Jacques Rivoirard

Unsupervised classification of multivariate geostatistical data

With the increasing development of remote sensing platforms and the evolution of sampling facilities in mining and oil industry, spatial datasets are becoming increasingly large, inform a growing number of variables and cover wider and wider areas. Therefore, it is often necessary to split the domain of study to account for radically different behaviors of the natural phenomenon over the domain and to simplify the subsequent modeling step. The definition of these areas can be seen as a problem of unsupervised classification, or clustering, where we try to divide the domain into homogeneous domains with respect to the values taken by the variables in hand. The application of classical clustering methods, designed for independent observations, does not ensure the spatial coherence of the resulting classes. Image segmentation methods, based on e.g. Markov random fields, are not adapted to irregularly sampled data. Other existing approaches, based on mixtures of Gaussian random functions estimated via the expectation-maximization algorithm, are limited to reasonable sample sizes and a small number of variables. In this work, we propose two algorithms based on adaptations of classical algorithms to multivariate geostatistical data. Both algorithms are model free and can handle large volumes of multivariate, irregularly spaced data. The first one proceeds by agglomerative hierarchical clustering. The spatial coherence is ensured by a proximity condition imposed for two clusters to merge. This proximity condition relies on a graph organizing the data in the coordinates space. The hierarchical algorithm can then be seen as a graph-partitioning algorithm. Following this interpretation, a spatial version of the spectral clustering algorithm is also proposed. The performances of both algorithms are assessed on toy examples and a mining dataset.

A Geostatistical Definition of Hotspots for Fish Spatial Distributions

Research surveys at sea are undertaken yearly to monitor the distribution and abundance of fish stocks. In the survey data, a small number of high fish concentration values are often encountered, which denote hotspots of interest. But statistically, they are responsible for important uncertainty in the estimation. Thus understanding their spatial predictability given their surroundings is expected to reduce such uncertainty. Indicator variograms and cross-variograms allow to understand the spatial relationship between values above a cutoff and the rest of the distribution under that cutoff. Using these tools, a “top” cutoff can be evidenced above which values are spatially uncorrelated with their lower surroundings. Spatially, the geometric set corresponding to the top cutoff corresponds to biological hotspots, inside which high concentrations are contained. The hotspot areas were mapped using a multivariate kriging model, considering indicators in different years as covariates. The case study considered here is the series of acoustic surveys Pelgas performed in the Bay of Biscay to estimate anchovy and other pelagic fish species. The data represent tonnes of fish by square nautical mile along transects regularly spaced. Top cutoffs were estimated in each year. The areas of such anchovy hotspots are then mapped by co-kriging using all information across the time series. The geostatistical tools were adapted for estimating hotspot habitat maps and their variability, which are key information for the spatial management of fish stocks. Tools used here are generic and will apply in many engineering fields where predicting high concentration values spatially is of interest.

From the Spatial Sampling of a Deposit to Mineral Resources Classification

Part I. Special session in honor of Professor Danie Krige -- Professor Danie Krige’s first memorial lecture: A summary of the basic tenets of evaluating the mineral resource assets of mining companies, as observed in Professor Danie Krige’s pioneering work over half a century (Winfred Assibey-Bonsu) -- Using classical Geostatistics to quantify the spatiotemporal dynamics of a neurodegenerative disease from brain MRI (Robert Marschallinger) -- Part II. Theory -- Can Measurement Errors be characterized from Duplicates? (Chantal de Fouquet) -- Modeling Asymmetrical facies successions using Pluri-Gaussian Simulations (Thomas Le Blevec) -- Considerations for the use of sequential sampling techniques (Jaap Leguijt) -- A truly multivariate Normal Score Transform based on Lagrangian Flow (Ute Mueller) -- Functional Decomposition Kriging for Embedding Stochastic Anisotropy Simulations (J. A. Vargas-Guzman) -- Part III. Mining Engineering -- Using samples of unequal length to estimate grades in a mineral deposit (Marcel Antonio Arcari Bassani) -- New Approach to Recoverable Resource Modelling: The Multivariate Case at Olympic Dam (Mario Rossi) -- Comparison of two grade multivariate simulation approaches on an iron oxide copper gold deposit (Antonio Cortes) -- Complexities in the geostatistics estimation of minerals deposits Besshi type on the nor-west of Pinar del Rio, Cuba (Jose Quintin Cuador-Gil) -- Definition of Operational Mining Unit (OMU) Size (Cassio Diedrich) -- Optimizing Infill Drilling Decisions using Multi-armed Bandits: Application in a Long-term, Multi-element Stockpile (Rein Dirkx) -- A new high-order statistical simulation that is non-stationary and transformation invariant (Amir Abbas Haji Abolhassani) -- Fixing Panel Artifacts in LIK Block Models (William Hardtke) -- Implications of algorithm and parameter choice: Impacts of geological uncertainty simulation methods on project decision making (Arja Jewbali) -- Approaching simultaneous local and global accuracy (Danile Jasper Kentwell) -- Geostatistics for Variable Geometry Veins (Alfredo Marin Suarez) -- Drilling Grid Analysis for Defining Open Pit and Underground Mineral Resources Catego-rization Using Brazilian Sulphide Deposit (Cu-Au) Production Data (Roberto Menin) -- A High-Order, Data-Driven Framework for Joint Simulation of Categorical Variables (Ilnur Minniakhmetov) -- Conditional Bias in Kriging - Lets Keep It (Marek Nowak) -- Operational SMU definition at a Brazilian copper operation (Roberto Menin) -- From the spatial sampling of a deposit to mineral resources classification (Jacques Rivoirard) -- Resource Model Dilution and Ore Loss: A Change of Support Approach (Oscar Rondon) -- Diamond Drill Holes and Blast Holes, a Formal Study (Serge Antoine Seguret) -- Building of a tonnage-surface function of metal grades and geological dilution: application to the massive and stockwork Zambujal ore deposit, Neves-Corvo mine (Jose Antonio Almeida) -- Application of direct sequential simulation and co-simulation for evaluation of resources and uncertainty of the Ncondezi coal deposit in Mozambique (Sara Matias Ferreira Sokhin) -- Castelo de Sonhos: Geostatistical quantification of the potential size of a Paleoproterozoic conglomerate-hosted gold deposit (R. Mohan Srivastava) -- A hybrid model for joint simulation of high-dimensional continuous and categorical variables (Hassan Talebi) -- Performance Analysis of Continuous Resource Model Updating in Lignite Production (Cansin Yuksel) -- Part IV. Petroleum Engineering -- Geostatistics on unstructured grids, theoretical background and applications (Biver Pierre) -- Using Spatial Constraints in Clustering for Electrofacies Calculation (Jean-Marc Chautru) -- Pore network modeling from multi-scale imaging using Multiple Point Statistics (Tatiana Chugunova) -- Bernstein copula-based spatial stochastic simulation of petrophysical properties using seismic attributes as secondary variable (Martin A. Diaz-Viera) -- Robust MPS-based modeling via Spectral Analysis (Morteza Elahi Naraghi) -- Efficient Uncertainty Quantification and History Matching of Large-Scale Fields through Model Reduction (Jianlin Fu) -- Revealing multiple geological scenarios through unsupervised clustering of posterior realizations from reflection seismic inversion (Mats Lundh Gulbrandsen) -- Object modelling in a time of modern well data configurations (Ragnar Hauge) -- Machine learning methods for sweet spot detection: a case study (Vera Louise Hauge) -- Theoretical generalization of Markov chain random field in reservoir lithofacies stochastic simulation (Xiang Huang) -- Deepwater Reservoir Connectivity Reproduction from MPS and Process-mimicking Geostatistical Methods (Michael J. Pyrcz) -- Modeling of depositional environments - Shoreline trajectory - The link between Sequence Stratigraphy and Truncated Gaussian Fields (Lars Edward Rygg Kjellesvik) -- Facies inversion with Plurigaussian lithotype rules (Lewis Li) -- Combined use of object-based models, multipoint statistics and direct sequential simulation for generation of the morphology, porosity and permeability of turbidite channel systems (Ines Alexandra Costa Marques) -- How to model interactions between reservoir properties for complex data structures (Havard Goodwin Olsen) -- Geostatistical Methods for Unconventional Reservoir Uncertainty Assessments (Michael J. Pyrcz) -- Productivity prediction using Alternating Conditional Expectations (Emmanuel T. Schnetzler) -- The adaptive plurigaussian simulation model (APS) versus the truncated plurigaussian simulation model (TPS) used in the presence of hard data (Bogdan Sebacher) -- A MPS Algorithm based on Pattern Scale-down Cluster (Yu Siyu) -- Integrating new data in reservoir forecasting without building new models (Sebastien Strebelle) -- Statistical scale-up of dispersive transport in heterogeneous reservoir (Vikrant Vishal) -- The comparative analysis of geostatistical methods on the square with a large number of wells (Evgeniy Kovalevskiy) -- Part V. Hydro(geo)logy -- Building piezometric maps: contribution of geostatistical tools (Bernard Bourgine) -- A gradient-based blocking Markov chain Monte Carlo method for stochastic inverse modeling (Jianlin Fu) -- Geoestatistical modeling and simulation scenarios as optimizing tools for curtain grouting design and construction at a dam foundation (Vasco Gavinhos) -- Inverse modeling aided by the Classification and Regression Tree (CART) algorithm (Julio Cesar Gutierrez-Esparza) -- Numerical Simulation of Solute Transport in Groundwater Flow System using Random Walk Method (Nilkanth H. Kulkarni) -- A Comparison of EnKF and EnPAT Inverse Methods: Non-Gaussianity (Liangping Li) -- Stochastic Inverse Modeling of Interbed Parameters and Transmissivity Using Land Subsidence and Drawdown Data via EnKF (Liangping Li) -- Influence of Heterogeneity on Heat Transport Simulations in Shallow Geothermal Systems (Javier Rodrigo-Ilarri) -- Part VI. Environmental Engineering and Sciences -- Building a geological reference platform using sequence stratigraphy combined with geostatistical tools (Bernard Bourgine) -- Constrained spatial clustering of climate variables for geostatistical reconstruction of optimal time series and spatial fields (Peter Dowd) -- Constraining geostatistical simulations of delta hydrofacies by using machine correlation (Peter Dowd) -- Assessing the performance of the gsimcli homogenisation method with precipitation monthly data from the COST-HOME benchmark (Sara Ribeiro) -- Ecological Risk Evaluation of Heavy Metal Pollution in Soil in YangGu (Yingjun Sun) -- Comparison of trend detection approaches in time series and their application to identify temperature changes in the Valencia region (Eastern Spain) (Peter Dowd) -- Part VII. Big Data -- Urban Dynamics Estimation using Mobile Phone logs and Locally Varying Anisotropy (Oscar F. Peredo).

Indicator-Based Geostatistical Models For Mapping Fish Survey Data

Marine research survey data on fish stocks often show a small proportion of very high-density values, as for many environmental data. This makes the estimation of second-order statistics, such as the variance and the variogram, non-robust. The high fish density values are generated by fish aggregative behaviour, which may vary greatly at small scale in time and space. The high values are thus imprecisely known, both in their spatial occurrence and order of magnitude. To map such data, three indicator-based geostatistical methods were considered, the top-cut model, min–max autocorrelation factors (MAF) of indicators, and multiple indicator kriging. In the top-cut and MAF approaches, the variable is decomposed into components and the most continuous ones (those corresponding to the low and medium values) are used to guide the mapping. The methods are proposed as alternatives to ordinary kriging when the variogram is difficult to estimate. The methods are detailed and applied on a spatial data set of anchovy densities derived from a typical fish stock acoustic survey performed in the Bay of Biscay, which show a few high-density values distributed in small spatial patches and also as solitary events. The model performances are analyzed by cross-validating the data and comparing the kriged maps. Results are compared to ordinary kriging as a base case. The top-cut model had the best cross-validation performance. The indicator-based models allowed mapping high-value areas with small spatial extent, in contrast to ordinary kriging. Practical guidelines for implementing the indicator-based methods are provided.

A Specific Volume to Measure the Spatial Sampling of Deposits

A concept is proposed that allows measuring the density of the spatial sampling of a regionalized variable in a domain. This “spatial sampling density variance” possesses an additivity property that enables combining the values from different parts of a domain. In the case of a regular sampling pattern, the spatial sampling density variance is constant throughout the domain. It depends on the sampling grid cell and on the variogram, not on the extension of the domain. It can also simply be expressed as a “specific volume”, similar to the inverse density of sample points in space, but taking into account the spatial structure. This can be used to compare different sampling patterns in a domain, as well as sampling patterns in different domains. In case of irregular sampling pattern, this can be mapped (like a density of points) using a moving window. The resulting map can be used to make the distinction between areas with different sampling densities. In the context of mineral resources, the concept can provide a description of the level of sampling for a deposit, or for parts of deposits sampled with different densities. This can be further used for classification, given expected production volumes.