Imaging and Computing Seminar

Maarten de Hoop, Mathematics, Purdue University

Title:
Construction and properties of solutions of the acoustic and elastic wave equations with coefficients of limited smoothness

Abstract:
We discuss the construction of weak solutions of the acoustic and elastic wave equations with $C^{1,1}$ coefficients using curvelets. We obtain a concentration of curvelets result and analyze polarization decoupling. We introduce a procedure to compute the approximate solutions appearing in the construction making use of prolate spheroidal wave functions and discuss the formation of caustics. We then establish a regularity estimate which implies the proper choice of quadrature to generate the curvelet-to-curvelet scattering. We briefly mention the possibility to incorporate random fluctuations in the coefficients and discuss applications in imaging based on reverse time migration.

Joint research with V. Brytik, S. Holman, H. Smith, G. Uhlmann, R.D. van der Hilst and H. Wendt.