DIFFERENTIAL GEOMETRY/PDE SEMINAR

Wednesday, October 11 Padelford C-36 3:45 PM

Reconstruction of discontinuities of wave velocities

Sönke Hansen (Universität Paderborn, Germany and UW)

We consider the wave equation in a medium X containing surfaces across which the wave velocity c is discontinuous. These discontinuities give rise to singularities in the Schwartz kernel Λ of the Dirichlet-to-Neumann operator on the space-time boundary of X. The formal derivative L of the map c ↦ Λ at a background wave velocity is used in the inverse problem of recovering c. Essentially L is a FIO associated with the canonical relation of single reflection. We show how a microlocal inverse of L reconstructs jump discontinuities of c.