- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, October 26, 2015 - 2:00pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Professor Maarten de Hoop – Rice University – mdehoop@purdue.edu – http://engineering.rice.edu/dehoop/
- Organizer
- Maryam Yashtini
We consider an inverse problem for an inhomogeneous wave equation with
discrete-in-time sources, modeling a seismic rupture. We assume that
the sources occur along an unknown path with subsonic velocity, and
that data is collected over time on some detection surface. We explore
the question of uniqueness for these problems, and show how to recover
the times and locations of sources microlocally first, and then the
smooth part of the source assuming that it is the same at each source
location. In case the sources (now all different) are (roughly
speaking) non-negative and of limited oscillation in space, and
sufficiently separated in space-time, which is a model for
microseismicity, we present an explicit reconstruction, requiring
sufficient local energy decay. (Joint research with L. Oksanen and J. Tittelfitz)