Aspects of Multivariate Statistical Analysis in Geology
Multivariate statistical methods have become commonplace in the Earth Sciences, What was once an exclusive area of activity is now within the reach of Everyman, owing to the ubiquitousness of mini-computers and the ready availability of software for doing the computing. In the days when one was required to do one's own programming, it was necessary to acquire considerable proficiency in linear algebra and one or more programming languages. Today, the vast majority of the people who use multivariate methods to analyse geological data have little or no idea of the matrix operations underlying a particular method, nor, for that matter, what the program is actually supposed to be doing. This situation can be both good and bad. It can do no harm if everything goes according to schedule, the program being used is competently constructed, which, alas, is far from being the general case, and there are no strong deviations from standard statistical theory in the data under examination. It is bad if the data do not fit the theoretical requirements of a particular method and even worse if the method of computation used is inappropriate. It is an inescapable and sad fact of life that much geological and biological material deviates in some manner or other from the theoretical requirements of a multivariate statistical procedure. The immediate relevance of this observation is that there are many sources of error in doing an analysis of geological data by means of standard statistical software.
Before undertaking any study of Geostatistics, it is necessary to become familiar with certain key concepts drawn from Classical Statistics, which form the basic building blocks of Geostatistics. Because the study of Statistics generally deals with quantities of data, rather than a single datum, we need some means to deal with that data in a manageable form. Much of Statistics deals with the organization, presentation, and summary of data. Isaaks and Srivastava (1989) remind us that “Data speaks most clearly when organized”.
Geoenv IV – geostatistics for environmental applications
This research focuses on two original statistical methods for analyzing large data sets in the context of climate studies. First, we propose a new way to introduce skewness to state-space models without losing the computational advantages of the Kalman filter operations. The motivation stems from the popularity of state-space models and statistical data assimilation techniques in geophysics, specially for forecasting purposes in real time. The added skewness comes from the extension of the multivariate normal distribution to the general multivariate skew-normal distribution. A new specific state-space model for which the Kalman Filtering operations are carefully described is derived.
Geostatistics for Seismic Data Integration in Earth Models
In the previous two chapters, we discussed the meaning of the geostatistical model and of its parameters. We will now discuss how this model can be applied. We will start with deterministic techniques, known under the generic name of kriging. Here, “deterministic” should be understood in the sense of “providing only one solution.” We will see that, although the model is probabilistic, kriging produces only one solution. Kriging covers a wide range of applications. The first one consists of interpolating one single variable in one, two, or three dimensions, and the second one consists of interpolating one variable but using the extra information provided by another variable that is related, of course, to the first one.
Applied geostatistic for reservoir characterization
The book is so easy to follow that many readers may not even need formal instruction and may find it suitable for self-tutoring. Those readers already proficient in geostatistics will enjoy reading about the authors' convictions on the subject. Honors for a well-produced book also go to Oxford University Press. I predict the volume will be a standard geostatistical reference for the decade." --Mathematical Geology
"This book is remarkable in the statistical literature and unique in geostatistics in that concepts and models are introduced from the needs of data analysis rather than from axioms or through formal derivations. Though academics will be rewarded with multiple challenges and seed ideas for new research work, the main public for this book will be undergraduates and practitioners who want to add geostatistics to their own toolbox." --Jrnl. of Canadian Petroleum Technology
Stochastic Modeling and Geostatistics Principles, Methods, and Case Studies
Producing a viable book about some aspect of mathematical geology that geologists will use is not easy to do. Many geologists simply do not like to deal with math on anything but a rudimentary level, if that! This is particularly true in the United States where courses in mathematics have not been a strong component of a general earth science curriculum. This is not a criticism or an implication that a mathematical approach to geology is in some way superior, nor is it meant to imply that earth sciences do not require the use of important mathematical principles. It is, however, a statement of priority. Traditional geology is a highly qualitative science resting soundly on classification schemes and descriptions associated with physical observations.