Ebook: Stochastic Models in Geosystems

This IMA Volume in Mathematics and its Applications STOCHASTIC MODELS IN GEOSYSTEMS is based on the proceedings of a workshop with the same title and was an integral part of the 1993-94 IMA program on "Emerging Applications of Probability." We would like to thank Stanislav A. Molchanov and Wojbor A. Woyczynski for their hard work in organizing this meeting and in edit­ ing the proceedings. We also take this opportunity to thank the National Science Foundation, the Office of N aval Research, the Army Research Of­ fice, and the National Security Agency, whose financial support made this workshop possible. A vner Friedman Willard Miller, Jr. v PREFACE A workshop on Stochastic Models in Geosystems was held during the week of May 16, 1994 at the Institute for Mathematics and Its Applica­ tions at the University of Minnesota. It was part of the Special Year on Emerging Applications of Prob ability program put together by an organiz­ ing committee chaired by J. Michael Steele. The invited speakers represented a broad interdisciplinary spectrum including mathematics, statistics, physics, geophysics, astrophysics, atmo­ spheric physics, fluid mechanics, seismology, and oceanography. The com­ mon underlying theme was stochastic modeling of geophysical phenomena and papers appearing in this volume reflect a number of research directions that are currently pursued in these areas.

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This volume contains the edited proceedings of a workshop on stochastic models in geosystems held during the week of May 16, 1994 at the Institute for Mathematics and its applications at the University of Minnesota. The authors represent a broad interdisciplinary spectrum including mathematics, statistics, physics, geophysics, astrophysics, atmospheric physics, fluid mechanics, seismology and oceanography. The common underlying theme was stochastic modeling of geophysical phenomena and papers appearing in this volume reflect a number of research directions that are currently pursued in this area. From the methodological mathematical point of view most of the contributions fall within the areas of wave propagation in random media, passive scalar transport in random velocity flows, dynamical systems with random forcing and self-similarity concepts including multifractals.

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This volume contains the edited proceedings of a workshop on stochastic models in geosystems held during the week of May 16, 1994 at the Institute for Mathematics and its applications at the University of Minnesota. The authors represent a broad interdisciplinary spectrum including mathematics, statistics, physics, geophysics, astrophysics, atmospheric physics, fluid mechanics, seismology and oceanography. The common underlying theme was stochastic modeling of geophysical phenomena and papers appearing in this volume reflect a number of research directions that are currently pursued in this area. From the methodological mathematical point of view most of the contributions fall within the areas of wave propagation in random media, passive scalar transport in random velocity flows, dynamical systems with random forcing and self-similarity concepts including multifractals.
Content:
Front Matter....Pages i-x
Seismic Coda Waves: A Stochastic Process in Earth’s Lithosphere....Pages 1-24
One Dimensional Random Walk in a Random Medium....Pages 25-56
Cascade of Scaling Gyroscopes: Lie Structure, Universal Multifractals and Self-Organized Criticality in Turbulence....Pages 57-81
A Non-Linear Model for Fluid Parcel Motions in the Presence of Many Large and Meso-Scale Vortices....Pages 83-96
Scale-Dependent Ocean Wave Turbulence....Pages 97-114
A Survey of Cascades with Applications from Geosciences....Pages 115-127
The Role of Statistical Models in Turbulence Theory....Pages 129-136
Ocean Circulation: Flow in Probability under Statistical Dynamical Forcing....Pages 137-148
Random Topography in Geophysical Models....Pages 149-169
Dynamical and Statistical Characteristics of Geophysical Fields and Waves and Related Boundary-Value Problems....Pages 171-208
Localization of Low Frequency Elastic Waves....Pages 209-217
Stochastic Forcing of Oceanic Motions....Pages 219-237
Radiative Transfer in Multifractal Atmospheres: Fractional Integration, Multifractal Phase Transitions and Inversion Problems....Pages 239-267
The Morphology and Texture of Anisotropic Multifractals Using Generalized Scale Invariance....Pages 269-311
Short-Correlation Approximation in Models of Turbulent Diffusion....Pages 313-352
Comments on Estimation and Prediction for Autoregressive and Moving Average Nongaussian Sequences....Pages 353-358
Probability Distributions of Passive Tracers in Randomly Moving Media....Pages 359-399
Three-Dimensional Burgers’ Equation as a Model for the Large-Scale Structure Formation in the Universe....Pages 401-413
Non-Mean Field Approach to Self-Organization of Landforms Via Stochastic Merger....Pages 415-425
Asymptotics of Solutions of Burgers’ Equation with Random Piecewise Constant Data....Pages 427-441
Modeling the Spatiotemporal Dynamics of Earthquakes with a Conservative Random Potential and a Viscous Force....Pages 443-458
Mass Transport by Brownian Flows....Pages 459-492
Back Matter....Pages 493-499

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This volume contains the edited proceedings of a workshop on stochastic models in geosystems held during the week of May 16, 1994 at the Institute for Mathematics and its applications at the University of Minnesota. The authors represent a broad interdisciplinary spectrum including mathematics, statistics, physics, geophysics, astrophysics, atmospheric physics, fluid mechanics, seismology and oceanography. The common underlying theme was stochastic modeling of geophysical phenomena and papers appearing in this volume reflect a number of research directions that are currently pursued in this area. From the methodological mathematical point of view most of the contributions fall within the areas of wave propagation in random media, passive scalar transport in random velocity flows, dynamical systems with random forcing and self-similarity concepts including multifractals.
Content:
Front Matter....Pages i-x
Seismic Coda Waves: A Stochastic Process in Earth’s Lithosphere....Pages 1-24
One Dimensional Random Walk in a Random Medium....Pages 25-56
Cascade of Scaling Gyroscopes: Lie Structure, Universal Multifractals and Self-Organized Criticality in Turbulence....Pages 57-81
A Non-Linear Model for Fluid Parcel Motions in the Presence of Many Large and Meso-Scale Vortices....Pages 83-96
Scale-Dependent Ocean Wave Turbulence....Pages 97-114
A Survey of Cascades with Applications from Geosciences....Pages 115-127
The Role of Statistical Models in Turbulence Theory....Pages 129-136
Ocean Circulation: Flow in Probability under Statistical Dynamical Forcing....Pages 137-148
Random Topography in Geophysical Models....Pages 149-169
Dynamical and Statistical Characteristics of Geophysical Fields and Waves and Related Boundary-Value Problems....Pages 171-208
Localization of Low Frequency Elastic Waves....Pages 209-217
Stochastic Forcing of Oceanic Motions....Pages 219-237
Radiative Transfer in Multifractal Atmospheres: Fractional Integration, Multifractal Phase Transitions and Inversion Problems....Pages 239-267
The Morphology and Texture of Anisotropic Multifractals Using Generalized Scale Invariance....Pages 269-311
Short-Correlation Approximation in Models of Turbulent Diffusion....Pages 313-352
Comments on Estimation and Prediction for Autoregressive and Moving Average Nongaussian Sequences....Pages 353-358
Probability Distributions of Passive Tracers in Randomly Moving Media....Pages 359-399
Three-Dimensional Burgers’ Equation as a Model for the Large-Scale Structure Formation in the Universe....Pages 401-413
Non-Mean Field Approach to Self-Organization of Landforms Via Stochastic Merger....Pages 415-425
Asymptotics of Solutions of Burgers’ Equation with Random Piecewise Constant Data....Pages 427-441
Modeling the Spatiotemporal Dynamics of Earthquakes with a Conservative Random Potential and a Viscous Force....Pages 443-458
Mass Transport by Brownian Flows....Pages 459-492
Back Matter....Pages 493-499
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