Journey to the Center of the Earth

Thursday, April 6, 2023 - 11:00am for 1 hour (actually 50 minutes)
Skiles 006
Gunther Uhlmann – University of Washington – gunther@math.washington.edu
Gong Chen, Benjamin Jaye, Tom Kelly

We will consider the inverse problem of determining the sound
speed or index of refraction of a medium by measuring the travel times of
waves going through the medium. This problem arises in global seismology
in an attempt to determine the inner structure of the Earth by measuring
travel times of earthquakes. It also has several applications in optics
and medical imaging among others.

The problem can be recast as a geometric problem: Can one determine
the Riemannian metric of a Riemannian manifold with boundary by
measuring the distance function between boundary points? This is the
boundary rigidity problem.

We will also describe some recent results, joint with Plamen Stefanov
and Andras Vasy, on the partial data case, where you are making
measurements on a subset of the boundary.