Ten Topics in Seismic Imaging

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
  • ‘Maslov asymptotic extension of generalized Radon transform (GRT) inversion in anisotropic elastic media: A least-squares approach’, Inverse Problems 16 (2000) 519–562, with S. Brandsberg-Dahl. 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

DMO, source-receiver continuation, range

  • ‘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
  • ‘Characterization and ‘source-receiver’ continuation of reflection seismic data’, Comm. Math. Phys. 263 (2006) 1–19, with G. Uhlmann. 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) doi:10.1029/2012GL052289, 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 (2009) WCA19-WCA34 with C.C. Stolk and W.W. Symes. View pdf

Evolution equations for imaging and velocity continuation

  • ‘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 (curvelets): A multi-scale approach to wave propagation and scattering – “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 (curvelets):  Imaging, illumination, partial reconstruction

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

Random media, Green’s functions and imaging with partly coherent waves via cross correlations

  • ‘Estimating a Green’s function from “field-field” correlations in a random medium’, SIAM J. Appl. Math. 69 (2009) 909-932, with K. Sølna. View pdf
  • ‘Retrieval of a Green’s function with reflections from partly coherent waves generated by a wave packet using cross correlations’, SIAM J. Appl. Math. 73 (2013) 493-522, with J. Garnier, S.F. Holman and K. Sølna. View pdf

Generalized Dix, time migration

  • ‘Recovering the isometry type of a Riemannian manifold from local boundary diffraction travel times’ , J. Math. Pures Appl. (2014) 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. (2014) with S.F. Holman, E. Iversen, M. Lassas and B. Ursin. View pdf
  • ‘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

Geodesic ray transform and (wave-equation) reflection tomography

  • ‘Sensitivity analysis of wave-equation tomography: A multi-scale approach’, J. Four. Anal. Appl. 16 (2010) 544-589, with V. Brytik and M. Salo. View pdf
  • ‘Wave-equation reflection tomography: Annihilators and sensitivity kernels’, Geoph. J. Int. 167 (2006) 1332–1352, with R.D. van der Hilst and P. Shen. View pdf

Addenda

  • ‘The resolv­ing power of seis­mic ampli­tude data: An anisotropic inversion/migration approach’, Geo­physics 64 (1999) 852–873, with C. Spencer and R. Burridge. View pdf
  • ‘Approximate dispersion relations for qP-qSV waves in transversely isotropic media’ , Geophysics 65 (2000) 919-933 , with M. Schoenberg. 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 (2006) S13-S28, with H. Douma. View pdf
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