CAAM 642

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 pdf
  • ‘Generalized Radon transform inversions for reflectivity in anisotropic elastic media’, Inverse Problems 13 (1997) 669-690, with N. Bleistein. View pdf
  • ‘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 pdf

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 pdf

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 pdf
  • ‘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 pdf

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 pdf
  • ‘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 pdf
  • ‘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 pdf

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 pdf
  • ‘Seismic inverse scattering in the downward continuation approach’, Wave Motion 43 (2006) 579-598, with C.C. Stolk. View pdf
  • ‘Kinematics of shot-geophone migration’, Geophysics 74 (6) (2009) WCA19-WCA34 with C.C. Stolk and W.W. Symes. View pdf

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 pdf
  • ‘Extended isochron rays in prestack depth (map) migration’, Geophysics 75 (4) (2010) S139-S150, with A.A. Duchkov. View pdf
  • Velocity continuation in the downward continuation approach to seismic imaging, Geoph. J. Int. 176 (2009) 909-924, with A.A. Duchkov. View pdf

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 pdf
  • ‘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 pdf
  • ‘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 pdf

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 pdf
  • ‘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 pdf
  • ‘Leading-order seismic imaging using curvelets’, Geophysics 72 (6) (2007) S231-S248, with H. Douma. View pdf

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 pdf
  • ‘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 pdf

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 pdf
  • ‘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 pdf
  • ‘Reconstruction along a geodesic from sphere data in Finsler geometry and anisotropic elasticity’ (2021) with J. Ilmavirta and M. Lassas. View pdf
  • ‘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 pdf
  • ‘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 pdf
  • ‘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 pdf

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 pdf
  • ‘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 pdf
  • ‘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 pdf

Ten Empirical Studies in Seismic Imaging »

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