In 2019 the U.S. Geological Survey reported over 1,600 significant earthquakes across the world. Modeling the planet as a manifold then an earthquake would represent a point source for a propagating wave on the manifold. In previous work they have used the wave's travel time from the point source to the boundary of the manifold to recover the structures of the manifold.
My goal is to determine the topological and differential structures of a convex manifold when we restrict our travel time measurements to a small region on the boundary.
- Properties for the Fréchet mean in Billera-Holmes-Vogtmann treespace. M. Anaya, O. Anipchenko-Ulaj, A. Ashfaq, M. Owen, E. Pavlechko, K. St.John et al., Advances in Applied Mathematics (2020) 120: 102072. https://doi.org/10.1016/j.aam.2020.102072
- On Determining if Tree-based Networks Contain Fixed Trees. M. Anaya, O. Anipchenko-Ulaj, A. Ashfaq, M. Owen, E. Pavlechko, K. St.John et al., Bull Math Biol (2016) 78: 961. https://doi.org/10.1007/s11538-016-0169-x