Catálogo de publicaciones - libros

Electrofacies are numerical combinations of petrophysical log responses that reflect specific physical and compositional characteristics of a rock interval; they are determined by multivariate procedures that include principal components analysis, cluster analysis, and discriminant analysis. As a demonstration, electrofacies were used to characterize the Amal Formation, the clastic reservoir interval in a giant oil field in Sirte Basin, Libya. Five electrofacies distinguish categories of Amal reservoir rocks, reflecting differences in grain size and intergranular cement. Electrofacies analysis guided the distribution of properties throughout the reservoir model, in spite of the difficulty of characterizing stratigraphic relationships by conventional means.

A morphological approach for studying coast lines time variations is proposed. It is based on interpolations and forecasts by means of weighted median sets, which allow to average the shorelines at different times. After a first translation invariant method, two variants are proposed. The first one enhances the space contrasts by multiplying the quench function, the other introduces homotopic constraints for preserving the topology of the shore (gulfs, islands).

Satellite remote sensing data have become available in meteorology, agriculture, forestry, geology, regional planning, hydrology or natural environment sciences since several decades ago, because satellites provide routinely high quality images with different temporal and spatial resolutions. Joining, combining or smoothing these images for a better quality of information is a challenge not always properly solved. In this regard, geostatistics, as the spatio-temporal stochastic techniques of geo-referenced data, is a very helpful and powerful tool not enough explored in this area yet. Here, we analyze the current use of some of the geostatistical tools in satellite image analysis, and provide an introduction to this subject for potential researchers.

The drinking water contamination crisis in Flint, Michigan has attracted national attention since extreme levels of lead were recorded following a switch in water supply that resulted in water with high chloride and no corrosion inhibitor flowing through the aging Flint water distribution system. Since Flint returned to its original source of drinking water on October 16, 2015, the State has conducted eleven bi-weekly sampling rounds, resulting in the collection of 4,120 water samples at 819 “sentinel” sites. This chapter describes the first geostatistical analysis of these data and illustrates the multiple challenges associated with modeling the space-time distribution of water lead levels across the city. Issues include sampling bias and the large nugget effect and short range of spatial autocorrelation displayed by the semivariogram. Temporal trends were modeled using linear regression with service line material, house age, poverty level, and their interaction with census tracts as independent variables. Residuals were then interpolated using kriging with three types of non-separable space-time covariance models. Cross-validation demonstrated the limited benefit of accounting for secondary information in trend models and the poor quality of predictions at unsampled sites caused by substantial fluctuations over a few hundred meters. The main benefit is to fill gaps in sampled time series for which the generalized product-sum and sum-metric models outperformed the metric model that ignores the greater variation across space relative to time (zonal anisotropy). Future research should incorporate the large database assembled through voluntary sampling as close to 20,000 data, albeit collected under non-uniform conditions, are available at a much greater sampling density.

Spatial fields represent a common representation of continuous geoscience and environmental variables. Examples include permeability, porosity, mineral content, contaminant levels, seismic impedance, elevation, and reflectance/absorption in satellite imagery. Identifying differences between spatial fields is often of interest as those differences may represent key indicators of change. Defining a significant difference is often problem specific, but generally includes some measure of both the magnitude and the spatial extent of the difference. This chapter demonstrates a set of techniques available for the detection of anomalies in difference maps represented as multivariate spatial fields. The multiGaussian model is used as a model of spatially distributed error and several techniques based on the Euler characteristic are employed to define the significance of the number and size of excursion sets in the truncated multiGaussian field. This review draws heavily on developments made in the field of functional magnetic resonance imaging (fMRI) and applies them to several examples motivated by environmental and geoscience problems.

John Aitchison died in December 2016 leaving behind an important inheritance: to continue to explore the fascinating world of compositional data. However, notwithstanding the progress that we have made in this field of investigation and the diffusion of the CoDA theory in different researches, a lot of work has still to be done, particularly in geochemistry. In fact most of the papers published in international journals that manage compositional data ignore their nature and their consequent peculiar statistical properties. On the other hand, when CoDA principles are applied, several efforts are often made to continue to consider the log-ratio transformed variables, for example the centered log-ratio ones, as the original ones, demonstrating a sort of resistance to thinking in relative terms. This appears to be a very strange behavior since geochemists are used to ratios and their analysis is the base of the experimental calibration when standards are evolved to set the instruments. In this chapter some challenges are presented by exploring water chemistry data with the aim to invite people to capture the essence of thinking in a relative and multivariate way since this is the path to obtain a description of natural processes as complete as possible.

A multi-element soil geochemical survey was conducted over the conterminous United States from 2007–2010 in which 4,857 sites were sampled representing a density of 1 site per approximately 1,600 km. Following adjustments for censoring and dropping highly censored elements, a total of 41 elements were retained. A logcentred transform was applied to the data followed by the application of a principal component analysis. Using the 10 most dominant principal components for each layer (surface soil, A-horizon, C-horizon) the application of random forest classification analysis reveals continental-scale spatial features that reflect bedrock source variability. Classification accuracies range from near zero to greater than 74% for 17 surface lithologies that have been mapped across the conterminous United States. The differences of classification accuracy between the Surface Layer, A- and C-Horizons do not vary significantly. This approach confirms that the soil geochemistry across the conterminous United States retains the characteristics of the underlying geology regardless of the position in the soil profile.

This chapter reviews the general concepts of uncertainty and probabilistic risk analysis with a focus on the sources of epistemic and aleatory uncertainty in natural resource and environmental applications together with examples of quantifying both types of uncertainty. The initial uncertainty in these applications arises from the in-situ spatial variability of variables and the relatively sparse data available to model this variability. Subsequent uncertainty arises from processes applied either to extract the in-situ variables or to subject them to some form of flow and/or transport. Various approaches to quantifying the impacts of these uncertainties are reviewed and several practical mining and environmental examples are given.

A comparative analysis of distance methods, kriging and stochastic simulation is conducted for evaluating their capabilities for predicting fluctuations in uncertainty due to changes in spatially correlated samples. It is concluded that distance methods lack the most basic capabilities to assess reliability despite their wide acceptance. In contrast, kriging and stochastic simulation offer significant improvements by considering probabilistic formulations that provide a basis on which uncertainty can be estimated in a way consistent with practices widely accepted in risk analysis. Additionally, using real thickness data of a coal bed, it is confirmed once more that stochastic simulation outperforms kriging.

In the study of molybdenum deposits and most other minerals deposits, including copper, lead and zinc, there is speculation that most undiscovered ore results from an increase (or “growth”) in the estimated size of a known deposit due to factors such as exploitation and advances in mining and exploration technology, rather than in discovering wholly new deposits. The purpose of this study is to construct a nonlinear model to estimate deposit “growth” for known deposits as a function of cutoff grade. The model selected for this data set was a truncated normal cumulative distribution function. Because the cutoff grade is commonly unknown, a model to estimate cutoff grade conditioned upon the deposit grade was constructed using data from 34 deposits with reported data on molybdenum grade, cutoff grade, and tonnage. Finally, an example is presented.