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Mineral target selection has been an important research subject for geoscientists around the world in the past three decades. Significant progress has been made in development of mathematical techniques and estimation methodologies for mineral mapping and resource assessment. Integration of multiple data sets, either by experts or statistical methods, has become a common practice in estimation of mineral potentials. However, real effect of these methodologies is at best very limited in terms of uses for government macro policy making, resource management, and mineral exploration in commercial sectors. Several major problems in data integration remain to be solved in order to achieve significant improvement in the effect of resource estimation. Geoscience map patterns are used for decision-making for mineral target selections. The optimal data integration methods proposed so far can be effectively applied by using GIS technologies. The output of these methods is a prognostic map that indicates where hidden ore bodies may occur. Issues related to randomness of mineral endowment, intrinsic statistical relations, exceptionalness of ore, intrinsic geological units, and economic translation and truncation, are addressed in this chapter. Moreover, a number of specific important technical issues in information synthesis are also identified, including information enhancement, spatial continuity, data integration and target delineation. Finally, a new concept of dynamic control areas is proposed for future development of quantification of mineral resources.

Samples are often taken to test whether they came from a specific population. These tests are performed at some level of significance (α). Even when the hypothesis is correct, we risk rejecting it in α percent of the cases—a Type I error. We also risk accepting it when it is not correct—a Type II error at β probability. In resource assessments much of the work is balancing these two kinds of errors. Remarkable advances in the last 40 years in mathematics, statistics, and computer sciences provide extremely powerful tools to solve many mineral resource problems. It is seldom recognized that perhaps the largest error—a third type—is solving the wrong problem. Most such errors are a result of the mismatch between information provided and information needed. Grade and tonnage or contained models can contain doubly counted deposits reported at different map scales with different names resulting in seriously flawed analyses because the studied population does not represent the target population of mineral resources. Among examples from mineral resource assessments are providing point estimates of quantities of recoverable materials that exist in Earth’s crust. What decision is possible with that information? Without conditioning such estimates with grades, mineralogy, remoteness, and their associated uncertainties, costs cannot be considered, and possible availability of the resources to society cannot be evaluated. Examples include confusing mineral occurrences with rare economically desirable deposits. Another example is researching how to find the exposed deposits in an area that is already well explored whereas any undiscovered deposits are likely to be covered. Some ways to avoid some of these type III errors are presented. Errors of solving the wrong mineral resource problem can make a study’s value negative.

Proximity regression is an exploratory method to predict multielement haloes (and multielement ‘vectors’) around a geological feature, such as a mineral deposit. It uses multiple regression directly to predict proximity to a geological feature (the response variable) from selected geochemical elements (explanatory variables). Lithogeochemical data from the Ben Nevis map area (Ontario, Canada) is used as an example application. The regression model was trained with geochemical samples occurring within 3 km of the Canagau Mines deposit. The resulting multielement model predicts the proximity to another prospective area, the Croxall property, where similar mineralization occurs, and model coefficients may help in understanding what constitutes a good multielement vector to mineralization. The approach can also be applied in 3-D situations to borehole data to predict presence of multielement geochemical haloes around an orebody. Residual principal components analysis is another exploratory multivariate method. After applying a conventional principal components analysis, a subset of PCs is used as explanatory variables to predict a selected (single) element, separating the element into predicted and residual parts to facilitate interpretation. The method is illustrated using lake sediment data from Nunavut Territory, Canada to separate uranium associated with two different granites, the Nueltin granite and the Hudson granite. This approach has the potential to facilitate the interpretation of multielement data that has been affected by multiple geological processes, often the situation with surficial geochemical surveys.

The quantitative estimation of mineralogy from wireline petrophysical logs began as an analytical stepchild. The calculation of porosity in reservoir lithologies is affected by mineral variability, and methods were developed to eliminate these components. Simple inversion methods were applied in pioneer applications by mainframe computers to a limited suite of digital log data. Over time, the value of lithological characterization of reservoirs and resource plays has been recognized. At the same time, the introduction of newer petrophysical measurements, particularly geochemical logs, in conjunction with increasingly sophisticated algorithms, has increased confidence in mineral profiles from logs as a routine evaluation tool.

In the oil industry, exploratory targets tend to be increasingly complex and located deeper and deeper offshore. The usual absence of well data and the increase in the quality of the geophysical data, verified in the last decades, make these data unavoidable for the practice of oil reservoir modeling and characterization. In fact the integration of geophysical data in the characterization of the subsurface petrophysical variables has been a priority target for geoscientists. Geostatistics has been a key discipline to provide a theoretical framework and corresponding practical tools to incorporate as much as possible different types of data for reservoir modeling and characterization, in particular the integration of well-log and seismic reflection data. Geostatistical seismic inversion techniques have been shown to be quite important and efficient tools to integrate simultaneously seismic reflection and well-log data for predicting and characterizing the subsurface lithofacies, and its petro-elastic properties, in hydrocarbon reservoirs. The first part of this chapter presents the state of the art and the most recent advances of geostatistical seismic inversion methods, to evaluate the reservoir properties through the acoustic, elastic and AVA seismic inversion methods with real case applications examples. In the second part we present a methodology based on seismic inversion to assess uncertainty and risk at early stages of exploration, characterized by the absence of well data for the entire region of interest. The concept of analog data is used to generate scenarios about the morphology of the geological units, distribution of acoustic properties and their spatial continuity. A real case study illustrates the this approach.

Publicly available large metal deposit size data bases allow new kinds of statistical modeling of regional and worldwide metal resources. The two models most frequently used are lognormal size-grade and Pareto upper tail modeling. These two approaches can be combined with one another in applications of the Pareto-lognormal size-frequency distribution model. The six metals considered in this chapter are copper, zinc, lead, nickel, molybdenum and silver. The worldwide metal size-frequency distributions for these metals are similar indicating that a central, basic lognormal distribution is flanked by two Pareto distributions from which it is separated by upper and lower tail bridge functions. The lower tail Pareto distribution shows an excess of small deposits which are not economically important. Number frequencies of the upper tail Pareto are mostly less than those of the basic lognormal. Parameters of regional metal size-frequency distributions are probably less than those of the worldwide distributions. Uranium differs from other metals in that its worldwide size-frequency distribution is approximately lognormal. This may indicate that the lognormal model remains valid as a standard model of size-frequency distribution not only for uranium but also for the metals considered in this chapter, which are predominantly mined from hydrothermal and porphyry-type orebodies. A new version of the model of de Wijs may provide a framework for explaining differences between regional and worldwide distributions. The Pareto tails may reflect history of mining methods with bulk mining taking over from earlier methods in the 20th century. A new method of estimating the Pareto coefficients of the economically important upper tails of the metal size-frequency distributions is presented. A non-parametric method for long-term projection of future metal resource on the basis of past discovery trend is illustrated for copper.

Bayesianism is currently one of the leading ways of scientific thinking. Due to its novelty, the paradigm still has many interpretations, in particular with regard to the notion of “prior distribution”. In this chapter, Bayesianism is introduced within the historical context of the evolving notions of scientific reasoning such as inductionism, deductions, falsificationism and paradigms. From these notions, the current use of Bayesianism in the geosciences is elaborated from the viewpoint of uncertainty quantification, which has considerable relevance to practical applications of geosciences such as in oil/gas, groundwater, geothermal energy or contamination. The chapter concludes with some future perspectives on building realistic prior distributions for such applications.

Geologists and geophysicists often approach the study of the Earth using different and complementary perspectives. To simplify, geologists like to define and study objects and make hypotheses about their origin, whereas geophysicists often see the earth as a large, mostly unknown multivariate parameter field controlling complex physical processes. This chapter discusses some strategies to combine both approaches. In particular, I review some practical and theoretical frameworks associating petrophysical heterogeneities to the geometry and the history of geological objects. These frameworks open interesting perspectives to define prior parameter space in geophysical inverse problems, which can be consequential in under-constrained cases.

Random function models and kriging constitute the core of the geostatistical methods created by Georges Matheron in the 1960s and further developed at the research center he created in 1968 at Ecole des Mines de Paris, Fontainebleau. Initially developed to avoid bias in the estimation of the average grade of mining panels delimited for their exploitation, kriging received progressively applications in all domains of natural resources evaluation and earth sciences, and more recently in completely new domains, for example, the design and analysis of computer experiments (DACE). While the basic theory of kriging is rather straightforward, its application to a large diversity of situations requires extensions of the random function models considered and sound solutions to practical problems. This chapter presents the origins of kriging as well as the development of its theory and its applications along the last fifty years. More details are given for methods presently in development to efficiently handle kriging in situations with a large number of data and a nonstationary behavior, notably the Gaussian Markov random field (GMRF) approximation and the stochastic partial differential (SPDE) approach, with a synthetic case study concerning the latter.

Geostatistical modeling is one of the most important tools for building an ensemble of probable realizations in earth science. Among them, multiple-point statistics (MPS) has recently gone under a remarkable progress in handling complex and more realistic phenomenon that can produce large amount of the expected uncertainty and variability. Such progresses are mostly due to the recent increase in more advanced computational techniques/power. In this review chapter, the recent important developments in MPS are thoroughly reviewed. Furthermore, the advantages and disadvantages of each method are discussed as well. Finally, this chapter provides a brief review on the current challenges and paths that might be considered as future research.