On Wave-Driven Inverse Problems: From Full-Waveform Imaging to Metamaterial Design

Monday, January 143 - 4 pmTechnological Institute, L211

Abstract: This seminar will include a discussion of recent progress in closely-related inverse problems driven by elastic waves. The full-waveform-based imaging of probed solids will be addressed, with geotechnical site characterization applications in mind. The driving problem is similar to geophysical probing -an inverse medium problem- albeit here the focus is in the characterization of the near-surface deposits. There are two key ingredients of the problem: a. modeling of the forward problem, which involves the numerical simulation of wave propagation in PML (perfectly-matched-layer)-truncated domains in the time-domain; and b. the inverse medium problem and the schemes we have implemented in an attempt to lend robustness to the inversion process. Numerical experiments with both synthetic and field data in 3D will be reported. Secondly, a PDE-constrained optimization approach for constructing optimal transient excitations capable of focusing energy to a target underground formation, by steering the wave energy to the formation will be discussed. The motivation stems from the possibility of "shaking" (via ground, wellbore, or other sources) a target reservoir zone strongly enough to increase oil mobility for Enhanced Oil Recovery (EOR) purposes. The method leads formally to an inverse source problem, where the tempo-spatial characteristics of the excitation are the unknown parameters. Numerical experiments with elastic and poroelastic targets demonstrating target illumination will be reported. Lastly, inverse metamaterial design for achieving user-defined band gaps in periodic structures with wave-shielding applications in mind will be discussed. A systematic procedure based either on a target group velocity profile or on the discriminant of the associated Bloch eigenvalue problem, is shown to be capable of producing metamaterial designs exhibiting the target band gaps, including omni-directional gaps. Numerical experiments in both the frequency and the time domain for scalar waves will be reported.

Biography: Loukas F. Kallivokas joined the Department of Civil, Architectural and Environmental Engineering at the University of Texas at Austin as an assistant professor in 1999. In 2003 he was the recipient of a National Science Foundation CAREER award for research in full-waveform-driven site characterization. He is currently a professor and the holder of the Carrol Allen Teaching Fellowship in Civil Engineering. His research interests are in computational engineering and sciences, with particular emphasis on wave mechanics and their applications, including seismic hazard problems, soil- and fluid-structure interaction, acoustic and elastic scattering and radiation problems, geotechnical site characterization, geophysics and geophysical probing, and non-destructive condition assessment. His most recent work focuses on wave-driven inverse medium, inverse scattering, and inverse source problems. From 2008 to 2011 he was the chair of the Computational Mechanics Committee of ASCE's Engineering Mechanics Institute, and he currently serves as an Associate Editor for ASCE's Journal of Engineering Mechanics.