Seminar

I will discuss the travel time tomography problem for the elastic wave equation, where the aim is to recover elastic coefficients in the interior of an elastic medium given the travel times of the corresponding elastic waves. I will consider in particular the transversely isotropic case, which provides a reasonable seismological model for the interior of the Earth or other planets. By applying techniques from boundary rigidity problems, our problem is reduced to the microlocal analysis of certain operators obtained from a pseudo-linearization argument. These operators are not quite elliptic, but they strongly resemble parabolic operators, for which a symbol calculus first constructed by Boutet de Monvel can be applied. I will describe how to use this calculus to solve the problem given certain global assumptions, and if time permits I will discuss current work to modify this calculus in order to solve the problem more locally.