Geo Mathematical Imaging Group, Purdue University

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For information regarding GMIG membership, please contact:

Barbara Doremire
Department of Mathematics
Purdue University
150 N. University Street
West Lafayette, IN 47907
Phone: 765-496-7678
bjd@purdue.edu

2012

GMIG Report 12-17: Sunyoung Park, Lingyun Qiu, Maarten V. de Hoop and Changsoo Shin, 'On time-harmonic seismic data and blending in full waveform inversion', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2012) pp. 305-318

GMIG Report 12-16: Christopher Petrovitch, Laura J. Pyrak-Nolte and David D. Nolte, 'From laboratory to field - critical scaling of single fractures', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2012) pp. 295-304

GMIG Report 12-15: Bradley C. Abell, Min-Kwang Choi and Laura J. Pyrak-Nolte 'Shear specific stiffness of fractures and fracture intersections', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2012) pp. 285-294

GMIG Report 12-14: Siyi Shao, Bradley C. Abell and Laura J. Pyrak-Nolte, 'Interface waves along fractures in anisotropic media', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2012) pp. 275-284

GMIG Report 12-X: Maarten V. de Hoop, Gunther Uhlmann and András Vasy, 'Diffraction from conormal singularities', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2012) pp. 231-274

GMIG Report 12-13: Maarten V. de Hoop, Josselin Garnier and Knut Sølna, 'Enhanced and specular backscattering in random media', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2012) pp. 209-230

GMIG Report 12-12: Zhaohui Guo and Maarten V. de Hoop, 'Shape optimization in full waveform inversion with sparse blocky model representations', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2012) pp. 189-208

GMIG Report 12-11: Maarten V. de Hoop, Lingyun Qiu and Otmar Scherzer, 'A convergence analysis of a multi-level projected steepest descent iteration for nonlinear inverse problems in Banach spaces subject to stability constraints', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2012) pp. 173-188

GMIG Report 12-10: Elena Beretta, Maarten V. de Hoop and Lingyun Qiu, 'Lipschitz stability of an inverse boundary value problem for a Schr ̈dinger type equation', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2012) pp. 155-172

GMIG Report 12-09: Scott Burdick, Maarten V. de Hoop, Shen Wang and Robert D. van der Hilst, 'Teleseismic wave-equation reflection tomography using free surface reflected phases', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2012) pp. 133-154

GMIG Report 12-08: Jianlin Xia, Yuanzhe Xi and Maarten V. de Hoop, 'Fast structured eigensolver for discretized partial differential operators on general meshes', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2012) pp. 123-132

GMIG Report 12-07: Shen Wang, Maarten V. de Hoop, Jianlin Xia and Xiaoye S. Li 'Massively parallel structured multifrontal solver for time-harmonic elastic waves in 3D anisotropic media', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2012) pp. 97-122

GMIG Report 12-06: Shen Wang, Jianlin Xia, Maarten V. de Hoop and Xiaoye S. Li, 'MFRS: An algorithm for the structured multifrontal solution of large sparse matrices via randomized sampling', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2012) pp. 81-96

GMIG Report 12-05: Maarten V. de Hoop, Sean F. Holman, Einar Iversen, Matti Lassas and Bjørn Ursin, 'Reconstruction of the metric of a Riemannian manifold from local boundary diffraction travel times II. A Dix-type algorithm', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2012) pp. 69-80

GMIG Report 12-04: Fredrik Andersson, Maarten V. de Hoop and Herwig Wendt, 'Multi-scale reverse-time-migration based inverse scattering using the dyadic parabolic decomposition of phase space', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2012) pp. 49-68

GMIG Report 12-03: Maarten V. de Hoop and Sean F. Holman, 'Up-down decoupling and paraxial wave equation estimates', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2012) pp. 29-48

GMIG Report 12-02: Fredrik Andersson, 'Time extended structure tensors for multiple directionality estimation' Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2012) pp. 13-28

GMIG Report 12-01: Fredrik Andersson, Marcus Carlsson and Maarten V. de Hoop, 'Frequency extrapolation through sparse sums of Lorentzians', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2012) pp. 1-12

2011

GMIG Report 11-16: Liu, Y., Nolte, D., and Pyrak-Nolte, L.J. 'Elastic films and reversibility in a microfluidic pore', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2011) pp. 267-274

GMIG Report 11-15: Li, W., Petrovitch, C.L., and Pyrak-Nolte, L.J. 'The effect of saturation on shear wave anisotropy in a transversely isotropic medium', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2011) pp. 253-266

GMIG Report 11-14: Petrovitch, C.L., Pyrak-Nolte, L.J., and De Hoop, M.V. 'Modeling of seismic wave scattering from rough fracture surfaces', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2011) pp. 243-252

GMIG Report 11-13: De Hoop, M.V. Garnier, J. Holman, S.F., and Sølna, K. 'Retrieval of a Green's function with reflections from partly incoherent waves generated by a wave packet using cross-correlations', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2011) pp. 221-242

GMIG Report 11-12: De Hoop, M.V. Qiu, L., and Scherzer, O. 'Local inverse problems: Hölder stability and iterative reconstruction', Inverse Problems (2012) pp. 203-220

GMIG Report 11-11: Brytik, V., De Hoop, M.V., Smith, H., and Uhlmann, G. 'Decoupling of modes for the elastic wave equation in media of limited smoothness', Comm. Partial Differential Equations 36 (2011) 1683-1693

GMIG Report 11-10: Wang, S., Xia, J. De Hoop, M.V., and Li, X. 'Frequency domain finite difference modelling of seismic wave propagation in TTI media via a massively parallel structured direct Helmholtz solver', Geophysics (2012)

GMIG Report 11-09: Wang, S., Li, X. Xia, J., Situ Y., and De Hoop, M.V. 'Efficient parallel algorithms for hierarchically semiseparable matrices', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2011) pp. 159-174

GMIG Report 11-08: De Hoop, M.V., Holman, S.F., Smith, H.F., and Uhlmann, F. 'Regularity in, and multi-scale discretization of the solution construction of hyperbolic evolution equations of limited smoothness', Applied and Computational Harmonic Analysis (2012)

GMIG Report 11-07: Wendt, H., De Hoop, M.V., Uhlmann, G., and Vasy, A. 'Fourier integral operator canonical computation with wave packets', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2011) pp. 113-130

GMIG Report 11-06: De Hoop, M.V., Iversen, E., Lassas, M., and Ursin, B. 'Reconstruction of the metric of a Riemannian manifold from local boundary diffraction travel times', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2011) pp. 95-112

GMIG Report 11-05: Iversen, E., Tygel, M., Ursin, B., and De Hoop, M.V. 'Kinematic time migration and demigration of reflections in prestack seismic data', Geophys. J. Int. (2012)

GMIG Report 11-04: Andersson F., and Strandmark P. 'Geometric segmentation using Gaussian wave packets', Proceedings of the Project Review, Geo-Mathematical Imaging Group (2011), Purdue University, West Lafayette, IN (2011) pp. 57-64

GMIG Report 11-03: Andersson, F., and Carlsson, M. 'Alternating projections on low-dimensional manifolds', Proceedings of the Project Review, Geo-Mathematical Imaging Group (2011), Purdue University, West Lafayette, IN (2011) pp. 37-56

GMIG Report 11-02: Andersson, F., and Carlsson, M. 'A fast alternating projection method for complex frequency estimation', Proceedings of the Project Review, Geo-Mathematical Imaging Group (2011) Purdue University, West Lafayette, IN (2011) pp. 21-36

GMIG Report 11-01: Tenorio, L., Andersson, F., De Hoop, M.V., and Ma, P. 'Data analysis tools for uncertainty quantification of inverse problems', Inverse Problems 27 (2011) doi:10.1088/0266-5611/27/4/045001

2010

GMIG Report 10-14: Pyrak-Nolte, L.J., and Olander, M.K. 'Particle swarms in smooth-walled fractures' Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2010) pp. 211-220

GMIG Report 10-13: Li, W., and Pyrak-Nolte, L.J. 'Seismic wave propagation in fractured carbonate rock', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2010) pp. 211-220

GMIG Report 10-12: Petrovitch, C.L., Pyrak-Nolte, L.J., and Nolte, D.D. 'The effect of initial contact area on the mechanical and hydraulic properties of single fractures', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2010) pp. 201-210

GMIG Report 10-11: Malcolm, A.E., De Hoop, M.V., and Ursin, B. 'Recursive imaging with multiply scattered waves using partial-image regularization: A North Sea case study', Geophysics 76 (2) (2011) B33-B42

GMIG Report 10-10: Qiu, L., De Hoop, M.V., and Sá Barreto, A.S. 'Modelling of time-harmonic seismic data with the Helmholtz equation and scattering series', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2010) pp. 169-186

GMIG Report 10-09: Brytik, V., De Hoop, M.V., and Van der Hilst, R.D. 'Elastic-wave inverse scattering with active and passive source reflection data', in Inside Out, Inverse Problems and Applications, Mathematical Sciences Research Institute Publications, edited by G. Uhlmann (2011)

GMIG Report 10-08: Tygel, M., Ursin, B., Iversen E., and De Hoop, M.V. 'Estimation of geological dip and curvature from time-migrated zero-offset reflections in heterogeneous anisotropic media', Geophys. Prosp. (2011) doi: 10.1111/j.1365-2478.2011.00989

GMIG Report 10-07: Andersson, F., De Hoop, M.V., and Wendt, H. 'Multi-scale discrete approximation of Fourier Integral Operators', MMS: A SIAM Interdisciplinary Journal (2011)

GMIG Report 10-06: Wang, S., De Hoop, M.V., and Xia J. 'On 3D modeling of seismic wave propagation via a structured massively parallel multifrontal direct Helmholtz solver', Geophys. Prosp. 59 (2011) 857-873

GMIG Report 10-05: Nowack, R.L. 'Seismic interferometry and estimation of the Green's function using Gaussian beams', Earthquake Science 23 (2010) 417-424

GMIG Report 10-04: Nowack, R.L., and Kainkaryam, S.M., 'The Gouy phase anomaly for harmonic and time-domain Gaussian beams', Geophys. J. Int. 184 (2011) 965-973

GMIG Report 10-03: Anderson, F., Carlsson, M., and Tenorio, L. 'On the representation of functions with Gaussian wave packets', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2010) pp. 25-50

GMIG Report 10-02: Carlsson, M. 'On truncated Wiener-Hopf operators and BMO', Proc. Amer. Math. Soc. 139 (2011) 1717-1733

GMIG Report 10-01: Carlsson, M. 'A complete AAK-theorem for weighted sequence spaces', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2010) pp. 1-8

2009

GMIG Report 09-12: Acosta-Colon, A.A., Olander, M.K., and Pyrak-Nolte, L.J. 'Seismic wave propagation across in-filled fractures', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2009) pp. 193-204

GMIG Report 09-11: Petrovitch, C.L., Pyrak-Nolte, L.J., and Nolte, D.D. 'Scaling of displacement and fluid flow in single fractures', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2009) pp. 181-192

GMIG Report 09-10: Yao, H., Campman, X., De Hoop, M.V., and Van der Hilst, R.D. 'Construction of empirical Green's functions from direct waves, coda waves, and ambient noise in SE Tibet', Physics of Earth and Planetary Interiors, (2009) doi:10.1016/j.pepi.2009.07.002

GMIG Report 09-09: Duchkov, A.A., De Hoop, M.V., and Anderson, F. 'Migration velocity analysis using wave packets - geometric approach', SEG Expanded Abstracts 28 (2009) 3999-4003

GMIG Report 09-08: Stolk, C.C., De Hoop, M.V., and Symes, W.W. 'Kinematics of shot-geophone migration', Geophysics 74 (6) (2009) WCA19-WCA34

GMIG Report 09-07: Wang, S., De Hoop, M.V., and Xia, J. 'Acoustic inverse scattering via Helmholtz operator factorization and optimization', J. Comput. Phys. 229 (2010) 8445-8462

GMIG Report 09-06: Op't Root, T.J.P.M., Stolk, C.C., and De Hoop, M.V. 'Linearized inverse scattering based on seismic Reverse-Time Migration', J. Math. Pures Appl. (2011)

GMIG Report 09-05: Wang, S., De Hoop, M.V., and Ursin, B. 'Illumination analysis of wave-equation imaging with curvelets', Inverse Problems 26 (2010) doi:10.1088/0266-5611/26/11/115013

GMIG Report 09-04: Nowack, R.L. 'Dynamically focused Gaussian beams for seismic imaging', Int. J. Geophys. 2011 (2011) doi:10.1155/2011/316581

GMIG Report 09-03: Nowack, R.L. 'A tale of two beams: Gaussian beams and Bessel beams', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2009) pp. 49-58

GMIG Report 09-02: Carlsson, M. 'AAK-Theory on weighted spaces', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2009) pp. 27-48

GMIG Report 09-01: Andersson, F., Carlsson, M., and De Hoop, M.V. 'Sparse approximations of functions using sums of exponentials', J. Approx. Theory 163 (2011) 213-248

2008

GMIG Report 08-12: Pyrak-Nolte, L.J., Nolte, D.D., Chen, D., and Giordano, N. 'Relating capillary pressure to interfacial areas', Water Resour. Res. 44 (2008) doi:10.1029/2007WR006434

GMIG Report 08-11: Acosta-Colon, A., Pyrak-Nolte, L.J., and Nolte, D.D. 'Laboratory-scale study of field of view and the seismic interpretation of fracture specific stiffness', Geophys. Prosp. 57 (2009) 209-224

GMIG Report 08-10: Sølna, K., and De Hoop, M.V. 'Estimating a Green's function from ''field-field'' correlations in a random medium', SIAM J. Appl. Math. 69 (2009) 909-932

GMIG Report 08-09: Malcolm, A.E., Ursin, B., and De Hoop, M.V. 'Seismic imaging and illumination with internal multiples', Geophys. J. Int. 176 (2009) 847-864

GMIG Report 08-08: Duchkov, A.A., and De Hoop, M.V. 'Velocity continuation in the downward continuation approach to seismic imaging', Geophys. J. Int. 176 (2009) 909-924
and:
Duchkov, A.A., and De Hoop, M.V. 'Extended isochron rays in prestack depth (map) migration', Geophysics 75 (4) (2010) S139-S150

GMIG Report 08-07: Nowack, R.L. 'Focused Gaussian beams for seismic imaging', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2008) pp. 129-139

GMIG Report 08-06: Nowack, R.L. 'Gaussian beam imaging for converted and surface reflected waves', Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2008) pp. 121-128

GMIG Report 08-05: Nowack, R.L. 'Frame-based Gaussian beam summation and seismic head waves',Proceedings of the Project Review, Geo-Mathematical Imaging Group, Purdue University, West Lafayette, IN (2008) pp. 113-119

GMIG Report 08-04: De Hoop, M.V., Smith, H. Uhlmann, G. and Van der Hilst, R.D. 'Seismic imaging with the generalized Radon transform: A curvelet transform perspective', Inverse Problems 25 (2009)doi:10.1088/0266-5611/25/2/025005

GMIG Report 08-03: Brytik, V., De Hoop, M.V., and Salo, M. 'Sensitivity analysis of wave-equation tomography: A multi-scale approach', J. Four. Anal. Appl. 16 (2010) 544-589

GMIG Report 08-02: Andersson, F., Carlsson, M. and De Hoop, M.V. 'Nonlinear approximation of functions in two dimensions by sums of exponential functions', Applied and Computational Harmonic Analysis 29 (2010) 156-181
and:
Andersson, F. and Carlsson, M., and De Hoop, M.V. 'Nonlinear approximation of functions in two dimensions by sums of wave packets', Applied and Computational Harmonic Analysis 29 (2010) 198-213

GMIG Report 08-01: Duchkov, A.A., Andersson, F., and De Hoop, M.V. 'Discrete, almost symmetric wave packets and multi-scale geometric representation of (seismic) waves', IEEE Trans. Geosc. and Remote Sensing 48 (2010) 3408-3423

2007

GMIG Report 07-01: Duchkov, A.A., De Hoop, M.V., and Sá Barreto, A.S. 'Evolution-equation approach to seismic image, and data, continuation', Wave Motion 45 (2008) 952-969