Introduction to the Mathematics of Seismic Imaging
Organized by Organizer: Gunther Uhlmann (Walker Family Endowed Professor in Mathematics, University of Washington and the University of California, Irvine)www.msri.org
Mathematical Sciences Research Institute, Berkeley, California, USA
Lecturers: Allison Malcolm (Assistant Professor, Department of Earth and Planetary Sciences, MIT) and William Symes (Noah Harding Professor of Computational and Applied Mathematics and Director of the Rice Inversion Project, Rice University)
The goal in seismic imaging is to determine the inner structure of the Earth from the crust to the inner core by using information provided by earthquakes in the case of the deep interior or by measuring the reflection of waves produced by acoustic or elastic sources on the surface of the Earth.
The mathematical problem can be formulated as an inverse problem for the wave equation: can one recover the sound speed of a medium by measuring information produced at the boundary by seismic waves? During the first week, the one dimensional case will be studied. During the second week, the higher dimensional case will be analyzed with mathematical techniques like geometrical optics and microlocal analysis.