Uniqueness of seismic inverse source problems modeling microseismicity and ruptures

Applied and Computational Mathematics Seminar
Monday, October 26, 2015 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 005
Professor Maarten de Hoop – Rice University – mdehoop@purdue.eduhttp://engineering.rice.edu/dehoop/
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)