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Books in Mathematical geology

  • Fractals and Multifractals in the Geosciences

    • 1st Edition
    • May 17, 2024
    • Behnam Sadeghi
    • English
    Fractals and Multifractals in the Geosciences details the application of a wide range of multifractal methods, including many novel ones developed by the author, along with the assessment of uncertainty in sample classification and stability of spatial patterns. This book also provides criteria for selection of the most effective combination of data pre-processing and multifractal modeling to extract desired features or signals in the data. The book specifically aims to introduce, apply, and test novel multifractal models that account directly for changes in relationships between variables, as well as the effects of distance between samples and the source of anomalous metal contents in geoscience samples. Linked to this will be assessment of the effects of different pre-processing of data prior to application of the models and quantification/model uncertainty in geochemical anomaly maps, associated with sample classification and spatial interpolation. Gaussian simulations such as Sequential Gaussian Simulation and Monte Carlo Simulation will be applied to the new multifractal models developed and a suite of existing models, including (simulated) concentration-area, spectrum-area, singularity and other models.Fractals and Multifractals in the Geosciences will be invaluable for mathematical geoscientists, geostatisticians, exploration, applied, urban and environmental geochemists, computational geoscientists, data scientists, and GIS professionals who need to better understand fractal geometry, along with its theory and applications in geochemical anomaly classification to generate maps that are helpful for decision-making for follow-up sampling and explorations.

  • Geographical Models with Mathematica

    • 1st Edition
    • February 1, 2017
    • Andre Dauphine
    • English
    Geographical Models with Mathematica provides a fairly comprehensive overview of the types of models necessary for the development of new geographical knowledge, including stochastic models, models for data analysis, for geostatistics, for networks, for dynamic systems, for cellular automata and for multi-agent systems, all discussed in their theoretical context. The author then provides over 65 programs, written in the Mathematica language, that formalize these models. Case studies are provided to help the reader apply these programs to their own studies.

  • Random Field Models in Earth Sciences

    • 1st Edition
    • October 22, 2013
    • George Christakos
    • English
    This book is about modeling as a prinicipal component of scientific investigations. In general terms, modeling is the funamental process of combining intellectual creativity with physical knowledge and mathematical techniques in order to learn the properties of the mechanisms underlying a physical phenomenon and make predictions. The book focuses on a specific class of models, namely, random field models and certain of their physical applications in the context of a stochastic data analysis and processing research program. The term application is considered here in the sense wherein the mathematical random field model is shaping, but is also being shaped by, its objects.

  • Precambrian Ophiolites and Related Rocks

    • 1st Edition
    • Volume 13
    • October 26, 2004
    • T.M. Kusky
    • English
    Recent developments have shown that many full and partial ophiolites are preserved in Precambrian cratons. This book provides a comprehensive description and discussion of the field aspects, geochemistry, geochronology and structure of the best of these ophiolites. It also presents syntheses of the characteristics of ophiolites of different ages, and an analysis of what the characteristics of these ophiolites mean for the thermal and chemical evolution of the earth.This title emphasizes new studies of Precambrian Geology that have documented ophiolites, ophiolitic fragments, and ophiolitic melanges in many Precambrian terranes. Each chapter focuses on individual Precambrian ophiolites or regions with numerous Precambrian ophiolites, and covers field aspects, petrology, geochemistry, geochronology, and other descriptive aspects of these ophiolites, it also delves into more theoretical and speculative aspects about the interpretation of the significance of these ancient ophiolites.

  • Geophysical Inverse Theory and Regularization Problems

    • 1st Edition
    • April 24, 2002
    • Michael S. Zhdanov
    • English
    This book presents state-of-the-art geophysical inverse theory developed in modern mathematical terminology. The book brings together fundamental results developed by the Russian mathematical school in regularization theory and combines them with the related research in geophysical inversion carried out in the West. It presents a detailed exposition of the methods of regularized solution of inverse problems based on the ideas of Tikhonov regularization, and shows the different forms of their applications in both linear and nonlinear methods of geophysical inversion. This text is the first to treat many kinds of inversion and imaging techniques in a unified mathematical manner.The book is divided in five parts covering the foundations of the inversion theory and its applications to the solution of different geophysical inverse problems, including potential field, electromagnetic, and seismic methods. The first part is an introduction to inversion theory. The second part contains a description of the basic methods of solution of the linear and nonlinear inverse problems using regularization. The following parts treat the application of regularization methods in gravity and magnetic, electromagnetic, and seismic inverse problems. The key connecting idea of these applied parts of the book is the analogy between the solutions of the forward and inverse problems in different geophysical methods. The book also includes chapters related to the modern technology of geophysical imaging, based on seismic and electromagnetic migration.This volume is unique in its focus on providing a link between the methods used in gravity, electromagnetic, and seismic imaging and inversion, and represents an exhaustive treatise on inversion theory.

  • Aspects of Multivariate Statistical Analysis in Geology

    • 1st Edition
    • November 24, 1999
    • E. Savazzi + 1 more
    • English
    The book presents multivariate statistical methods useful in geological analysis. The essential distinction between multivariate analysis as applied to full-space data (measurements on lengths, heights, breadths etc.) and compositional data is emphasized with particular reference to geochemical data. Each of the methods is accompanied by a practically oriented computer program and backed up by appropriate examples. The computer programs are provided on a compact disk together with trial data-sets and examples of the output.An important feature of this book is the graphical system developed by Dr. Savazzi which is entitled Graph Server. Geological data often deviate from ideal statistical requirements. For this reason, close attention has been paid to the analysis of data that contain atypical observations.