Mathematics in Geosciences

September 01, 2001 - June 30, 2002

Tabs

Overview

This image of the earth and moon "Blue Marble 2000" was created by R. Stöckli, A. Nelson and F. Hasler, Laboratory for Atmospheres, NASA Goddard Space Flight Center, using data from NASA, the USGS and NOAA. It is a mosaic of data from three satelites based on conditions on September 9, 1997.

The geosciences began their modern incarnation in 1957 with the 18-month long International Geophysical Year (IGY). The IGY saw a global mobilization of effort to investigate all aspects of the Earth and the space environment. While American and Soviet space vehicles made startling new discoveries about the Earth's magnetic field and the Van Allen belt, strong observational evidence was added to reinforce the plate tectonic revolution. New insights were obtained relating to the structure and dynamics of the earth's interior, both mantle and core. During the 1950s and 1960s, digital computers made it possible to model the atmosphere and oceans and, ultimately, to predict weather and climate as fluid media.

The last four decades have been monumental years of discovery and accumulation of facts and detailed data on the solid earth, ocean, atmosphere, and space sciences. Significant theoretical insight concerning these topics has emerged, but deep problems remain to challenge conventional methodologies and insights derived from the physical sciences. The time is ripe to apply mathematical modeling and analysis techniques, including newer methods in continuous and discrete dynamical systems, stochastic processes, homogenization, and multiscale asymptotics to our investigation of these problems.

Organizing Committee:

William I. Newman	UCLA, Earth and Space Sciences
David R. Brillinger	UC Berkeley, Statistics
Michael Ghil	UCLA, Atmospheric Sciences
J.M. Hyman	Los Alamos National Laboratory, Center for Nonlinear Studies
Frederic Schoenberg	UCLA, Statistics
William W. Symes	Rice University, Computational and Applied Mathematics
Donald L. Turcotte	Cornell University, Geological Sciences
Mary F. Wheeler	University of Texas, Center for Subsurface Modeling

Poster

Events

June 10 - 14, 2002	Point Process Modeling and Seismological Application of Statistics	Annual Program Workshop
May 13, 2002	Earthquake Probability Models and Forecasting	Tutorial
April 29 - May 03, 2002	Data Assimilation in the Oceanic and Atmospheric Sciences	Annual Program Workshop
April 22 - 26, 2002	Workshop: Inverse Problems and Quantification of Uncertainty	Annual Program Workshop
April 19, 2002	Inverse Problems and the Quantification of Uncertainty	Tutorial
March 18 - 22, 2002	Nonlinear Continuum Mechanics, Rheology and the Dynamo	Annual Program Workshop
March 13 - 15, 2002	Minisymposium: Numerical Methods in the Geosciences	Annual Program Workshop
March 04 - 06, 2002	Ray Theory for the Elastic Wave Equation	Tutorial
February 18 - 20, 2002	Wavelet Methods in Seismology: Application of Wavelets to Multiscale Analysis and Non-linear Estimation	Tutorial
February 11 - 15, 2002	Reduced Descriptions of Coupled GFD Systems (Slow Manifolds in the Ocean and Atmosphere)	Annual Program Workshop
January 07 - 11, 2002	Quantifying Uncertainty and Multiscale Phenomena in Subsurface Processes	Annual Program Workshop
November 12 - 15, 2001	Time Series Analysis and Applications to Geophysical Systems	Annual Program Workshop
October 29 - November 02, 2001	Dynamical Systems in Celestial Mechanics and Climate Dynamics	Annual Program Workshop
October 08 - 12, 2001	Complexity in Geophysical Systems	Annual Program Workshop
October 05 - 06, 2001	Special Event: Keilis-Borok Festschrift	Annual Program Workshop
September 25 - 29, 2001	Spatio-Temporal Patterns in the Geosciences	Annual Program Workshop
September 24, 2001	Spatio-Temporal Patterns in the Geosciences	Tutorial

Full Description

The geosciences today provide an impressive array of important problems that should command the attention of applied mathematicians. In addition, the geosciences offer the opportunity as well as the need to advance the foundations and techniques of applied mathematics to meet this challenge. The time is right to initiate an International Mathematical Geosciences Year (IMGY) to bring mathematicians and geoscientists together in the investigation of our planet and the environment within which it resides.

We present a three-quarter program designed to introduce mathematicians to the major themes and techniques of the geosciences, and create a focal point for a multidisciplinary assault on some of the outstanding problems emerging from them. Accordingly, the three quarters are organized along methodological lines, beginning with dynamical systems and ergodic theory, then moving on to multiscale problems and renormalization, and concluding with inverse problems and the quantification of uncertainty.

Fall Quarter (September - December, 2001)

Dynamical Systems and Ergodic Theory

Important progress has been made in understanding the dynamics of the earth's crust, especially earthquakes. The availability of new data opens new applications for modern mathematical technique. The theoretical understanding of large-scale atmospheric and oceanic flows, and of the coupled atmosphere-ocean-cryosphere-biosphere climate system, is being revolutionized by the insights provided by dynamical systems theory and its statistical complement, these systems' ergodic theory. Similarly, significant new insights have emerged in applications of dynamical systems theory to problems relevant to the earth's interior. Analysis, simulation, and prediction of geophysical processes, ranging from climates to earthquakes, are likely to make much more rapid progress by bringing the appropriate mathematical and statistical tools to bear on them.

Winter Quarter (January - March, 2002)

Multiscale Phenomena and Renormalization

The description of many natural phenomena naturally introduces a high degree-of-freedom system which takes the form of a continuum, described by partial differential equations, or of discrete systems. Another venue for multiscale phenomena manifests in the field of point processes, and the development of linear and nonlinear models.

Spring Quarter (April - June, 2002)

Inverse Problems and the Quantification of Uncertainty

This quarter addresses the quantification of uncertainty in geosciences, through two workshop programs. The first program concerns state and parameter estimation in the presence of imperfection in data acquisition, physical modeling, and numerical simulation. This theme separates into two subthemes in a rough way, according to whether the system changes substantially while it is being observed, or not. In the former case the state estimation problem has come to be called the problem of data assimilation, whereas in the latter case it is often called model inversion. The first two workshops address these two aspects of the first theme. The second theme deals with the application of statistical time series and point process modeling and inference, seismic

Long-Term Visitors

Name	Affiliation	Department	Visit
Donald Aronson	University of Minnesota, Twin Cities	Mathematics Department	10/08/01-11/02/01
Mark Bebbington	Massey University	Department of Statistics	04/02/02-06/15/02
Robert Burridge	Massachusetts Institute of Technology	Earth Resources Laboratory	01/06/02-06/30/02
Carme Calderer	University of Minnesota, Twin Cities	School of Mathematics	09/01/01-08/31/02
Valera Chtcherbakov	Geophysical Observatory Borok		02/14/02-06/14/02
Vittorio Cristini	University of Minnesota, Twin Cities	Institute for Mathematics and its Applications	09/01/01-08/31/02
Fabio D'Andrea	Massachusetts Institute of Technology	Department of Earth, Atmospheric and Planetary Sciences	09/23/01-10/16/01
Emmanuel Detournay	University of Minnesota, Twin Cities	Department of Civil, Environmental, and Geo-Engineering	09/24/01-03/15/02
Douglas Dokken	University of St. Thomas	Department of Mathematics	09/01/01-06/30/02
Roger Fosdick	University of Minnesota, Twin Cities	Department of Aerospace Engineering and Mechanics	03/01/02-03/31/02
Andrei Gabrielov	Purdue University	Department of Mathematics	09/16/01-10/16/01
Hongjun Gao	Nanjing Normal University	School of Mathematics and Computer Sciences	09/22/01-03/23/02
David Gubbins	University of Leeds	School of Earth Sciences	03/18/02-04/12/02
Robert Gulliver	University of Minnesota, Twin Cities	Institute for Mathematics and its Applications	09/01/01-08/31/02
David Harte	Statistics Research Associates Limited		05/28/02-06/28/02
Agnes Helmstetter	University of California, Los Angeles	Department of Earth and Space Science	09/23/01-10/13/01
Felix Herrmann	Massachusetts Institute of Technology	Department of Earth, Atmospheric, and Planetary Sciences	10/01/01-05/31/02
Steven Jaume	College of Charleston	Department of Geology and Environmental	06/01/02-06/30/02
Alexey Kaplan	Columbia University	Lamont-Doherty Earth Observatory	04/15/02-05/15/02
Vladimir Keilis-Borok	University of California, Los Angeles	Department of Earth and Space Sciences	09/17/01-10/13/01
Rachel Kuske	University of Minnesota, Twin Cities	School of Mathematics	09/01/01-08/31/02
John Lowengrub	University of Minnesota, Twin Cities	Department of Mathematics	09/01/01-08/31/02
Peter Lynch	Met Eireann	School of Mathematics	02/01/02-02/28/02
Alexey Lyubushin	Russian Academy of Sciences	Institute of Physics of the Earth	06/02/02-07/01/02
Dan Marchesin	Instituto de Matematica Pura e Aplicada		01/07/02-02/09/02
Willard Miller Jr.	University of Minnesota, Twin Cities	Institute for Mathematics and its Applications	09/01/01-08/31/02
Gueorgui Moltchan	Russian Academy of Sciences	Int'l Inst. of Earthquake Pred. Theory and Math Geophysics	09/20/01-10/14/01
Robert Nadeau	Lawrence Livermore National Laboratory	Department of Earth Science	06/01/02-06/30/02
Jean-Claude Nédélec	École Polytechnique	Centre de Mathématiques Appliquées	10/04/01-11/03/01
William Newman	University of California, Los Angeles	Planetary Physics, Astronomy and Mathematics	09/07/01-12/15/01
Yosihiko Ogata	The Institute of Statistical Mathematics		06/09/02-07/02/02
Robert O'Malley	University of Washington	Department of Mathematical Sciences	01/02/02-01/26/02 01/02/02-03/31/02
Jeong-Soo Park	Chonnam National University	Department of Statistics	09/05/01-08/31/02
Concepcion Patino	University of Cádiz	CASEM - Facultad de Ciencias del Mar y	09/17/01-10/26/01
Thomas Pence	Michigan State University	Department of Mechanical Engineering	03/17/02-04/08/02
Fernando Reitich	University of Minnesota, Twin Cities	School of Mathematics	09/01/01-08/31/02
Yanick Ricard	École Normale Supérieure de Lyon	Laboratoire de Sciences de la Terre	03/01/02-03/31/02
Arnd Scheel	University of Minnesota, Twin Cities	School of Mathematics	10/29/01-02/15/02
Kurt Scholz	University of St. Thomas	Department of Mathematics	01/01/02-06/30/02
Gerard Schuster	The University of Utah	Department of Geology and Geophysics	04/03/02-06/30/02
George Sell	University of Minnesota, Twin Cities	School of Mathematics	09/01/01-08/31/02
Alexandr Shapoval	Russian Academy of Science	Int'l Inst. of Earthquake Pred. Theory and Math Geophysics	09/23/01-10/22/01
Robert Shcherbakov	Cornell University	Department of Earth and Atmospheric Sciences	09/01/01-12/31/01
Jianhong Shen	University of Minnesota, Twin Cities	Department of Earth and Atmospheric Sciences	09/01/01-08/31/02
Stefan Siegmund	Johann Wolfgang Goethe-Universität Frankfurt	Department of Mathematics	04/08/02-09/19/02
Vladimir Sverak	University of Minnesota, Twin Cities	School of Mathematics	09/01/01-08/31/02
Javier Thayer	The Mitre Corporation		09/01/01-08/31/02
Donald Turcotte	Cornell University	Department of Geological Science	09/01/01-11/30/01
David Vere-Jones	University of Victoria		04/01/02-07/03/02
Jianhua Wu	Shaanxi Normal University	Department of Mathematics	01/08/02-03/07/02
Ilia Zaliapin	University of California, Los Angeles	Institute of Geophysics and Planetary Physics	09/17/01-10/15/01