| Date: | October 24, 2018 |
| Time: | Noon |
| Location: | Blocker 628 |
| Speaker: | Dr. Ngoc T. Do, University of Arizona |
| Title: | Inverse source problem for the wave equation with reduced data: an explicit solution |
| Abstract: | The inverse source problem for the standard wave equation is a mathematical foundation for several promising emerging modalities of medical imaging. I will review the physical and biological motivation behind these techniques, and will concentrate on the theoretical and algorithmic aspects of this problem. Of special interest here are theoretically exact inversion formulas, explicitly expressing solution of the problem in terms of the measured data. Practically all such formulas require data to be taken on a surface completely surrounding the object under investigation, which, in many cases, cannot be done in practice. The alternative approach we present yields explicit, theoretically exact reconstruction from data measured on an open surface. This is the first result of this kind. Numerical simulations illustrating the work of the method will be also presented.
This is a joint work with Prof. L. Kunyansky. |
|
| Date: | October 31, 2018 |
| Time: | Noon |
| Location: | BLOC 628 |
| Speaker: | Dr. Teemu Saksala, Rice University, Department of computational and applied mathema |
| Title: | Seeing inside the Earth with micro earthquakes |
| Abstract: | Earthquakes produce seismic waves. They provide a way to obtain
information about the deep structures of our planet. The typical
measurement is to record the travel time difference of the seismic
waves produced by an earthquake. If the network of seismometers is
dense enough and they measure a large number of earthquakes, we can
hope to recover the wave speed of the seismic wave from the travel
time differences.
In this talk we will consider geometric inverse problems related to
different data sets produced by seismic waves. We will state
uniqueness results for these problems and consider the mathematical
tools needed for the proofs. The talk is based on joint works with:
Maarten de Hoop, Joonas Ilmavirta, Matti Lassas and Hanming Zhou. |
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