Inversion and imaging with waves is of fundamental importance in both radar and seismic reconstruction. Mathematics provides the key technology in both areas and, despite differing in many important respects, they have much in common in their underlying mathematical frameworks, approaches, and challenges. This semester program will focus on advancing their common mathematical and computational methodologies, as well as selected subjects distinct to each area, in the context of new challenges and opportunities that have arisen in recent years. Both theory and applications will be of interest. Participants will be drawn from academia, industry, and governmental laboratories in order to broadly address theory, applications, and their synergy.
The program will be influenced by recent developments in wave propagation and imaging, data acquisition and analysis, and high-performance computing. Driven by the ongoing need for more realistic mathematical models and simulations, recent advances in wave propagation and imaging in complex media are increasingly convincing and competitive but present new challenges. New sensor technologies have led to new types of data that can be collected, as well as to unprecedented volumes of data. This wealth of data offers new potential for gaining insights but also poses new needs for large-scale data-analysis algorithms that can effectively exploit advances in computing.
There is an outstanding opportunity to build on these developments and to bring the field to new levels of realistic inversion scenarios and problem scales. Topics to be considered in the semester program include wave propagation, inversion, and imaging in random media; statistical aspects of inverse problems, including homogenization and uncertainty quantification; optimization methods for inversion and imaging; large-scale computation and inverse problems, including methods for model reduction and large-scale optimization; and subjects of particular interest in radar reconstruction or in seismic inversion.
Synthetic aperture radar (SAR) image of Shenandoah National Park, Virginia, shaded relief colored by elevation, Shuttle Radar Topography Mission. Image credit: NASA/JPL.
Seismic image of thrust and fold structural geometry offshore Namibia. Image credit: Rob Butler, Virtual Seismic Atlas.
Loading...
Loading participant list in background...
Publications
Jacob Lange, Richard O'Shaughnessy, Kevin Barkett, Vijay Varma, Scott Field, Reassessment of GW170817 and GW190425 using higher order mode models, APS April Meeting Abstracts, APS Meeting Abstracts, vol. 2022, 2022, pp. D17.007.
Liliana Borcea, Josselin Garnier, Alexander V. Mamonov, Jörn Zimmerling, Waveform inversion via reduced order modeling, borcea2022waveform:2202.01824, 2022.
L Borcea, V Druskin, A Mamonov, S Moskow, M Zaslavsky, Reduced order models for spectral domain inversion: embedding into the continuous problem and generation of internal data, Inverse Problems 36 (2020) no. 5, 055010.
Liliana Borcea, Vladimir Druskin, Alexander V. Mamonov, Mikhail Zaslavsky, Jörn Zimmerling, Reduced Order Model Approach to Inverse Scattering, borcea2020reduced:1910.13014, 2020.
Liliana Borcea, Josselin Garnier, Alexander V Mamonov, Jörn Zimmerling, Reduced order model approach for imaging with waves, Inverse Problems 38 (2021) no. 2, 025004.
Liliana Borcea, Vladimir Druskin, Jörn Zimmerling, A reduced order model approach to inverse scattering in lossy layered media, borcea2021reduced:2012.00861, 2021.
Liliana Borcea, Fioralba Cakoni, Shixu Meng, A direct approach to imaging in a waveguide with perturbed geometry, Journal of Computational Physics 392 (2019), 556–577.
Wei Li, John C Schotland, Yang Yang, Yimin Zhong, Inverse Source Problem for Acoustically-Modulated Electromagnetic Waves, arXiv preprint arXiv:2202.11888 (2022).
Mikhail Gilman, Semyon Tsynkov, Polarimetric radar interferometry in the presence of differential Faraday rotation, Inverse Problems 38 (2022) no. 4, 045010.
Wei Li, Yang Yang, Yimin Zhong, Inverse transport problem in fluorescence ultrasound modulated optical tomography with angularly averaged measurements, Inverse Problems 36 (2020) no. 2, 025011.
Mengmeng Yang, Marie Graff, Rajiv Kumar, Felix J Herrmann, Low-rank representation of omnidirectional subsurface extended image volumes, Geophysics 86 (2021) no. 3, S165-S183.
Raluca Felea, Romina Gaburro, Allan Greenleaf, Clifford Nolan, Microlocal analysis of borehole seismic data, arXiv preprint arXiv:2110.01682 (2021).
Raluca Felea, and Romina Gaburro, Allan Greenleaf, Clifford Nolan, and, Microlocal analysis of Doppler synthetic aperture radar, Inverse Problems {\&}amp$\mathsemicolon$ Imaging 13 (2019) no. 6, 1283-1307.
Ali M Alfaraj, Eric Verschuur, Felix J Herrmann, Non-surface-consistent short-wavelength statics correction for dense and subsampled data: A rank-based approach, SEG Technical Program Expanded Abstracts 2020, Society of Exploration Geophysicists, 2020, pp. 2784-2788.
Reza Mollapourasl, Majid Haghi, Alfa Heryudono, Numerical Simulation and Applications of the Convection--Diffusion--Reaction Equation with the Radial Basis Function in a Finite-Difference Mode, Journal of Computational Finance 23 (2020) no. 5.
Gabriel Parrish, Jan MH Hendrickx, Fred M Phillips, Daniel Cadol, Brian Borchers, Parameterizing the Root Zone Soil Water Holding Capacity for a Soil Water Balance Model in Water-Limited Ecosystems of New Mexico., AGU Fall Meeting Abstracts, vol. 2019, 2019, pp. H33H-2011.
Mikhail Gilman, Semyon Tsynkov, Cross-channel contamination of PolSAR images due to frequency dependence of Faraday rotation angle, 2018 IEEE Conference on Antenna Measurements \& Applications (CAMA), IEEE, 2018, pp. 1-4.
Jonathan Popa, Susan E Minkoff, Yifei Lou, Improving seismic data completion via low-rank tensor optimization, SEG International Exposition and Annual Meeting, OnePetro, 2020.
Jonathan Popa, Susan Minkoff, Yifei Lou, Improving seismic data completion and efficiency using tensors, SEG International Exposition and Annual Meeting, OnePetro, 2019.
Miguel Moscoso, Alexei Novikov, George Papanicolaou, Chrysoula Tsogka, Imaging with highly incomplete and corrupted data, Inverse Problems 36 (2020) no. 3, 035010.
Symeon Papadimitropoulos, Dimitrios A Mitsoudis, Chrysoula Tsogka, Imaging in three-dimensional waveguides with partial aperture data, Journal of Theoretical and Computational Acoustics 29 (2021) no. 03, 2050018.
Mikhail Gilman, Semyon Tsynkov, Divergence measures and detection performance for dispersive targets in SAR, Radio Science 56 (2021) no. 1, 1-17.
Vladimir Druskin, Alexander V Mamonov, Mikhail Zaslavsky, Distance preserving model order reduction of graph-Laplacians and cluster analysis, Journal of Scientific Computing 90 (2022) no. 1, 1-30.
Mikhail Gilman, Semyon Tsynkov, Differential Faraday rotation and polarimetric SAR, SIAM Journal on Applied Mathematics 78 (2018) no. 3, 1422-1449.
Mikhail Gilman, Semyon Tsynkov, Detection of delayed target response in SAR, Inverse Problems 35 (2019) no. 8, 085005.
John Lagergren, Kevin Flores, Mikhail Gilman, Semyon Tsynkov, Deep learning approach to the detection of scattering delay in radar images, Journal of Statistical Theory and Practice 15 (2021) no. 1, 1-19.
Wen Ding, Kui Ren, Lu Zhang, Coupling Deep Learning with Full Waveform Inversion, arXiv preprint arXiv:2203.01799 (2022).
Kui Ren, Yimin Zhong, Unique determination of absorption coefficients in a semilinear transport equation, SIAM Journal on Mathematical Analysis 53 (2021) no. 5, 5158-5184.
Liliana Borcea, Josselin Garnier, Alexander V Mamonov, J{\"o}rn Zimmerling, Waveform inversion via reduced order modeling, arXiv preprint arXiv:2202.01824 (2022).
Alexander V Mamonov, Liliana Borcea, Josselin Garnier, J{\"o}rn Zimmerling, Velocity estimation via model order reduction, SEG/AAPG International Meeting for Applied Geoscience \& Energy, OnePetro, 2022.
Liliana Borcea, Vladimir Druskin, A Mamonov, Shari Moskow, Mikhail Zaslavsky, Reduced order models for spectral domain inversion: embedding into the continuous problem and generation of internal data, Inverse Problems 36 (2020) no. 5, 055010.
Liliana Borcea, Vladimir Druskin, Alexander V Mamonov, Mikhail Zaslavsky, Jörn Zimmerling, Reduced order model approach to inverse scattering, SIAM Journal on Imaging Sciences 13 (2020) no. 2, 685-723.
Liliana Borcea, Josselin Garnier, Alexander V Mamonov, J{\"o}rn Zimmerling, Reduced order model approach for imaging with waves, Inverse Problems 38 (2021) no. 2, 025004.
Liliana Borcea, Shixu Meng, Factorization method versus migration imaging in a waveguide, Inverse Problems 35 (2019) no. 12, 124006.
Liliana Borcea, Vladimir Druskin, J{\"o}rn Zimmerling, A reduced order model approach to inverse scattering in lossy layered media, Journal of Scientific Computing 89 (2021) no. 1, 1-36.
Yijun Zhang, Shashin Sharan, Oscar Lopez, Felix J Herrmann, Wavefield recovery with limited-subspace weighted matrix factorizations, SEG International Exposition and Annual Meeting, OnePetro, 2020.
Gabriel Kropf, Chlo{\"e} Bonamici, Brian Borchers, Updating the Fast Grain Boundary program: Temperature-time paths from intragrain oxygen isotope zoning, Computers \& Geosciences 151 (2021), 104753.
Mario J Bencomo, William W Symes, Preconditioner for estimation of multipole sources via full waveform inversion, Journal of Computational Physics 419 (2020), 109667.
Ratan Mani Prasad, Santimoy Kundu, Torsional surface wave dispersion in pre-stressed dry sandy layer over a gravitating anisotropic porous half-space, ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift f{\"u}r Angewandte Mathematik und Mechanik 97 (2017) no. 5, 550-560.
Chloe E Bonamici, Gabriel Kropf, Brian Borchers, Gabriel Parrish, Time-temperature paths from intragrain oxygen isotope zoning, AGU 2019 Fall Meeting, 2019.
Jonathan Popa, Susan E Minkoff, Yifei Lou, Tensor-based reconstruction applied to regularized time-lapse data, Geophysical Journal International 231 (2022) no. 1, 638-649.
Polina Zheglova, Matteo Ravasi, Ivan Vasconcelos, Alison Malcolm, Target-enclosing inversion using an interferometric objective function, Geophysical Journal International 232 (2023) no. 1, 37-52.
Semyon V Tsynkov, Mikhail Gilman, Synthetic Aperture Radar Imaging through a Turbulent Ionosphere, 2021 Joint Mathematics Meetings (JMM), AMS, 2021.
Miguel Moscoso, Alexei Novikov, George Papanicolaou, Chrysoula Tsogka, Synthetic aperture imaging with intensity-only data, IEEE Transactions on Computational Imaging 6 (2019), 87-94.
Mikhail Gilman, Semyon Tsynkov, Statistical characterization of scattering delay in synthetic aperture radar imaging, arXiv preprint arXiv:1908.08124 (2019).
Alec Yonika, Alfa Heryudono, Gaurav Khanna, Space-time collocation method: Loop quantum Hamiltonian constraints, International Journal of Modern Physics C 31 (2020) no. 11, 2050166.
Ali M Alfaraj, Eric Verschuur, Felix J Herrmann, Residual statics correction without NMO—A rank-based approach, First International Meeting for Applied Geoscience \& Energy, Society of Exploration Geophysicists, 2021, pp. 2565-2569.
Jonathan Popa, Susan E Minkoff, Yifei Lou, An improved seismic data completion algorithm using low-rank tensor optimization: Cost reduction and optimal data orientation, Geophysics 86 (2021) no. 3, V219-V232.
Wei Li, John C Schotland, Yang Yang, Yimin Zhong, An Acousto-electric Inverse Source Problem, SIAM Journal on Imaging Sciences 14 (2021) no. 4, 1601-1616.
Alfa Heryudono, Mehdi Raessi, Adaptive Partition of Unity Interpolation Method with Moving Patches, arXiv preprint arXiv:2207.09614 (2022).
Bojan B Guzina, Shixu Meng, Othman Oudghiri-Idrissi, A rational framework for dynamic homogenization at finite wavelengths and frequencies, Proceedings of the Royal Society A 475 (2019) no. 2223, 20180547.
Curt Da Silva, Yiming Zhang, Rajiv Kumar, Felix J Herrmann, Applications of low-rank compressed seismic data to full-waveform inversion and extended image volumes, Geophysics 84 (2019) no. 3, R371-R383.
Yijun Zhang, Felix J Herrmann, A practical workflow for land seismic wavefield recovery with weighted matrix factorization, SEG/AAPG/SEPM First International Meeting for Applied Geoscience \& Energy, OnePetro, 2021.
Mikhail Gilman, Semyon Tsynkov, A mathematical perspective on radar interferometry, Inverse Problems \& Imaging 16 (2022) no. 1, 119.
Igor Tominec, Elisabeth Larsson, Alfa Heryudono, A least squares radial basis function finite difference method with improved stability properties, SIAM Journal on Scientific Computing 43 (2021) no. 2, A1441-A1471.
Wei Li, Yang Yang, Yimin Zhong, A hybrid inverse problem in the fluorescence ultrasound modulated optical tomography in the diffusive regime, SIAM Journal on Applied Mathematics 79 (2019) no. 1, 356-376.
Liliana Borcea, Fioralba Cakoni, Shixu Meng, A direct approach to imaging in a waveguide with perturbed geometry, Journal of Computational Physics 392 (2019), 556-577.
Jia Shi, Elena Beretta, Maarten de Hoop, Elisa Francini, Sergio Vessella, A numerical study of multi-parameter full waveform inversion with iterative regularization using multi-frequency vibroseis data, Computational Geosciences 24 (2020).
Mario Bencomo, William Symes, Discretization of Multipole Sources in a Finite Difference Setting for Wave Propagation Problems, Journal of Computational Physics 386 (2019).
Hui Guo, Yang Yang, Bound-Preserving Discontinuous Galerkin Method for Compressible Miscible Displacement in Porous Media, SIAM J. Sci. Comput. 39 (2017).
Shujuan Mao, Michel Campillo, Robert van der Hilst, Florent Brenguier, Laurent Stehly, Gregor Hillers, High Temporal Resolution Monitoring of Small Variations in Crustal Strain by Dense Seismic Arrays, Geophysical Research Letters 46 (2018).
Chrysoula Tsogka, D. Mitsoudis, Symeon Papadimitropoulos, Imaging Extended Reflectors in a Terminating Waveguide, SIAM Journal on Imaging Sciences 11 (2017).
Kui Ren, Yimin Zhong, Imaging point sources in heterogeneous environments, Inverse Problems 35 (2019).
Josselin Garnier, Knut Sølna, Imaging through a scattering medium by speckle intensity correlations, Inverse Problems 34 (2018).
Li Wei, Yang Yang, Yimin Zhong, Inverse transport problem in fluorescence ultrasound modulated optical tomography with angularly averaged measurements, Inverse Problems 36 (2019).
Thibaud Blondel, J. Chaput, Derode Arnaud, Michel Campillo, Alexandre Aubry, Matrix Approach of Seismic Imaging: Application to the Erebus Volcano, Antarctica, Journal of Geophysical Research: Solid Earth 123 (2018).
Polina Zheglova, S.M. Akrami, Alison Malcolm, Developments in Vector Acoustic Full Waveform Inversion, 2018.
Mikhail Gilman, Semyon Tsynkov, Detection of delayed target response in SAR, Inverse Problems 35 (2019) no. 8, 085005.
Elena Beretta, Maarten V. de Hoop, Elisa Francini, Sergio Vessella, Jian Zhai, Uniqueness and Lipschitz stability of an inverse boundary value problem for time-harmonic elastic waves, arXiv: Analysis of PDEs (2014).
Chunquan Yu, Elizabeth Day, Maarten de Hoop, Michel Campillo, S. Goes, Rachel Blythe, Robert van der Hilst, Compositional heterogeneity near the base of the mantle transition zone beneath Hawaii, Nature communications 9 (2018), 1266.
Mario J. Bencomo, William W. Symes, Preconditioner for estimation of multipole sources via full waveform inversion, Journal of Computational Physics 419 (2020), 109667.
Andrea Aspri, Elena Beretta, Anna L. Mazzucato, Maarten V. De Hoop, Analysis of a Model of Elastic Dislocations in Geophysics, Archive for Rational Mechanics and Analysis 236 (2019) no. 1, 71–111.
Herurisa Rusmanugroho, Alison Malcolm, Meghdad Darijani, A numerical modeling of how cracks influence the nonlinear interactions of P- and S-waves, 2018, pp. 3828-3832.
Herurisa Rusmanugroho, Alison Malcolm, Meghdad Darijani, A numerical model for the nonlinear interaction of elastic waves with cracks, Wave Motion 92 (2019), 102444.
Wei Li, Yang Yang, Yimin Zhong, A Hybrid Inverse Problem in the Fluorescence Ultrasound Modulated Optical Tomography in the Diffusive Regime, SIAM J. Appl. Math. 79 (2019), 356-376.
Hongkai Zhao, Yimin Zhong, A Hybrid Adaptive Phase Space Method for Reflection Traveltime Tomography, SIAM J. Imaging Sci. 12 (2019), 28-53.
Gerrit Olivier, J. Chaput, Brian Borchers, Using Supervised Machine Learning to Improve Active Source Signal Retrieval, Seismological Research Letters 89 (2018).
Maria Kotsi, Alison Malcolm, Gregory Ely, 4D Full-Waveform Metropolis Hastings Inversion Using a Local Acoustic Solver, 2018.
Vladimir Druskin, Alexander V. Mamonov, Mikhail Zaslavsky, Distance preserving model order reduction of graph-Laplacians and cluster analysis., arXiv 1809.03048 (2020).
Miguel Moscoso, Alexei Novikov, George Papanicolaou, Chrysoula Tsogka, Data structures for robust multifrequency imaging, 2020.
Liliana Borcea, Josselin Garnier, Knut Sølna, Wave Propagation and Imaging in Moving Random Media, Multiscale Modeling & Simulation 17 (2019), 31-67.
Liliana Borcea, Vladimir Druskin, Alexander Mamonov, Mikhail Zaslavsky, Untangling nonlinearity in inverse scattering with data-driven reduced order models, Inverse Problems 34 (2017).
Liliana Borcea, Vladimir Druskin, Alexander Mamonov, Mikhail Zaslavsky, Robust nonlinear processing of active array data in inverse scattering via truncated reduced order models, Journal of Computational Physics 381 (2019).
Liliana Borcea, Vladimir Druskin, Alexander Mamonov, Shari Moskow, Mikhail Zaslavsky, Reduced order models for spectral domain inversion: embedding into the continuous problem and generation of internal data, Inverse Problems 36 (2020).
Liliana Borcea, Vladimir Druskin, Alexander Mamonov, Mikhail Zaslavsky, Jörn Zimmerling, Reduced Order Model Approach to Inverse Scattering, SIAM Journal on Imaging Sciences 13 (2020), 685-723.
Christophe Gomez, Knut Sølna, Wave Propagation in Random Waveguides with Long-Range Correlations, Communications in Mathematical Sciences 16 (2015).
Evren Yarman, Margaret Cheney, MIMO-SAR Imaging and Waveform Design, 2018, pp. 1-5.
Ruichao Ye, Maarten de Hoop, Kundan Kumar, Michel Campillo, The impacts of material and geometrical heterogeneities on the simulation of rate and state dependent ruptures, 2018, pp. 3823-3827.
Baptiste Rousset, Roland Burgmann, Michel Campillo, Slow slip events in the roots of the San Andreas fault, Science Advances 5 (2019).
Miguel Moscoso, Alexei Novikov, George Papanicolaou, Chrysoula Tsogka, Robust multifrequency imaging with MUSIC, Inverse Problems 35 (2018).
Raju Kumhar, Santimoy Kundu, Chandani Kumari, Propagation of torsional wave at a corrugated interface between viscoelastic sandy medium and inhomogeneous half-space, 2019, pp. 020012.
Jia Shi, Elena Beretta, Maarten de Hoop, Elisa Francini, Sergio Vessella, A numerical study of multi-parameter full waveform inversion with iterative regularization using multi-frequency vibroseis data, Computational Geosciences 24 (2020).
Josselin Garnier, Knut Sølna, Noninvasive Imaging Through Random Media, SIAM Journal on Applied Mathematics 78 (2018).
Christophe Gomez, Olivier Pinaud, Monte Carlo Methods for Radiative Transfer with Singular Kernels, SIAM Journal on Scientific Computing 40 (2018), A1714-A1741.
