M. Armstrong – författare

ACKNOWLEDGEMENTS xvii LIST OF PARTICIPANTS xix PLENARY SESSIQNS KRIGE D.G., GUARASCIO M. and CAMISANI-CALZOLARI F.A. Early South African qeostatistical techniques in today's perspective ...1 MATHERON G. The internal consistency of models in qeostatistics...21 MONESTIEZ P., HABIB R. and AUDERGON J.M. Estimation de la covariance et du varioqramme pour une fonction aleatoire a support arborescent : application a l'etude des arbres fruitiers ...39 CHILES J.P. Modelisation qeostatistique de reseaux de fractures...57 BRUNO R. and RASPA G. Geostatistical characterization of fractal models of surfaces 17 RIVOIRARD J. Models with orthoqonal indicator residuals...91 OMRE H., HALVORSEN K.B. and BERTEIG V. A Bayesian approach to kriqinq ...109 THEQRY I SWITZER P. Non-stationary spatial covariances estimated from monitorinq data ...127 CHAUVET P. Quelques aspects de l'analyse structurale des FAI-k a 1 dimension...139 vi TABLE OF CONTENTS DOWD P.A. Generalised cross-covariances ...151 CRESSIE N. The many faces of spatial prediction ..**...*...**.*.*..*. 163 OBLED C. & BRAUD I. Analogies entre geostatistique et analyse en composantes principales de processus ou analyse EOFs...177 THEORY II JEULIN D. Sequential random functions models...189 CHAUTRU J.M. The use of Boolean random functions in geostatistics *.**.**...201 SOARES A.O. Use of a mathematical morphology tool in characterizing covariance& of indicator data...213 ALLISON H.J. Regularization in geostatistics and in ill-posed inversed problems ...* . . * . * . . * ...* * ...225 DONG A.

When this two-day meeting was proposed, it was certainly not conceived as a celebration, much less as a party. However, on reflection, this might have been a wholly appropriate gesture because geostatistical simulation came of age this year: it is now 21 years since it was first proposed and implemented in the form of the turning bands method. The impetus for the original development was the mining industry, principally the problems encountered in mine planning and design based on smoothed estimates which did not reflect the degree of variability and detail present in the real, mined values. The sustained period of development over recent years has been driven by hydrocarbon applications. In addition to the original turning bands method there are now at least six other established methods of geostatistical simulation. Having reached adulthood, it is entirely appropriate that geostatistical simulation should now be subjected to an intense period of reflection and assessment. That we have now entered this period was evident in many of the papers and much of the discussion at the Fontainebleau meeting. Many questions were clearly articulated for the first time and, although many ofthem were not unambiguously answered, their presentation at the meeting and publication in this book will generate confirmatory studies and further research.

The 15 contributions, of which five are on applications in petroleum science and ten are on mining geostatistics, were presented at the 31st International Geological Congress, held in Rio de Janeiro, Brazil, from 6th - 17 August, 2000. Stochastic simulation was the key theme of these case studies. A wide range of methods was used: truncated Gaussian and pluriGaussian, SIS and SGS, Boolean methods and multi-point attractors. The five contributions on petroleum science focus on different aspects of reservoir characterization. All use stochastic simulations to generate 3D numerical models that reproduce the key features of questions such as reconciling reserve estimates with production figures. None of the contributions discuss theory; instead they show readers how to incorporate geology into geostatistical case studies in a meaningful way.

It is now nearly 25 years since the first textbook on geostatistics ("Traitj de gjostatistique appliquje" by G. Matheron) appeared in print in 1962. In that time geostatis­ tics has grown from an arcane theory regarded with scepticism by statisticians and miners alike, to a reputable scientific disci­ pline which is routinely used in the geosciences. In the mining industry, in particularly, comparisons between predicted reserve estimates and actual production figures have proved its worth. Few now doubt its usefulness as a statistical tool in the earth sciences. Over the past quarter of a century, many geostatistical case studies have been published but the vast majority of these are routine applications of kriging. Our objective with this volume is to present a series of innovative applications of geostatistics. These range from a careful variographic analysis on uranium data, through detailed studies on geologically complex deposits right up to the latest nonlinear methods applied to deposits with highly skew data distributions. Applications of new techniques such as the external drift method for combining well data with seismic information have also been included. Throughout the volume the accent has been put on how to apply geostatistics in practice. Notation has been kept to a mininmum and mathematical details have been relegated to annexes. We hope that this will encourage readers to put the more sophis­ ticated techniques into practice in their own fields.

When this two-day meeting was proposed, it was certainly not conceived as a celebration, much less as a party. However, on reflection, this might have been a wholly appropriate gesture because geostatistical simulation came of age this year: it is now 21 years since it was first proposed and implemented in the form of the turning bands method. The impetus for the original development was the mining industry, principally the problems encountered in mine planning and design based on smoothed estimates which did not reflect the degree of variability and detail present in the real, mined values. The sustained period of development over recent years has been driven by hydrocarbon applications. In addition to the original turning bands method there are now at least six other established methods of geostatistical simulation. Having reached adulthood, it is entirely appropriate that geostatistical simulation should now be subjected to an intense period of reflection and assessment. That we have now entered this period was evident in many of the papers and much of the discussion at the Fontainebleau meeting. Many questions were clearly articulated for the first time and, although many ofthem were not unambiguously answered, their presentation at the meeting and publication in this book will generate confirmatory studies and further research.

Geostatistics Rio 2000 includes fifteen contributions, five of which are on applications in petroleum science and ten are on mining geostatistics. These contributions were presented at the 31st International Geological Congress, held in Rio de Janeiro, Brazil, from 6-17 August, 2000. Stochastic simulation was the key theme of these case studies. A wide range of methods was used: truncated gaussian and plurigaussian, SIS and SGS, boolean methods and multi-point attractors. Audience: The volume will be of value to scientists, researchers, and professionals in geology, mining engineering, petroleum engineering, mathematics and statistics, as well as those working for mining and oil companies.

It is now nearly 25 years since the first textbook on geostatistics ("Traitj de gjostatistique appliquje" by G. Matheron) appeared in print in 1962. In that time geostatis­ tics has grown from an arcane theory regarded with scepticism by statisticians and miners alike, to a reputable scientific disci­ pline which is routinely used in the geosciences. In the mining industry, in particularly, comparisons between predicted reserve estimates and actual production figures have proved its worth. Few now doubt its usefulness as a statistical tool in the earth sciences. Over the past quarter of a century, many geostatistical case studies have been published but the vast majority of these are routine applications of kriging. Our objective with this volume is to present a series of innovative applications of geostatistics. These range from a careful variographic analysis on uranium data, through detailed studies on geologically complex deposits right up to the latest nonlinear methods applied to deposits with highly skew data distributions. Applications of new techniques such as the external drift method for combining well data with seismic information have also been included. Throughout the volume the accent has been put on how to apply geostatistics in practice. Notation has been kept to a mininmum and mathematical details have been relegated to annexes. We hope that this will encourage readers to put the more sophis­ ticated techniques into practice in their own fields.

It is now nearly 25 years since the first textbook on geostatistics ("Traitj de gjostatistique appliquje" by G. Matheron) appeared in print in 1962. In that time geostatis­ tics has grown from an arcane theory regarded with scepticism by statisticians and miners alike, to a reputable scientific disci­ pline which is routinely used in the geosciences. In the mining industry, in particularly, comparisons between predicted reserve estimates and actual production figures have proved its worth. Few now doubt its usefulness as a statistical tool in the earth sciences. Over the past quarter of a century, many geostatistical case studies have been published but the vast majority of these are routine applications of kriging. Our objective with this volume is to present a series of innovative applications of geostatistics. These range from a careful variographic analysis on uranium data, through detailed studies on geologically complex deposits right up to the latest nonlinear methods applied to deposits with highly skew data distributions. Applications of new techniques such as the external drift method for combining well data with seismic information have also been included. Throughout the volume the accent has been put on how to apply geostatistics in practice. Notation has been kept to a mininmum and mathematical details have been relegated to annexes. We hope that this will encourage readers to put the more sophis­ ticated techniques into practice in their own fields.

ACKNOWLEDGEMENTS xvii LIST OF PARTICIPANTS xix PLENARY SESSIQNS KRIGE D.G., GUARASCIO M. and CAMISANI-CALZOLARI F.A. Early South African qeostatistical techniques in today's perspective ...1 MATHERON G. The internal consistency of models in qeostatistics...21 MONESTIEZ P., HABIB R. and AUDERGON J.M. Estimation de la covariance et du varioqramme pour une fonction aleatoire a support arborescent : application a l'etude des arbres fruitiers ...39 CHILES J.P. Modelisation qeostatistique de reseaux de fractures...57 BRUNO R. and RASPA G. Geostatistical characterization of fractal models of surfaces 17 RIVOIRARD J. Models with orthoqonal indicator residuals...91 OMRE H., HALVORSEN K.B. and BERTEIG V. A Bayesian approach to kriqinq ...109 THEQRY I SWITZER P. Non-stationary spatial covariances estimated from monitorinq data ...127 CHAUVET P. Quelques aspects de l'analyse structurale des FAI-k a 1 dimension...139 vi TABLE OF CONTENTS DOWD P.A. Generalised cross-covariances ...151 CRESSIE N. The many faces of spatial prediction ..**...*...**.*.*..*. 163 OBLED C. & BRAUD I. Analogies entre geostatistique et analyse en composantes principales de processus ou analyse EOFs...177 THEORY II JEULIN D. Sequential random functions models...189 CHAUTRU J.M. The use of Boolean random functions in geostatistics *.**.**...201 SOARES A.O. Use of a mathematical morphology tool in characterizing covariance& of indicator data...213 ALLISON H.J. Regularization in geostatistics and in ill-posed inversed problems ...* . . * . * . . * ...* * ...225 DONG A.

When this two-day meeting was proposed, it was certainly not conceived as a celebration, much less as a party. However, on reflection, this might have been a wholly appropriate gesture because geostatistical simulation came of age this year: it is now 21 years since it was first proposed and implemented in the form of the turning bands method. The impetus for the original development was the mining industry, principally the problems encountered in mine planning and design based on smoothed estimates which did not reflect the degree of variability and detail present in the real, mined values. The sustained period of development over recent years has been driven by hydrocarbon applications. In addition to the original turning bands method there are now at least six other established methods of geostatistical simulation. Having reached adulthood, it is entirely appropriate that geostatistical simulation should now be subjected to an intense period of reflection and assessment. That we have now entered this period was evident in many of the papers and much of the discussion at the Fontainebleau meeting. Many questions were clearly articulated for the first time and, although many ofthem were not unambiguously answered, their presentation at the meeting and publication in this book will generate confirmatory studies and further research.