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For many years, digital signal processing has been governed by the theory of Fourier transform and its numerical implementation. The main disadvantage of Fourier theory is the underlying assumption that the signals have time-wise or space-wise invariant statistical properties. In many applications the deviation from a stationary behavior is precisely the information to be extracted from the signals. Wavelets were developed to serve the purpose of analysing such instationary signals. The book gives an introduction to wavelet theory both in the continuous and the discrete case. After developing

Wavelets (Mathematics) --- Geology --- Geomathematics --- Mathematical geology --- Wavelet analysis --- Harmonic analysis --- Mathematics. --- Wavelets (Mathematics).

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What is fuzzy logic? -- A system of concepts and methods for exploring modes of reasoning that are approximate rather than exact. While the engineering community has appreciated the advances in understanding using fuzzy logic for quite some time, fuzzy logic's impact in non-engineering disciplines is only now being recognized. The authors of Fuzzy Logic in Geology attend to this growing interest in the subject and introduce the use of fuzzy set theory in a style geoscientists can understand. This is followed by individual chapters on topics relevant to earth scientists: sediment modeling, fracture detection, reservoir characterization, clustering in geophysical data analysis, ground water movement, and time series analysis. George Klir is the Distinguished Professor of Systems Science and Director of the Center for Intelligent Systems, Fellow of the IEEE and IFSA, editor of nine volumes, editorial board member of 18 journals, and author or co-author of 16 books Foreword by the inventor of fuzzy logic -- Professor Lotfi Zadeh

Fuzzy logic. --- Geology --- Geografie --- Mathematics. --- Fysische geografie --- Algemeen. --- Fuzzy logic --- Geomathematics --- Mathematical geology --- Nonlinear logic --- Fuzzy mathematics --- Logic, Symbolic and mathematical --- Fuzzy systems --- Mathematics

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A Complutense International Seminar on "Earth Sciences and Mathematics" was organised and held in Madrid at the Facultad de Ciencias Matemáticas of the Universidad Complutense de Madrid in September 2006. Scientists from both fields, Mathematics and Earth Sciences, took part in this International Seminar, addressing scientific problems related to our planet from clearly complementary approaches, seeking to gain and learn from this dual approach and proposing a closer collaboration in the near future. This volume is the second one of a Topical Issue on "Earth Sciences and Mathematics" and contains papers addressing different topics as analysis of InSAR time series, fuzzy classification for remote sensing, modelling gravitational instabilities, geodynamical evolution of the Alboran Sea, statistical warning systems for volcanic hazards, analysis of solutions for the hydrological cycle, study of the ice flow, magma intrusion in elastic layered media, river channel formation, Hartley transform filters for continuous GPS, and deformation modeling.

Earth sciences --Mathematics. --- Earth sciences --Statistical methods. --- Geography --- Geology --- Earth & Environmental Sciences --- Physical Geography --- Geology - General --- Earth sciences. --- Mathematics. --- Geosciences --- Geomathematics --- Mathematical geology --- Earth Sciences. --- Earth Sciences, general. --- Environmental sciences --- Physical sciences --- Geography. --- Cosmography --- Earth sciences --- World history

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Nonrenewable natural resources --- Mines and mineral resources --- Geology --- Mathematics --- Ressources non-renouvelables --- Ressources minérales --- Géologie --- Périodiques. --- Mathématiques --- Geognosy --- Geoscience --- Non-renewable natural resources --- Exhaustible resources --- Natural resources, Nonrenewable --- Economic aspects --- Mines and mineral resources. --- Nonrenewable natural resources. --- Mathematics. --- Deposits, Mineral --- Mineral deposits --- Mineral resources --- Mines and mining --- Mining --- Geomathematics --- Mathematical geology --- Earth sciences --- Natural history --- Natural resources --- Geology, Economic --- Minerals --- Ressources non renouvelables

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The authors introduce geomathematics as an active research area to a wider audience. Chapter 1 presents an introduction to the Earth as a system to apply scientific methods. Emphasis is laid on transfers from virtual models to reality and vice versa. In the second chapter geomathematics is introduced as a new scientific area which nevertheless has its roots in antiquity. The modern conception of geomathematics is outlined from different points of view and its challenging nature is described as well as its interdisciplinarity. Geomathematics is shown as the bridge between the real world and the virtual world. The complex mathematical tools are shown from a variety of fields necessary to tackle geoscientific problems in the mathematical language. Chapter 3 contains some exemplary applications as novel exploration methods. Particular importance is laid on the change of language when it comes to translate measurements to mathematical models. New solution methods like the multiscale mollifier technique are presented. Further applications discussed are aspects of reflection seismics. Chapter 4 is devoted to the short description of recent activities in geomathematics. The Appendix (Chapter 5) is devoted to the GEM – International Journal on Geomathematics founded ten years ago. Besides a detailed structural analysis of the editorial goals an index of all papers published in former issues is given.

Geology --- Mathematics. --- Geomathematics --- Mathematical geology --- Differential equations, partial. --- Integral equations. --- Potential theory (Mathematics). --- Partial Differential Equations. --- Integral Equations. --- Potential Theory. --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Equations, Integral --- Functional equations --- Functional analysis --- Partial differential equations --- Partial differential equations. --- Potential theory (Mathematics)