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SUMMARY:Nikolas Eptaminitakis (Purdue University)
DTSTART:20220217T170000Z
DTEND:20220217T180000Z
DTSTAMP:20260423T035639Z
UID:Inverse/80
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Inverse/80/"
 >The Solid-Fluid Transmission Problem</a>\nby Nikolas Eptaminitakis (Purdu
 e University) as part of International Zoom Inverse Problems Seminar\, UC 
 Irvine\n\n\nAbstract\nWe will discuss a problem motivated from geophysics\
 , where one is interested in understanding the propagation of seismic wave
 s in the interior of the Earth. It is known that the interior of the Earth
  consists of several layers\, some of which are solid and some of which ar
 e fluid. When a seismic wave meets the interface between two layers\, part
  of its energy is reflected back (possibly with mode conversion)\, and\, i
 f the angle of incidence is not too large\, part of it is transmitted to t
 he other side of the interface. We are particularly interestred in underst
 anding reflection\, transmission and mode conversion of waves at the inter
 face between a linear elastic solid and an inviscid fluid. For simplicity\
 , we consider the case of two layers\, with the fluid layer being enclosed
  by the solid one. The two media are described by a system of PDEs modelin
 g the displacement in the solid and pressure-velocity in the fluid\, with 
 these quantities being coupled at the interface by transmission conditions
 . We study the problem microlocally: to understand the behavior of singula
 rities of solutions of the system\, we construct a parametrix for it (appr
 oximate solution up to smooth error) using geometric optics. As an applica
 tion of our study\, we consider the inverse problem of recovering the wave
  speeds in the two layers and the material density in the solid outer laye
 r from the Neumann-to-Dirichlet map for the solid-fluid system correspondi
 ng to the exterior boundary. Based on joint work with Plamen Stefanov.\n
LOCATION:https://researchseminars.org/talk/Inverse/80/
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