Stochastic Models in Geosystems: (85 The IMA Volumes in Mathematics and its Applications)

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.

Table of Contents:
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.