黑料导航

Vitaly Katsnelson鈥檚 research focuses partial differential equations鈥攕pecifically, microlocal analysis and inverse problems. He received his Ph.D. in Mathematics from Stanford University, where he used microlocal analysis to study elastic wave propagation on singular manifolds (elastic objects with edges and corners) to better understand how waves experienced during an earthquake interact with sharp objects.

Katsnelson continued his research through postdoctoral work at Rice University under the supervision of Professor Maarten V. de Hoop. The focus of his study was on inverse problems where they attempt to reconstruct material properties of the Earth using seismic surface data or by conducting seismic experiments on the surface itself. This process is not unlike medical imaging where scientists try to detect cancer cells or obtain an image of the body noninvasively by sending certain waves and then taking measurements of these scattered waves outside the body, akin to a CT scan.

In 2017, Katsnelson and his collaborators obtained a fundamental uniqueness result for the inverse boundary value problem associated with the acoustic wave equation with piecewise smooth wave speeds, based on the scattering control series they developed. The scattering control allowed for disentanglement of internal multiple scattering without knowledge of the wave speed or interfaces, which was the key to recovering the full wave speed without linearization. This research was then carried into the realm of the elastic wave equation in developing a scattering-control-based approach to the recovery of P-and S-wave speeds, and showing the extent that internal multiples may be suppressed and eliminated.

Currently, Vitaly鈥檚 research looks at the frequencies of the Earth鈥檚 free oscillations during an earthquake and how much structure of the planet鈥檚 interior one can reconstruct from such frequencies that are measured in practice.