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.