Knowledge-Driven and Data-Driven Fuzzy Models for Predictive Mineral Potential Mapping

In this paper, we describe new fuzzy models for predictive mineral potential mapping: (1) a knowledge-driven fuzzy model that uses a logistic membership function for deriving fuzzy membership values of input evidential maps and (2) a data-driven model, which uses a piecewise linear function based on quantified spatial associations between a set of evidential evidence features and a set of known mineral deposits for deriving fuzzy membership values of input evidential maps. We also describe a graphical defuzzification procedure for the interpretation of output fuzzy favorability maps. The models are demonstrated for mapping base metal deposit potential in an area in the south-central part of the Aravalli metallogenic province in the state of Rajasthan, western India. The data-driven and knowledge-driven models described in this paper predict potentially mineralized zones, which occupy less than 10% of the study area and contain at least 83% of the model and validation base metal deposits. A cross-validation of the favorability map derived from using one of the models with the favorability map derived from using the other model indicates a remarkable similarity in their results. Both models therefore are useful for predicting favorable zones to guide further exploration work.     

Data-Driven Index Overlay and Boolean Logic Mineral Prospectivity Modeling in Greenfields Exploration

Index overlay and Boolean logic are two techniques customarily applied for knowledge-driven modeling of prospectivity for mineral deposits, whereby weights of values in evidential maps and weights of every evidence map are assigned based on expert opinion. In the Boolean logic technique for mineral prospectivity modeling (MPM), threshold evidential values for creating binary maps are defined based on expert opinion as well. This practice of assigning weights based on expert opinion involves trial-and-error and introduces bias in evaluating relative importance of both evidential values and individual evidential maps. In this paper, we propose a data-driven index overlay MPM technique whereby weights of individual evidential maps are derived from data. We also propose a data-driven Boolean logic MPM technique, whereby thresholds for creating binary maps are defined based on data. For assigning weights and defining thresholds in these proposed data-driven MPM techniques, we applied a prediction-area plot from which we can estimate the predictive ability of each evidential map with respect to known mineral occurrences, and we use that predictive ability estimate to assign weights to evidential map and to select thresholds for generating binary predictor maps. To demonstrate these procedures, we applied them to an area in the Kerman province in southeast Iran as a MPM case study for porphyry-Cu deposits.     

Application of Radial Basis Functional Link Networks to Exploration for Proterozoic Mineral Deposits in Central Iran

The metallogeny of Central Iran is characterized mainly by the presence of several iron, apatite, and uranium deposits of Proterozoic age. Radial Basis Function Link Networks (RBFLN) were used as a data-driven method for GIS-based predictive mapping of Proterozoic mineralization in this area. To generate the input data for RBFLN, the evidential maps comprising stratigraphic, structural, geophysical, and geochemical data were used. Fifty-eight deposits and 58 ‘nondeposits’ were used to train the network. The operations for the application of neural networks employed in this study involve both multiclass and binary representation of evidential maps. Running RBFLN on different input data showed that an increase in the number of evidential maps and classes leads to a larger classification sum of squared error (SSE). As a whole, an increase in the number of iterations resulted in the improvement of training SSE. The results of applying RBFLN showed that a successful classification depends on the existence of spatially well distributed deposits and nondeposits throughout the study area. An erratum to this article can be found at     

'How green is my valley?' Desktop geographic information systems as a community-based participatory mapping tool

Communities can be encouraged to participate in countryside conservation through mapping, expressing what they feel to be important or distinct locally. Established UK community 'parish map' projects focus on artwork. 'Public participation geographic information systems' potentially offer an alternative community mapping approach. Research sought to compare artwork and GIS mapping and their ease of use. Raster maps, digitizing of features and data table creation encouraged community groups to undertake thematic mapping themselves. Seamless maps removed perceived neighbourhood boundaries. Linking attribute data to maps offers an interactive approach to projects, including internet mapping. Findings indicated that hands-on use of GIS, with support, could benefit and empower community groups when responding to local geographic issues.     

Use of Fuzzy Membership Input Layers to Combine Subjective Geological Knowledge and Empirical Data in a Neural Network Method for Mineral-Potential Mapping

Use of GIS layers, in which the cell values represent fuzzy membership variables, is an effective method of combining subjective geological knowledge with empirical data in a neural network approach to mineral-prospectivity mapping. In this study, multilayer perceptron (MLP), neural networks are used to combine up to 17 regional exploration variables to predict the potential for orogenic gold deposits in the form of prospectivity maps in the Archean Kalgoorlie Terrane of Western Australia. Two types of fuzzy membership layers are used. In the first type of layer, the statistical relationships between known gold deposits and variables in the GIS thematic layer are used to determine fuzzy membership values. For example, GIS layers depicting solid geology and rock-type combinations of categorical data at the nearest lithological boundary for each cell are converted to fuzzy membership layers representing favorable lithologies and favorable lithological boundaries, respectively. This type of fuzzy-membership input is a useful alternative to the 1-of-N coding used for categorical inputs, particularly if there are a large number of classes. Rheological contrast at lithological boundaries is modeled using a second type of fuzzy membership layer, in which the assignment of fuzzy membership value, although based on geological field data, is subjective. The methods used here could be applied to a large range of subjective data (e.g., favorability of tectonic environment, host stratigraphy, or reactivation along major faults) currently used in regional exploration programs, but which normally would not be included as inputs in an empirical neural network approach.     

Application of Data-Driven Evidential Belief Functions to Prospectivity Mapping for Aquamarine-Bearing Pegmatites,Lundazi District,Zambia

A case application of data-driven estimation of evidential belief functions (EBFs) is demonstrated to prospectivity mapping in Lundazi district (eastern Zambia). Spatial data used to represent recognition criteria of prospectivity for aquamarine-bearing pegmatites include mapped granites, mapped faults/fractures, mapped shear zones, and radioelement concentration ratios derived from gridded airborne radiometric data. Data-driven estimates EBFs take into account not only (a) spatial association between an evidential map layer and target deposits but also (b) spatial relationships between classes of evidences in an evidential map layer. Data-driven estimates of EBFs can indicate which spatial data provide positive or negative evidence of prospectivity. Data-driven estimates of EBFs of only spatial data providing positive evidence of prospectivity were integrated according to Dempster’s rule of combination. Map of integrated degrees of belief was used to delineate zones of relative degress of prospectivity for aquamarine-bearing pegmatites. The predictive map has at least 85% prediction rate and at least 79% success rate of delineating training and validation deposits, respectively. The results illustrate usefulness of data-driven estimation of EBFs in GIS-based predictive mapping of mineral prospectivity. The results also show usefulness of EBFs in managing uncertainties associated with evidential maps.     

Comparison of satellite and air photo based landslide susceptibility maps

Landslide susceptibility maps can be prepared in a variety of ways. Many geoscientists favour the use of an overlay model approach in which several map layers are combined by some arithmetic rules to determine the potential for sliding in an area or region. The resulting susceptibility maps, although based on a subjective weighting of relevant factors, can often be of high accuracy and utility. In order to obtain the relevant input data for this type of analysis, remotely sensed data are often used. To date, susceptibility mapping, just as the mapping of historic and individual landslides, has tended to require higher-resolution imagery. This has somewhat limited the application of landslide susceptibility mapping. While high-resolution air photo or satellite imagery is superior to lower resolution imagery for the purpose of mapping of historic and individual landslides, such higher levels of resolution may not be required for the development of landslide susceptibility maps. In order to determine if medium-resolution satellite imagery, such as SPOT or ASTER, could provide the needed data for landslide susceptibility mapping, a comparison was undertaken of landslide susceptibility model output resulting from the use of stereo NAPP aerial photography versus the use of data obtained from stereo SPOT imagery. The test area selected for this study consisted of two watersheds, Pena Canyon and Big Rock Canyon, situated west of Santa Monica, California, USA, along the Pacific Coast Highway. Both watersheds have a long and well-documented history of landslide activity and sufficient geologic variability and complexity to provide a good test site. The specific overlay model used in this evaluation required input data consistent with the needs of many other models of this type. The model output derived from the two different data sources and presented here in the form of susceptibility maps were virtually identical. Statistical and difference analysis confirmed that both methods of obtaining input data provide similar results and successfully identified landslide prone areas. These results suggest that satellite imagery, in this instance, SPOT images, could potentially be used in lieu of conventional air photos, to evaluate landslide susceptibility. In many situations, especially in the case of remote locations and/or developing countries, this capability should result in substantial savings in terms of time, financial resources, and overall viability.     

基于临近相似性考虑的犯罪热点密度图预测准确性比较——以DP半岛街头抢劫犯罪为例

在无时空考虑的密度估计算法基础上,分别加入了案件点之间的时间临近相似性、空间临近相似性和时空临近相似性的考虑,利用DP半岛2006~2007年的街头抢劫犯罪数据为基础计算无时空临近相似性、时间临近相似性、空间临近相似性和时空临近相似性4种不同算法所得到的犯罪热点图,并以之预测2008年的街头抢劫。通过Natural breaks（Jenks）分级方法和等比例面积选取两种方式来划定热点区域进行预测并进行PAI指数得分比较,结果表明时空临近相似性的密度估计算方法在犯罪预测的优势比较显著。     

Mapping potential evapotranspiration: the smooth interpolation of isolines with a low density station network

The criteria which may be employed when selecting an approach to a particular evapotranspiration mapping problem are discussed in the light of previous attempts at mapping evapotranspiration. Evapotranspiration mapping involves two main stages: firstly the derivation of point evapotranspiration estimates, and secondly the interpolation of isolines around these estimates. Many studies have emphasized the first stage, frequently applying estimation formulae to data from climate stations, and have given substantially less attention to the interpolation of isolines. In the present study, where potential evapotranspiration estimates were derived for only 70 stations over the area of the European Economic Community and where maps showing the general trends in potential evapotranspiration were required, the technique of isoline interpolation was of great importance. Two forms of polynomial trend surface analysis were applied to the point estimates and a technique employing a restricted use of all three dimensions of location was found to be appropriate for denning the position of the smoothed evapotranspiration isolines.     

Identifying strengths and limitations of pan-European forest cover maps through spatial comparison

Detailed and harmonized information on spatial forest distribution is an essential input for forest-related environmental assessments, in particular, for biomass and growing stock modeling. In the last years, several mapping approaches have been developed in order to provide such information for Europe in a harmonized way. Each of these maps exhibits particular properties and varies in accuracy. Yet, they are often used in parallel for different modeling purposes. A detailed spatial comparison seemed necessary in order to provide information on the advantages and limitations of each of these forest cover maps in order to facilitate their selection for modeling purposes.

This article confronts the high-resolution forest cover map recently developed by the Joint Research Centre for the year 2000 (FMAP2000) with previously existing maps for the same time period: the CORINE Land Cover 2000 (CLC2000) and the Calibrated European Forest Map 1996 (CEFM1996). The spatial comparison of these three maps was carried out based on forest proportion maps of 1 km derived from the original maps. To characterize differences according to biogeographic regions, two criteria were used: detail of thematic content within each map and local spatial agreement.

Concerning thematic content, CLC2000 displayed a surfeit of non-forested areas at the cost of low forest proportions, while FMAP2000 showed a more balanced distribution likely to preserve more detail in forest spatial pattern. Good spatial agreement was found for CLC2000 and FMAP2000 within about 70% of the study area, while only 50% agreement was found when compared with CEFM1996. The largest spatial differences between all maps were found in the Alpine and Mediterranean regions. Reasons for these might be different input data and classification techniques and, in particular, the calibration of CEFM1996 to reported national statistics.     

Predictive modelling of gold potential with the integration of multisource information based on random forest: a case study on the Rodalquilar area,Southern Spain

Mineral exploration activities require robust predictive models that result in accurate mapping of the probability that mineral deposits can be found at a certain location. Random forest (RF) is a powerful machine data-driven predictive method that is unknown in mineral potential mapping. In this paper, performance of RF regression for the likelihood of gold deposits in the Rodalquilar mining district is explored. The RF model was developed using a comprehensive exploration GIS database composed of: gravimetric and magnetic survey, a lithogeochemical survey of 59 elements, lithology and fracture maps, a Landsat 5 Thematic Mapper image and gold occurrence locations. The results of this study indicate that the use of RF for the integration of large multisource data sets used in mineral exploration and for prediction of mineral deposit occurrences offers several advantages over existing methods. Key advantages of RF include: (1) the simplicity of parameter setting; (2) an internal unbiased estimate of the prediction error; (3) the ability to handle complex data of different statistical distributions, responding to nonlinear relationships between variables; (4) the capability to use categorical predictors; and (5) the capability to determine variable importance. Additionally, variables that RF identified as most important coincide with well-known geologic expectations. To validate and assess the effectiveness of the RF method, gold prospectivity maps are also prepared using the logistic regression (LR) method. Statistical measures of map quality indicate that the RF method performs better than LR, with mean square errors equal to 0.12 and 0.19, respectively. The efficiency of RF is also better, achieving an optimum success rate when half of the area predicted by LR is considered.     

Landslide susceptibility mapping based on Support Vector Machine: A case study on natural slopes of Hong Kong, China

The Support Vector Machine (SVM) is an increasingly popular learning procedure based on statistical learning theory, and involves a training phase in which the model is trained by a training dataset of associated input and target output values. The trained model is then used to evaluate a separate set of testing data. There are two main ideas underlying the SVM for discriminant-type problems. The first is an optimum linear separating hyperplane that separates the data patterns. The second is the use of kernel functions to convert the original non-linear data patterns into the format that is linearly separable in a high-dimensional feature space. In this paper, an overview of the SVM, both one-class and two-class SVM methods, is first presented followed by its use in landslide susceptibility mapping. A study area was selected from the natural terrain of Hong Kong, and slope angle, slope aspect, elevation, profile curvature of slope, lithology, vegetation cover and topographic wetness index (TWI) were used as environmental parameters which influence the occurrence of landslides. One-class and two-class SVM models were trained and then used to map landslide susceptibility respectively. The resulting susceptibility maps obtained by the methods were compared to that obtained by the logistic regression (LR) method. It is concluded that two-class SVM possesses better prediction efficiency than logistic regression and one-class SVM. However, one-class SVM, which only requires failed cases, has an advantage over the other two methods as only “failed” case information is usually available in landslide susceptibility mapping.     

A Comparative Analysis of Weights of Evidence,Evidential Belief Functions,and Fuzzy Logic for Mineral Potential Mapping Using Incomplete Data at the Scale of Investigation

Large amounts of digital data must be analyzed and integrated to generate mineral potential maps, which can be used for exploration targeting. The quality of the mineral potential maps is dependent on the quality of the data used as inputs, with higher quality inputs producing higher quality outputs. In mineral exploration, particularly in regions with little to no exploration history, datasets are often incomplete at the scale of investigation with data missing due to incomplete mapping or the unavailability of data over certain areas. It is not always clear that datasets are incomplete, and this study examines how mineral potential mapping results may differ in this context. Different methods of mineral potential mapping provide different ways of dealing with analyzing and integrating incomplete data. This study examines the weights of evidence (WofE), evidential belief function and fuzzy logic methods of mineral potential mapping using incomplete data from the Carajás mineral province, Brazil to target for orogenic gold mineralization. Results demonstrate that WofE is the best one able to predict the location of known mineralization within the study area when either complete or unacknowledged incomplete data are used. It is suggested that this is due to the use of Bayes’ rule, which can account for “missing data.” The results indicate the effectiveness of WofE for mineral potential mapping with incomplete data.     

Data-Driven Predictive Modeling of Mineral Prospectivity Using Random Forests: A Case Study in Catanduanes Island (Philippines)

The Random Forests (RF) algorithm is a machine learning method that has recently been demonstrated as a viable technique for data-driven predictive modeling of mineral prospectivity, and thus, it is instructive to further examine its usefulness in this particular field. A case study was carried out using data from Catanduanes Island (Philippines) to investigate further (a) if RF modeling can be used for data-driven modeling of mineral prospectivity in areas with few (i.e., <20) mineral occurrences and (b) if RF modeling can handle predictor variables with missing values. We found that RF modeling outperforms evidential belief (EB) modeling of prospectivity for hydrothermal Au–Cu deposits in Catanduanes Island, where 17 hydrothermal Au–Cu prospects are known to exist. Moreover, just like EB modeling, RF modeling allows analysis of the spatial relationships between known prospects and individual layers of predictor data. Furthermore, RF modeling can handle missing values in predictor data through an RF-based imputation technique whereas in EB modeling, missing values are simply represented by maximum uncertainty. Therefore, the RF algorithm is a potentially useful method for data-driven predictive modeling of mineral prospectivity in regions with few (i.e., <20) occurrences of mineral deposits of the type sought. However, further testing of the method in other regions with few mineral occurrences is warranted to fully determine its usefulness in data-driven predictive modeling of mineral prospectivity.     

Error assessment of grid-based flow routing algorithms used in hydrological models

This paper reports an investigation on the accuracy of grid-based routing algorithms used in hydrological models. A quantitative methodology has been developed for objective and data-independent assessment of errors generated from the algorithms that extract hydrological parameters from gridded DEM. The generic approach is to use artificial surfaces that can be described by a mathematical model, thus the ‘true’ output value can be pre-determined to avoid uncertainty caused by uncontrollable data errors. Four mathematical surfaces based on an ellipsoid (representing convex slopes), an inverse ellipsoid (representing concave slopes), saddle and plane were generated and the theoretical ‘true’ value of the Specific Catchment Area (SCA) at any given point on the surfaces could be computed using mathematical inference. Based on these models, tests were made on a number of algorithms for SCA computation. The actual output values from these algorithms on the convex, concave, saddle and plane surfaces were compared with the theoretical ‘true’ values, and the errors were then analysed statistically. The strengths and weaknesses of the selected algorithms are also discussed.     

From Land Cover to Land Use: A Methodology for Efficient Land Use Mapping over Large Areas

Land use information over large areas is increasingly important for many studies related to environment in general and global change in particular. Yet there is a dearth of methodological knowledge in this area, especially regarding the practical task of producing land use maps. In this article, a systematic land use mapping approach is developed, based on land cover maps that in turn are produced through remote sensing. The concept is based on the recognition of varying strengths of land cover (LC) – land use (LU) relationships, from the thematic and spatial points of view. Several categories of relationships are identified, ranging from direct (case 1) to multiple/complex (case 4), and appropriate mapping strategies are discussed for these cases. Using a mapping study in Lebanon, it is shown that the principles embodied in this approach correspond to issues and conditions in real mapping situations. Finally, the concepts are translated into a series of steps through which the method can be applied to large areas, taking into consideration the specific requirements and constraints of each case. The final land use map represents an acceptable compromise between accuracy, level of detail, and cost.     

A Review of “Knowledge Externalities,Innovation Clusters and Regional Development”

Land use information over large areas is increasingly important for many studies related to environment in general and global change in particular. Yet there is a dearth of methodological knowledge in this area, especially regarding the practical task of producing land use maps. In this article, a systematic land use mapping approach is developed, based on land cover maps that in turn are produced through remote sensing. The concept is based on the recognition of varying strengths of land cover (LC) – land use (LU) relationships, from the thematic and spatial points of view. Several categories of relationships are identified, ranging from direct (case 1) to multiple/complex (case 4), and appropriate mapping strategies are discussed for these cases. Using a mapping study in Lebanon, it is shown that the principles embodied in this approach correspond to issues and conditions in real mapping situations. Finally, the concepts are translated into a series of steps through which the method can be applied to large areas, taking into consideration the specific requirements and constraints of each case. The final land use map represents an acceptable compromise between accuracy, level of detail, and cost.     

Landslide susceptibility mapping using geological data, a DEM from ASTER images and an Artificial Neural Network (ANN)

An efficient and accurate method of generating landslide susceptibility maps is very important to mitigate the loss of properties and lives caused by this type of geological hazard. This study focuses on the development of an accurate and efficient method of data integration, processing and generation of a landslide susceptibility map using an ANN and data from ASTER images. The method contains two major phases. The first phase is the data integration and analysis, and the second is the Artificial Neural Network training and mapping. The data integration and analysis phase involve GIS based statistical analysis relating landslide occurrence to geological and DEM (digital elevation model) derived geomorphological parameters. The parameters include slope, aspect, elevation, geology, density of geological boundaries and distance to the boundaries. This phase determines the geological and geomorphological factors that are significantly correlated with landslide occurrence. The second phase further relates the landslide susceptibility index to the important geological and geomorphological parameters identified in the first phase through ANN training. The trained ANN is then used to generate a landslide susceptibility map. Landslide data from the 2004 Niigata earthquake and a DEM derived from ASTER images were used. The area provided enough landslide data to check the efficiency and accuracy of the developed method. Based on the initial results of the experiment, the developed method is more than 90% accurate in determining the probability of landslide occurrence in a particular area.     

Combining AHP with GIS for Predictive Cu Porphyry Potential Mapping: A Case Study in Ahar Area (NW,Iran)

Using the analytic hierarchy process (AHP) method for multi-index evaluation has special advantages, while the use of geographic information systems (GIS) is suitable for spatial analysis. Combining AHP with GIS provides an effective approach for studies of mineral potential mapping evaluation. Selection of potential areas for exploration is a complex process in which many diverse criteria are to be considered. In this article, AHP and GIS are used for providing potential maps for Cu porphyry mineralization on the basis of criteria derived from geologic, geochemical, and geophysical, and remote sensing data including alteration and faults. Each criterion was evaluated with the aid of AHP and the result mapped by GIS. This approach allows the use of a mixture of quantitative and qualitative information for decision-making. The results of application in this article provide acceptable outcomes for copper porphyry exploration.     

Mapping uncertain geographical attributes: incorporating robustness into choropleth classification design

ABSTRACT

Choropleth mapping provides a simple but effective visual presentation of geographical data. Traditional choropleth mapping methods assume that data to be displayed are certain. This may not be true for many real-world problems. For example, attributes generated based on surveys may contain sampling and non-sampling error, and results generated using statistical inferences often come with a certain level of uncertainty. In recent years, several studies have incorporated uncertain geographical attributes into choropleth mapping with a primary focus on identifying the most homogeneous classes. However, no studies have yet accounted for the possibility that an areal unit might be placed in a wrong class due to data uncertainty. This paper addresses this issue by proposing a robustness measure and incorporating it into the optimal design of choropleth maps. In particular, this study proposes a discretization method to solve the new optimization problem along with a novel theoretical bound to evaluate solution quality. The new approach is applied to map the American Community Survey data. Test results suggest a tradeoff between within-class homogeneity and robustness. The study provides an important perspective on addressing data uncertainty in choropleth map design and offers a new approach for spatial analysts and decision-makers to incorporate robustness into the mapmaking process.