The Role of Nolinearity in Inverse Problems

Wednesday, April 24, 2002 - 9:30am - 10:30am
Keller 3-180
Roel Snieder (Colorado School of Mines)
Inverse problems are often formulated as a minimization problem of a quantity that mesures the misfit between the recorded data and synthetic data for a given model. One normally assumes that the main effect of nonlinearity of the forward problem is to create secondary minima of the mistfit function. Several examples are shown that this is an oversimplification of the real situation and that nonlinearity can have much more pathological effects. The related instability of that can occur in nonlinear inverse problems is illustrated using perturbation theory. Modern optimization techniques generate not single models that are compatible with the data, but a large class of models that is compatible with the data. A technique is presented to extract the robust features from these populations of models.

Biographical sketch: Roel Snieder holds the Keck Foundation Endowed Chair of Basic Exploration Science at the Colorado School of Mines. He received in 1984 a Masters degree in Geophysical Fluid Dynamics from Princeton University, and in 1987 a Ph.D. in seismology from Utrecht University. In 1993 he was appointed as professor of seismology at Utrecht University, where from 1997-2000 he was appointed as Dean of the Faculty of Earth Sciences. In 1997 he was a visiting professor at the Center for Wave Phenomena. Roel served on the editorial boards of Geophysical Journal International, Inverse Problems, and Reviews of Geophysics. In 2000 he was elected as Fellow of the American Geophysical Union for important contributions to geophysical inverse theory, seismic tomography, and the theory of surface waves.