Overview and details of the sessions of this conference. Please select a date or location to show only sessions at that day or location. Please select a single session for detailed view (with abstracts and downloads if available).
Inverse scattering: Regularized Lanczos method for the Lippmann-Schwinger equation
Justin Baker1, Elena Cherkaev1, Vladimir Druskin2, Shari Moskow3, Mikhail Zaslavsky4
1University of Utah, U.S.A.; 2Worcester Polytechnic Institute, U.S.A.; 3Drexel University, U.S.A.; 4Southern Methodist University, U.S.A.
Inverse scattering techniques have broad applicability in geophysics, medical imaging,
and remote sensing. This talk presents a robust direct reduced-order model method for solving inverse scattering problems. The
approach is based on a Lippmann-Schwinger-Lanczos (LSL) algorithm in the frequency domain with two levels of regularization. Numerical experiments for Helmholtz and
Schrödinger problems show that the proposed regularization
scheme significantly improves the performance of the LSL algorithm, allowing
for good reconstructions with noisy data.
Travel Time Tomography in Transversely Isotropic Elasticity via Microlocal Analysis
Yuzhou Zou
Northwestern University
We will discuss recent results of the author regarding the travel time tomography problem in the context of transversely isotropic elasticity. The works build on previous works regarding X-ray and (elastic) travel time tomography and boundary rigidity problems studied by de Hoop, Stefanov, Uhlmann, Vasy, et al., which reduce the inverse problems to the microlocal analysis of certain operators obtained from a pseudolinearization argument. We will discuss the additional analytic complications in this situation, due to the degenerating ellipticity of certain key operators obtained in the pseudolinearization argument, as well as the machinery developed to tackle these additional complications.
An inverse source problem for the elasto-gravitational equations
Lorenzo Baldassari2, Maarten V. de Hoop2, Elisa Francini1, Sergio Vessella1
1Università di Firenze, Italy; 2Rice University, USA
We study an inverse source problem for a system of elastic-gravitational equations, describing the oscillations of the Earth due to an earthquake.
The aim is to determine the seismic-moment tensor and the position of the point source by using only measurements of the disturbance in the gravity field induced by the earthquake, for an arbitrarily small time window.
The problem is inspired by the recently discovered speed-of-light prompt elasto-gravity signals (PEGS), which can prove beneficial for earthquake early warning systems (EEWS).
