GIS-based mineral potential modeling by advanced spatial analytical methods in the southeastern Yunnan mineral district,China

This paper demonstrates a modeling procedure of mineral potential mapping based on singularity theory, and further presents an idea to look into metallogeny of Sn–Cu polymetallic deposits in southeastern Yunnan mineral district, China by applying a localized regression method. Mineralization is a typical cascade process generally accompanied by irregular geological, geochemical and geophysical signatures. Singularity index as an efficient anomaly analytical tool helps to identify anomalies as well as characterize formation processes of these anomalies. In this study, the singularity-based mineral potential mapping method was utilized to characterize hydrothermal mineralization associated with magmatic, tectonic and sedimentary processes in this district. Based on the results, a mineral prospectivity model was constructed to delineate target areas. In addition to mineral prospectivity, controlling effects of geo-processes on mineralization are spatially non-stationary. Geographically-weighted regression analysis was thus employed to investigate these spatially-varied controlling effects and it has contributed to improve understanding to local metallogeny in the study area. Results of the spatial analysis presented can be used to guide following stages of mineral exploration in the district.     

Data- and knowledge-driven mineral prospectivity maps for Canada's North

Data- and knowledge-driven techniques are used to produce regional Au prospectivity maps of a portion of Melville Peninsula, Northern Canada using geophysical and geochemical data. These basic datasets typically exist for large portions of Canada's North and are suitable for a “greenfields” exploration programme. The data-driven method involves the use of the Random Forest (RF) supervised classifier, a relatively new technique that has recently been applied to mineral potential modelling while the knowledge-driven technique makes use of weighted-index overlay, commonly used in GIS spatial modelling studies. We use the location of known Au occurrences to train the RF classifier and calculate the signature of Au occurrences as a group from non-occurrences using the basic geoscience dataset. The RF classification outperformed the knowledge-based model with respect to prediction of the known Au occurrences. The geochemical data in general were more predictive of the known Au occurrences than the geophysical data. A data-driven approach such as RF for the production of regional Au prospectivity maps is recommended provided that a sufficient number of training areas (known Au occurrences) exist.     

From 2D to 3D: Prospectivity modelling in the Taupo Volcanic Zone,New Zealand

A 2D prospectivity model of epithermal gold mineralisation has been completed over the Taupo Volcanic Zone (TVZ), using the weights of evidence modelling technique. This study was used to restrict a 3D geological interpretation and prospectivity model for the Ohakuri region. The TVZ is commonly thought of as a present-day analogue of the environment in which many epithermal ore deposits, such as in the Hauraki Goldfield, Coromandel Volcanic Zone, are formed. The models utilise compiled digital data including historical exploration data, geological data from the Institute of Geological and Nuclear Sciences Ltd. Quarter Million Mapping Programme, recent Glass Earth geophysics data and historic exploration geochemical data, including rock-chip and stream sediment information. Spatial correlations between known deposits and predictive maps are determined from the available data, which represent each component of the currently accepted mineral system model for epithermal gold. The 2D prospectivity model confirms that the TVZ has potential for gold mineralisation. However, one of the weaknesses of this weights of evidence model is that the studies are carried out in 2D, with an approximation of 3D provided by geophysical and drilling data projected to a 2D plane. Consequently, a 3D prospectivity model was completed over the Ohakuri area, constrained by the results of the 2D model and predictive maps. The 3D model improved the results allowing more effective exploration targeting. However, the study also highlighted the main issues that need to be resolved before 3D prospectivity modelling becomes standard practise in the mineral exploration industry. The study also helped develop a work flow that incorporates preliminary 2D spatial data analysis from the weights of evidence technique to more effectively restrict and develop 3D predictive map interpretation and development.     

Controls on mineral deposit occurrence inferred from analysis of their spatial pattern and spatial association with geological features

In this paper, point pattern analysis, fractal analysis and Fry analysis were employed to study the spatial pattern of known occurrences of mineral deposits of the type sought, whereas distance distribution method was applied to study the spatial associations between various geological features and known occurrences of mineral deposits of the type sought. In the Aroroy district (Philippines), the results of the applications of these spatial analytical techniques support a conceptual model of district-scale mechanism of geologic controls on low-sulphidation epithermal Au mineralization, which involves a more-or-less regular mesh of interlinked zones of extension faults/fractures at and/or around intersections of NNW- and NW-trending strike-slip faults/fractures. Integration of spatial evidential data layers representing these structural controls and surficial geochemical anomalies, via knowledge-guided application of data-driven evidential belief functions, results in delineation of prospective areas occupying about 25% of the district, in which there is about 70% likelihood of undiscovered occurrences of low-sulphidation epithermal Au deposits.     

Assessing the impact of conceptual mineral systems uncertainty on prospectivity predictions

The past two decades have seen a rapid adoption of artificial intelligence methods applied to mineral exploration. More recently, the easier acquisition of some types of data has inspired a broad literature that has examined many machine learning and modelling techniques that combine exploration criteria, or ‘features’, to generate predictions for mineral prospectivity. Central to the design of prospectivity models is a ‘mineral system’, a conceptual model describing the key geological elements that control the timing and location of economic mineralisation. The mineral systems model defines what constitutes a training set, which features represent geological evidence of mineralisation, how features are engineered and what modelling methods are used. Mineral systems are knowledge-driven conceptual models, thus all parameter choices are subject to human biases and opinion so alternative models are possible. However, the effect of alternative mineral systems models on prospectivity is rarely compared despite the potential to heavily influence final predictions. In this study, we focus on the effect of conceptual uncertainty on Fe ore prospectivity models in the Hamersley region, Western Australia. Four important considerations are tested. (1) Five different supergene and hypogene conceptual mineral systems models guide the inputs for five forest-based classification prospectivity models model. (2) To represent conceptual uncertainty, the predictions are then combined for prospectivity model comparison. (3) Representation of three-dimensional objects as two-dimensional features are tested to address commonly ignored thickness of geological units. (4) The training dataset is composed of known economic mineralisation sites (deposits) as ‘positive’ examples, and exploration drilling data providing ‘negative’ sampling locations. Each of the spatial predictions are assessed using independent performance metrics common to AI-based classification methods and subjected to geological plausibility testing. We find that different conceptual mineral systems produce significantly different spatial predictions, thus conceptual uncertainty must be recognised. A benefit to recognising and modelling different conceptual models is that robust and geologically plausible predictions can be made that may guide mineral discovery.     

Prospectivity for epithermal gold–silver deposits in the Deseado Massif,Argentina

Previous prospectivity modelling for epithermal Au–Ag deposits in the Deseado Massif, southern Argentina, provided regional-scale prospectivity maps that were of limited help in guiding exploration activities within districts or smaller areas, because of their low level of detail. Because several districts in the Deseado Massif still need to be explored, prospectivity maps produced with higher detail would be more helpful for exploration in this region.We mapped prospectivity for low- and intermediate-sulfidation epithermal deposits (LISEDs) in the Deseado Massif at both regional and district scales, producing two different prospectivity models, one at regional scale and the other at district-scale. The models were obtained from two datasets of geological evidence layers by the weights-of-evidence (WofE) method. We used more deposits than in previous studies, and we applied the leave-one-out cross validation (LOOCV) method, which allowed using all deposits for training and validating the models. To ensure statistical robustness, the regional and district-scale models were selected amongst six combinations of geological evidence layers based on results from conditional independence tests.The regional-scale model (1000 m spatial resolution), was generated with readily available data, including a lithological layer with limited detail and accuracy, a clay alteration layer derived from a Landsat 5/7 band ratio, and a map of proximity to regional-scale structures. The district-scale model (100 m spatial resolution) was generated from evidence layers that were more detailed, accurate and diverse than the regional-scale layers. They were also more cumbersome to process and combine to cover large areas. The evidence layers included clay alteration and silica abundance derived from ASTER data, and a map of lineament densities. The use of these evidence layers was restricted to areas of favourable lithologies, which were derived from a geological map of higher detail and accuracy than the one used for the regional-scale prospectivity mapping.The two prospectivity models were compared and their suitability for prediction of the prospectivity in the district-scale area was determined. During the modelling process, the spatial association of the different types of evidence and the mineral deposits were calculated. Based on these results the relative importance of the different evidence layers could be determined. It could be inferred which type of geological evidence could potentially improve the modelling results by additional investigation and better representation.We conclude that prospectivity mapping for LISEDs at regional and district-scales were successfully carried out by using WofE and LOOCV methods. Our regional-scale prospectivity model was better than previous prospectivity models of the Deseado Massif. Our district-scale prospectivity model showed to be more effective, reliable and useful than the regional-scale model for mapping at district level. This resulted from the use of higher resolution evidential layers, higher detail and accuracy of the geological maps, and the application of ASTER data instead of Landsat ETM + data. District-scale prospectivity mapping could be further improved by: a) a more accurate determination of the age of mineralization relative to that of lithological units in the districts; b) more accurate and detailed mapping of the favourable units than what is currently available; c) a better understanding of the relationships between LISEDs and the geological evidence used in this research, in particular the relationship with hydrothermal clay alteration, and the method of detection of the clay minerals; and d) inclusion of other data layers, such as geochemistry and geophysics, that have not been used in this study.     

A hybrid AHP-VIKOR approach for prospectivity modeling of porphyry Cu deposits in the Varzaghan District,NW Iran

Identifying highly favorable areas related to a particular mineralization type is the main objective of mineral prospectivity modeling (MPM). The northwestern portion of Ahar-Arasbaran porphyry copper belt (AAPCB) is situated within the Urumieh-Dokhtar magmatic belt (UDMB). Because of owning many worthwhile Cu-Mo and Cu-Au porphyry deposits, this area is entitled to incorporate diverse spatial evidence layers for the MPM. In this paper, a hybrid AHP-VIKOR, as an improved knowledge-driven MPM procedure has been proposed for integration of various exploration evidence layers. For this, the AHP is used to calculate important weights of spatial criteria while the VIKOR is applied to outline ultimate prospectivity model. Six effective spatial evidence layers pertaining to the Varzaghan District are selected: (1) multi-elemental geochemical layer of Cu-Mo-Bi-Au; (2) remotely sensed data of argillic, phyllic, and iron oxide alteration layers; and (3) geological and structural layers of Oligo-Miocene intrusions and fault. In addition, a fuzzy prospectivity model (γ?=?0.9) is implemented to assess the AHP-VIKOR approach. Two credible validation methods comprising normalized density index and success rate curve are adapted for quantitative evaluation of predictive models and enhancing the probability of exploration success. The achieved results proved the higher accuracy of the AHP-VIKOR model compared with the fuzzy model in delimiting the favorable areas.     

Mapping mineral prospectivity by using one-class support vector machine to identify multivariate geological anomalies from digital geological survey data

Mineral targets are local geological anomalies. In a study area of a number of unit cells, mapping mineral prospectivity can be implemented by identifying anomaly cells from the unit cell population. One-class support vector machine (OCSVM) models can yield useful results in anomaly detection in high-dimensional data or without any assumptions on the distribution of the inlying data. The OCSVM model was applied to mapping gold prospectivity of the Laotudingzi-Xiaosiping district, an area with a complex geological background, in Jilin Province, China. The decision function value of each unit cell belonging to an anomaly was computed on the basis of the trained OCSVM model and used to express gold prospectivity of the cell. The receiver operating characteristic (ROC) curve, area under curve (AUC) and data-processing efficiency were used to compare the performance of the OCSVM model and a restricted Boltzmann machine (RBM) model in mapping gold prospectivity. The results show that the OCSVM model outperforms the RBM model in terms of ROC, AUC and data-processing efficiency. Gold targets were optimally delineated by using the Youden index to maximise the spatial association between the delineated gold targets and known gold deposits. The gold targets delineated by the OCSVM model occupy 11% of the study area and contain 88% of the known gold deposits; and the gold targets delineated by the RBM model occupy 10% of the study area and contain 81% of the known gold deposits. Therefore, the OCSVM model is a feasible mineral prospectivity mapping approach.     

西藏铁格隆南铜(金)矿床三维模型分析与深部预测

铁格隆南铜(金)矿床是近年来在班公湖-怒江成矿带西段多龙矿集区新发现的超大型Cu(Au-Ag)矿床。本文针对铁格隆南矿区深部找矿问题,以现代成矿地质理论和多元地学信息综合分析技术为支撑,以构建矿床找矿模型为指导,依托数据库技术、3S技术、三维建模与可视化技术及地质统计学理论与方法,开展基于矿产地质、地球物理、地球化学等成矿条件及找矿标志的三维地质实体建模与矿化异常三维空间重构,将铁格隆南矿床的预测评价研究拓展到三维空间,揭示了区内成矿地质特征、地球化学及地球物理异常表征,据此探讨了矿床的成因及矿体分布特征。并在此基础上,开展了矿区的地质-地球化学-地球物理综合信息分析与预测评价,以期减少单一信息多解性和成矿条件不确定性,为铁格隆南矿区深部找矿工作提供参考。研究结果表明:在地质找矿模型指导下,基于深部成矿空间三维结构重构基础上的三维地质、地球物理、地球化学异常信息提取与综合分析,可以有效的识别成矿地质体和矿致异常信息,实现深部矿产资源靶区空间定位预测,为深部找矿预测研究提供了新思路。综合分析结果显示铁格隆南矿床深部找矿潜力巨大。     

新疆塔尔巴哈台-萨吾尔地区多重分形地球化学异常提取及成矿预测

塔尔巴哈台-萨吾尔地区位于中国新疆西北部,目前已发现若干处铜、金矿床,具有很好的成矿潜力。成矿定量预测方法常被用于综合成矿标志信息,进行成矿远景区的定量预测和评价。本文首先结合多重分形理论-奇异性指数模型进行地球化学异常提取,之后通过对区域成矿条件进行综合分析,基于地球化学异常以及构造、岩浆岩、地层与矿化的相关关系构建了塔尔巴哈台-萨吾尔地区铜-金成矿预测模型;研究进一步基于新近的找矿成果,以已知矿床和新近发现的矿化点信息作为依据,利用证据权重方法对研究区铜-金矿化的远景区进行了定量预测。预测结果显示出塔尔巴哈台-萨吾尔地区具有良好的找矿前景,区内存在多个新的成矿远景区,可作为新的找矿勘探的目标,开展进一步找矿勘查工作。     

三维成矿定量预测系统设计与应用实例研究

隐伏矿体三维成矿定量预测是以多元地学大数据为基础的矿产预测新技术与方法。本文基于隐伏矿体三维成矿定量预测的实际需要及相关方法步骤,采用集成二次开发的方式,设计实现了一套可在三维环境下基于大数据开展定量化成矿预测工作的软件系统。本文阐述了系统的总体架构及开发方式,并对系统中各个功能模块的设计及实现过程进行详细阐述。系统融合了当前三维成矿定量预测研究的最新方法及成果,内含数据库管理、三维地球物理正演、三维空间分析以及三维预测评价等功能模块,能够对多元地学大数据进行集成和分析预测。为了验证系统的适用性和有效性,该系统被应用于长江中下游成矿带钟姑矿田三维成矿定量预测研究,相关成果表明系统的建立不但能够深化和发展三维成矿预测理论,也为新时期基于大数据的隐伏矿体找矿勘探工作提供了新方法及有力工具。     

Mineral systems approach applied to GIS-based 2D-prospectivity modelling of geological regions: Insights from Western Australia

GIS-based 2D prospectivity modelling of three greenfield geological regions of Western Australia, namely, the West Arunta Orogen, West Musgrave Orogen and Gascoyne Province, was implemented for a range of deposit types including orogenic and intrusion-related gold, volcanic sediment-hosted base-metal sulfides, magmatic nickel–copper and magmatic platinum group element sulfides, iron-oxide copper gold, tin–tungsten, igneous and metamorphic related rare earth elements, surficial uranium and unconformity-related uranium.Conceptual mineral systems models were generated to identify the targeting criteria. The inputs to the models were the spatial proxies derived from 1:100,000 to 1:500,000 scale public domain data. The results showed similar prospectivity patterns for all of the targeted deposit types except sediment-hosted uranium and surficial uranium deposit types. Once a favourable geodynamic architecture is established, it can sustain different mineral systems and produce diverse deposit types depending on the nature of ligands in the source regions and physical–chemical environment in the trap regions through repeated reactivation in the subsequent geological history. A model is proposed to explain the formation of different deposit types at different stages of tectonic evolution of a province. The implication for GIS-based 2D prospectivity modelling at the scale of geological region is that the prospectivity model may not be deposit type specific. Further, prospectivity modelling should be carried out sequentially at progressively finer scales (regional- to district- to camp-scale), using only the targeting criteria that are relevant at the specific scale to delineate targets for specific deposit types.     

Application of singularity mapping technique to identify local anomalies using stream sediment geochemical data,a case study from Gangdese,Tibet, western China

Identifying geochemical anomalies from background is a fundamental task in exploration geochemistry. The Gangdese mineral district in western China has complex geochemical surface expression due to complex geological background and was chosen as a study area for recognition of the spatial distribution of geochemical elements and separating anomalies from background using stream sediment geochemical data. The results illustrate that weak anomalies are hidden within the strong variance of background and are not well identified by means of inverse distance weighted; neither are they clearly identified by the C–A method if this method is applied to the whole study area. On the other hand, singularity values provide new information that complements use of original concentration values and can quantify the properties of enrichment and depletion caused by mineralization. In general, producing maps of singularities can help to identify relatively weak metal concentration anomalies in complex geological regions. Application of singularity mapping technique in Gangdese district shows local anomalies of Cu are not only directly associated with known deposits in the central part of the study area, but also with E–W and N–E oriented faults in the north of the study area. Both types of anomalies should be further investigated for undiscovered Cu mineral deposits.     

Data fusion and porphyry copper prospectivity models,southeastern Arizona

Mineral exploration programs commonly use a combination of geological, geophysical and remotely sensed data to detect sets of optimal conditions for potential ore deposits. Prospectivity mapping techniques can integrate and analyse these digital geological data sets to produce maps that identify where optimal conditions converge. Three prospectivity mapping techniques – weights of evidence, fuzzy logic and a combination of these two methods – were applied to a 32,000 km² study area within the southeastern Arizona porphyry Cu district and then assessed based on their ability to identify new and existing areas of high mineral prospectivity. Validity testing revealed that the fuzzy logic method using membership values based on an exploration model identified known Cu deposits considerably better than those that relied solely on weights of evidence, and slightly better than those that used a combination of weights of evidence and fuzzy logic. This led to the selection of the prospectivity map created using the fuzzy logic method with membership values based on an exploration model. Three case study areas were identified that comprise many critical geological and geophysical characteristics favourable to hosting porphyry Cu mineralisation, but not associated with known mining or exploration activity. Detailed analysis of each case study has been performed to promote these areas as potential targets and to demonstrate the ability of prospectivity modelling techniques as useful tools in mineral exploration programs.     

Mapping mineral prospectivity for Cu polymetallic mineralization in southwest Fujian Province,China

In this study, both the fuzzy weights of evidence (FWofE) and random forest (RF) methods were applied to map the mineral prospectivity for Cu polymetallic mineralization in southwestern Fujian Province, which is an important Cu polymetallic belt in China. Recent studies have revealed that the Zijinshan porphyry–epithermal Cu deposit is associated with Jurassic to Cretaceous (Yanshanian) intermediate to felsic intrusions and faulting tectonics. Evidence layers, which are key indicators of the formation of Zijinshan porphyry–epithermal Cu mineralization, include: (1) Jurassic to Cretaceous intermediate–felsic intrusions; (2) mineralization-related geochemical anomalies; (3) faults; and (4) Jurassic to Cretaceous volcanic rocks. These layers were determined using spatial analyses in support by GeoDAS and ArcGIS based on geological, geochemical, and geophysical data. The results demonstrated that most of the known Cu occurrences are in areas linked to high probability values. The target areas delineated by the FWofE occupy 10% of the study region and contain 60% of the total number of known Cu occurrences. In comparison with FWofE, the resulting RF areas occupy 15% of the study area, but contain 90% of the total number of known Cu occurrences. The normalized density value of 1.66 for RF is higher than the 1.15 value for FWofE, indicating that RF performs better than FWofE. Receiver operating characteristics (ROC) were used to validate the prospectivity model and check the effects of overfitting. The area under the ROC curve (AUC) was greater than 0.5, indicating that both prospectivity maps are useful in Cu polymetallic prospectivity mapping in southwestern Fujian Province.     

Data-driven predictive mapping of gold prospectivity,Baguio district,Philippines: Application of Random Forests algorithm

The Random Forests (RF) algorithm has recently become a fledgling method for data-driven predictive mapping of mineral prospectivity, and so it is instructive to further study its efficacy in this particular field. This study, carried out using Baguio gold district (Philippines), examines (a) the sensitivity of the RF algorithm to different sets of deposit and non-deposit locations as training data and (b) the performance of RF modeling compared to established methods for data-driven predictive mapping of mineral prospectivity. We found that RF modeling with different training sets of deposit/non-deposit locations is stable and reproducible, and it accurately captures the spatial relationships between the predictor variables and the training deposit/non-deposit locations. For data-driven predictive mapping of epithermal Au prospectivity in the Baguio district, we found that (a) the success-rates of RF modeling are superior to those of weights-of-evidence, evidential belief and logistic regression modeling and (b) the prediction-rate of RF modeling is superior to that of weights-of-evidence modeling but approximately equal to those of evidential belief and logistic regression modeling. Therefore, the RF algorithm is potentially much more useful than existing methods that are currently used for data-driven predictive mapping of mineral prospectivity. However, further testing of the method in other areas is needed to fully explore its usefulness in data-driven predictive mapping of mineral prospectivity.     

Regional prospectivity analysis for hydrothermal-remobilised nickel mineral systems in western Victoria,Australia

Fuzzy logic mineral prospectivity modelling was performed to identify camp-scale areas in western Victoria with an elevated potential for hydrothermal-remobilised nickel mineralisation. This prospectivity analysis was based on a conceptual mineral system model defined for a group of hydrothermal nickel deposits geologically similar to the Avebury deposit in Tasmania. The critical components of the conceptual model were translated into regional spatial predictor maps combined using a fuzzy inference system. Applying additional criteria of land use restrictions and depth of post-mineralisation cover, downgrading the exploration potential of the areas within national parks or with thick barren cover, allowed the identification of just a few potentially viable exploration targets, in the south of the Grampians-Stavely and Glenelg zones. Uncertainties of geological interpretations and parameters of the conceptual mineral system model were explicitly defined and propagated to the final prospectivity model by applying Monte Carlo simulations to the fuzzy inference system. Modelling uncertainty provides additional information which can assist in a further risk analysis for exploration decision making.     

GIS-based 3D prospectivity mapping: A case study of Jiama copper-polymetallic deposit in Tibet,China

This paper reports a deposit-scale GIS-based 3D mineral potential assessment of the Jiama copper-polymetallic deposit in Tibet, China. The assessment was achieved through a sequential implementation of metallogenic modelling and 3D modelling of geology, geochemistry and prospectivity. A metallogenic model for the Jiama deposit and 3D modelling workflow were used to construct multiple 3D layers of volumetric and triangular mesh models to represent geology, geochemistry and ore-controlling features in the study area. A GIS-based 3D weights-of-evidence analysis was then used to estimate the subsurface prospectivity for Cu (Mo) orebodies in the area, which led to the identification of three prospective deep-seated exploration targets. Additionally, the geochemical modelling indicates three potential fluid flow pathways based on the 3D zonation of major geochemical elements and their ratios, particularly the Zn/Pb ratios, which support the results of the weights of evidence model.     

Separation of a geochemical anomaly from background by fractal and U-statistic methods,a case study: Khooni district,Central Iran

Separation of geochemical anomalies from background are one of the important steps in mineral exploration. The Khooni mineral district (Central Iran) has complex geochemical surface expression due to a complex geological background. This region was chosen as a study area for recognition of the spatial distribution of geochemical elements and separating anomalies from background using stream sediment geochemical data. In the past decades, geochemical anomalies have been identified by means of various methods. Some of these separation methods include: statistical analysis methods, spatial statistical methods and fractal and multi-fractal methods. In this article, two efficient methods, i.e. U-statistics and the fractal concentration-area for separation and detection of anomalous areas of the background were used. The U spatial statistic method is a weighted mean, which considers sampling point positions and their spatial relation in the estimation of anomaly location. Also, fractal and multi-fractal models have also been applied to separate anomalies from background values. In this paper, the concentration–area model (C–A) was suggested to separate the anomaly of background. For this purpose, about 256 stream sediment samples were collected and analyzed. Then anomaly maps of elements were generated based on U spatial statistics and the C-A fractal methods for Au, As and Sb elements. According to obtained results, the U-statistics method performed better than C-A method. Because the comparisons of the known deposits and occurrences against the anomalous area created using thresholds from U-statistics and C-A method show that the spatial U-statistics method hits all of 3 known deposits and occurrences, the C-A fractal method hits 1 and fails 2. In addition, the results showed that these methods with regard to spatial distribution and variability within neighboring samples, in addition to concentration value frequency distributions and correlation coefficients, have more accurate results than the traditional approaches.