Department of Mathematics and Statistics, University of Helsinki
Room: A414 (Exactum)
Address: P.O. Box 68 (Gustaf Hällströmin katu 2b)
FI-00014 University of Helsinki
I'm interested in inverse problems on manifolds. In my Phd Thesis I study certain geometric inverse problems related to geophysical prospecting. The rough idea is that earthquakes produce seismic waves that propagate through the Earth and can be measured on different locations on the surface of Earht with instruments called geophones. Therefore it possible to measure travel time differences of seismic waves. Doing this kind of measurements, we can find indirect information about the inner structure of Earth.
Mathematically speaking we study an inverse problem of a wave equation on Riemannian manifold with Dirichlet or Neumann boundary values. The goal is to reconstruct the unknown wave speed in the interior of the manifold or equivalently the Riemannian metric tensor. That is a mathematical consept that corresponds to the material parameters of the soil and in this way tells us about the structure of Earth.
At the moment I work with my advisor Matti Lassas, Hangming Zhou, Tapio Helin and Lauri Oksanen. I'm planing to defend my thesis at the fall of 2017.
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