Geoscientists Meet in Colorado to Explore Increasingly Complex, Multidisciplinary Problems

November 13, 2001

Invited speaker Max Morris of Iowa State University brought a statistician's perspective to problems in the geosciences, with an emphasis on inverse problems. Various forms of computational uncertainty analysis, he pointed out, are the result of effective combinations of statistical analysis with methods from traditional applied mathematics.
Lea Jenkins and Béatrice Rivière

Boulder, Colorado, provided a scenic backdrop for the 2001 SIAM Conference on Mathematical and Computational Issues in the Geosciences, which was held June 12-16. The conference, sponsored by the SIAM Activity Group on Geosciences, gave researchers in the field a tremendous opportunity to meet and discuss ways to address current problems. The natural beauty of the national parks surrounding Boulder also gave participants a chance to relax and enjoy some of the scenery of the Rocky Mountains. By taking advantage of the tennis courts and hiking path right behind the hotel, people could ruminate on the conference sessions without leaving the grounds.

The organizers of the conference strive to bring people from a variety of backgrounds together. Accordingly, this year's meeting-the sixth in a series sponsored by SIAG/GS-included talks on statistics, scaling issues, multiphysics couplings, and the increasing complexity of systems being solved. The growing involvement of statisticians in SIAG/GS is important as applied mathematicians, scientists, and engineers need to account for more uncertainty in their models. Bringing the various groups together can be a tremendous boon to fostering research partnerships.

The conference began on Sunday, when conference attendees were welcomed at a reception on the patio of the grand Millennium Hotel near downtown Boulder. The plenary talks, which began on Monday, are summarized here to give readers an idea of the most active research areas in the geosciences.

Richard Anderson of Sandia National Laboratories, the first plenary speaker, discussed the design and implementation of performance assessments (PAs) for radioactive waste disposal facilities. Anderson's extensive experience includes work on the Yucca Mountain Project for the disposal of high-level radioactive waste, assessments of the Waste Isolation Pilot Plant (WIPP) for the disposal of transuranic waste (in the Chihuahuan Desert of southeastern New Mexico), and exploratory studies related to the seabed disposal of radioactive waste. In particular, Anderson led the PA effort that supported the successful Compliance Certification Application by the U.S. Department of Energy to the U.S. Environmental Protection Agency for WIPP. Upon certification in 1998, WIPP became the first operational facility in the United States for the deep geologic disposal of radioactive waste.

In his talk, Anderson outlined the significant conceptual, computational, and organizational considerations needed for a successful PA for radioactive waste disposal. These considerations consist of uncertainty analyses, selection and modeling of physical and anthropogenic processes, and communication among all parties involved in the PA process. Thus, a full performance assessment doesn't begin or end with the solution of partial differential equations, and it can be extremely important for geoscientists to help in the overall team effort.

The afternoon session on Monday led off with an address by Keith Bedford, chair of the Department of Civil and Environmental Engineering and Geodetic Science at Ohio State University. An expert in the area of coastal and ocean modeling, Bedford recently received a special award from the American Meteorological Society for inventing the first coastal forecasting system. He gave a very informative lecture on multiphysics coupling of ocean, atmospheric, sediment, and wave modeling in nearshore environments.

Bedford's group has been involved recently in the development of a fully coupled mathematical formulation and parallel numerical model called COMAPS (Coastal Marine Prediction System). The COMAPS model consists of five modules, including three-dimensional circulation and thermal codes, a three-dimensional, three-class sediment transport code, an Eulerian particle-tracking code, a spectral-based wind wave code, and codes for the air-sea and water column-sediment-bottom coupling physics. Bedford showed applications to an NSF-funded study of alongshore-offshore sediment transport resulting from storms in Lake Michigan, and to a Department of Defense-sponsored project in the Adriatic Sea. These simulations revealed the need for local space-time grid refinement so that important transient behavior in sediment movement can be captured. This capability, among others, will be the subject of future research on the COMAPS model.

The reception at the poster session on Monday evening gave attendees the opportunity to socialize and to view research results in a more relaxed setting. The poster session allowed for more interaction between the researchers and the presenters, and provided a more casual venue for attendees to talk about their work.

Multiscaling issues were highlighted on Tuesday morning in the address of William G. Gray of the Department of Civil Engineering at the University of Notre Dame. Gray is widely known for his work in a variety of areas of hydrology and currently serves as editor of the journal Water Resources Research. For more than two decades, one of the themes of his research has been an effort to understand the physics of multiphase flow in porous media from first principles. To be practical, such an understanding must include macroscale averaging of complex microscale phenomena. The motivation is to replace empirical macroscale models, to the extent possible, with theoretically based models.

Gray's presentation on thermodynamically constrained averaging theory described theoretical advances that provide the impetus for targeted experimental and computational studies of multiphase flow. Capillary pressure and hysteresis are among the effects that it may be possible to understand more deeply from such studies, and interfacial areas between phases are among the parameters that have been pinpointed as potentially important to this understanding.

Plenary speaker Max D. Morris of the Department of Statistics at Iowa State University discussed the insights to be gained by combining the rather different traditional viewpoints of statistics and applied mathematics toward scientific problems: the former with its emphasis on uncertainty and goodness or lack of fit, the latter with its deterministic explanations of observations based on the modeling of physical processes. Specific examples were related to the computational uncertainty analysis of inverse problems from models of fluid flow and acoustic wave scattering. Morris has a long history of interaction with scientists, engineers, and applied mathematicians, particularly in his previous positions at Oak Ridge National Laboratory and as editor of the applied statistics journal Technometrics.

Scaling issues received further attention on Tuesday evening at the SIAG/GS Business Meeting. Thomas Fogwell of the National Science Foundation, the guest speaker at the meeting, discussed opportunities for geosciences researchers at NSF. In addition to providing insight on current trends for funding activities in the geosciences, he pointed to a significant interest on the part of NSF in the problems of upscaling and multiscaling.

Seismic problems in geophysics were the focus for both plenary speakers on Wednesday. Norman Bleistein, professor emeritus of mathematics, research professor of geophysics, and past director of the Center for Wave Phenomena at the Colorado School of Mines, has been for three decades a leading figure in applications of seismic migration and inversion, particularly to petroleum exploration.

One of two invited speakers on seismic problems in geophysics was Norman Bleistein of the Colorado School of Mines. Using the (1954) Hagedoorn string construction for seismic reflector imaging as a point of departure, Bleistein showed how the Kirchhoff migration/inversion methods widely used for imaging seismic data in the oil industry today can be developed from the earlier method.

His presentation traced the history of two longstanding threads of the field, the Hagedoorn string construction and Kirchhoff migration and inversion. The Hagedoorn method finds reflectors directly, by using travel-time curves from reflection responses on a seismic trace. The more recent Kirchhoff techniques, which have long been the method of choice in the petroleum industry, use an integral representation of the solution of the wave equation to recover structural subsurface features and reflection coefficients. Using the Hagedoorn construction as a starting point to develop the Kirchhoff methods, Bleistein explained the recent observation that these approaches are actually related.

Harnessing the power of large-scale computing, a primary interest for researchers who study earthquake phenomena, was discussed in Wednesday afternoon's plenary session by John Rundle. Rundle is a professor of physics at the University of Colorado, Boulder, where he also directs the Colorado Center for Chaos and Complexity, and he chairs the American Geophysical Union's Committee on Nonlinear Geophysics. He specializes in the statistical physics of earthquakes, certainly a strikingly nonlinear problem. Serious attempts to simulate and forecast earthquakes are beginning, based on a concept of earthquakes as examples of nucleation and critical phenomena in driven threshold systems. In this framework, space-time patterns can be studied statistically to seek understanding of the underlying dynamics. Large-scale computing is making possible such efforts, which were not feasible only a short time ago.

John Rundle of the University of Colorado, Boulder, who studies the statistical physics of earthquakes, explained that advances in large-scale computing are just now making possible serious attempts to simulate and forecast earthquakes.

Petroleum engineers are highly aware of the difficulties associated with the mischaracterization of uncertainty in petroleum reservoir performance. On Thursday morning, Hamdi Tchelepi of Chevron Petroleum Technology Company gave a plenary talk on the assessment of uncertainty in petroleum reservoir performance predictions, pointing out that the management of production from a petroleum reservoir is often determined by performance predictions obtained from numerical simulations. These simulations are often based on limited reservoir data of varying quality, and the uncertainty in the data brings into question the reliability of these simulations.

Monte Carlo simulations are one method for quantifying this uncertainty. Monte Carlo methods are generally impractical in this setting, however, because of the large number of equiprobable realizations of the reservoir description and the cost of performing even a single reservoir simulation. In his talk, Tchelepi focused on the use of direct approaches based on the formulation of stochastic partial differential equations for certain statistical moments. He concentrated on the specific case of two-phase, immiscible flow and derived equations for the moments of total velocity, travel time, transverse displacement, water saturation, production rate, and cumulative recovery. These equations were solved numerically, and the results compared very favorably with those of more computationally intensive Monte Carlo simulations.

Expanding on and complementing the plenary talks, the minisymposia and contributed paper sessions allowed attendees to learn more about cutting-edge research in today's geosciences community. These sessions covered many areas, including multiphysics and multiscaling issues, locally conservative algorithms, ocean and atmospheric modeling, modeling of fractured porous media, and statistical methods for problems in the geosciences. These problems require multidisciplinary solutions, which is why SIAG/GS continually seeks the in-volvement of researchers from other fields.

Do these problems sound interesting to you? Information about the activity group, and the next SIAM conference on the geosciences (to be held in 2003), can be found at

Lea Jenkins and Béatrice Rivière are research associates at the Center for Subsurface Modeling, TICAM, University of Texas, Austin. Also contributing to this article were Clint Dawson, Jon Helton, and Tom Russell.

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