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Role of Wavelets in the Physical and Statistical Modelling of Complex Geological Processes

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Computational Earthquake Science Part II

Part of the book series: PAGEOPH Topical Volumes ((PTV))

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Abstract

Today wavelets are recognized to have a wide range of useful properties that allow them to treat effectively multifacet problems, such as data compression, scale-localization analysis, feature extraction, statistics, numerical simulation, visualization, and communication. Second-generation wavelets represent a recent improvement of the wavelet algorithm, allowing for greater flexibility in the spatial domain and other computational advantages. We will show how these wavelets can be employed to extract large-scale coherent structures from (1) three-dimensional turbulent flows and (2) high Rayleigh number thermal convection. We will discuss the concept of modelling via decomposition into coherent and incoherent fields, taking into account the effect of the incoherent field via statistical modelling. We will discuss wavelet properties and how they can be utilized and integrated in handling large-scale problems in earthquake physics and other nonlinear phenomena in the geosciences.

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Author information

Authors and Affiliations

  1. Minnesota Supercomputer Institute, Department of Geophysics, University of Minnesota, Minneapolis, MN

    D. A. Yuen

  2. Department of Mathematics/ Computer Science, School of Computational Science and Information Technology, Florida State University, Tallahassee, FL

    G. Erlebacher

  3. Department of Mechanical Engineering, University of Colorado, Boulder, CO

    O. V. Vasilyev

  4. Department of Mechanical Engineering, University of Colorado, Boulder, CO

    D. E. Goldstein

  5. Department of Statistics, North Carolina State University, Raleigh, NC

    M. Fuentes

Authors
  1. D. A. Yuen
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  2. G. Erlebacher
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  3. O. V. Vasilyev
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  4. D. E. Goldstein
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  5. M. Fuentes
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Editor information

Editors and Affiliations

  1. Earth and Space Sciences Division, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, 91109-8099, USA

    Andrea Donnellan

  2. QUAKES, Earth Systems Science Computational Centre (ESSCC), Department of Earth Sciences, The University of Queensland, Brisbane, Qld, 4072, Australia

    Peter Mora

  3. Department of Earth and Planetary Science, The University of Tokyo, Bunkyo-ku, Tokyo, 113-0033, Japan

    Mitsuhiro Matsu’ura

  4. Center for Analysis and Prediction, CSB & Laboratory of Nonlinear Mechanics, Institute of Mechanics, China Academy of Sciences, Beijing, 100080, China

    Xiang-chu Yin

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© 2004 Springer Basel AG

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Yuen, D.A., Erlebacher, G., Vasilyev, O.V., Goldstein, D.E., Fuentes, M. (2004). Role of Wavelets in the Physical and Statistical Modelling of Complex Geological Processes. In: Donnellan, A., Mora, P., Matsu’ura, M., Yin, Xc. (eds) Computational Earthquake Science Part II. PAGEOPH Topical Volumes. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7875-3_9

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  • DOI: https://doi.org/10.1007/978-3-0348-7875-3_9

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-7643-7143-2

  • Online ISBN: 978-3-0348-7875-3

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