势。     

新疆昌吉州耕地土壤有机质空间变异动态研究

土壤有机质在提高土壤肥力和作物生产力方面发挥重要作用,研究其空间变异性可为精准施肥以及可持续的土地利用和管理提供科学依据。本文以新疆昌吉州为研究区,基于多重分形方法,使用第二次土壤普查（1980年前后）、2010年和2018年共3期土壤有机质数据,计算多重分形参数来探究土壤有机质空间变异的动态。结果表明：① 第二次土壤普查—2018年期间,昌吉州土壤有机质含量呈增加趋势。② 第二次土壤普查—2018年期间,昌吉州土壤有机质的空间分布总体上具有非均匀的多重分形特征,土壤有机质值域范围逐渐变窄,空间分布变异性降低,趋于均一化。其中阜康市、吉木萨尔县和木垒哈萨克自治县的有机质变异程度在2010—2018年略有上升。③ 2018年,昌吉州土壤有机质在空间上自西向东值域分布范围逐渐变宽,变异程度增加,内部差异变大,趋向于非均匀化。④ 三个时期昌吉州土壤有机质数值中均是低值数据分布概率较大,其变异程度高于高值数据,仅阜康市和木垒哈萨克自治县在2018年由高值数据占主导地位。长时间的耕作经营使得土壤有机质含量有所提高,空间分布逐渐趋向均一化,但仍存在部分区域有机质较高,部分区域较低的情况。分区管理措施可以有效提高区域的整体肥力水平,应在阜康市、吉木萨尔县和木垒哈萨克自治县等有机质变异程度较高的区域继续推进精准施肥,改进灌溉和耕作措施以降低土壤有机质空间变异性。     

Multifractal process of runoff fluctuation of the Kaidu River in Xinjiang,China

Based on the hydrological data in the headwater region of the Kaidu River during 1972–2011, the multifractal process of runoff fluctuation was analyzed. Results indicated that, in the past 40 years, the overall runoff of the Kaidu River in Xinjiang has shown significant multifractal behavior. Its singular curve lnχ_q(ε)–ln(ε) verified a favorable scale invariance over the entire time scale. τ(q)–q proved that evolution of the runoff time series presented multifractal characteristics. Moreover,the multifractal spectrum f(α)–α curve was hooklike leftward which indicated that, compared to relatively large runoff events. And Δf0 indicated that these relatively small events took the leading role; B0 explained the Kaidu River's daily-runoff ascending tendency presented during 1972–2011. Besides that, the multifractal behavior of the Kaidu River's runoff variability over four decades was also analyzed. Generally speaking, by decades, their four corresponding spectrum variations were not noticeable. These Δα values showed larger runoff events occupied the leading position with some local values falling. During the 1970 s to the 1990 s, Δf0 illustrated the probability of the daily runoff at the lowest point is always larger than that of the highest during three continuous decades. At the beginning of the 21 st century, for Δf0 the trend presented was contrary from the 1970 s to the 1990 s. B values suggested an overall trend of increases during1972–2011. Until the 21 st century, the runoff with a slightly descending tendency on the whole explained these relatively large runoff events taking the leading role for the Kaidu River; but sometimes, some small events also played the dominant role.     

Multifractal analysis of the spatial distribution of earthquakes in southern Italy

We evaluate the complete spectrum of the generalized fractal dimension of the spatial pattern of microearthquakes in Southern Italy, revealing a multifractal distribution structure. Our analysis is focused on the dependence of the multifractal distribution on the size of the selected area and the kind of seismicity in the area. As the size of the window varies, we observe that the capacity, information and correlation dimensions vary significantly, while both d _∞ and d _−infin; remain unchanged within their errors limits. We interpret this result in terms of the observation that our data are mainly clustered around a linear fault (the Sisifo fault). When we restrict the selected windows around the fault, clustering around a line (the fault) is highlighted. The capacity dimension changes from about 1.8 to about 1.4 and the correlation dimension decreases because we observe in detail the clustering of the seismicity along the fault, which approximates the maximum intense clustering of the whole data set. Although our results are strongly influenced by the fact that the data are dominated by the epicentres located on the fault, we can conclude that multifractal analysis can be a very useful tool to discriminate the seismicity linked to a particular fault in a given area.     

Fractal pattern integration for mineral potential estimation

Concepts of fractal/multifractal dimensions and fractal measure were used to derive the prior and posterior probabilities that a small unit cell on a geological map contains one or more mineral deposits. This has led to a new version of the weights of evidence technique which is proposed for integrating spatial datasets that exhibit nonfractal and fractal patterns to predict mineral potential. The method is demonstrated with a case study of gold mineral potential estimation in the Iskut River area, northwestern British Columbia. Several geological, geophysical, and geochemical patterns (Paleozoic-Mesozoic sedimentary and volcanic clastic rocks; buffer zones around the contacts between sedimentary rocks and Mesozoic intrusive rocks; a linear magnetic anomaly; and geochemical anomalies for Au and associated elements in stream sediments) were integrated with the gold mineral occurrences which have fractal and multifractal properties with a box-counting dimension of 1.335±0.077 and cluster dimension of 1.219±0.037.     

Joint Modeling Based on Singularity Mapping and U-statistical Methods for Geo-Anomaly Characterization

Natural Resources Research - Geo-anomalies play an important role in GIS-assisted mineral exploration. Statistical and fractal/multifractal methods are commonly applied to characterize...     

Multifractal Modeling of Worldwide and Canadian Metal Size-Frequency Distributions

The Pareto-lognormal frequency distribution, which can result from multifractal cascade modeling, previously was shown to be useful to describe the worldwide size-frequency distributions of metals including copper, zinc, gold and silver in ore deposits. In this paper, it is shown that the model also can be used for the size-frequency distributions of these metals in Canada which covers 6.6% of the continental crust. Like their worldwide equivalents, these Canadian deposits show two significant departures from the Pareto-lognormal model: (1) there are too many small deposits, and (2) there are too few deposits in the transition zone between the central lognormal and the upper tail Pareto describing the size-frequency distribution of the largest deposits. Probable causes of these departures are: (1) historically, relatively many small ore deposits were mined before bulk mining methods became available in the twentieth century, and (2) economically, giant and supergiant deposits are preferred for mining and these have strongest geophysical and geochemical anomalies. It is shown that there probably exist many large deposits that have not been discovered or mined. Although overall the samples of the size-frequency distributions are very large, frequencies uncertainties associated with the largest deposits are relatively small and it remains difficult to estimate more precisely how many undiscovered mineral deposits there are in the upper tails of the size-frequency distributions of the metals considered.

     

A Novel Hunger Games Search Optimization-Based Artificial Neural Network for Predicting Ground Vibration Intensity Induced by Mine Blasting

Innovation efforts in developing soft computing models (SCMs) of researchers and scholars are significant in recent years, especially for problems in the mining industry. So far, many SCMs have been proposed and applied to practical engineering to predict ground vibration intensity (BIGV) induced by mine blasting with high accuracy and reliability. These models significantly contributed to mitigate the adverse effects of blasting operations in mines. Despite the fact that many SCMs have been introduced with promising results, but ambitious goals of researchers are still novel SCMs with the accuracy improved. They aim to prevent the damages caused by blasting operations to the surrounding environment. This study, therefore, proposed a novel SCM based on a robust meta-heuristic algorithm, namely Hunger Games Search (HGS) and artificial neural network (ANN), abbreviated as HGS–ANN model, for predicting BIGV. Three benchmark models based on three other meta-heuristic algorithms (i.e., particle swarm optimization (PSO), firefly algorithm (FFA), and grasshopper optimization algorithm (GOA)) and ANN, named as PSO–ANN, FFA–ANN, and GOA–ANN, were also examined to have a comprehensive evaluation of the HGS–ANN model. A set of data with 252 blasting operations was collected to evaluate the effects of BIGV through the mentioned models. The data were then preprocessed and normalized before splitting into individual parts for training and validating the models. In the training phase, the HGS algorithm with the optimal parameters was fine-tuned to train the ANN model to optimize the ANN model's weights. Based on the statistical criteria, the HGS–ANN model showed its best performance with an MAE of 1.153, RMSE of 1.761, R² of 0.922, and MAPE of 0.156, followed by the GOA–ANN, FFA–ANN and PSO–ANN models with the lower performances (i.e., MAE?=?1.186, 1.528, 1.505; RMSE?=?1.772, 2.085, 2.153; R²?=?0.921, 0.899, 0.893; MAPE?=?0.231, 0.215, 0.225, respectively). Based on the outstanding performance, the HGS–ANN model should be applied broadly and across a swath of open-pit mines to predict BIGV, aiming to optimize blast patterns and reduce the environmental effects.

     

京津冀城镇用地空间结构的多分维谱分析

城市形态和城镇体系都具有分形性质,但简单分形模型不能有效揭示城市系统的复杂结构特征及其背后的问题。多分形模型及分析方法是研究城市空间复杂性和描述城市异质性的有效手段。利用城镇建设用地和总建设用地的多分维谱分析,可以发现京津冀城镇体系及主要城市的空间演化问题。主要结果如下：①京津冀总建设用地的全局谱线不正常,代表中心区的谱线收敛过快,而代表边缘区和乡村地区的谱线收敛位置严重越界;②局部谱线单峰左偏,左(趋向中心区)高密、右(趋向边缘区)低疏,且右边数值越界;③多分维增长曲线服从二次logistic函数,但不同区域和城市的增长曲线的拐点位置不同。深入分析谱线特征及其异常根源,得出如下结论：①京津冀主要城市的中心区填充过密,没有太多缓冲空间,而边缘区无序扩展,需要通过规划进行优化;②京津冀城市生长以外延扩展模式为主,但河北省总建设用地有中心集聚迹象;③京津冀地区特别是主要城市用地接近饱和,土地扩展速度高峰已经过去,只有河北省部分区域例外。     

Numerical modelling of Quaternary terrace staircase formation in the Ebro foreland basin,southern Pyrenees,NE Iberia

The southern foreland basin of the Pyrenees (Ebro basin) is an exorheic drainage basin since Late Miocene times. Remnants of an early exorheic Ebro drainage system are not preserved, but morphology provides evidence for the Pliocene–Quaternary drainage development. The incision history of the Ebro system is denoted by (i) extensive, low gradient pedimentation surfaces which are associated with the denudation of the southern Pyrenean piedmont around the Pliocene–Quaternary transition and (ii) deeply entrenched Quaternary river valleys. Presumably since the Middle Pleistocene fluvial incision intensified involving the formation of extensive terrace staircase in the Ebro basin. Terrace exposure dating in major Ebro tributary rivers indicates climate‐triggered terrace formation in response to glacial–interglacial climate and glacier fluctuations in the Pyrenean headwaters. The overall (semi)parallel longitudinal terrace profiles argue for progressive base level lowering for the whole Ebro drainage network. The landscape evolution model, TISC, is used to evaluate climatic, tectonic and base level scenarios for terrace staircase formation in the Ebro drainage system. Model simulations are compared with morpho‐climatic, tectonic and chronologic data. Results show that climatic fluctuations cause terrace formation, but the incision magnitudes and convergent terrace profiles predicted by this climate model scenario are not consistent with the (semi)parallel terraces in the Ebro basin. A model including previous (late Pliocene) uplift of the lower Ebro basin results in rapid base‐level lowering and erosion along the drainage network, small late stage incision magnitudes and terrace convergence, which are not in agreement with observations. Instead, continuous Quaternary uplift of both the Pyrenees and the Ebro foreland basin triggers (semi)parallel terrace staircase formation in southern Pyrenean tributary rivers in consistency with the observed longitudinal terrace profiles and Middle–Late Pleistocene incision magnitudes. Forward model simulations indicate that the present Ebro drainage system is actively incising, providing further evidence for uplift.     

A MaxEnt Model for Mineral Prospectivity Mapping

Mineral prospectivity mapping is an important preliminary step for mineral resource exploration. It has been widely applied to distinguish areas of high potential to host mineral deposits and to minimize the financial risks associated with decision making in mineral industry. In the present study, a maximum entropy (MaxEnt) model was applied to investigate its potential for mineral prospectivity analysis. A case study from the Nanling tungsten polymetallic metallogenic belt, South China, was used to evaluate its performance. In order to deal with model over-fitting, varying levels of β _j -regularization were set to determine suitable β value based on response curves and receiver operating characteristic (ROC) curves, as well as via visual inspections of prospectivity maps. The area under the ROC curve (AUC = 0.863) suggests good performance of the MaxEnt model under the condition of balancing model complexity and generality. The relative importance of ore-controlling factors and their relationships with known deposits were examined by jackknife analysis and response curves. Prediction–area (P–A) curves were used to determine threshold values for demarcating high probability of tungsten polymetallic deposit occurrence within small exploration area. The final predictive map showed that high favorability zones occupy 14.5% of the study area and contain 85.5% of the known tungsten polymetallic deposits. Our study suggests that the MaxEnt model can be efficiently used to integrate multisource geo-spatial information for mineral prospectivity analysis.     

Knowledge-Driven Prospectivity Mapping for Granite-Related Polymetallic Sn–F–(REE) mineralization,Bushveld Igneous Complex,South Africa

This paper presents mineral prospectivity mapping to identify potential new exploration ground for polymetallic Sn–F–REE mineralization associated with the Bushveld granites of the Bushveld Igneous Complex, South Africa. The Lebowa Granite Suite, commonly known as the Bushveld granites, is host to a continuum of polymetallic mineralization with a wide range of metal assemblages (Sn–Mo–W–Cu–Pb–Zn–As–Au–Ag–Fe–F–U–REE), ranging from a high-temperature to a low-temperature magmatic hydrothermal mineralizing environment. The prospectivity map was generated by fuzzy logic modeling and a selection of targeting criteria (or spatial proxies) based on a conceptual mineral system highlighting critical processes responsible for the formation of the polymetallic mineralization. The spatial proxies include proximity to differentiated granites (as heat and metal-rich fluid sources), Rb geochemical map (fluid-focusing mechanism such as fractionation process), principal component maps (PC 4 Y–Th and PC 14 Sn–W, fluid pathways for both high- and low-temperature mineralization) and proximity to roof rocks (traps for fluids). Logarithmic functions were used to rescale rasterized evidential maps into continuous fuzzy membership scores in a range of [0, 1]. The evidential maps were combined in two-staged integration matrix using fuzzy AND, OR and gamma operators to produce the granite-related polymetallic Sn–F–(REE) prospectivity map. The conceptual mineral system model and corresponding prospectivity model developed in this study yielded an encouraging result by delineating the known mineral deposits and occurrences of Sn–F–(REE) mineralization that were not used to assign weights to the evidential maps. The prospectivity model predicted, on average, 77% of the known mineral occurrences in the BIC (i.e., 56 of 73 Sn occurrences, 12 of 15 F occurrences and 6 of 8 REE occurrences). Based on this validation, 13 new targets were outlined in this study.     

Integrating Fire Behavior and Pedestrian Mobility Models to Assess Potential Risk to Humans from Wildfires Within the U.S.–Mexico Border Zone∗

Wildfires create a risk to pedestrians traveling through rural areas, because they might not be aware of the presence of a wildfire or its direction and rate of spread until is too late to successfully evacuate. In wildland areas of southern San Diego County, immigrants crossing the U.S.–Mexico border and border security agents are particularly at risk to wildfires. The objective of this study is to develop a framework of analysis and associated tools for examining the combined behavior of wildfires and pedestrian mobility to assess the potential threat of fire to pedestrians in wildland areas. Outputs from a geographic information system (GIS) overlay model for determining potentially dangerous fire zones, the Wildland–Urban Interface Evacuation (WUIVAC) model, and a model of pedestrian mobility in wildland areas were combined to generate wildfire risk to pedestrian maps. The key technical contributions of the study are the development and testing of the pedestrian mobility model and the framework and logic for integrating the results of three GIS-based models. The applied geography contribution is the testing of two scenarios of high risk from wildfires to pedestrians within the U.S.–Mexico border zone of San Diego County, California.

The study results show that the travel times calculated by the pedestrian mobility model appear to be realistic and are affected by the terrain and vegetation characteristics of a study site, whereas the evacuation trigger buffers (ETBs) from WUIVAC are mostly influenced by the wind speed and direction parameters of the FlamMap fire spread model. A moderate fire danger to pedestrians in the most remote wildland locations of the study area is determined. The scenario test results suggest that if a wildfire occurs within 2 km (extreme southwesterly winds) or 6 km (extreme northeasterly wind) of pedestrians in the worst case location within the San Diego border region they would likely not have a sufficient amount of time to reach a nearby safety zone.     

An intelligent method to discover transition rules for cellular automata using bee colony optimisation

This paper presents a new, intelligent approach to discover transition rules for geographical cellular automata (CA) based on bee colony optimisation (BCO–CA) that can perform complex tasks through the cooperation and interaction of bees. The artificial bee colony miner algorithm is used to discover transition rules. In BCO–CA, a food source position is defined by its upper and lower thresholds for each attribute, and each bee searches the best upper and lower thresholds in each attribute as a zone. A transition rule is organised when the zone in each attribute is connected to another node by the operator ‘And’ and is linked to a cell status value. The transition rules are expressed by the logical structure statement ‘IF-Then’, which is explicit and easy to understand. Bee colony optimisation could better avoid the tendency to be vulnerable to local optimisation through local and global searching in the iterative process, and it does not require the discretisation of attribute values. Finally, The BCO–CA model is employed to simulate urban development in the Xi’an-Xian Yang urban area in China. Preliminary results suggest that this BCO approach is effective in capturing complex relationships between spatial variables and urban dynamics. Experimental results indicate that the BCO–CA model achieves a higher accuracy than the NULL and ACO–CA models, which demonstrates the feasibility and availability of the model in the simulation of complex urban dynamic change.     

Selection of Optimal Thresholds for Estimation and Simulation Based on Indicator Values of Highly Skewed Distributions of Ore Data

This study strives to outline a geostatistics model for estimation and simulation of the Qolqoleh gold ore deposit located in Saqqez, NW of Iran. Considering that this gold deposit contains high-grade values, accurate evaluation of such values is of high importance, and therefore different methods based on indicator values, such as full indicator kriging (FIK) and sequential indicator simulation (SIS), have been employed to improve the accuracy of estimation and simulation of high-grade values. FIK and SIS cover the full range of grades based on several thresholds on the indicator data. The cumulative distribution function (CDF) is typically used for selection of threshold values. Given the highly skewed distribution of gold grade and its intense fluctuations, the number of thresholds is increased using CDF, which in turn results in a whole lot of calculations. To reduce the volume of calculations, the number–size (N–S) fractal model has been used to select thresholds. From such a model, all optimal thresholds are chosen with respect to geology and the unnecessary thresholds are excluded from selection. Thus, a study of the selection of optimal thresholds for estimation and simulation of a gold ore resource by means of FIK and SIS, respectively, based on thresholds selected using the N–S fractal model is presented. Finally, it is proved that results of these geostatistical methods based on thresholds selection from the N–S model appear to be better-positioned to explain ore grade variability compared to thresholds selected from the CDF and threshold selection from the N–S model is more effective for reducing the volume of required calculations.     

A climatological study of the effect of sea-surface temperature on North Atlantic hurricane intensification

The climatic influence of sea-surface temperature (SST) on intensification is examined for North Atlantic hurricanes by averaging hourly intensity increases from best-track data over the period 1986–2013 in 4° by 4° latitude–longitude grid cells. Independent monthly SST data over the same period are averaged in the same cells. After removing cells with cold water or fast moving hurricanes, the SST effect on intensification, at the climate scale, is quantified by regressing intensification onto SST while controlling for average intensity. The regression is performed using a generalized linear model from a gamma family and a logarithmic link function. The model shows a statistically significant relationship, with higher intensification values associated with higher SST values. On average, mean intensification increases by 16% [(9,?20)% uncertainty interval] for every 1 °C increase in mean SST. A clustered region where the model underpredicts intensification is noted over the southeastern Caribbean Sea, perhaps related to the fresh water plume from the Orinoco River.