Maarten V. de Hoop

PROGRAM IN MICROLOCAL ANALYSIS AND SEISMIC IMAGING

Description: Content varies from year to year. Instructor permission required. Repeatable for credit.

Class Resources:

Bolker condition, DSR condition, convex foliation condition

Generalized Radon transform (GRT), annihilators – “Kirchhoff migration, MVA”

‘Microlocal analysis of seismic inverse scattering in anisotropic, elastic media’, Comm. Pure Appl. Math. 55 (2002) 261-301, with C.C. Stolk. View
‘Generalized Radon transform inversions for reflectivity in anisotropic elastic media’, Inverse Problems 13 (1997) 669-690, with N. Bleistein. View
‘Linearized 2.5-dimensional parameter imaging-inversion in anisotropic elastic media’, Geoph. J. Int. 161 (2005) 722-738, with S.-K. Foss and B. Ursin. View

AVA analysis

‘Recovery of wave speeds and density of mass across a heterogeneous smooth interface from acoustic and elastic wave reflection operators’, GEM – International Journal on Geomathematics 13 (2022) 9, with S. Bhattacharyya, V. Katsnelson and G. Uhlmann. View

DMO, source-receiver continuation, range

‘Characterization and ‘source-receiver’ continuation of reflection seismic data’, Comm. Math. Phys. 263 (2006) 1-19, with G. Uhlmann. View
‘Seismic wavefield ‘continuation’ in the single scattering approximation: A framework for Dip and Azimuth Moveout’, Can. Appl. Math. Q. 10 (2002) 199-238, with A.E. Malcolm and J.H. Le Rousseau. View

Reverse-time-continuation based imaging (RTM) and inverse scattering

‘Linearized inverse scattering based on seismic Reverse-Time Migration’, J. Math. Pures Appl. 98 (2012) 211-238, with T.J.P.M. op’t Root and C.C. Stolk. View
‘Elastic-wave inverse scattering based on reverse time migration with active and passive source reflection data’, in Inside Out II, Inverse Problems and Applications, Mathematical Sciences Research Institute Publications 60, edited by G. Uhlmann, Cambridge University Press, Cambridge, (2013) 411-453 with V. Brytik and R.D. van der Hilst. View
‘Beyond receiver functions: Passive source Reverse Time Migration and inverse scattering of converted waves’, Geophys. Res. Lett. 39 (2012) L15308, with X. Shang and R.D. van der Hilst. View

Downward-continuation (DSR) based extended imaging and inverse scattering

‘Modeling of seismic data in the downward continuation approach’, SIAM J. Appl. Math. 65 (2005) 1388-1406, with C.C. Stolk. View
‘Seismic inverse scattering in the downward continuation approach’, Wave Motion 43 (2006) 579-598, with C.C. Stolk. View
‘Kinematics of shot-geophone migration’, Geophysics 74 (6) (2009) WCA19-WCA34 with C.C. Stolk and W.W. Symes. View

Imaging and velocity continuation or flows

‘Evolution-equation approach to seismic image, and data, continuation’, Wave Motion 45 (2008) 952-969, with A.A. Duchkov and A.S. Sá Barreto. View
‘Extended isochron rays in prestack depth (map) migration’, Geophysics 75 (4) (2010) S139-S150, with A.A. Duchkov. View
‘Velocity continuation in the downward continuation approach to seismic imaging‘, Geoph. J. Int. 176 (2009) 909-924, with A.A. Duchkov. View

Wave packets: Ray-wave “duality”

‘A multi-scale approach to hyperbolic evolution equations with limited smoothness’, Comm. Partial Differential Equations 33 (2008) 988-1017, with F. Andersson, H. Smith and G. Uhlmann. View
‘Regularity and multi-scale discretization of the solution construction of hyperbolic evolution equations with limited smoothness’, Applied and Computational Harmonic Analysis 33 (2012) 330-353, with S.F. Holman, H. Smith and G. Uhlmann. View
‘Decoupling of modes for the elastic wave equation in media of limited smoothness’, Comm. Partial Differential Equations 36 (2011) 1683-1693, with V. Brytik, H. Smith and G. Uhlmann. View

Wave packets: Imaging and illumination

‘Multi-scale discrete approximation of Fourier Integral Operators’, Multiscale Modelling and Simulation 10 (2012) 111-145, with F. Andersson and H. Wendt. View
‘Seismic imaging with the generalized Radon transform: A curvelet transform perspective’, Inverse Problems 25 (2009) 025005, with H. Smith, G. Uhlmann and R.D. van der Hilst. View
‘Leading-order seismic imaging using curvelets’, Geophysics 72 (6) (2007) S231-S248, with H. Douma. View

Time migration

‘Kinematic time migration and demigration of reflections in pre-stack seismic data’, Geoph. J. Int. 189 (2012) 1635-1666, with E. Iversen, M. Tygel and B. Ursin. View
‘Explicit expressions for pre-stack map time-migration in isotropic and VTI media and the applicability of map depth-migration in heterogeneous anisotropic media’, Geophysics 71 (1) (2006) S13-S28, with H. Douma. View

Generalized Dix

‘Recovering the isometry type of a Riemannian manifold from local boundary diffraction travel times’, J. Math. Pures Appl. 103 (2015) 830-848, with S.F. Holman, E. Iversen, M. Lassas and B. Ursin. View
‘Reconstruction of a conformally Euclidean metric metric from local boundary diffraction travel times’, SIAM J. Math. Anal. 46 (2014) 3705-3726, with S.F. Holman, E. Iversen, M. Lassas and B. Ursin. View
‘Reconstruction along a geodesic from sphere data in Finsler geometry and anisotropic elasticity’ (2021) with J. Ilmavirta and M. Lassas. View
‘Recovering the universal cover of a Finsler manifold from sphere data’ (2023), coming soon.

Transmission and reflection tomography

‘Inverting the local geodesic ray transform of higher rank tensors’, Inverse Problems 35 (2019) 115009, with G. Uhlmann and J. Zhai. View
‘Generic uniqueness and stability for the mixed ray transform in three-dimensional compact simple Riemannian manifolds’ Trans. AMS 374 (2021) 6085-6144, with T. Saksala, G. Uhlmann and J. Zhai. 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

Addenda

‘Solving the three-dimensional high-frequency Helmholtz equation using contour integration and polynomial preconditioning’, SIAM J. Matrix Anal. Appl. 41 (2020) 58-82, with X. Liu, Y. Xi and Y. Saad. View
‘Uniform asymptotic expansion of the square-root Helmholtz operator and the one-way wave propagator’, SIAM J. Appl. Math. 63 (2003) 777-800, with A.K. Gautesen. View
‘A multi-scale Gaussian beam parametrix for the wave equation: The Dirichlet problem’, J. Diff. Eqs. 309 (2022) 949-993, with M. Berra and J.L. Romero. View