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Jeroen Tromp
Blair Professor of Geology
Professor of Applied & Computational Mathematics

Department of Geosciences
320 Guyot Hall
Princeton University
Princeton, NJ 08544

Phone: (609) 258-4128
E-Mail: email


Theoretical & Computational Seismology

The quality of tomographic images of the Earth's interior is closely tied to our ability to efficiently and accurately simulate 3-D seismic wave propagation on global, regional, and local scales. For decades seismologists have attempted to use asymptotic and numerical methods to address the forward problem in seismology, i.e., given a 3-D Earth model, accurately simulate the associated ground motions. In collaboration with Dimitri Komatitsch at the University of Pau, we have facilitated simulations of 3-D acoustic, (an)elastic, and poroelastic wave propagation at unprecedented resolution and accuracy by taking advantage of modern numerical methods and harnessing parallel computers. As a result of our efforts, on a modest PC cluster one can now simulate 3-D global seismic wave propagation at periods of 20 s and longer, accounting for heterogeneity in the crust and mantle, topography, anisotropy, attenuation, fluid-solid interactions, self-gravitation, rotation, and the oceans. On the next generation petaflops machines we will able to reach a shortest period of 1 s in global simulations.

The challenge now lies in harnessing these new found forward modeling capabilities to enhance the quality of images of Earth's interior and the earthquake rupture process, i.e., to address the seismological inverse problem. The objective here is to go beyond classical 'travel time' (time-of-flight) tomography, and to use information contained in entire seismic waveforms. On the face of it, this seems like a Herculean task, because hundreds or even thousands of model parameters are involved in such inversions. In principle, the sensitivity of a seismogram with respect to the model parameters may be calculated numerically, but this would require a number of forward calculations equal to the number of model parameters (typically thousands). By drawing connections between seismic tomography, adjoint methods popular in climate and ocean dynamics, and time-reversal imaging, we have demonstrated that one iteration in tomographic inversions may be performed based upon just two numerical simulations for each earthquake: one calculation for the current model and a second adjoint calculation that uses time-reversed signals at the receivers as simultaneous, fictitious sources. This has finally opened the door to solving the 3-D inverse problem, i.e., the problem of using the remaining differences between the data and the simulations to improve images of the Earth's interior. Our current research efforts are focused on using adjoint methods to 'image' earth structure on all scales.



Updated 12/09/08