PROGRAM IN ANALYSIS OF INVERSE PROBLEMS IN GEOPHYSICS
Prerequisites: CAAM 423
Description: Content varies from year to year. Instructor permission required. Repeatable for credit.
Class Resources:
EIT
- Lecture 1. View
- Lecture 2 and 3. View
- Lecture 4. View
- Lecture 5. View
- Lecture 6. View
- ‘Uniqueness for the electrostatic inverse boundary value problem with piecewise constant anisotropic conductivities’, Inverse Problems 33 (2017) 125013, with G. Alessandrini and R. Gaburro. View
Geometric inverse problems
- ‘Abel transforms with low regularity with applications to X-ray tomography on spherically symmetric manifolds’, Inverse Problems 33 (2017) 124003, with J. Ilmavirta. View
- ‘Recovery of material parameters in transversely isotropic media’, Archive for Rational Mechanics and Analysis 235 (2020) 141-165, with G. Uhlmann and A. Vasy. View
- ‘A foliated and reversible Finsler manifold is determined by its broken scattering relation’, Pure and Applied Analysis 3-4 (2021) 789-811, with J. Ilmavirta, M. Lassas and T. Saksala. View
Microseismic cloud
- ‘Stable reconstruction of simple Riemannian manifolds from unknown interior sources’, Inverse Problems (2023) 095002, with J. Ilmavirta, M. Lassas and T. Saksala. View
Algebraic geometry meets differential geometry, elastic geometry
- ‘Reconstruction of generic anisotropic stiffness tensors from partial data around one polarization’ (2023), with J. Ilmavirta, M. Lassas and Anthony Várilly-Alvarado. View
Spectral rigidity of spherically symmetric manifolds with boundary and discontinuities
- ‘Spectral rigidity for spherically symmetric manifolds with boundary’, J. Math. Pures Appl. 160 (2022) 54-98, with J. Ilmavirta and V. Katsnelson. View
- ‘Spherically symmetric terrestrial planets with discontinuities are spectrally rigid’, Comm. Math. Phys. (2024) 405:31, with J. Ilmavirta and V. Katsnelson. View
Rotation and Concentric MacLaurin Centroids
- not available yet
Semiclassical inverse spectral problems for surface waves
- ‘Semiclassical inverse spectral problem for seismic surface waves in isotropic media I: Love waves’, Inverse Problems 36 (2020) 075015, with A. Iantchenko, R.D. van der Hilst, and J. Zhai. View
- ‘Semiclassical inverse spectral problem for seismic surface waves in isotropic media II: Rayleigh waves’, Inverse Problems 36 (2020) 075016, with A. Iantchenko, R.D. van der Hilst, and J. Zhai. View
System of radiative transfer equations and monitoring
- ‘Three-dimensional random wave coupling along a boundary and an associated inverse problem’, Multiscale Modelling and Simulation 22(1) (2023) 39-65, with J. Garnier and K. Sølna. View
- ‘Inverse problem for Love waves in a layered, elastic half-space’, Inverse Problems 40 (2023) 045013, with J. Garnier, A. Iantchenko and J. Ricaud. View
Inverse problems for the Rayleigh system with spectral data and resonances
- ‘Inverse problem for the Rayleigh system with spectral data’, J. Math. Phys. 63 (2022) 031505, with A. Iantchenko. View
- ‘Analysis of wavenumber resonances for the Rayleigh system in a half space’, Proc. R. Soc. A (Mathematical, Physical and Engineering Sciences) 479:20220845 (2023), with A. Iantchenko. View
- ‘Inverse problem for the Rayleigh system with wavenumber resonances’, (2023) with A. Iantchenko, not available yet
Inverse boundary value problems for time-harmonic waves
- ‘Stable determination of polyhedral interfaces from boundary data for the Helmholtz equation’, Comm. Partial Differential Equations 40 (2015) 1365-1392, with E. Beretta, E. Francini and S. Vessella. View
- ‘Lipschitz stability for a piecewise linear Schrödinger potential from local Cauchy data’, Asympt. Anal. 108 (2017) 115-149, with G. Alessandrini, R. Gaburro and E. Sincich. View
- ‘Uniqueness and Lipschitz stability of an inverse boundary value problem for time harmonic elastic waves’, Inverse Problems 33 (2017) 035013, with E. Beretta, E. Francini, S. Vessella and J. Zhai. View
Dynamical inverse boundary value problems
Anisotropy
- ‘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, with G. Nakamura and J. Zhai. View
Boundary control
- ‘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, 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, 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, with P. Kepley and L. Oksanen. View
Scattering control
- ‘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, with P. Caday, V. Katsnelson and G. Uhlmann. View
- ‘Recovery of discontinuous Lamé parameters from exterior Cauchy data’, Comm. Partial Differential Equations 46 (2021) 680-715, with P. Caday, V. Katsnelson, and G. Uhlmann. View
- ‘Recovery of piecewise smooth density and Lamé parameters from high-frequency exterior Cauchy data’, SIAM J. Imaging Sci. 15 (2022) 1910-1943, with S. Bhattacharyya, V. Katsnelson and G. Uhlmann. View
Self gravitation
- ‘Recovery of piece-wise smooth parameters from exterior Cauchy data associated with the wave equation containing a nonlocal contribution’ (2023), with S. Bhattacharyya and V. Katsnelson, not available yet
Gliding rays
- not available yet
Nonlinear waves
- ‘Nonlinear responses from the interaction of two progressing waves at an interface’, Annales de l’Institut Henri Poincaré/ Analyse non linéaire 36 (2019) 347-363, with G. Uhlmann and Y. Wang. View
- ‘Nonlinear interaction of waves in elastodynamics and an inverse problem’, Math. Ann. 376 (2019) 765-795, with G. Uhlmann and Y. Wang. View
Inverse problems in viscoelasticity
- ‘Holmgren-John unique continuation theorem for viscoelastic systems’, in Time-dependent Problems in Imaging and Parameter Identification (2021) 287-301, with C.-L. Lin and G. Nakamura, edited by B. Kaltenbacher, T. Schuster and A. Wald. View
- ‘Resolvent estimates for viscoelastic systems of extended Maxwell type and their applications’, SIAM J. Math. Anal. (2024) in print, with M. Kimura, C.-L. Lin and G. Nakamura. View
- ‘Anisotropic extended Burgers model, its relaxation tensor and properties of the associated Boltzmann viscoelastic system’, ArXiv (2024), with M. Kimura, C.-L. Lin, G. Nakamura and K. Tanuma. View
- ‘Exact boundary controllability for the extended Maxwell systems’, with C.-L. Lin and G. Nakamua, not available yet
Inverse problems in nonlocal elasticity: Mitigating static stress singularities
- ‘Uniqueness in an inverse problem of fractional elasticity’, Proc. R. Soc. A (Mathematical, Physical and Engineering Sciences) 479 (2023) doi:10.1098/rspa.2023.0474, with G. Covi and M. Salo. View
- ‘Dynamic case’, not available yet
Inverse “source” problems and faults
Inverse dislocation problems
- ‘Analysis of a model of elastic dislocations in geophysics’, Archive for Rational Mechanics and Analysis 236 (2020) 71-111, with A. Aspri, E. Beretta and A. Mazzucato. View
Inverse problems for contact mechanics
- ‘Inverse Signorini obstacle problem’, with M. Lassas, J. Lu, L. Oksanen and Z. Zhao, not available yet
Inverse problems for friction and rupture dynamics
- ‘Uniqueness for a seismic inverse source problem modeling a subsonic rupture’, Comm. Partial Differential Equations 41 (2016) 1895-1917, with L. Oksanen and J. Tittelfitz. View
- ‘Quantitative unique continuation for elasticity and Maxwell systems with application to the kinematic inverse rupture problem’, Comm. Partial Differential Equations 48 (2023) 286-314, with M. Lassas, J. Lu and L. Oksanen. View
- ‘Stable recovery of coefficients in an inverse fault friction problem’, Comm. Partial Differential Equations (2024) in print, with M. Lassas, J. Lu and L. Oksanen. View
Inverse problems for Prompt Elasto-Gravity Signals (PEGS)
- ‘Early-warning inverse source problem for the elasto-gravitational equations’, SIAM J. Appl. Math. 84(3) (2024) 831-855, with L. Baldassari, E. Francini and S. Vessella. View
- ‘Prompt elasto-gravity inverse source problem in inhomogeneous media’, not available yet
Variational Formulations and Empirical Studies »
