Dr. Michael Slawinski
Office: ER 4032
My research deals with seismic ray theory in elastic media. My work investigates a geometrical formulation of seismic ray theory that is grounded in variational principles, in particular the classical results of Fermat and Hamilton. The geometrical approach used in this investigation, which is based on the geometries of Finsler and Cartan, has been developed during the past century and forms a natural context for seismic ray theory research. In view of Fermat's principle, raypaths are geodesics in the space wherein the arclength is the traveltime. Moreover, in view of Huygens' principle, the elementary wavefronts are indicatrices in the tangent bundle over the medium while the phase-slowness surfaces are figuratrices in the cotangent bundle. The relationship between these two bundles is none other than the Legendre transformation, which allows one to express wavefronts as Legendre images of the phase-slowness curves.
My research is based on collaborations with mathematicians possessing expertise in differential geometry and is conducted in conjunction with petroleum and geophysical companies who also provide financial support for the research project, graduate students, post-doctoral fellows and visiting scholars.