Geologically Constrained Fuzzy Mapping of Gold Mineralization Potential,Baguio District,Philippines

An application of the theory of fuzzy sets to the mapping of gold mineralization potential in the Baguio gold mining district of the Philippines is described. Proximity to geological features is translated into fuzzy membership functions based upon qualitative and quantitative knowledge of spatial associations between known gold occurrences and geological features in the area. Fuzzy sets of favorable distances to geological features and favorable lithologic formations are combined using fuzzy logic as the inference engine. The data capture, map operations, and spatial data analyses are carried out using a geographic information system. The fuzzy predictive maps delineate at least 68% of the known gold occurrences that are used to generate the model. The fuzzy predictive maps delineate at least 76% of the unknown gold occurrences that are not used to generate the model. The results are highly comparable with the results of previous stream-sediment geochemical survey in the area. The results demonstrate the usefulness of a geologically constrained fuzzy set approach to map mineral potential and to redirect surficial exploration work in the search for yet undiscovered gold mineralization in the mining district. The method described is applicable to other mining districts elsewhere.     

Spatial interpolation using conditional generative adversarial neural networks

ABSTRACT

Spatial interpolation is a traditional geostatistical operation that aims at predicting the attribute values of unobserved locations given a sample of data defined on point supports. However, the continuity and heterogeneity underlying spatial data are too complex to be approximated by classic statistical models. Deep learning models, especially the idea of conditional generative adversarial networks (CGANs), provide us with a perspective for formalizing spatial interpolation as a conditional generative task. In this article, we design a novel deep learning architecture named conditional encoder-decoder generative adversarial neural networks (CEDGANs) for spatial interpolation, therein combining the encoder-decoder structure with adversarial learning to capture deep representations of sampled spatial data and their interactions with local structural patterns. A case study on elevations in China demonstrates the ability of our model to achieve outstanding interpolation results compared to benchmark methods. Further experiments uncover the learned spatial knowledge in the model’s hidden layers and test the potential to generalize our adversarial interpolation idea across domains. This work is an endeavor to investigate deep spatial knowledge using artificial intelligence. The proposed model can benefit practical scenarios and enlighten future research in various geographical applications related to spatial prediction.     

Exploring Spatially Non-stationary Relationships in the Determinants of Mineralization in 3D Geological Space

Exploring the spatial relationships between various geological features and mineralization is not only conducive to understanding the genesis of ore deposits but can also help to guide mineral exploration by providing predictive mineral maps. However, most current methods assume spatially constant determinants of mineralization and therefore have limited applicability to detecting possible spatially non-stationary relationships between the geological features and the mineralization. In this paper, the spatial variation between the distribution of mineralization and its determining factors is described for a case study in the Dingjiashan Pb–Zn deposit, China. A local regression modeling technique, geological weighted regression (GWR), was leveraged to study the spatial non-stationarity in the 3D geological space. First, ordinary least-squares (OLS) regression was applied, the redundancy and significance of the controlling factors were tested, and the spatial dependency in Zn and Pb ore grade measurements was confirmed. Second, GWR models with different kernel functions in 3D space were applied, and their results were compared to the OLS model. The results show a superior performance of GWR compared with OLS and a significant spatial non-stationarity in the determinants of ore grade. Third, a non-stationarity test was performed. The stationarity index and the Monte Carlo stationarity test demonstrate the non-stationarity of all the variables throughout the area. Finally, the influences of the degree of non-stationary of all controlling factors on mineralization are discussed. The existence of significant non-stationarity of mineral ore determinants in 3D space opens up an exciting avenue for research into the prediction of underground ore bodies.

     

Modelling uncertainty and spatial dependence: Stochastic imaging

Abstract

The most vibrant area of research in geostatistics is stochastic imaging, that is, the modelling of spatial uncertainty through alternative, equiprobable, numerical representations (maps) of spatially distributed phenomena. These stochastic images are conditioned to a variety of data accounting for their specific measurement scale and reliability.

Any geostatistical prediction is built on a prior model of spatial correlation that ties data to unsampled values and, equally importantly, unsampled values at different locations together. Since a major goal in the exercise of mapping is to display organization in space, spatial correlation is a necessity. As for uncertainty it is so pervasive that it is imperative to account for it.     

Weights of Evidence Modeling of Mineral Potential: A Case Study Using Small Number of Prospects,Abra, Philippines

Weights of evidence (WofE) modeling usually is applied to map mineral potential in areas with large number of deposits/prospects. In this paper, WofE modeling is applied to a case study area measuring about 920 km² with 12 known porphyry copper prospects. A pixel size of 100 m × 100 m was used in the spatial data analyses to represent in a raster-based GIS lateral extents of prospects and of geological features considered as spatial evidence. Predictor maps were created based on (a) estimates of studentized values of positive spatial association between prospects and spatial evidence; (b) proportion of number of prospects in zones where spatial evidence is present; and (c) geological interpretations of positive spatial association between prospects and spatial evidence. Uncertainty because of missing geochemical evidence is shown to have an influence on tests of assumption of conditional independence (CI) among predictor maps with respect to prospects. For the final predictive model, assumption of CI is rejected based on omnibus test but is accepted based on a new omnibus test. The final predictive model, which delineates 30% of study area as zones with potential for porphyry copper, has 83% success rate and 73% prediction rate. The results demonstrate plausibility of WofE modeling of mineral potential in large areas with small number of mineral prospects.     

Non-stationary Geostatistical Modeling: A Case Study Comparing LVA Estimation Frameworks

Incorporating locally varying anisotropy (LVA) in geostatistical modeling improves estimates for structurally complex domains where a single set of anisotropic parameters modeled globally do not account for all geological features. In this work, the properties of two LVA-geostatistical modeling frameworks are explored through application to a complexly folded gold deposit in Ghana. The inference of necessary parameters is a significant requirement of geostatistical modeling with LVA; this work focuses on the case where LVA orientations, derived from expert geological interpretation, are used to improve the grade estimates. The different methodologies for inferring the required parameters in this context are explored. The results of considering different estimation frameworks and alternate methods of parameterization are evaluated with a cross-validation study, as well as visual inspection of grade continuity along select cross sections. Results show that stationary methodologies are outperformed by all LVA techniques, even when the LVA framework has minimal guidance on parameterization. Findings also show that additional improvements are gained by considering parameter inference where the LVA orientations and point data are used to infer the local range of anisotropy. Considering LVA for geostatistical modeling of the deposit considered in this work results in better reproduction of curvilinear geological features.

     

Multiple Point Metrics to Assess Categorical Variable Models

Geostatistical models should be checked to ensure consistency with conditioning data and statistical inputs. These are minimum acceptance criteria. Often the first and second-order statistics such as the histogram and variogram of simulated geological realizations are compared to the input parameters to check the reasonableness of the simulation implementation. Assessing the reproduction of statistics beyond second-order is often not considered because the “correct” higher order statistics are rarely known. With multiple point simulation (MPS) geostatistical methods, practitioners are now explicitly modeling higher-order statistics taken from a training image (TI). This article explores methods for extending minimum acceptance criteria to multiple point statistical comparisons between geostatistical realizations made with MPS algorithms and the associated TI. The intent is to assess how well the geostatistical models have reproduced the input statistics of the TI; akin to assessing the histogram and variogram reproduction in traditional semivariogram-based geostatistics. A number of metrics are presented to compare the input multiple point statistics of the TI with the statistics of the geostatistical realizations. These metrics are (1) first and second-order statistics, (2) trends, (3) the multiscale histogram, (4) the multiple point density function, and (5) the missing bins in the multiple point density function. A case study using MPS realizations is presented to demonstrate the proposed metrics; however, the metrics are not limited to specific MPS realizations. Comparisons could be made between any reference numerical analogue model and any simulated categorical variable model.     

Geostatistical Simulation with a Trend Using Gaussian Mixture Models

Geostatistics applies statistics to quantitatively describe geological sites and assess the uncertainty due to incomplete sampling. Strong assumptions are required regarding the location independence of statistical parameters to construct numerical models with geostatistical tools. Most geological data exhibit large-scale deterministic trends together with short-scale variations. Such location dependence violates the common geostatistical assumption of stationarity. The trend-like deterministic features should be modeled prior to conventional geostatistical prediction and accounted for in subsequent geostatistical calculations. The challenge of using a trend in geostatistical simulation algorithms for the continuous variable is the subject of this paper. A stepwise conditional transformation with a Gaussian mixture model is considered to provide a stable and artifact-free numerical model. The complex features of the regionalized variable in the presence of a trend are removed in the forward transformation and restored in the back transformation. The Gaussian mixture model provides a seamless bin-free approach to transformation. Data from a copper deposit were used as an example. These data show an apparent trend unsuitable for conventional geostatistical algorithms. The result shows that the proposed algorithm leads to improved geostatistical models.     

Direct induction of compact rule-based classifiers for resource mapping

Abstract

Rule-based classifiers are used regularly with geographical information systems to map categorical attributes on the basis of a set of numeric or unordered categorical attributes. Although a variety of methods exist for inducing rule-based classifiers from training data, these tend to produce large numbers of rules when the data has noise. This paper describes a method for inducing compact rule-sets whose classification accuracy can, at least in some domains, compare favourably with that achieved by larger less succinct rule-sets produced by alternative methods. One rule is induced for each output class. The condition list for this rule represents a box in n-dimensional attribute space, formed by intersecting conditions which exclude other classes. Despite this simplicity, the classifier performed well in the test application prediction of soil classes in the Port Hills, New Zealand, on the basis of regolith type and topographic attributes obtained from a digital terrain model.     

Predictive land value modelling in Guatemala City using a geostatistical approach and Space Syntax

ABSTRACT

Spatial information of land values is fundamental for planners and policy makers. Individual appraisals are costly, explaining the need for predictive modelling. Recent work has investigated using Space Syntax to analyse urban access and explain land values. However, the spatial dependence of urban land markets has not been addressed in such studies. Further, the selection of meaningful variables is commonly conducted under non-spatialized modelling conditions. The objective of this paper is to construct a land value map using a geostatistical approach using Space Syntax and a spatialized variable selection. The methodology is applied in Guatemala City. We used an existing dataset of residential land value appraisals and accessibility metrics. Regression-kriging was used to conduct variable selection and derive a model for spatial prediction. The prediction accuracy is compared with a multivariate regression. The results show that a spatialized variable selection yields a more parsimonious model with higher prediction accuracy. New insights were found on how Space Syntax explains land value variability when also modelling the spatial dependence. Space Syntax can contribute with relevant spatialized information for predictive land value modelling purposes. Finally, the spatial modelling framework facilitates the production of spatial information of land values that is relevant for planning practice.     

Improving Coal Quality Estimations with Geostatistics and Geophysical Logs

In most modern coal mines, there are many coal quality parameters that are measured on samples taken from boreholes. These data are used to generate spatial models of the coal quality parameters, typically using inverse distance as an interpolation method. At the same time, downhole geophysical logging of numerous additional boreholes is used to measure various physical properties but no coal quality samples are taken. The work presented in this paper uses two of the most important coal quality variables—ash and volatile matter—and assesses the efficacy of using a number of geostatistical interpolation methods to improve the accuracy of the interpolated models, including the use of auxiliary variables from geophysical logs. A multivariate spatial statistical analysis of ash, volatile matter and several auxiliary variables is used to establish a co-regionalization model that relates all of the variables as manifestations of an underlying geological characteristic. A case study of a coal mine in Queensland, Australia, is used to compare the interpolation methods of inverse distance to ordinary kriging, universal kriging, co-kriging, regression kriging and kriging with an external drift. The relative merits of these six methods are compared using the mean error and the root mean square error as measures of bias and accuracy. The study demonstrates that there is significant opportunity to improve the estimations of coal quality when using kriging with an external drift. The results show that when using the depth of a sample as an external drift variable there is a significant improvement in the accuracy of estimation for volatile matter, and when using wireline density logs as the drift variable there is improvement in the estimation of the in situ ash. The economic benefit of these findings is that cheaper proxies for coal quality parameters can significantly increase data density and the quality of estimations.

     

A case study of model selection and parameter inference by maximum likelihood with application to uncertainty analysis

One of the uses of geostatistical conditional simulation is as a tool in assessing the spatial uncertainty of inputs to the Monte Carlo method of system uncertainty analysis. Because the number of experimental data in practical applications is limited, the geostatistical parameters used in the simulation are themselves uncertain. The inference of these parameters by maximum likelihood allows for an easy assessment of this estimation uncertainty which, in turn, may be included in the conditional simulation procedure. A case study based on transmissivity data is presented to show the methodology whereby both model selection and parameter inference are solved by maximum likelihood.     

Sediment‐budget modelling of multi‐sourced basin fills: application to recent deposits of the western Adriatic mud wedge (Italy)

We analysed modern mass‐accumulation patterns on the western Adriatic mud wedge (Italy), an elongated belt of shelf mud formed by coalesced prodeltas of the Adige, Po, and Apennine rivers, as part of an integrated strategy aimed at producing a quantitative sediment budget model for muddy continental shelves sourced by multiple compositionally distinct fluvial systems. Sediment provenance and source‐specific accumulation rates of surface sediments were quantified by combining results of grain‐size analysis and geochemical analysis of specific size fractions with bulk mass accumulation rates. Statistical classification algorithms adapted to compositional data were used to partition the total (geochemical) variation of sediment properties into size‐related and provenance‐specific factors. We identified geochemically distinct fluvial end‐member sediment types in two different grain‐size fractions, which were grouped into sediments derived from the Apennine rivers, and sediments derived from the Po and Adige rivers. Compositional fingerprints (end‐member compositions) of each source area were estimated by taking into account relative rates of fluvial sediment supply from rivers as predicted by numerical modelling. The end members allow us to explain geochemical compositional variation of mud‐wedge surface sediments in terms of provenance and size‐selective dispersal, and map mass accumulation rates of sediments from individual source areas (grain size<63 μm), as well as bulk sand accumulation rates (grain size>63 μm) across the western Adriatic mud wedge. The source‐specific rates of fine‐grained sediment supply derived from geostatistical estimates of mass‐accumulation rates were used to calibrate the numerical model of sediment supply to present‐day conditions.     

Evaluation of vegetative criteria for near-surface groundwater detection using multispectral mapping and GIS techniques in semi-arid Botswana

The critical need to consider all options in the search for groundwater in semi-arid areas has promoted work on the possible association of near-surface groundwater and vegetation characteristics using a combination of remote-sensing data and geographic information systems (GIS) techniques. Two vegetative criteria (dense woody cover and abundance of deep-rooting species) are identified as being indicative of near-surface groundwater, and their spatial distribution is tested against the location of aquifers in southeast Botswana. Vegetative criteria classes were combined in a GIS environment with the distribution of geomorphic units and bedrock geology to determine the degree of coincidence with assumed or known aquifers. Results indicate that the distribution of dense woody vegetation as mapped from Thematic Mapper imagery has some potential in identifying especially surficial but also bedrock near-surface groundwater sources in mostly naturally vegetated semi-arid areas. Dense woody cover classes tend to select aquifers in topographically higher areas while classes comprising some deep-rooting species tend to select low-lying aquifers such as those occurring in fossil valleys. Deep-rooting species, however, are less successful as a vegetative criterion. Although various technical refinements are suggested, this work shows that vegetative criteria mapping can however be used in conjunction with conventional geological/geophysical techniques to enhance the prospects for groundwater location in relatively undisturbed semi-arid areas.     

基于XGBoost的多源降水数据融合方法研究

气象站点观测降水难以精确反映降水时空分布与变化,而雷达降水存在复杂地形区域精度不高等问题。为了最大限度发挥两者的优势,文章以广东省北部山区为研究区域,选择2018-08-26—30一次暴雨过程为研究对象,结合地形、与海岸线距离、植被指数、经纬度等地表辅助参量,分析地面站点降水与地表辅助参量、雷达降水的相关关系,利用XGBoost算法与克里金插值方法,构建地面-雷达日降水数据融合模型,得到了空间分辨率为1 km的日降水融合数据集。此外,采用多元线性回归（LM）与克里金插值方法,实现了地面-雷达日降水数据的融合,并利用地面降水数据分别对XGBoost与LM日降水融合性能进行精度验证。结果表明：1）地面降水与雷达降水存在显著的正相关,地面降水与地表辅助参量之间的相关性随时间变化;2）XGBoost预测精度整体上高于LM预测结果;经模型残差校正后,XGBoost融合模型的精度整体上优于LM融合模型,这是因为XGBoost方法在捕捉地面降水与地表辅助参量、雷达降水之间关系性能上优于LM方法。     

Nonparametric Geostatistical Simulation of Subsurface Facies: Tools for Validating the Reproduction of,and Uncertainty in,Facies Geometry

Delineation of facies in the subsurface and quantification of uncertainty in their boundaries are significant steps in mineral resource evaluation and reservoir modeling, which impact downstream analyses of a mining or petroleum project. This paper investigates the ability of nonparametric geostatistical simulation algorithms (sequential indicator, single normal equation and filter-based simulation) to construct realizations that reproduce some expected statistical and spatial features, namely facies proportions, boundary regularity, contact relationships and spatial correlation structure, as well as the expected fluctuations of these features across the realizations. The investigation is held through a synthetic case study and a real case study, in which a pluri-Gaussian model is considered as the reference for comparing the simulation results. Sequential indicator simulation and single normal equation simulation based on over-restricted neighborhood implementations yield the poorest results, followed by filter-based simulation, whereas single normal equation simulation with a large neighborhood implementation provides results that are closest to the reference pluri-Gaussian model. However, some biases and inaccurate fluctuations in the realization statistics (facies proportions, indicator direct and cross-variograms) still arise, which can be explained by the use of a single finite-size training image to construct the realizations.

     

Spatial Scale Problems and Geostatistical Solutions: A Review

The concept of spatial scale is fundamental to geography, as are the problems of integrating data obtained at different scales. The availability of GIS has provided an appropriate environment to re-scale data prior to subsequent integration, but few tools with which to implement the re-scaling. This sparsity of appropriate tools arises primarily because the nature of the spatial variation of interest is often poorly understood and, specifically, the patterns of spatial dependence and error are unknown. Spatial dependence can be represented and modelled using geostatistical approaches providing a basis for the subsequent re-scaling of spatial data (e.g., via spatial interpolation). Geostatistical techniques can also be used to model the effects of re-scaling data through the geostatistical operation of regularization. Regularization provides a means by which to re-scale the statistics and functions that describe the data rather than the data themselves. These topics are reviewed in this paper and the importance of the spatial scale problems that remain is emphasized.     

Mineral Potential Mapping Using a Conjugate Gradient Logistic Regression Model

Mineral potential prediction is a process of establishing a statistical model that describes the relationship between evidence variables and mineral occurrences. In this study, evidence variables were constructed from geological, remote sensing, and geochemical data collected from the Lalingzaohuo district, Qinghai Province, China. Based on these evidence variables, a conjugate gradient logistic regression (CG-LR) model was established to predict exploration targets in the study area. The receiver operating characteristic (ROC) and prediction–area (P-A) curves were used to evaluate the effectiveness of the CG-LR model in mineral potential mapping. The difference between the vertical and horizontal coordinates of each point on the ROC curve was used to determine the optimal threshold for classifying the exploration targets. The optimal threshold corresponds to the point on the ROC curve where the difference between the vertical coordinate and the horizontal coordinate is the largest. In exploration target prediction in the study area, the CG algorithm was used to optimize iteratively the LR coefficients, and the prediction effectiveness was tested for different epochs. With increasing iterations, the prediction performance of the model becomes increasingly better. After 60 iterations, the LR model becomes stable and has the best performance in exploration target prediction. At this point, the exploration targets predicted by the CG-LR model occupy 14.39% of the study area and contain 93% of the known mineral deposits. The exploration targets predicted by the model are consistent with the metallogenic geological characteristics of the study area. Therefore, the CG-LR model can effectively integrate geological, remote sensing, and geochemical data for the study area to predict targets for mineral exploration.

     

Using Mahalanobis Distance to Detect and Remove Outliers in Experimental Covariograms

Experimental variograms are crucial for most geostatistical studies. In kriging, for example, the variography has a direct influence on the interpolation weights. Despite the great importance of variogram estimators in predicting geostatistical features, they are commonly influenced by outliers in the dataset. The effect of some randomly spatially distributed outliers can mask the pattern of the experimental variogram and produce a destructuration effect, implying that the true data spatial continuity cannot be reproduced. In this paper, an algorithm to detect and remove the effect of outliers in experimental variograms using the Mahalanobis distance is proposed. An example of the algorithm’s application is presented, showing that the developed technique is able to satisfactorily detect and remove outliers from a variogram.