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Scholarly Interest Report
         
Maarten Valentijn de Hoop
Professor
Simons Chair in Computational and Applied Mathematics and Earth Science; Professor of Computational and Applied Mathematics and Professor of Earth, Environmental and Planetary Sciences
 
e-mail:mdehoop@rice.edu
 
  • B.Sc. Physics (1981) Utrecht University, Netherlands
  • Ph.D. Technical Sciences (1992) Delft University of Technology, Netherlands
  • M.Sc. Theoretical Physics (1984) Utrecht University, Netherlands
 
Primary Department
   Department of Computational and Applied Mathematics
   Department of Earth, Environmental & Planetary Sciences
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Department Affiliations
 
  • Department of Computational and Applied Mathematics
  • Department of Earth, Environmental & Planetary Sciences
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    Websites
     Maarten V. de Hoop
     Maarten V. de Hoop
     
    Research Areas
     (1) Scattering, imaging and inverse problems, theoretical and computational seismology, geodesy. (2) Multi-dimensional imaging, inverse scattering and tomography. (3) Nonlinear inverse boundary value problems: direct and iterative reconstruction; geometric inverse problems; inverse spectral problems; inverse problems with nonlinear wave interaction; coupled physics and hybrid inverse problems. (4) Deep learning and inverse problems. (5) Development of multiscale methods and nonlinear theories of generalized functions applied to scattering and inverse scattering in media of low regularity, and in highly discontinuous and random media. (6) Large-scale computational modeling of acoustic, elastic and electromagnetic wave phenomena in complex media, earthquakes, normal modes and fast iterative methods for nonlinear inverse problems; techniques from microlocal analysis and computational harmonic analysis, structured matrix based methods, and massively parallel algorithms.
     
    Teaching Areas
     Applied inverse problems, mathematical theory of seismology, applied microlocal analysis, advanced real analysis, advanced applied mathematics, theory of distributions for the graduate curriculum; calculus, differential equations, linear algebra, numerical analysis, partial differential equations for the undergraduate curriculum.
     
    Selected Publications
     Refereed articles
     

    M.V. de Hoop, P. Kepley and L. Oksanen "An exact redatuming procedure for the inverse boundary value problem for the wave equation." SIAM Journal on Scientific Computing, 78 (1) (2018) : 171-192.

     
     

    C. Yu, E.A. Day, M. V. de Hoop, M. Campillo, S. Goes, R.A. Blythe and R.D. van der Hilst "Mapping mantle transition zone discontinuities beneath the Central Pacific with array processing of SS precursors." Journal of Geophysical Research, 122 (12) (2017) : 10364-10378.

     
     

    C. Yu, E.A. Day, M. Campillo, S. Goes, R.A. Blythe, M. V. de Hoop and R.D. van der Hilst "Compositional heterogeneity near the base of the mantle transition zone beneath Hawaii." Submitted

     
     

    E. Beretta, M. V. de Hoop, E. Francini, S. Vessella and J. Zhai "Uniqueness and Lipschitz stability of an inverse boundary value problem for time harmonic elastic waves." Inverse Problems, 33(3) (2017) : 035013.

     
     

    E. Beretta, M. V. de Hoop, F. Faucher and O. Scherzer. "Inverse boundary value problem for the Helmholtz equation: Quantitative conditional Lipschitz stability estimates." SIAM Journal on Mathematical Analysis, 48(6) (2016) : 3962-3983.

     
     

    G. Alessandrini, M. V. de Hoop, R. Gaburro and E. Sincich "EIT in a layered anisotropic medium." Inverse Problems and Imaging (2018) Accepted

     
     

    G. Alessandrini, M. V. de Hoop, R. Gaburro and E. Sincich. "Lipschitz stability for the electrostatic inverse boundary value problem with piecewise linear conductivities." Journal de Mathématiques Pures et Appliquées, 107(5) (2017) : 638-633.

     
     

    G. Alessandrini, M. V. de Hoop. R. Gaburro and E. Sincich. "Lipschitz stability for a piecewise linear Schrödinger potential from local Cauchy data." Asymptotic AnalysisAccepted

     
     

    G. Alessandrini, M.V. de Hoop and R. Gaburro "Uniqueness for the electrostatic inverse boundary value problem with piecewise constant anisotropic conductivities." Inverse Problems, 33 (2017)

     
     

    J. Chen and M. V. de Hoop "The inverse problem for electroseismic conversion: Stable recovery of the conductivity and the electrokinetic mobility parameter." Inverse Problems and Imaging, 10(3) (2016) : 641-658.

     
     

    J. Shi, E. Beretta, E. Francini, M. V. de Hoop and S. Vessella "Multi-parameter iterative reconstruction with the multi-frequency Neumann-to-Dirichlet map for elastic waves as the data." Submitted

     
     

    K. Brazda, M. V. de Hoop and G. Hormann. "Variational formulation of Earth’s elasto-gravitational deformations under low regularity conditions’." Submitted

     
     

    M. Berra, M. V. de Hoop and J.L. Romero "A multi-scale Gaussian beam parametrix for the wave equation: The Dirichlet boundary value problem." Submitted

     
     

    M. V de Hoop, P. Kepley, and L. Oksanen "Recovery of a smooth metric via wave field and coordinate transformation reconstruction." Submitted

     
     

    M. V. de Hoop and J. Ilmavirta "Abel transforms with low regularity with applications to X-ray tomography on spherically symmetric manifolds." Inverse Problems, 33 (2017)

     
     

    M. V. de Hoop, G. Nakamura and J. Zhai "Reconstruction of Lamé moduli and density at the boundary enabling directional elastic wavefield decomposition." SIAM Journal on Applied Mathematics, 77(2) (2017) : 520-536.

     
     

    M. V. de Hoop, G. Uhlmann and Y. Wang "Nonlinear responses from the interaction of two progressing waves at an interface." Submitted

     
     

    M. V. de Hoop, J. Garnier and K. Sølna. "Global acoustic daylight imaging in a stratified earth-like model." Inverse Problems, 33 (2017)

     
     

    M. V. de Hoop, J. Ilmavirta and V. Katsnelson "Spectral rigidity for spherically symmetric manifolds with boundary." Submitted

     
     

    M. V. de Hoop, L. Oksanen and J. Tittelfitz "Uniqueness for a seismic inverse source problem modeling a subsonic rupture." Communications in Partial Differential Equations , 41(12) (2016) : 1895-1917.

     
     

    M. V. de Hoop. A. Iantchenko, G. Nakamura, and J. Zhai "Semiclassical analysis of elastic surface waves." Submitted

     
     

    M.V. de Hoop, S.F. Holman and H. Pham "On the system of elastic-gravitational equations describing the oscillations of the earth." Submitted

     
     

    P. Caday, M. V. de Hoop, V. Katsnelson and G. Uhlmann "Scattering control for the wave equation with unknown wavespeed." Submitted

     
     

    P. Caday, V. Katsnelson, M. V. de Hoop and G. Uhlmann "Reconstruction of piecewise smooth wave speeds using multiple scattering." Submitted

     
     

    P. Poli, M. Campillo and M. V. de Hoop "Analysis of intermediate period correlations of coda from deep earthquakes." Earth and Planetary Science Letters, 477 (2017) : 147-155.

     
     

    R. Ye, M. V. de Hoop, C.L. Petrovitch, L.J. Pyrak-Nolte and L.C. Wilcox "A Discontinuous Galerkin method with a modified penalty flux for the propagation and scattering of acousto-elastic waves." Geophysical Journal International, 205(2) (2016) : 1267-1289.

     
     

    X. Liu, J. Xia and M. V. de Hoop "Interconnected hierarchical rank-structured methods for directly solving and preconditioning the Helmholtz equation." Submitted

     
     

    X. Liu, J. Xia and M. V. de Hoop "Parallel randomized and matrix-free direct solvers for large structured dense linear systems." SIAM Journal on Scientific Computing, 38(5) (2016) : S508-S538.

     
     

    X. Shang, M. V. de Hoop and R.D. van der Hilst "Common conversion point stacking of receiver functions versus passive source reverse time migration and wavefield regularization." Geophysical Journal International, 209(2) (2017) : 923-934.

     
     

    Z. Xin, J. Xia, M. V. de Hoop, S. Cauley, and V. Balakrishnan "A distributed-memory randomized structured multifrontal method for sparse direct solutions." SIAM Journal on Scientific Computing, 39(4) (2017) : C292-C318.

     
     

    K. Datchev and M. V. de Hoop "Iterative reconstruction of the wave speed for the wave equation with bounded frequency boundary data." Inverse Problems, 32 (2016) : 025008.

     
     

    M. V. de Hoop, M. Lassas, M. Santacesaria, S. Siltanen and J.P. Tamminen "Positive-energy D-bar method for acoustic tomography: A computational study." Inverse Problems, 32(2) (2016) : 025003.

     
     

    M.V. de Hoop and J. Chen "The inverse problem for electroseismic conversion: Stable recovery of the conductivity and the electrokinetic mobility parameter." Inverse Problems and Imaging, 10 (3) (2016) : 641-658.

     
     

    M.V. de Hoop, L. Oksanen and J. Tittelfitz "Uniqueness for a seismic inverse source problem modeling a subsonic rupture." Communications in Partial Differential Equations, 41 (12) (2016) : 1895-1917.

     
     

    M.V. de Hoop, P. Kepley and L. Oksanen "On the construction of virtual interior point-source traveltime distances from the hyperbolic Neumann-to-Dirichlet map." SIAM J. Appl. Math, 76 (2) (2016) : 805-825.

     
     

    M.V. de Hoop, X. Liu and J. Xia "Parallel randomized and matrix-free direct solvers for large structured dense linear systems." SIAM Journal on Scientific Computing, 38 (5) (2016) : S508-S538.

     
     

    S. Wang, X.S. Li, F.H. Rouet, J. Xia and M. V. de Hoop "A parallel geometric multifrontal solver using hierarchically semiseparable structure." ACM Transactions on Mathematical Software, 42(3) (2016)

     
     

    V. Albani, P. Elbau, M. V. de Hoop and O. Scherzer "Optimal convergence rates results for linear inverse problems in Hilbert spaces." Numerical Functional Analysis and Optimization, 37 (2016) : 521-540.

     
     

    E. Beretta, Maarten V. de Hoop, E. Francini and S. Vessella "Stable determination of polyhedral interfaces from boundary data for the Helmholtz equation." Comm. Partial Differential Equations, 40 (2015) : 1365-1392.

     
     

    F. Andersson, M.V. de Hoop, and H. Wendt "Multi-scale reverse-time-migration-type imaging using the dyadic parabolic decomposition of phase space." SIAM Imaging , 8 (2015) : 2383-2411.

     
     

    M.V. de Hoop and J. Tittelfitz "An inverse source problem for a variable speed wave equation with discrete-in-time sources." Inverse Problems, 31 (2015) : 075007.

     
     

    M.V. de Hoop, G. Uhlmann and A. Vásy "Diffraction from conormal singularities." Annales Scientifiques de l’ENS serie 4, 48 (2015) : 351-408.

     
     

    M.V. de Hoop, L. Qiu. and O. Scherzer "An analysis of a multi-level projected steepest descent iteration for nonlinear inverse problems in Banach spaces subject to stability constraints." Numerische Mathematik, 129 (2015) : 127-148.

     
     

    M.V. de Hoop, S.F. Holman, E. Iversen, M. Lassas and B. Ursin "Recovering the isometry type of a Riemannian manifold from local boundary diffraction travel times." Journal de Mathématiques Pures et Appliquées, 103 (2015) : 830-848.

     
     

    R. Andreev, P. Elbau, M.V. de Hoop, L. Qiu and O. Scherzer "Generalized convergence rates results for linear inverse problems in Hilbert spaces." Numerical Functional Analysis and Optimization, 36 (2015) : 549-566.

     
    Presentations
     Conference Paper
     

    "Controlling multiple scattering without knowing the wavespeed in bounded domans containing co-normal sungularities’, Applied Inverse Problems Conference, Hangzhou." (2 Jun - 29 May, 2017)

     
     Invited Talks
     

    "Can we solve the seismic inverse problem?." Department of Mathematics, University of Texas at Austin. (1 Feb, 2017)

     
     

    "Frame-based multi-scale Gaussian beams, wavefield approximation and boundary value problems." CIMPA 2017 Research School on Harmonic Analysis, Geometric Measure Theory and Applications, Buenos Aires, Argentina. (7 Aug, 2017)

     
     

    "Scattering control and inverse problem for the wave equation with piecewise smooth wave speed ." Mathematisches Forschungsinstitut Oberwolfach (MFO) Workshop on Computational Inverse Problems for Partial Differential Equations, Oberwolfach, Germany. (14-20 May, 2017)

     
     

    "Scattering control and inverse problem for the wave equation with piecewise smooth wavespeeds." Institute for Pure and Applied Mathematics Workshop II: Full Waveform Inversion and Velocity Analysis, University of California, Los Angeles. (1-5 May, 2017)

     
     

    "Scattering control without knowing the wave speed – inverse problem for the wave equation with piecewise smooth wave speeds." Cargèse International School on Ambient Noise Imaging and Monitoring, Cargèse, France. (5-9 June, 2017)

     
     

    "‘Controlling multiple scattering in wavefields without knowing the wavespeed in bounded domains containing conormal singularities’, LIASFMA Workshop on Control and Inverse Problems for Partial Differential Equations ." Zhejiang University, Hangzhou, China.

     
     

    "‘Dirichlet-to-Neumann maps in geophysics and inverse problems’, Dirichlet-to-Neumann Maps: Spectral Theory, Inverse Problems and Applications (Casa Matem´atica Oaxaca - Banff International Research Station, Oaxaca, Mexico)."

     
     

    "‘Frame-based multi-scale Gaussian beams, wavefield approximation and boundary value problems’, Sparse Interpolation, Rational Approximation and Exponential Analysis." Casa Matem´atica Oaxaca - Banff International Research Station, Oaxaca, Mexico.

     
     

    "‘Inverse problems in seismology with a view to the mantle’, Melt in the Mantle (Isaac Newton Institute for Mathematical Sciences, Cambridge, England)."

     
     

    "‘Scatterign control for the wave equation with an unkown wavespeed containing conormal singularities’, Workshop on Inverse Problems, Imaging and PDEs." Jockey Club Institute for Advanced Study, HKUST, Hong Kong.

     
     

    "‘Seismic inverse problems: Iterative reconstruction with bounded frequency boundary data’, Computational Seismology Workshop (Tsinghua Sanya International Mathematics Forum, Sanya, China)."

     
     

    "Inverse Problems in Exploration and Global Seismology." Computer, Electrical and Mathematical Science and Engineering Division, KAUST, Saudi Arabia. (November)

     
     

    "Seismic inverse problems: Revealing Earth’s interior." Lagrange Lecture, Dipartimento di Matematica “Giuseppe Peano”, Universtit`a degli Studi di Torino, Turin, Italy. (February)

     
     

    "‘Seismic applications – Parallel randomized structured direct solvers for multi-frequency full waveform inversion’, Second EAGE Workshop on High Performance Computing for Upstream (Dubai, UAE)."

     
     

    "‘Uniqueness of seismic inverse source problems modelling microseismicity and ruptures’, Workshop on Inverse Problems, Imaging and PDEs (Jockey Club Institute for Advanced Study, HKUST, Hong Kong)."

     
     

    "Construction of high-frequency direct waves generated by interior point sources from the Neumann-to-Dirichlet map’, Passive Imaging and Monitoring in Wave Physics (Institut d’Etudes Scientifiques de Carg`ese, Carg`ese, Corsica, France)."

     
     

    "Full waveform inversion: Iterative regularization and convergence’, Lofoten Seminar at Spitsbergen ." Longyearbyen, Svalbard.

     
     

    "Seismic inverse problems." IMPACT Distinguished Lecture, School of Mathematics, Georgia Institute of Technology, Atlanta, GA. (October)

     
     

    "The seismic inverse problem: Stability and reconstruction." Mathematics Program, New York University Abu Dhabi, Abu Dhabi, UAE.

     
     

    "Uniqueness of seismic inverse source problems modeling microseismicity and ruptures and Construction of high-frequency direct waves generated by virtual interior point sources from the Neumann-to-Dirichlet map." Dipartimento di Matematica e Geoscienze, Sezione di Matematica e Informatica, Universtit`a degli Studi di Trieste, Trieste, Italy.

     
     Other
     

    "Nonlinear responses from the interaction of two progressing waves at an interface and corresponding inverse problems." Mathias Total 2017 Conference, Paris, France. (26 Oct, 2017)

     
     

    "Research program of the Geo-Mathematical Imaging Group." ConocoPhillips, Houston. (2 Nov, 2017)

     
     

    "Research program of the Geo-Mathematical Imaging Group." NASA Astromaterials Research & Exploration Science Division, Johnson Space Centre, France. (29 Nov, 2017)

     
     Seminar Speaker
     

    "On the spectrum of the earth." Séminaire Problèmes Inverses I, Laboratoire Jean Kuntzmann, Université Grenoble-Alpes, France. (21 Dec, 2017)

     
     

    "On the spectrum of the earth." Department of Mathematics, University of Washington, Seattle. (8 May, 2017)

     
    Editorial Positions
     Member of the Editorial Board, Journal of Pseudodifferential Operators and Applications. (2017 - 2018)

     Member of the Editorial Board, Inverse Problems. (2000 - 2003)

     Member of the Editorial Board, Inverse Problems. (2017 - 2018)

    Awards, Prizes, & Fellowships
     Fellow of the Institute of Physics (IOP), (2001)

    Positions Held
     Visiting Professor, Massachusetts Institute of Technology, Department of Earth, Atmospheric and Planetary Sciences. (2017 - 2018)

     Visiting Professor, Chinese Academy of Sciences, Graduate University. (2017 - 2018)