MMES'98 MATHEMATICAL METHODS IN EARTH SCIENCES
One-day workshop




W1 Spatio/temporal analysis of natural systems

Lecturers: George Christakos
DESE, School of Public Health, University of North Carolina
111 Rosenau Hall, Chapel Hill, NC 27599-7400
e-mail: george_christakos@unc.edu

The course aims at introducing models and methods of stochastic spatio-temporal analysis, which have a wide range of applications including geology, hydrology, geostatistics, atmospheric environment, epidemiology, medical geography, mining and petroleum engineering. The topics to be discussed in the course include the modern stochastics paradigm, space/time random field models, mapping techniques, bayesian and information-theoretic methods of space/time analysis and prediction. Space/time concepts and tools have a variety of important features, including the ability to demonstrate with a unique efficiency the distribution of natural processes and exposures in space/time, convey factual information and stimulate the formation of hypotheses. The composite space/time approach offers valuable physical insight that could not have been obtained on the basis a purely spatial or a purely temporal analysis. Space/time maps represent computer-generated and -reproduced empirical realities.
Depending on a number of factor (e.g., data quality, scale, and physically motivated criteria), the space/time analysis and mapping offer alternative images of the dynamic evolution of physical systems. The space/time theory is formulated in a way that preserves most of the references of earlier theories, which are its limited cases. Minimum mean square error estimators (such as the various forms of kriging) obtained on the basis of hard data and lower-order statistics (e.g., mean and covariance, semi-variogram) are derived as special cases of the general space/time theory. Space/time estimation techniques are presented and guidelines for their application in practice are given. Important aspects of scientific reasoning are taken into consideration in the development of the bayesian maximum entropy approach. The unique features that make this approach a loyal guardian of plausible reasoning in natural sciences are highlighted.
Emphasis will be given in the study of natural variables with spatially non-homogeneous and temporally non-stationary characteristics. The case of vector mapping analysis (modeling and mapping more than one natural variables simultaneously) will be discussed. Scale issues—which are prominent in composite space/time mapping applications—will be investigated. Comparisons are made between the various space/time mapping techniques. The variety of applications provides a framework for evaluation, and a realization that there can be a systematic organization for many concepts, tools and perspectives. The approach of the course is conceptual with a number of examples and case studies presented for edification and assimilation. A valuable aid in the implementation of the models is offered by computerized visualization techniques. Case studies will be discussed, which demonstrate the advantages of composite space/time analysis in the study of earth and environmental problems.


W2 New methods and concepts in mathematical geology

Lecturers: Frits P. Agterberg1 and Qiuming Cheng2
1Natural Resources Canada
601 Booth Street Ottawa K1A 0E8 - Canada
tel.: +1 613 996 2374
fax.: +1 613 996 0473
e-mail: agterberg@gsc.NRCan.gc.ca

2Dept. of Earth and Atmospheric Science
Dep. of Geography, Faculty of Pure and Applied Science,
York University, North York, Ontario M3J 1P3, Canada
tel.: +1 416 736 5529
fax.: +1 416 736 5950
e-mail: qiuming@yorku.ca


The one-day workshop covers three new fields of research in mathematical geology.
a) Multifractal modelling in relation to geostatistics:
multifractal semivariogram; frequency distributions of variables with different spatial supports; multiplicative cascade simulation models; discrete versus continuous multifractals.
Applications are to element concentration values in geochemistry, sizes and grades of mineral deposits, distribution of fractures in crystalline rocks.
b) Data integration techniques: multivariate statistical analysis for estimating probabilities of discrete events; Bayesian decision models; weights of evidence; fuzzy set theory; neural networks; definition of nackground and anomalies. Applications to mineral potential mapping of ore deposits and geochemical data analysis.
c) Geological time and quantitative stratigraphy: Integration of geochronological data with stratigraphic information to construct numerical geological time scales; analysis of superpositional relations for stratigraphic events observed in sedimentary rocks with wildcat drilling applications.

Each set of techniques is backed up by computer programs and applications to large datasets will be demonstrated.


W3 Geostatistical simulation in geology

Lecturers: Alain Galli and Margaret Armstrong
Centre de Geostatistique de l'Ecole des Mines de Paris
35 Rue Saint Honore
77305 Fontainebleau - France
e-mail: galli@cg.ensmp.fr
e-mail: armstrong@cg.ensmp.fr

When geostatistical simulations were first invented 20-25 years ago, people simulated variables like porosity or permeability, or grades directly. But as the geology controls the variability to a large extent, it became clear that it was better to carry out the simulations in two steps: first simulate the geology (the facies, the rocktypes, geological objects) then infill the variables according to the geology. As the second step is well known, this course focuses on the practical aspects of simulating geology. After briefly reviewing simulation methods, their main features will be illustrated by a series of case studies in mining and petroleum.


W4 Basic geostatistics: a one day introductory course

Lecturers: Vera-Pawlowsky-Glahn
Universitat Politècnica de Catalunya
Departamento de Matemática Aplicada III
ETS de Ing. de Caminos, Canales y Puertos
c/ Gran Capitán, s/n
E-08034 Barcelona, Spain
e-mail: pawlowsky@etseccpb.upc.es

Vera Pawlowsky-Glahn is professor at the School of Civil Engineering of the Technical University of Catalonia and is assigned to the Department of Applied Mathematics III. She is the head of a research group working in the fields both of statistical analysis of compositional data and in spatial statistics. She has been teaching courses on statistics, multivariate statistics and geostatistics, mainly to civil and geological engineers, during the last 10 years.

Course content
The course is conceived as an introductory course to univariate geostatistics. It is intended for practitioners and students, both graduate and undergraduate, with a basic background in classical statistics. Topics addressed include: exploratory data analysis; theoretical foundations of geostatistics; the semi-variogram: estimation, theoretical models, properties; measures of spatial variability; spatial prediction; kriging.

Course structure
The course will alternate theoretical presentations with examples and case studies; available software will be presented.


W5 Environmental spatial data analysis. Do it yourself with spatial statistics and neural networks

Subtitle
Case studies of soil pollution for decision system support with spatial statistics packages (Geostat Office, Faipack, Multigeo) and with neural network residual kriging and generalized regression.

Lecturers
Prof. Michel Maignan, University of Lausanne, Switzerland;
e-mail: michel.maignan@imp.unil.ch
Prof. Mikhail Kanevski, IBRAE Institute of Nuclear Safety, Moscow, Russia;
Prof. Roberto Bruno, University of Bologna, Italy;
Prof. Giuseppe Raspa, University of Roma, La Sapienza, Italy;
Dr. S. Canu, Heudyasic, University of Compiegne, France.

Chapters
Topology of monitoring networks: Voronoi polygons, fractal dimensions, Morishita index
Variography/trend analysis and modeling (VarRose)
Geostatistical predictions and simulations (WinGSLIB)
Multivariate spatial data analysis (Multigeo)
Neural networks function approximations and spatial interpolations (ANN/GR)
NNRK neural network residual kriging/cokriging NNRC
Non stationary IRF-k analysis (FAIPACK)
GIS and cartographic display (Geoplot)

Practice
The workshop will alternate presentation of methods and actual practice on PCs, so that the participants are in a position to redo themselves the whole workshop. The case studies will refer to completed/ongoing studies of the group according to Russian-Swiss-Japanese-European cooperation for radionuclides in the Russian soils, and in the Swiss soils and for heavy metals in the Japanese and in the Swiss soils.

Content
The study of soil pollution requires new adaptations and new methods beyond the classical ones because of their specific types of monitoring networks, and because of their characteristic non-stationarities. Furthermore, the results must be presented and analyzed on the basis of existing geographical maps. The first topic which is presented deals with the topological characterization of the monitoring networks and with the relevant indexes, and not only with declustering. The topology of a monitoring network, especially for pollution cartography, must not be underestimated. New programs developed under windows are presented in order to illustrate the analysis of non-stationarities and the measurement of spatial correlations. Estimations proposed are based on classical estimators: deterministic estimators or stochastic BLUE kriging estimators. Simulations are done with classical programs, easy to use under windows. Constraints on variography in case of multivariate data are presented and treated by use of a new and-hoc package for multivariate geostatistics. Beyond the classical interpolation methods developed during the last 40 years, neural networks represent a new possibility, which is still in controversial development, but that we have successfully used for the non-stationary cases of large-scale soil pollution. The specific developments which have been done lead to neural network residual kriging in the case of complex non-stationarities. Another manner to solve the problem of non-stationarities follows the methods of generalized covariances and of intrinsic random functions of order-k; these methods have been implemented on PCs since several years by Italian authors. The positive contribution of a study of spatial statistics for pollution to a DSS (Decision Support System) requires a precise mapping on the basis of existing geographical maps, and a subsequent possibility of queries; this is done when the results of spatial statistics are moved to a GIS (Geographical Information System), either vector based or raster based; this will be demonstrated.


W6 Environmental Geostatistics

Lectures:
Roberto BRUNO
Dip. di Ing. Chimica, Mineraria e delle Tecnologie Ambientali
Univ. of Bologna
V.le Risorgimento, 2 - 40136 Bologna, Italy
Tel.(+39-51) 6443393; fax (+39-51) 6443392;
E-mail: roberto.bruno@mail.ing.unibo.it

Chantal DE FOUQUET
Centre de Geostatistique del l'Ecole Nationale Superieure des Mines de Paris
35 Rue Saint-Honoré - 77305 Fontainebleau - France
Tel.(+33-1) 64694761; fax (+33-1) 64694705;
E-mail: fouquet@cg.ensmp.fr

Giuseppe RASPA
Dip. di Ing. Chimica, dei Materiali, delle Materie Prime e Metall.
Univ. of Rome "La Sapienza"
V. Eudossiana, 18 - 00187 Roma, Italy
Tel.(+39-6) 44585627; fax (+39-6) 44585618;
E-mail: raspa@columbus.it

R.Bruno is Associate Professor in the Department of Mining, Chemical and Environmental Technologies Engineering at University of Bologna where teaches "Georesources Characterisation" and "Applied Geostatistics". He has been active in the area of Geostatistics for over 20 years in both, industrial and academic fields.

Ch. De Fouquet , Civil Mining Engineer, Doct.Ing., is Master of Research of the Geostatistics Center of "Ecole Nationale Superieure de Mines de Paris", where she is charged of Environmental Geostatistics Applications.

G.Raspa is Associate Professor in the Department of Chemical, Materials, Raw Materials and Metallurgy Engineering at University of Rome "La Sapienza" where teaches "Applied Geostatistics". He has been active in the area of Geostatistics for over 20 years in both, industrial and academic fields.

Course Content

The course aims at giving a wide range of examples of environmental problems that can be at best studied and solved by a geostatistical approach. In fact most of environmental problems accounts for topological data as information, often known at limited number of points of the spatio-temporal working space. Moreover the problem solutions, be a monitoring or a reclamation problem, are basically linked to decisions which today need an optimality criterion, as for example sampling, selection processes, estimations, and so on: i.e. the classical framework where geostatistics grew and succeeded over last 20 years. It is then very important to know the widest range of tools available, the knowledge of the proper field of applications of each one, as well as their limits. In effect there are no general geostatistical procedures (and Sw's), but each particular problem needs its own specific procedure, to be built on gestatistical base functions; and some experience is needed to do it, also considering that geostatistical methods evolve and grow richer.
This course will provide a grounding for the analysis of the problem, the comparison of different methodologies at hand, a guide for a practical choice of the strategic and tactical approach. A large part of geostatistics field would be considered: stationary/non-stationary, monovariate/multivariate, linear/non-linear, but always only on the practical point of view as a tool for problem solving.

Course structure:
The analysis of two main problems will give the opportunity of a commented review on various methods available:
A) Spatial reconstruction of environmental variables.
How to improve the spatial reconstruction of many environmental variables, as acquifer or soil characteristics, noise, pollution, etc.: external drift, multivariable processing, stationary or non-stationary approach, estimation or simulation. B) Identification and characterisation of polluted areas (or risk of exceeding a threshold).
How to improve the confidence on space partitions: estimation or simulation, linear or non linear approach, indicator or full variable.
PC/Workstations software will be available both for case studies presentations supporting the lectures, as well, whenever possible, for quick applications in real time.