Program in Inverse Problems for the Elastic Wave Equation

Inverse problems for the (elastic) wave equation


Boundary control, recovery of smooth wave speed

‘On the construction of virtual interior point-source traveltime distances from the hyperbolic Neumann-to-Dirichlet map’ , SIAM J. Appl. Math. 76 (2016) 805-825, doi: 10.1137/15M1033010, with P. Kepley and L. Oksanen. View
‘An exact redatuming procedure for the inverse boundary value problem for the wave equation, SIAM J. Appl. Math. 78 (2018) 171-192, doi:10.1137/16M1106729, with P. Kepley and L. Oksanen. View
Recovery of a smooth metric via wave field and coordinate transformation reconstruction, SIAM J. Appl. Math. 78 (2018) 1931-1953, doi:10.1137/17M1151481, with P. Kepley and L. Oksanen. View

Scattering control, recovery of piecewise smooth P- and S- wave speeds

‘Scattering control for the wave equation with unknown wavespeed’, Archive for Rational Mechanics and Analysis 231 (2019) 409-464, with P. Caday, V. Katsnelson and G. Uhlmann. View
‘Reconstruction of piecewise smooth wave speeds using multiple scattering’, Trans. AMS 372 (2019) 1213-1235, doi:10.1090/tran/7632, with P. Caday, V. Katsnelson and G. Uhlmann. View
‘Recovery of discontinuous Lamé parameters from exterior Cauchy data’, Comm. Partial Differential Equations 46 (4) (2021) 680-715, doi:10.1080/03605302.2020.1857399, with P. Caday, V. Katsnelson and G. Uhlmann. View

Anisotropy, land acquisition

‘Unique recovery of a piecewise analytic density and stiffness tensor from the elastic-wave Dirichlet-to-Neumann map’, SIAM J. Appl. Math. 79 (2019) 2359-2384, doi:10.1137/18M1232802, with G. Nakamura and J. Zhai . View

Geometric inverse problems, high-frequency waves and scattering

‘Generic uniqueness and stability for the mixed ray transform in three-dimensional compact simple Riemannian manifolds’, Trans. AMS 374 (2021) 6085-6144, doi:10.1090/tran/8342, with T. Saksala, G. Uhlmann and J. Zhai. View
‘Recovery of material parameters in transversely isotropic media’, Archive for Rational Mechanics and Analysis 235 (2020) 141-165, doi:10.1007/s00205-019-01421-5, with G. Uhlmann and A. Vasy. View
‘A foliated and reversible Finsler manifold is determined by its broken scattering relation’, Pure and Applied Analysis (2021) in print, with J. Ilmavirta, M. Lassas and T. Saksala. View