Multivariate geostatistics. Non stationary geostatistics. Non linear geostatistics. Simulations

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1 Earth & Environment Sciences Geosciences & Geoengineering Research Department 35 rue Saint-Honoré F Fontainebleau Cedex PROFESSIONAL TRAINING IN GEOSTATISTICS Linear geostatistics Linear geostatistics modeling Linear geostatistics estimation Multivariate geostatistics Non stationary geostatistics Non linear geostatistics Simulations in Mastère spécialisé CGE or in modular continuing professional education 0

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3 Founded in 1783, the skills of the School followed the development of the industry. Mines ParisTech, nowadays, studies, develops and teaches all the useful techniques for engineers, including economic and social sciences. Installed since 1816 in the heart of the Latin Quarter in Paris, in the old Hotel de Vendome, near the Luxembourg Gardens, the School has grown in 1967 in Fontainebleau (500 m from the castle), Corbeil and Evry (in local SNECMA), and finally in 1976 in the technology park of Sophia Antipolis, Valbonne near Nice. Originally responsible for civil engineering teaching of MINES ParisTech and the Corps technique de l État, the school has developed, since the sixties, research and postgraduate education (Specialized Masters, PhD) in ), in partnership between industry and ARMINES Association (founded in 1967 by the School). School, founding member of PRES ParisTech, continues to be at the heart of multiple projects. 2

4 Located in Paris, MINES ParisTech trains, since its creation in 1783, very high-level engineers able to solve complex problems in various fields, including mining. First school of engineers in France by its volume of research contracts, MINES ParisTech provides an important activity of oriented research toward industry and organized into five departments: earth sciences and environment, energy and processes engineering, materials sciences and engineering, mathematics and systems, economics, management and society. The engineering school also develops the creation of chairs for teaching and research on emerging topics. MINES ParisTech is a founding member of ParisTech which brings together 12 of the famous engineering and management schools in Paris. The school is also a founding member of the PRES Paris sciences and letters which brings together 16 institutions of higher education and research. Created in 1967 at the initiative of MINES ParisTech, ARMINES is an association of research, partners of several schools of engineers. ARMINES supports oriented research for industry and brings to the common research laboratories of partner schools means in staff andequipment in relation to its volume of contracting activity. This research partnership with industry led to a unique culture where the scientific approach is facing the industrial dimension. With about 544 employees in more than 50 laboratories, the participation of schools teachers-researchers and a contractual activity close to 44.7 million in 2013, it is the first French research structure performedby institutions of higher education. ARMINES strengthens the R & D activity of the network of French Schools of Mines, Polytechnique ParisTech, ENSTA ParisTech, the École Navale and the École des Ponts ParisTech. MINES ParisTech Earth & Environment Sciences Geosciences & Geoengineering Research Department 35 rue Saint-Honoré F Fontainebleau Cedex Tel : +33 (0) ARMINES Structure of research contract 60 Boulevard Saint-Michel F Paris Cedex 06 Tel : +33 (0) training@geosciences.mines-paristech.fr 3

5 GEOSCIENCES & GEOENGINEERING RESEARCH DEPARTMEMT Located in Fontainebleau, at 60km southwards from Paris, MINES ParisTech research site is in the heart of the worldwide known Fontainebleau forest, near to the national domain of the Fontainebleau castle, inscribed on the UNESCO World Heritage List. The Geosciences & Geoengineering Research Department (research structure common to MINES ParisTech and ARMINES) focuses on research and teaching activities in the field Earth and Environmental Sciences. Research expertise focuses on geology, geophysics, geostatistics, hydrogeology, engineering geology and geomechanics, geochemistry. With 50 teachers-researchers, working in close relationship with the industry, the Geosciences Research Department is involved in the civil engineer education of MINES ParisTech, the doctoral training programs and proposes postgraduate and regular professional training programs. The programs presented in this document cover different aspects of the mineral raw material industry including the role of the State in the development of the mining industry, the assessment of the resources through geostatistical techniques and the technical and economic aspects related to mining operations. Participants to these training programs come from all over the world. They are mine engineers, mine and exploration geologists, production managers, geophysicists, civil engineering, environment and landuse engineers, administrative and financial directors, technical directors, members of government agencies, and students of higher education institutes. Intra-company training can be organized also scheduled, in France and abroad. 4

6 google earth 2014 GEOSCIENCES & GEOENGINEERING RESEARCH DEPARTMEMT Since the beginning of the 1980 s, more than 1800 students from 75 countries and major mining companies have been trained in one of the Geosciences & Geoengineering Research Department training programmes: France: Areva Mines, Eramet, Imerys, Lafarge Romania: Technical university of Petrosani Poland: Central mining institute of Katowice Russia: St Petersbourg mining Institute Europe India: Coal India Ltd, Indian Bureau of Mines Indonesia: Geology and mineral ressources department, PT Bukit Asam, PT Antam, PT Kaltim Primacoal, PT Freeport McMoran, PT Indominco Kazakhstan: Katco Saudi Arabia: Saudi Arabian Mining Company (Ma aden), Saudi Geological Survey (SGS) Thaïland: EGAT, Bampu Asia participants 40 et + 20 à à 20 5 à 12 - de 5 South America Brazil: Vale, National Dept of Mining Production Colombia: Ingeominas, Cerrejon Coal SA, BHP Billiton Peru: Centromin Chili: CODELCO, Anglo American Chile Mexico: various companies Venezuela: CVG Ferrominera Orinoco, CVG Minerven, Carbones del Guasare, Mining ministry, Environment ministry Africa South Africa: Dept of Mineral Affairs, De Beers Guinea: Natural ressources ministry, Minig companie of Bauxite Gabon: Ministère des Mines, COMILOG Niger: Ministère des Mines, Areva Niger, Somaïr, Cominak, Imouraren S.A. Morocco: Mining ministry, MANAGEM-ONA 5

7 Professional training in GEOSTATISTICS Mining production supplies many base processing industries and generates induced activities in the fields of equipment manufacturing (mining, handling, explosives...), resources management and consulting (environmental audit, economic analyses, resource evaluations...). Today, awareness regarding the need for a sustainable use of non-renewable natural resources increased the constraints that weigh on mines. The entire mining process (exploration, mining, processing and site reclamation at the end of mining operations) should be optimized at best to satisfy needs in raw materials, environmental protection, sustainable mining of resources, economic viability of the mining companies and societal aspects. Social benefits for local populations are today at the heart of discussions and development strategies for the States in charge of mining operations. This training programme is aimed at providing answers to these important issues for the future of the actors involved in the exploitation of the natural resources indispensable to the functioning and the development of human societies. These actors are now committed to ensuring the sustainability of their activities for greater economic competitiveness. GEOSTATISTICS (CFSG) training provides solutions for the study of regionalized variables, at the border between mathematics and the Earth sciences. This training helps to improve quantitative estimation and mapping of the resources available, whose data are useful for optimization of mining operations, the implementation of a corporate strategy and the overall organization of a mine site. If this training is very oriented towards the mining industry, discussed mathematical techniques can be used for other areas of activity (environmental pollution, oil reservoirs, aquifers, soil science...). CFSG caters primarily to mining engineers, exploration and exploitation geologists, engineers responsible for the management of water resources, or geophysicists. This training, taught in English language, may be attended either as a 10 months long postgraduate training (6 months of lectures and 4 months of personal project), or as modular professional training Location : MINES ParisTech - Geosciences Research Department 35, rue Saint-Honoré Fontainebleau (France) Training Team To register for MS CFSG or in modular continuing professional education, send your curriculum vitae indicating the name of the chosen modules to: resp_cfsg@geosciences.mines-paristech.fr Mrs Gaëlle LE LOC H Training manager Mrs Nathalie DIETRICH Assistant manager

8 GEOSCIENCES & GEOENGINEERING RESEARCH DEPARTMEMT PROGRAMME CFSG Geostatistics in Mastère spécialisé CGE Duration 10 months Dates Cost Language Pages 04/09/17-06/07 / English 7 in m odular professional continuing education Linear geostatistics (CFSG 2) 20 day s 1 8/09/ /1 0/ English 8-9 Linear geostatistics modeling (CFSG 2a) Linear geostatistics - estimation (CFSG 2b, CFSG 2a required) 10 day s 18/09/17-29/09/ English 9 10 day s 02/10/17-13/10/ English 9 Multivariate geostatistics (CFSG 3) 10 day s 06/11/17-17 /11/ English 10 Non stationary geostatistics (CFSG 4) 5 day s 27 /11/17-01/12/ English 11 Non linear geostatistics (CFSG 5) 1 0 day s 1 5/01/1 8-26/01/ English 14 Sim ulations (CFSG 6) 1 0 day s 05/02/ /02/ English 14 NB: Management reserves the right to cancel training or module if number of registrants is insufficient. 7

9 GEOSTATISTICS (CFSG) Mastère spécialisé CGE 10 months Target audience Engineers, geologists, reservoirs engineers, geophysicists, Professional experience and good level of math is required Programme CFSG 1: Introduction (2 weeks 4 ECTS) Recalls of basic knowledge and homogenization of the student s levels on prerequisites. CFSG 2: LINEAR GEOSTATISTICS (course+personal work, 7 weeks 15 ECTS) Characterization of spatial variability (variogram), local estimation (kriging), confidence intervals (kriging variances and dispersion) and global estimation of in situ resources. CFSG 3: MULTIVARIATE (course+personal work, 2 weeks 5 ECTS) Tools and methods complementing those of linear geostatistics when several variables must be studied simultaneously (polymetallic orebodies, layer cake sedimentary environments, geochemical prospecting...): cross covariance and cross variogram, cokriging, external drift, factorial kriging analysis... CFSG 4: NON STATIONARY (1 weeks 3 ECTS) Methods for phenomena with a systematic trend or "drift": universal kriging (simple global drift) intrinsic random functions of order k (complex drift) CFSG 5: NON LINEAR - (course+personal work, 3 weeks 7 ECTS) Estimation of quantities above cut-off thresholds. Two major themes: Support Effect (sample size different of selection unit size) Information effect (selection on estimator). CFSG 6 - SIMULATIONS - (course+personal work, 3 weeks 7 ECTS) Generating different versions of random functions or random sets which reproduce the data variability, as well as data values by "conditioning". We thus solve problems that are beyond estimation methods, linear or not. The 3rd week corresponds to a small computer project and is mandatory for all of the CFSG registrants. Short workshops or conferences (1 semaines - 2 ECTS) Technical visits (mines, quarries and other) in France or abroad (1 weeks 2 ECTS) Personal application work (4 months 30 ECTS) Degree Successful trainees are awarded a Mastère spécialisé diploma CGE and a national French post-graduate degree issued by MINES ParisTech CFSG1 Cost : Duration : 10 m onths Dates : 04/09/17-06/07 /18 Language : English Tuition fees and information to resp_cfsg@geosciences.mines-paristech.fr 8

10 (CFSG 2) Regular professional training LINEAR GEOSTATISTICS Objectives: to estimate the value of a regionalized variable at a point or within a block, key parameter of a mining project, using the tools of linear geostatistics (regionalized variable: elevation of a horizon, porosity of a rock, grade in metal or concentration content in pollutant...),. These tools describe and model the spatial variability of the phenomenon under study reporting for example anisotropy, correlation distances or nested variability scales. Programme Theory and practice of basic geostatistics : Variography : exploratory data analysis, experimental variogram, theoretical models, variogram fitting; Dispersion variance, estimation variance; Local estimation : theory and practice of kriging; Global estimation. This programme can be divided into two parts: Modeling: it provides a better understanding of the spatial variability of the studied variable. Critical analysis of data; Experimental variogram: an experimental view of the variability of the data; Calculation methods for this experimental variogram both in cases of regular and irregular sampling; Theoretical model of variogram: fitting and consequences of the choice of variogram model on the variable properties, meaning of the the model parameters; Regularization: taking account of the variability of sample volume and consequences on modeling. Estimation Variance estimation: evaluation of confidence intervals of the estimators; Global estimation (on the whole deposit, or on large parts of the studied domain); Kriging: «best linear unbiased estimator»; Various methods of kriging: punctual and block kriging with known or unknown mean; kriging neighborhood (choice of data points used for kriging). Prerequisite: solid background in mathematics This module can be divided into two parts: linear geostatistics I and II (see next page). CFSG2 Cost : Duration : 20 day s Including lunch Dates : 18/09/17-13/10/17 Language : English 9

11 (CFSG 2a et 2b) - Regular professional training LINEAR GEOSTATISTICS I AND II CFSG 2a: Linear Geostatistics I / modeling Objectives: Description and modeling of the spatial variability of the variable of interest from experimental data. Programme Experimental variogram: experimental quantification of data variability (later taken into account at modeling stage), calculation methods of this experimental variogram in the case of regular or irregular sampling; Modeling: structural geostatistical analysis, quantification of the studied phenomenon spatial variability (anisotropies, correlation distances, nested scales of variability); Concept of variogram model: importance of variogram fitting and consequences of the model choice on the variable properties, meaning of the model parameters; Regularization: combining data from different sample size; its consequences on modeling; Dispersion Variance: quantification of variable dispersion in a finished field, based on its geometry and its size; application to homogenization stockpiles. Prerequisite: solid background in mathematics. CFSG2A Cost : Duration : 10 day s Including lunch Dates : 18/09/17-29/09/17 Language : English CFSG 2b: Linear Geostatistics II / estimation Objectives: estimate the variable interest already modeled, as well as an assessment of the possible errors magnitude (deviation of estimation, confidence intervals); methods optimize estimating by minimizing the estimation error, difference between calculated and real value. Programme Estimation variance: evaluation of confidence intervals for the different estimators; Global estimation (on the whole deposit, or on large areas of operation); Kriging : «best linear unbiased estimator»; Various types of kriging: punctual and block kriging with known or unknown mean, kriging neighborhood (choice of data points used for kriging). Prerequisite: Linear Geostatistics I or equivalent CFSG2B Cost : Duration : 10 day s Including lunch Dates : 02/10/17-13/10/17 Language : English 10

12 (CFSG 3) - Regular professional training MULTIVARIATE GEOSTATISTICS Objectives: to provide additional tools for the characterization and estimation of resources when there are several variables to consider simultaneously. It allows to highlight spatial relationships between variables, to improve the estimation of a variable using secondary variables,collected at the same points [isotopic case] or not [heterotopic case], to improve consistency between several variables estimation, to simulate several variables together. Programme Several variables are investigated at the same time, in the case of polymetallic deposits, sedimentary geometry multi-surface environments or geochemical prospecting. Basic statistics: reminders on linear regression; Multivariate structural tools: cross covariance and cross variogram (these tools allow to quantify the spatial relationships between variables); Intrinsic correlation model, linear model of coregionalization; Cokriging: estimation method proposed by geostatistics for multivariate applications (general equations for isotopic or heterotopic cases) and cokriging simplifications for specific models or specific types of sampling (collocated cokriging, kriging with external drift...); Factorial kriging analysis: to filter or map one or more of the spatial components of the model (used for mapping anomalies on small or large scale, as for geophysical and geochemical survey); Multivariate statistical tools such as principal components analysis; Elements for multivariate simulation (a simulation module is proposed later in the year). Prerequisite: Proficiency in basic geostatistics is required (see Linear Geostatistics training). CFSG3 Cost : Duration : 10 day s Including lunch Dates : 06/11/17-17 /11/17 Language : English 11

13 (CFSG 4) - Regular professional training NON STATIONARY GEOSTATISTICS Objectives: to provide tools adapted to phenomena too complex to be represented by stationary or intrinsic models, expanding the hypotheses of stationarity. To study phenomena with drift or partly regular behavior (behavior at low frequencies, for example) for which there is not allowed variogram model compatible with the experimental variograms. Programme Study of phenomena with a systematic trend or "drift" with two groups of methods: Universal kriging (case of a global drift of simple form): in a first approach, very intuitive, the studied variable is the sum of two components, one (the residual) that can be treated using the methods of linear geostatistics, the other is considered as a drift (or trend). An extension of this KU approach leads to the method of external drift, in which two types of information are present: the variable of interest, measured in a small number of samples, and an auxiliary variable, densely sampled, which is supposed to provide information on the general behavior of the variable of interest. Intrinsic random functions of order k (IRFk, case of a complex drift): functions that transform the data into stationary quantities (analogous to a differentiation of order k), and that filter the more regular components of the phenomenon. The advantage of this technique is that it broadens the range of models by introducing the generalized covariance (generally, the choice of these generalized covariance and their parameters are handled by an automatic module). The methods differ only in the nature of the stationary objects. The first part of the course focuses on the identification of non-stationary behavior. A numerical example with some regularly spaced 1D data allows us to imagine a simple solution. Prerequisite: Proficiency in basic geostatistics is required see Linear Geostatistics training. CFSG4 Cost : Duration : 5 day s Including lunch Dates : 27 /11/17-01/12/17 Language : English 12

14 (CFSG 5) - Regular professional training NON-LINEAR GEOSTATISTICS Objectives: to provide estimates when linear geostatistics reached its limits: very asymmetric distributions (including change of support models to go from the scale of the sample to that of the block), estimates of non-linear functions of the variable of interest (for example, the average content above a threshold) etc. Programme For example, we seek to estimate the quantities exceeding thresholds from data and a model, or even improve estimation and calculation of variance estimation in the case of variables a very asymmetrical distribution. Two main themes will be discussed: the support effect (the samples size is different from that of the selection units); the information effect (selection from the estimator instead of the true values); The following methods will be presented: indicator kriging (estimates the indicator above a cut-off); multiple indicator kriging (estimate different classes of indicator corresponding to different cutoffs); disjunctive kriging (cokriging of indicators, taking into account the relations between the different indicator variables); conditional distribution (after transformation of the variable into a Gaussian variable). These methods provide for instance the probability that the grade exceeds a given cut-off on the sample support. However the support of interest (block, or selectivity mining unit, for instance) is generally much larger than the quasi-point sample support. This results in a lower selectivity, the distribution of block values presenting for instance less low or high values than the distribution of point support values. Change of support models will be studied, that allow predicting the global distribution of block values within the whole domain, from the known distribution of sample values. Techniques will also be seen, that take into account change of support locally, using the previously mentioned estimators of indicators, or other specific estimators (service variables, uniform conditioning). Prerequisite: Proficiency in basic geostatistics is required (see Linear Geostatistics training). CFSG5 Cost : Duration : 10 day s Including lunch Dates : 15/01/18-26/01/18 Language : English 13

15 (CFSG 6) - Regular professional training GEOSTATISTICS SIMULATIONS Objectives: to provide "digital equivalents of ore body" which have the same spatial variability than the studied deposit, at the cost of a local error greater than for estimations. Blocks models obtained by simulation are less smooth and more realistic than those provided by estimation methods. They can be used to test digitally various production methods. Programme Introduction and concepts; Simulation of random variables; process; Simulation of random sets by the Truncated Gaussian or the Plurigaussian methods; Boolean stationary and non-stationary models. These techniques allow getting different versions of random functions or sets that reproduce the variability of the data, as well as their values by "conditioning". It solves problems that escape to estimation methods, linear or not. Prerequisite: Proficiency in basic geostatistics is required (see Linear Geostatistics training). CFSG6 Cost : Duration : 10 days Including lunch Dates : 05/02/18-16/02/18 Language : English 14

16 Access map to Mines ParisTech Fontainebleau site Charles de Gaulle Airport Antony ORLYVAL Orly Orly ouest sud Paris Gare du Nord ORLYVAL Paris Orly Airport Paris Gare de Lyon Fontainebleau/Avon train To the bus station of Avon : Bus line 1 Les Bouleaux Les Lilas: stop at Saint Honoré Mines ParisTech, 35 rue Saint Honoré, Fontainebleau - France 15

17 MINES PARISTECH: MINING PROFESSIONAL TRAINING PROGRAMES Location: MINES ParisTech Geosciences Research Department Training team 35, rue Saint-Honoré Fontainebleau (France) To register for MS CFSG or in modular continuing professional education, send your curriculum vitae indicating the name of the chosen training to: Portail historique du Quartier Boufflers à Fontainebleau Mrs Gaëlle LE LOC H Training manager resp_cfsg@geosciences.mines-paristech.fr Mrs Nathalie DIETRICH Assistant manager Other trainings exist: CESECO: Technical and economic analysis of mining operations Mr. Jean-Alain FLEURISSON Training manager Mrs Claudie DE VREESE Assistant manager resp_ceseco@geosciences.mines-paristech.fr CESAM: Mining administration M. Hugues ACCARIE Training manager resp_cesam@geosciences.mines-paristech.fr Mme Claudie DE VREESE Assistant manager

18 What is a "Mastère spécialisé "? A "Mastère spécialisé " (MS ) is a post-master degree, a (registered) collective label owned by the Conférence des Grandes Écoles. It was created in 1983 to respond to demand from French companies who wanted to recruit graduates with skills in specialized fields. It guarantees the course's vocational focus, rigour and technical nature. It allows students to develop their strengths and is a springboard for their professional career. What are its objectives? To enable students to become highly specialised in an area corresponding to the needs identified by businesses, therefore giving them dual expertise recognised in the labour market; To enable foreign students to obtain a diploma upon completion of a vocational course in a French or foreign Grande École. What does it consist of? This is a set of teachings full time professional guidance including for MS CFSG: At least 720 hours of theoretical work, practical work and group work (45 ECTS credits); An independent project prepared as part of a mission and leading the defense of a professional thesis. The minimum duration of the mission is 4 months (30 ECTS credits). Only schools which are members of the CGE may issue a post-master degree labelled MS. Who is elligible? Graduates of an engineering school accredited by the Commission on Engineering Degrees (CTI) Graduates of a management school accredited by the Management Training and Qualifications Assessment Committee (CEFDG) to deliver Master's level degrees; Students with a postgraduate degree or equivalent, the list of which is drawn up by the Conférence des Grandes Écoles; Foreign students whose diploma is equivalent to the French diplomas listed above. Our trumps Our network of companies and industry partners ; Professional thesis topics at the heart of economic issue ; Our quality of teaching and interactive teaching ; Some small promotion and personalized coaching. 17

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20 Sculpture above the entrance of Mines ParisTech in Paris 19