Seismic coda waves: A stochastic process in earth's lithosphere.- One dimensional random walk in a random medium.- Cascade of scaling gyroscopes: lie structure, universal multifractals and self-organized criticality in turbulence.- A non-linear model for fluid parcel motions in the presence of many large and meso-scale vortices.- Scale-dependent ocean wave turbulence.- A survey of cascades with applications from geosciences.- The role of statistical models in turbulence theory.- Ocean circulation: flow in probability under statistical dynamical forcing.- Random topography in geophysical models.- Dynamical and statistical characteristics of geophysical fields and waves and related boundary-value problems.- Localization of low frequency elastic waves.- Stochastic forcing of oceanic motions.- Radiative transfer in multifractal atmospheres: fractional integration, multifractal phase transitions and inversion problems.- The morphology and texture of anisotropic multifractals using generalized scale invariance.- Short-correlation approximation in models of turbulent diffusion.- Comments on estimation and prediction for autoregressive and moving average nonGaussian Sequences.- Probability distributions of passive tracers in randomly moving media.- Three-dimensional Burgers' equation as a model for the large-scale structure formation in the universe.- Non-mean field approach to self-organization of landforms via stochastic merger.- Asymptotics of solutions of Burgers' equation with random piecewise constant data.- Modeling the spatiotemporal dynamics of earthquakes with a conservative random potential and a viscous force.- Mass transport by Brownian flows.
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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