Geostatistics: concepts and applications

Jorge Kazuo Yamamoto , Paulo M. Barbosa Landim

Essential to all the steps of a mining project, since the mineral research to the study of the technical and economic viability, Geostatistics is also used in the most modern softwares for georeferenced information systems.

The book deals with the sampling, spatial inference and the random variables nature; calculation and modeling of the experimental variograms; geostatistics techniques on estimation and interpolation to continuous and discrete random variables; geostatistic coestimation; and stochastic simulation.

Geostatistics: concepts and applications is designed for Geology, Geophysics, Mining Engineering, Agronomy, Oceanography and Forest Engineering students, as well as professionals and researchers involved in the analysis of the geological or georeferenced data.

Original title
Geoestatística: conceitos e aplicações
Year of publication

About the authors

Paulo M. Barbosa Landim

Paulo M. Barbosa Landim majored in Geology, from Universidade de São Paulo, in 1961, where he also completed his PhD degree in Stratigraphy. He has made his entire academic career in Universidade Estadual Paulista (Unesp), where he retired as a full professor in 1998. Nowadays he works as a volunteer professor in the same university, in the Applied Geology Department. In 2000 he received the title of Professor Emeritus from the University Council.

Author's CV (in portuguese).

Jorge Kazuo Yamamoto

Jorge Kazuo Yamamoto majored in Geology from Universidade de São Paulo, in 1976. He worked as a geology researcher of the Instituto de Pesquisas Tecnológicas (IPT) from 1977 to 1988. Nowadays he is a full professor at USP, in the Sedimentary and Environmental Geology Department, where he teaches Geostatistics in undergraduate and graduate courses.

Author's CV (in portuguese).

1 Basic concepts

1.1 Spatial phenomenon

1.2 Samples and sampling methods

1.3 Spatial inference

1.4 Random and regionalized variables

1.5 Ungrouping


2 Experimental variograms calculation and modeling

2.1 Spatial statistics

2.2 Calculation of experimental variograms

2.3 Types of variograms

2.4 Anisotropies

2.5 Variogram perfomance next to the origin

2.6 Final considerations


3 Geostatistics estimation

3.1 Transformation of data

3.2 Geostatistics estimation

3.3 Nonlinear kriging

3.4 Interpolation of categorical variables

3.5 Final considerations


4 Geostatistics coestimation

4.1 Cokriging

4.2 Kriging with external drift

4.3 Final considerations


5 Stochastic simulation

5.1 Smoothing error

5.2 Stochastic simulation methods

5.3 Sequential simulation methods

5.4 Considerations on the stochastic simulation methods


Appendix A – Mathematical and statistical basic elements

A.1 Graphical methods of presenting the data

A.2 Descriptive statistics

A.3 Bivariate data

A.4 Theoretical probabilities distribution

A.5 Derivatives

A.6 Integrals

A.7 Matrixes

A.8 Systems of linear equations

A.9 Softwares


Appendix B – Data files


About the authors


Geostatistics: concepts and applications is an introductory book to the bases and fundamental concepts of the field. Is an essential reading to all of those who seek in Geostatistics a set of instruments to solve concrete problems in natural resources management. The authors, Jorge Yamamoto and Paulo Landim, scientists involved in the praxis of Earth sciences, conceived this book in a format all fundamental books of applied sciences should be: from problems to solutions.

Starting by underlining the birth of Geostatistics in a geological and mining environmental (with the “creators” Georges Matheron, Daniel Krige, André Journel and Alain Marechal), the authors are concerned to show through the book the methods applicability to the several domains of Earth and environmental sciences, i.e., to characterize physical phenomena from any natural phenomena structured in space. As the authors quote, the book “dedicated to analyze geological data controlled by their spatial distribution but can perfectly be used in other fields which also use geo-referenced data”.

But Jorge Yamamoto and Paulo Landim are also teachers, which makes Geostatistics: concepts and applications have a strong pedagogic feature, conferring to all approached subjects a clear exposition and a great concern with details of mathematical formalisms and its algorithms. Indeed, considering Geostatistics is spread in countless fields of application, with algorithms and methodologies implemented in appealing and friendly softwares, this book is fundamental to reeducate most of Geostatistics users, who became button-pushers favoring experimental and repetitive exercises of huge methods menus instead of its comprehension and misuse error evaluation.

Divided in five chapters the book starts analyzing spatial patterns of structured phenomena and simple instrument models, such as variograms and spatial covariance. However, most of it is dedicated to spatial inference methods of the extensive family of linear estimators, the kriging. In this noble part of te book is evident the authors’ intention in refer and detail the most usual methods in geostatistic praxis. They end the book with a chapter dedicated to the spatial uncertainty quantification by the new models of stochastic simulation.

I am certain the teaching and practice of Geostatistics will get substantially richer with the publication of this book.

Prof. Dr. Amilcar Soares
Director of Centre for Natural Resources and Environment (Cerena) of Superior Technic Institute IST) of Lisbon Technical University, Portugal