Concentration-area Fractal Model Research Articles

Fractal-Based Multi-Criteria Feature Selection to Enhance Predictive Capability of AI-Driven Mineral Prospectivity Mapping

AI-driven mineral prospectivity mapping (MPM) is a valid and increasingly accepted tool for delineating the targets of mineral exploration, but it suffers from noisy and unrepresentative input features. In this study, a set of fractal and multifractal methods, including box-counting calculation, concentration–area fractal modeling, and multifractal analyses, were employed to excavate the underlying nonlinear mineralization-related information from geological features. Based on these methods, multiple feature selection criteria, namely prediction–area plot, K-means clustering, information gain, chi-square, and the Pearson correlation coefficient, were jointly applied to rank the relative importance of ore-related features and their fractal representations, so as to choose the optimal input feature dataset readily used for training predictive AI models. The results indicate that fault density, the multifractal spectrum width (∆α) of the Yanshanian intrusions, information dimension (D1) of magnetic anomalies, correlation dimension (D2) of iron-oxide alteration, and the D2 of argillic alteration serve as the most effective predictor features representative of the corresponding ore-controlling elements. The comparative results of the model assessment suggest that all the AI models trained by the fractal datasets outperform their counterparts trained by raw datasets, demonstrating a significant improvement in the predictive capability of fractal-trained AI models in terms of both classification accuracy and predictive efficiency. A Shapley additive explanation was employed to trace the contributions of these features and to explain the modeling results, which imply that fractal representations provide more discriminative and definitive feature values that enhance the cognitive capability of AI models trained by these data, thereby improving their predictive performance, especially for those indirect predictor features that show subtle correlations with mineralization in the raw dataset. In addition, fractal-trained models can benefit practical mineral exploration by outputting low-risk exploration targets that achieve higher capturing efficiency and by providing new mineralization clues extracted from remote sensing data. This study demonstrates that the fractal representations of geological features filtered by multi-criteria feature selection can provide a feasible and promising means of improving the predictive capability of AI-driven MPM.

Application of data-driven multi-index overlay and BWM-MOORA MCDM methods in mineral prospectivity mapping of porphyry Cu mineralization

The present study applies proposed hybrid mathematical frameworks, namely Data-driven Multi-Index Overlay Method (DMIO) and Best Worst Method-multi objective optimization by ratio analysis (BWM-MOORA) techniques, for generating robust predictive models enhancing mineral prospectivity analysis is demonstrated. These are used for (i) weighting multiple groups of evidence maps acquired from geological databases, such as remote sensing, geological, geochemical, and geophysical, and then (ii) integrating these weighted layers into robust predictive models to assess porphyry copper prospectivity. This case study of the Chahargonbad area is a district of the volcano-plutonic Urumieh–Dokhtar magmatic arc belt. Porphyry copper deposit (exploration and development) models were used for distilling geoscientific datasets that are available into a group of evidence-based layers. The BWM-MOORA method combines two separate processes in which BWM is applied to weight each criterion and sub-criteria, whereas the MOORA approach helps rank these attributes. Each layer is first converted to another space of [0,1] by the sigmoidal logistic function to perform the critical process of integrating each of the evidence layers. Then, a concentration-area fractal model was used to classify evidences into some geospatial populations. In addition, a prospectivity / mineral potential mapping (MPM) analysis is performed using the DMIO, a well-proven, and accurate data-based methodology, to verify the satisfactoriness and validation of the applied methodology. Prediction-area (P-A) and normalized density (Nd) analysis (plots) were performed as validation methods to estimate the reliability and evaluate the relative efficiency of the MPM models. Therefore, these detailed outcomes confirm the validity of the BWM-MOORA model (Nd = 3.17), which is slightly higher than the valid and proper model DMIO (Nd = 3) in determining the specific potential mineralization regions.

Combination of Machine Learning Algorithms with Concentration-Area Fractal Method for Soil Geochemical Anomaly Detection in Sediment-Hosted Irankuh Pb-Zn Deposit, Central Iran

Prediction of geochemical concentration values is essential in mineral exploration as it plays a principal role in the economic section. In this paper, four regression machine learning (ML) algorithms, such as K neighbor regressor (KNN), support vector regressor (SVR), gradient boosting regressor (GBR), and random forest regressor (RFR), have been trained to build our proposed hybrid ML (HML) model. Three metric measurements, including the correlation coefficient, mean absolute error (MAE), and means squared error (MSE), have been selected for model prediction performance. The final prediction of Pb and Zn grades is achieved using the HML model as they outperformed other algorithms by inheriting the advantages of individual regression models. Although the introduced regression algorithms can solve problems as single, non-complex, and robust regression models, the hybrid techniques can be used for the ore grade estimation with better performance. The required data are gathered from in situ soil. The objective of the recent study is to use the ML model’s prediction to classify Pb and Zn anomalies by concentration-area fractal modeling in the study area. Based on this fractal model results, there are five geochemical populations for both cases. These elements’ main anomalous regions were correlated with mining activities and core drilling data. The results indicate that our method is promising for predicting the ore elemental distribution.

Data-driven multi-index overlay gold prospectivity mapping using geophysical and remote sensing datasets

The comparative relevance of each geospatial component of mineralization differs from one geological terrane to the other because various sought-after mineral deposit-types synonymously differ in different geological terranes. Hence, the possibility of employing a conceptual model to obtain a relationship or a quantitative function between various geospatial features (evidential layers) with respect to the mineral being sought is laudable, though these features may not necessarily have a generically related effect with the mineral being sought. As a consequence, there is the need to employ a technique that has the capacity to recognize the efficient and inefficient geospatial indicators of the mineral deposit-type being sought. In view of this, this study employed the logistic function, concentration-area fractal model and the prediction-area (P-A) plot to transform and discretize the continuous value of each evidential layer as well as generating intersection points of prediction rate indicators that are essential in obtaining the normalized densities, which were subsequently employed in generating the objective weight for each evidential layer in a data-driven way. The P-A and the normalized density techniques employed were vital in recognizing the indicator and non-indicator criteria. The results obtained acknowledged the potassium concentration layer as a non-indicator of gold mineralization within the study area and subsequently recognized the hydroxyl bearing mineral concentration layer as the most plausible indicator criteria among the six evidential layers (lineament density, iron concentration, hydroxyl concentration, gravity anomaly, magnetic anomaly and potassium concentration) employed in this study. These five indicator criteria were integrated to generate a mineral prospectivity map (MPM) over the study area based on the data-driven multi-index overlay approach adopted. The prediction rate for each of the 6 evidential layers (5 of which were the indicator criteria) as well as the MPM produced indicates that, the generation of objective weights in a data-driven manner via normalized density enhances the predicting ability of the MPM produced in comparison with the individual evidential layers.

Introducing a new approach of geochemical anomaly intensity index (GAII) for increasing the probability of exploration of shear zone gold mineralization

Increasing the prediction rate in the identification of mineralization zones using the stream sediment geochemical data is an essential issue in the regional exploration stage. The various univariate (such as fractal and probability plot (PP) methods) and multivariate methods (such as principal component analysis (PCA)) have been performed for interpreting the geochemical data and detecting the mineralization areas. In this study, a new geochemical criterion named geochemical anomaly intensity index (GAII) was proposed for geochemical anomaly mapping. This approach was developed based on the PCA method and the catchment basin coefficient (CBC). The GAII as a weighted geochemical index is calculated using the mineralization principal component (MPC) scores and CBC. GAII can be mapped and utilized for geochemical anomaly mapping and detecting the mineralization areas. Besides, GAII can identify paragenesis elements better than the current methods. In this research, GAII was successfully used to generate geochemical anomaly maps on shear zone gold mineralization in the southwest of Saqqez, NW Iran. The geochemical data have been divided into three groups based on catchment basins and the host rock type. Then the MPCs and paragenesis elements of Au mineralization have been obtained individually using PCA. Three mineralization paragenesis groups consisting of (Au, Sn), (Au, W), and (Au, As, Sb and Ba) have been recognized for different catchment basins of the southwest of Saqqez district using PCA. GAII was calculated and mapped based on the CBC(Au, Sn), CBC(Au, W), CBC(Au, As, Sb, Ba), and their MPC scores. GAII accurately detected the Au mineralization zones and improved the geochemical anomaly map in this area compared to the PP method, concentration-area fractal model, and U-spatial statistics method. The results demonstrated that GAII was successfully used for (a) identifying the mineralization paragenesis elements, (b) intensifying the geochemical anomaly, and (c) increasing the prediction rate of mineralization zones. The shear zone gold mineralization areas in the southwest of Saqqez district were effectively detected using this new data analysis approach. GAII has provided better results than the current PP method, concentration-area fractal model, and U-spatial statistics method.

Integration of concentration-area fractal model and relative absorption band depth method for mapping hydrothermal alterations using ASTER data

Those image processing methods which use both spatial and spectral properties of remotely sensed images often increase accuracy of image classification. In this study, the concentration-area (C-A) fractal model and Relative absorption Band Depth (RBD) were applied to map hydrothermal alteration zones using ASTER data covering the northern part of Rabor area, Iran. Based on the field observations and spectral analysis of rock samples, three types of RBD were calculated and applied to map hydrothermal altered rocks (RBD6 for phyllic, RBD8 for propylitic, and RBD5 for argillic). A log-log plot of area-digital number value for RBD images showed that there are three populations in each image. Representation of these populations revealed that the third population of each RBD has enhanced separation of alteration zones. To verify the results, a spectral library of ground rock samples was built and used to compare with 10 spectra derived from each image. Spectral Angle Mapping, Spectral Feature Fitting, and Binary Encoding were applied to assess the matching of image spectra with the spectral library spectra. Results confirmed that third population of RBD6 and RBD8 contain pure pixels of phyllic and propylitic alterations, respectively whereas there are some interference between argillic and phyllic alterations in RBD5.

Integration of airborne geophysics and satellite imagery data for exploration targeting in porphyry Cu systems: Chahargonbad district, Iran

ABSTRACTThis study illustrates the application of a geometric average integration of aeromagnetic, radiometric and satellite imagery data over a region prone to Cu‐bearing mineralization at Chahargonbad area in Kerman province of Iran. Processing aeromagnetic, radiometric and Advanced Spaceborne Thermal Emission and Reflection Radiometer satellite data can provide exploratory insights about favourable zones in association with porphyry‐type ore occurrences, which can be synthesized through a combination of knowledge‐ and data‐driven approaches as a geometric average and be represented in a mineral prospectivity map. The existence of known deposits in a prospect region can facilitate the investigation of significant exploratory footprints extracted from airborne data by calculating each indicator layer's weight by plotting a prediction–area curve accompanied by a concentration–area fractal curve. Among various indicators, the most important ones are determined based on derived weights from the prediction–area plots to be synthesized in a single Cu favorability map. To fulfil this aim, indicator layers from airborne geophysics (magmatic bodies, magnetic lineaments and potassium radiometry) and remote‐sensing data (alterations such as argillic, phyllic, propylitic and iron oxide along with geological lineaments) were prepared and evaluated using the known porphyry Cu mineralization by the simultaneous plot of the concentration–area fractal model and the prediction–area curve to attain the ore prediction rate and the relevant occupied area of each map for weight assignment of indicators. The geometric average prospectivity model was applied to synthesize the leading indicators, and the result was compared with a multi‐class index overlay map. This study's significance lies in improvement of the performance of the mineral prospectivity/potential mapping after running a geometric average by a higher ore prediction rate of 79%, which has occupied 21% of the area as potential zones for further mining investigations.

Category-based fractal modelling: A novel model to integrate the geology into the data for more effective processing and interpretation

Parent lithology exerts a major influence on the associated regolith geochemistry and affects the setting of population or domain boundaries. In regional geochemical mapping and anomaly detection, a lack of samples pertaining to one or more key lithologies may results in interpolation errors. Such errors can be addressed via category-based fractal modelling to characterise different background and anomalous populations by taking both error propagation and geochemical data values into account. Such geochemical anomaly classification models have been developed using Monte Carlo simulation (MCSIM) within a given lithological domain to provide estimates of population breaks. Two types of category-based fractal models used are (i) related lithological groups representative samples where there is an adequate number of samples derived from a given lithological or geological domain, and (ii) related lithological groups whole samples and a group of Gaussian simulated samples regenerated based on the mean and standard deviation of the available samples per lithological group. Both models were applied to VMS-related element concentrations in the low-density till geochemical mapping of Sweden following centred log-ratio (clr) transformation. Compared with the concentration-area fractal model the category-based fractal models provided more reliable estimates for population thresholds and identification of anomalous classes.

Weighted Photolineaments Factor (WPF): An Enhanced Method to Generate a Predictive Structural Evidential Map with Low Uncertainty, a Case Study in Chahargonbad Area, Iran

Decreasing the uncertainty and increasing the prediction rate of evidential maps are two important objectives in mineral prospectivity mapping (MPM). In this paper, we proposed weighted photolineaments factor (WPF) to generate a continuous weighted structural evidential map with high prediction rate and low uncertainty in Chahrgonbad area. The WPF which has four components was defined as weighted sum of the values related to four following characteristics of lineaments: (a) number, (b) length, (c) number of intersection and (d) number of directional sets. We used the extracted lineaments from geological map and processing of aeromagnetic data in our analysis to enhance the prediction rate of WPF map. The process was implemented using an effective multistage algorithm including: texture analysis, phase symmetry analysis, non-maximal suppression, thresholding, skeletonization and line fitting process. Afterward, values related to various characteristics of lineaments were extracted and transformed by a logistic function to improve their predictive ability. Then, using the concentration-area fractal model and prediction-area plot, the prediction rate of WPF components was derived and their importance weights were calculated using normalized density. Finally, the WPF map was generated and evaluated using location of 18 known mineral occurrences in the study area. The results demonstrated a good concordance with our previous geological knowledge and experience about Cu mineralization in Chahrgonbad area. The number of lineaments directional sets and the number of lineaments were recognized as structural criteria with the highest prediction rate for Cu prospectivity. The generated WPF map has a higher prediction rate (80%) in comparison with each individual component and delineated 20% of the study area as prospective target. Eventually, three zones with high structural permeability which are fertile environment for emplacement of intrusions, circulation of magmatic-hydrothermal fluids and Cu mineralization were delineated on the WPF map and proposed for further exploration.

Stream sediment geochemical data analysis for district-scale mineral exploration targeting: Measuring the performance of the spatial U-statistic and C-A fractal modeling

Recognition of mineralization-related geochemical footprints and modeling their multi-element dispersion patterns are important aspects to consider when “vectoring” toward undiscovered ore deposits. The collection, analysis, and interpretation of stream sediment geochemical data together make an exploration method that has proven to be successful at the district scale mineral exploration targeting. Identifying the possible sources of stream sediment geochemical anomalies and mapping evidence (i.e., footprints) of the underlying ore-forming processes, however, are not trivial tasks. This is because stream sediment samples represent transported material reflecting the entire geology upstream from the sample locations. Furthermore, indicator element distribution patterns are commonly strongly affected by local factors such as regolith, topographic gradient, vegetation density, and/or climate. Therefore, there is a need for finding a better geochemical anomaly separation method regarding the nature of geochemical data obtained from the area sampled. The main objectives of this study were (1) evaluating and comparing the spatial U-statistic and concentration–area fractal modeling methods of anomaly identification, both amenable to spatial analysis, for recognizing geochemical footprints of porphyry copper mineralization, and (2) measuring their performance in the context of district-scale exploration targeting in an area located in southeast Iran. Subsequently, the methods were first evaluated on a dataset of element contents to decompose anomalous populations. Finally, the geochemical model that proved more efficient with respect to predicting the known mineral deposits was integrated with additional evidence maps to delineate exploration targets. Our evaluation of the resulting geochemical targeting model demonstrated that the targets derived from this method are robust and worthy of follow-up exploration.

Constraining the distribution of elements and their controlling factors in the Zhaojikou Pb–Zn ore deposit, SE China, via fractal and compositional data analysis

The distribution of elements in soil is affected by various natural processes, and therefore, it is essential that exploration geochemists are able to recognize whether an elemental concentration is related to mineralization or other processes. This research aimed to recognize the elemental distribution and its controlling factors around the Zhaojikou Pb–Zn ore deposit, SE China, via fractal and compositional data analysis. Firstly, histograms over the raw data and log-ratio transformations were used to check whether the concentration data followed a normal distribution or not. The concentration distribution maps of elements were then generated via spretrum–area fractal plot to show the spatial relationships. Afterward, the inter-relationships among different elements were studied through robust principal component analysis based on compositional data theory. The factors controlling the distribution of elements were discussed and geochemical indices were proposed for future exploration. Finally, a comprehensive anomaly map was generated to show important prospecting areas. Results showed how the interpretation of distributions of elements was enhanced due to the application of data log-ratio transformation in univariate and multivariate analysis compared to the use of raw data. The histograms based on isometric log-ratio performed best among the three log-ratio transformations. The concentration distribution maps showed three anomalous areas at the surface. It clearly allowed identifying the relationships between the elements and their possible source patterns. Area I with anomalous assemblage of Pb–Zn–Ag–Cu–Cd corresponded to the current known ore deposits, while Area II with anomalous assemblage of Pb–Zn–Ag–Cu–Cd may indicate the occurrence of new potential base metal (Pb–Zn) ore bodies, and Area III with anomalous assemblage of W–As–Sb may indicate the occurrence of new potential Au mineralization/ore occurences. The robust biplot of PCA shows that the distributions of elements of interest were generally controlled by three geological processes: Pb–Zn ore-forming process, Au mineralization and weathering. Lead, Zn, Ag, Cu, and Cd, were affected mainly by Pb–Zn ore-forming processes; W, Sb, and As were affected mainly by Au mineralization, whereas Al2O3, K2O, Rb, Ba, Sr, Na2O, CaO, MgO, and SiO2 were affected to a greater extent by weathering processes. Sulphur, a mineralizing agent, was controlled by the ore-forming processes, being affected greatly by weathering. Finally, we proposed Pb > 160 ppm, Zn > 120 ppm, Ag > 193 ppb, Cu > 50 ppm, Cd > 210 ppb, W > 5 ppm, As > 25 ppm, Sb > 3.5 ppm, and S > 120 ppm as geochemical indices based on concentration-area fractal model analysis for future surficial geochemical prospecting in the Zhaojikou District.

Mapping of single- and multi-element geochemical indicators based on catchment basin analysis: Application of fractal method and unsupervised clustering models

The study aimed to recognize significant single- and multi-elemental geochemical indicators associated with porphyry and skarn copper deposits in the Varzaghan district, NW Iran, from stream sediment geochemical data. In this regard, because of the diversity and complexity of geological processes that influence dispersion patterns of geochemical elements in different areas, sample catchment basin (SCB) modeling of stream sediments was applied. To judge the capability of each single-element geochemical indicator to predict exploration targets of mineral deposits of the type sought, prediction-area plot analysis was employed. Then, concentration-area fractal modeling was performed on the SCB models to delineate geochemical anomalies of each indicator element. Next, a Cu-Au-Mo-Bi association was considered to reflect multi-element indicator of porphyry-skarn Cu mineralization. Different populations of the SCB multi-element geochemical indicators were delineated by three unsupervised clustering methods, namely K-means, K-medoids and fuzzy c-means. Silhouette Width and Xie-Beni validation indices were calculated for selecting the optimal cluster number to optimize delineation of significant anomalies. Finally, for quantitative evaluation of the efficiency of single- and multi-element indicator anomalies in delineating exploration targets, we applied normalized density and success-rate curve based on the known Cu occurrences in the study area.

Comparative analysis between concentration- number (C-N) and concentration- area (C-A) fractal models for separating anomaly from background in Siahrood 100,000 sheet, NW Iran

Summary In this paper Concentration-Number (C-N) and Concentration-Area (C-A) fractal models were used for separating anomaly from background for Cu, Mo, Fe2O3 and Sb in Siahrood 1:100,000 sheet, NW Iran. First, 1238 stream sediment samples were taken and analyzed. Then, the threshold values were obtained for anomaly separation from the log- log plots. The log–log plots can be divided into three segments or phases that correlate with lithological formation, faults and alteration in the study area. Using the results of fractal modelling, the anomaly maps were drawn and anomalous areas were identified. Elemental anomaly maps resulted from the C-A and C- N fractal models were compared withthe locations of mineralization/deposits in the study area.Results showed thatthere was a good correlation between the locations of mineralization/deposits and anomaly region for both fractal models. But the concentration-area fractal model could hit more mineralization/deposits. This is more obvious for Cu. Results also showed that most of the Cu, Fe and Mo anomalies located in igneous rocks, altered igneous rocks and faults. Because of activity of hydrothermal solutions in intrusive rocks in the northern part of the study area and volcanic rocks in central parts, intrusive and volcanic rocks, altered and quartzite veins, and mineralization zones occur. Introduction Delineation of anomalies from background is an essential task in geochemical exploration. Geochemical data are usually characterized by their spatial positions, meaning that elemental concentration varies spatially. The concentration–area model (C–A model) has been developed and applied by many geoscientists. Another useful model for separating anomaly from background is the number–size model (N–S model), which has been widely used by many geoscientists. Methodology and Approaches Concentration-number and concentration-area fractal models were used for separating anomaly from background. Then with drawingthe log-log elemental plot the threshold values obtained for anomaly separation. Using the results of fractal modelling the anomaly maps were drawn and anomaly regions were identified. Elemental anomaly maps resulted from the concentration-area and concentration- number fractal models were compared withthe locations of mine indexes in the study area. Results and Conclusions Results showed thatthere was a good correlation between the locations of mine indexes and anomaly region for both fractal models. In other words most of anomalies derived from C-A and N-S models hits mine indexes in the region. But the concentration-area fractal model hit more mine indexes. This is more obvious for Cu. Results also showed that most of the Cu, Fe and Mo anomalies located in igneous rocks, altered igneous rocks and faults.

Separation of rock types in reservoir rock using concentration-area multifractal model

Separation and identification of rock type is one of the most important and key stages in reservoir simulation. There are various methods for separation and diagnosis of rock type varying from simple statistical tests (based on statistical parameters of distribution function) to complex fractal (based on special structure of data). Fractal geometry has proved its practical aspects with increasing expansion in various sciences and techniques. One of the main applications of fractal geometry in estimation of threshold and separation of anomaly from background is based on the difference between their fractal dimensions. In this paper, after modeling porosity parameter in a reservoir rock in south of Iran by Kriging method, the area of rock communities was separated using concentration-area fractal model. The results of fractal analysis indicate five rock types based on porosity parameter in this reservoir rock and threshold limit of 10.80% for separation of porosity related to background from anomaly.

Integration of Concentration-Area Fractal Modeling and Spectral Angle Mapper for Ferric Iron Alteration Mapping and Uranium Exploration in the Xiemisitan Area, NW China

The high-grade uranium deposits in the Xiemisitan area, northwestern China, are genetically associated with the faulting of felsic volcanic or sub-volcanic rocks. Ferric iron alteration indicates that oxidizing hydrothermal fluids percolated through the rocks. In this study, we measured the gamma-ray intensities of rocks in the Xiemisitan area and we propose a hybrid method for the mapping of ferric iron alteration using concentration-area fractal modeling and spectral angle mapper. The method enables ferric iron alteration to be distinguished from potash-feldspar granitic rocks. The mapping results were integrated with structural data to assist with exploration for uranium in the study area. Using this approach, six prospective areas of mineralization were proposed. Of these areas, two anomalies with high gamma-ray intensities of 104 and 650 Uγ were identified and verified by field inspection. These observations suggest that Enhanced Thematic Mapper Plus images are a valuable tool that can improve the efficiency of uranium exploration.

Supervised geochemical anomaly detection by pattern recognition

Geochemical anomaly detection is an important issue in mineral exploration. The availability of a training dataset consisting of labeled geochemical samples of background and anomaly classes enables us to define a supervised pattern recognition framework for geochemical anomaly detection. Therefore, various classification and feature selection algorithms can be utilized to build a predictive model and classify the unseen geochemical samples into the pre-defined anomaly and background classes. In this study, some of the state-of-art feature selection and classification algorithms were utilized for supervised anomaly detection in the Kuh Panj porphyry-Cu district. Filter, wrapper and embedded mode feature selection algorithms were used to remove redundant and irrelevant elements from the classification procedure. Subsequently, AdaBoost (ADB), support vector machine (SVM) and Random Forest (RF) algorithms were trained with borehole and surface rock samples from the drilled parts of the study area to create a classified map depicting anomalous areas in the undrilled parts of the district. Results show that feature selection algorithms could play an important role in increasing the accuracy and generalization ability of the classifiers used. Wrapper mode subset selection method combined with a genetic algorithm (GA) search method resulted in the best performance in the study area. Applied classification algorithms outperform Gaussian linear discriminant analysis (GLDA) and provide more accurate, robust and reliable results. Among the applied classification methods, ADB achieved the best leave-one-out cross-validation (LOO) error rate of 0.06. Meanwhile, comparison of the resulted classified map using ADB with another one created via concentration–area fractal model indicated advantage of the former one in terms of detecting high-promising prospective target areas in the study region.

A MATLAB-based program for processing geochemical data using fractal/multifractal modeling

In the field of applied geochemistry, it is important to obtain quantitative descriptions of geochemical patterns and identify geochemical anomalies. In this paper, we present a MATLAB-based program for processing geochemical data by means of fractal/multifractal modeling. The procedure consists of two functional parts. First, we quantify the spatial distribution characteristics of geochemical patterns using the multifractal spectrum. Second, geochemical anomalies are identified using various fractal/multifractal models. These models include the concentration-area fractal model, spectrum-area multifractal model, and multifractal singularity analysis. The results can be visualized in the MATLAB platform or saved for further analysis, i.e., by geographic information systems software. We demonstrate the applicability of this program by processing a geochemical dataset from soil samples taken in Inner Mongolia, China. We examine the concentrations of Ag in these soil samples, and show that the results obtained by our program are highly correlated with known Ag deposits in the region of interest.

Site effect classification based on microtremor data analysis using a concentration–area fractal model

Abstract. The aim of this study is to classify the site effect using concentration–area (C–A) fractal model in Meybod city, central Iran, based on microtremor data analysis. Log–log plots of the frequency, amplification and vulnerability index (k−g) indicate a multifractal nature for the parameters in the area. The results obtained from the C–A fractal modelling reveal that proper soil types are located around the central city. The results derived via the fractal modelling were utilized to improve the Nogoshi and Igarashi (1970, 1971) classification results in the Meybod city. The resulting categories are: (1) hard soil and weak rock with frequency of 6.2 to 8 Hz, (2) stiff soil with frequency of about 4.9 to 6.2 Hz, (3) moderately soft soil with the frequency of 2.4 to 4.9 Hz, and (4) soft soil with the frequency lower than 2.4 Hz.

Cu- and Zn-Soil Anomalies in the NE Border of the South Portuguese Zone (Iberian Variscides, Portugal) Identified by Multifractal and Geostatistical Analyses

Extensive Cu- and Zn-soil geochemical data in the Albernoa/Entradas–S. Domingos region (NE border of the Iberian Pyrite Belt, South Portuguese Zone) were examined to separate anomalies from background using the concentration–area fractal model. Distribution patterns of Cu and Zn concentrations in soil are primarily influenced by bedrock. The regional threshold values of Cu- and Zn-soil contents over metasedimentary sequences are 20–25 and 20–60 ppm, respectively, becoming 30–50 and 20–90 ppm, respectively, when metavolcanic rocks are present. The first-order threshold values for Cu are 80–90 ppm in soils over metasediments and 70–80 ppm in soils over sequences bearing metavolcanics. For Zn, the first-order threshold values are 40–80 and 90–100 ppm in soils over metasediments and metavolcanic rocks, respectively. Metasediments and metavolcanics comprising significant sulphide disseminations are outlined by Cu- and Zn-soil values above 100 and 300 ppm in soil, respectively. On the basis of these results, Alvares and Albernoa/Entradas areas emerge as the first priority targets for exploration. The observed non-coincidence of Cu- and Zn-soil anomalies in soil in the area could reflect difference in element dispersion during weathering, they mostly indicate distinct metal sources related to the original composition of different rock types or to chemical changes developed during Variscan deformation/re-crystallization path. The established regional baseline data can be used as reference for environmental studies.

Image Segmentation for Hydrothermal Alteration Mapping Using PCA and Concentration–Area Fractal Model

Information extraction from processed remotely sensed images, in the case of missing initial spectra of pixels, can be a challenge for the users. In such situations, application of conventional methods based on spectral properties of pixels is impractical. We took advantage of the fractal theory for image segmentation of a principal component (PC) image for hydrothermal alteration mapping. The selected input images included short wave infrared bands of ASTER imagery covering the Darrehzar porphyry copper mine and surrounding areas with well-known hydrothermal alteration zones. Hydrothermal alteration like other geological processes can show spatial distribution with fractal properties. Principal component analysis was used to enhance hydrothermal alteration associated with the Darrehzar porphyry copper deposit. None of the resulting PCs were appropriate to portray clearly important alteration types in the study area. The PC1 image, which contains more than 98% of variance of the input bands, was selected for image segmentation using a digital number–area technique based on the established concentration–area fractal model. This technique was proposed based on frequency distributions and spatial correlation and variability of pixel values. The resulting hydrothermal alteration map indicates intense phyllic, weak phyllic, and propylitic as the main alteration types exposed at the surface of the Darrehzar area. In addition, the proposed technique delineated the phyllic zone in the exposed mine pit and a transition zone between inner phyllic and surrounding propylitic alteration zones. Field investigation and sampling in 23 locations including spectral measurements, XRD and thin section studies, confirmed the accuracy of the classified image by the proposed technique.