Full-Waveform Inversion with Gauss- Newton-Krylov Method
|
|
- Marylou Cain
- 6 years ago
- Views:
Transcription
1 Full-Waveform Inversion with Gauss- Newton-Krylov Method Yogi A. Erlangga and Felix J. Herrmann Seismic Laboratory for Imaging and Modeling The University of British Columbia (UBC), Vancouver The 79th SEG Meeting: SI3 Methods Houston, October 27, 29
2 Full-Waveform Inversion (FWI) Given experiment data P. With the misfit functional: E[m] = 1 2 P F[m] 2 2 Optimization Problem: Find ˆm = arg min m M E[m] subject to the (forward) modeling wavefields D receivers by. U F[m] = DU[m] restricted to the Lailly, 1983 Tarantola, 1984, 1986, 1987 Pratt and co-authors, 1996, 1998, 1999, 23
3 Frequency domain FWI Forward model: Helmholtz equation H[ω, m]u = Q, m = (m 1... m M ) T H : the Helmholtz matrix, function of angular freq ω Q = [q 1... q ns ] U = [u 1... u ns ] : the source matrix, with shots : the wavefield matrix n s
4 Impediments Fast, scalable solver for the forward and adjoint systems iterative method with Preconditioning with shifted Laplacian [E. et al. (26), Riyanti et al., (26)] Multilevel Krylov method [E. & Nabben (29), E. & Herrmann (28)] Multidimensional experiments (shots, frequencies): more data than model Data reduction via frequency subsampling [Sirgue & Pratt (24), Mulder & Plessix (24)] Compressive Sampling (CS) framework : data reduction via shot and frequency subsampling compressive wavefield computation [Lin, Herrmann (27), Herrmann, E. & Lin (29)] extension to compressive imaging Fast minimization solver (GN-type: Hessian) Gauss-Newton method with implicit computation of Hessian
5 Our solution Gauss-Newton with implicit Hessian (Gauss-Newton-Krylov, GNK) Dimensionality reduction [Herrmann, E. & Lin (29)] [Tim Lin: Compressive simultaneous full-waveform simulation, this meeting, SM1] Q = D HU = Q y = RMDU s }{{} single shots Q = D HU = Q y = DU RMs }{{} simul. shots FWI with CS
6 FWI with CS The misfit functional: E[m] = 1 2 RM(P F[m]) 2 2 with RM a CS-sampling matrix (reduces data size). Optimization Problem: Find ˆm = arg min m M E[m] subject to F[m] = DU[m]
7 Main contribution: [Hermann et al. (29), EAGE] See also: Krebs et al. (29), this meeting E[m] = 1 2 P F[m] 2 2 In line with this: Sampling of overdetermined systems [Drineas, Mahoney & Muthukhrisnan (26)] min E min E but is a bounded approximation.
8 Outline Newton method: Hessian Implicit computation of the GN Hessian Extension to CS framework Reduced numbers of shots and frequencies Examples related work: in time domain [Akcelic, Biros & Ghattas (22)] PDE-constrained optimization: KKT sytems, reduced systems, etc [Heinkenschloss (1991), Biros & Ghattas (25),...]
9 Newton Method E[m + δm] = E[m] + g T δm δmt Hδm m Initial model ; Update until convergence: δm = H 1 k 1 g k 1; m k = m k 1 + γ k 1 δm; with g k 1 g[m k 1 ] H k 1 H[m k 1 ] : the gradient, : the Hessian, γ k 1 : the step length.
10 H = [h i,j ] with ( ) E h i,j = m i m j ( 2 U = rowsum U m i m j m i Hessian: F m j ). Negative sign: not necessarily SP(S)D Fast/quadratic convergence only if close to the minimizer From the adjoint system: U m i V (back-propagated)
11 Gauss-Newton Method Simplify the Hessian by setting U m i nonlinear wave phenomena (e.g. multiples) F m j = Giving h GN i,j = rowsum ( 2 U m i m j ). This is associated with setting the back-propagated wavefield V = in the Hessian H GN = [h GN i,j ] is SP(S)D.
12 Inverting the Hessian: Krylov H GN k 1δm = g k 1 SP(S)D Hessian: compute Four important steps in CG: δm with Conjugate Gradient (CG). compute: w := H GN k 1p solution update: residual update: search dir. update: δm δm + αp r r αw p r + βw α, β : CG step lengths, satisfying orthogonal projection p δ 2 m m : second variation (of the Lagrangian) of.
13 Second variation system of GN - derived from second variations of the Lagrange minimization functional - detailed treatment in weak (bilinear) formulation, see the abstract. Forward model: H[m]Ũ = ω2 diag(p)u Ũ : second variation of U Adjoint system/back propagation: H[m]Ṽ = D DŨ Ṽ : the second variation of V The action of Hessian on p H GN p := ω 2 rowsum(u Ṽ)
14 FWI: Examples Marmousi model: 742 x 298 m, 372 x 15 gridpoints, 37 shots. Freqs: 3, 5, 9 Hz. 1 CG iters for the Hessian Hard model Smooth model
15 First Update (in δm ) Gradient Method GNK Note: different scale (by 1^3)
16 Velocity after the first update Gradient Method GNK
17 After 5 iterations Hard model Inverted Result
18 FWI with compressive simultaneous source (CFWI) Minimization problem: ˆm R = arg min m M 1 2 RM(P F) 2 2 RM : CS-sampling matrix turns single shots into randomized simultaneous shots subsamples the shots (fewer shots) and frequencies Simultaneous shots: Beasley, Chambers & Jiang (1998), Beasley (28) Berkhout (28) Neelamani, Krohn, Krebs, Deffenbaugh & Romberg (28) Herrmann, E. & Lin (29)
19 Gradient method of CFWI Minimize functional: E = 1 2 RM(P DU) 2 2 Gradient update: = 1 2 (RM(P DU))T RM(P DU) ( ) g R = rowsum J T (RM(P DU)) J J(RMDU) ( ) g R = rowsum J (RM(P DU)) with the Jacobian.
20 Using wavefield-source equivalence [Herrmann, E., & Lin, 29] Gradient update with J J(DU) : the (compressed) Jacobian w.r.t. to the compressed simultaneous sources P δm = g = J T (P DU) : data obtained with simultaneous shot
21 Computing the Jacobian Compressed forward model: U m i = H 1 H m i U. δm = rowsum [ U T H T... HT m 1 m M HU = Q {}}{ H T (P DU) ] V V : backpropagated wavefield ass. with Q = RMQ. The GN Hessian can be derived in the similar way!
22 Complexity Analysis Gauss-Newton-Krylov (GNK) Gradient : forward + back-propagation n f n s n 2 log n Hessian : forward + back-propagation per CG iteration n CG n f n s n 2 log n Overall : Compressive FWI with GNK: n CG n f n s n 2 log n n CG n f n sn 2 log n n f n f, n s n s Construction of RM negligible compared to FWI
23 CFWI: Examples, GNK Iter #1 9% subsampled 37 randomized simul. shots 37 periodic shots Noisy image --> recover the image via sparsity promoting
24 CFWI: Examples, GNK Iter #5 9% subsampled 37 randomized simul. shots 37 periodic shots
25 CFWI: Examples, GNK Iter #1 99% subsampled 4 randomized simul. shots 4 periodic shots
26 CFWI: Examples, GNK Iter #5 99% subsampled 4 randomized simul. shots 4 periodic shots
27 Conclusion Viable inversion of GN Hessian with Krylov method Accuracy of the inversion of Hessian depends on the number of iterations --> better FWI result Faster convergence of CG by preconditioners Implicit BFGS-type preconditioner Curvelet-based preconditioner [Herrmann, Brown, E. & Moghaddam (29)] Memory-friendly algorithm (gradient and Hessian can be computed on the fly) With scalable implicit solver for forward and adjoint systems, matrixfree algorithm [E., Oosterlee & Vuik (26), E. & Nabben (29), E. & Herrmann (28)] Natural extension to compressive FWI Similar results but less computational work In the CS framework: l1 inversion
28 Acknowledgments This work was in part financially supported by the Natural Sciences and Engineering Research Council of Canada Discovery Grant (22R81254) and the Collaborative Research and Development Grant DNOISE ( ) of Felix J. Herrmann. This research was carried out as part of the SINBAD II project with support from the following organizations: BG Group, BP, Petrobras, and Schlumberger. Further information: slim.eos.ubc.ca
Migration with Implicit Solvers for the Time-harmonic Helmholtz
Migration with Implicit Solvers for the Time-harmonic Helmholtz Yogi A. Erlangga, Felix J. Herrmann Seismic Laboratory for Imaging and Modeling, The University of British Columbia {yerlangga,fherrmann}@eos.ubc.ca
More informationCompressive sampling meets seismic imaging
Compressive sampling meets seismic imaging Felix J. Herrmann fherrmann@eos.ubc.ca http://slim.eos.ubc.ca joint work with Tim Lin and Yogi Erlangga Seismic Laboratory for Imaging & Modeling Department of
More informationCompressive Sensing Applied to Full-wave Form Inversion
Compressive Sensing Applied to Full-wave Form Inversion Felix J. Herrmann* fherrmann@eos.ubc.ca Joint work with Yogi Erlangga, and Tim Lin *Seismic Laboratory for Imaging & Modeling Department of Earth
More informationCompressive-wavefield simulations
Compressive-wavefield simulations Felix Herrmann Yogi Erlangga, Tim. Lin To cite this version: Felix Herrmann Yogi Erlangga, Tim. Lin. Compressive-wavefield simulations. Laurent Fesquet and Bruno Torrésani.
More informationSimultaneous estimation of wavefields & medium parameters
Simultaneous estimation of wavefields & medium parameters reduced-space versus full-space waveform inversion Bas Peters, Felix J. Herrmann Workshop W- 2, The limit of FWI in subsurface parameter recovery.
More informationWavefield Reconstruction Inversion (WRI) a new take on wave-equation based inversion Felix J. Herrmann
Wavefield Reconstruction Inversion (WRI) a new take on wave-equation based inversion Felix J. Herrmann SLIM University of British Columbia van Leeuwen, T and Herrmann, F J (2013). Mitigating local minima
More informationSUMMARY. The main contribution of this paper is threefold. First, we show that FWI based on the Helmholtz equation has the advantage
Randomized full-waveform inversion: a dimenstionality-reduction approach Peyman P. Moghaddam and Felix J. Herrmann, University of British Columbia, Canada SUMMARY Full-waveform inversion relies on the
More informationFWI with Compressive Updates Aleksandr Aravkin, Felix Herrmann, Tristan van Leeuwen, Xiang Li, James Burke
Consortium 2010 FWI with Compressive Updates Aleksandr Aravkin, Felix Herrmann, Tristan van Leeuwen, Xiang Li, James Burke SLIM University of British Columbia Full Waveform Inversion The Full Waveform
More informationCompressive simultaneous full-waveform simulation
Compressive simultaneous full-waveform simulation Felix J. Herrmann 1, Yogi Erlangga 1 and Tim T. Y. Lin 1 (August 14, 2008) Running head: compressive simulations ABSTRACT The fact that the numerical complexity
More informationSource estimation for frequency-domain FWI with robust penalties
Source estimation for frequency-domain FWI with robust penalties Aleksandr Y. Aravkin, Tristan van Leeuwen, Henri Calandra, and Felix J. Herrmann Dept. of Earth and Ocean sciences University of British
More informationSeismic wavefield inversion with curvelet-domain sparsity promotion
Seismic wavefield inversion with curvelet-domain sparsity promotion Felix J. Herrmann* fherrmann@eos.ubc.ca Deli Wang** wangdeli@email.jlu.edu.cn *Seismic Laboratory for Imaging & Modeling Department of
More informationSUMMARY. H (ω)u(ω,x s ;x) :=
Interpolating solutions of the Helmholtz equation with compressed sensing Tim TY Lin*, Evgeniy Lebed, Yogi A Erlangga, and Felix J Herrmann, University of British Columbia, EOS SUMMARY We present an algorithm
More informationSparsity-promoting migration with multiples
Sparsity-promoting migration with multiples Tim Lin, Ning Tu and Felix Herrmann SLIM Seismic Laboratory for Imaging and Modeling the University of British Columbia Courtesy of Verschuur, 29 SLIM Motivation..
More informationComparison between least-squares reverse time migration and full-waveform inversion
Comparison between least-squares reverse time migration and full-waveform inversion Lei Yang, Daniel O. Trad and Wenyong Pan Summary The inverse problem in exploration geophysics usually consists of two
More informationUncertainty quantification for Wavefield Reconstruction Inversion
Uncertainty quantification for Wavefield Reconstruction Inversion Zhilong Fang *, Chia Ying Lee, Curt Da Silva *, Felix J. Herrmann *, and Rachel Kuske * Seismic Laboratory for Imaging and Modeling (SLIM),
More informationSUMMARY REVIEW OF THE FREQUENCY DOMAIN L2 FWI-HESSIAN
Efficient stochastic Hessian estimation for full waveform inversion Lucas A. Willemsen, Alison E. Malcolm and Russell J. Hewett, Massachusetts Institute of Technology SUMMARY In this abstract we present
More informationMatrix Probing and Simultaneous Sources: A New Approach for Preconditioning the Hessian
Matrix Probing and Simultaneous Sources: A New Approach for Preconditioning the Hessian Curt Da Silva 1 and Felix J. Herrmann 2 1 Dept. of Mathematics 2 Dept. of Earth and Ocean SciencesUniversity of British
More informationA projected Hessian for full waveform inversion
CWP-679 A projected Hessian for full waveform inversion Yong Ma & Dave Hale Center for Wave Phenomena, Colorado School of Mines, Golden, CO 80401, USA (c) Figure 1. Update directions for one iteration
More informationMitigating data gaps in the estimation of primaries by sparse inversion without data reconstruction
Mitigating data gaps in the estimation of primaries by sparse inversion without data reconstruction Tim T.Y. Lin SLIM University of British Columbia Talk outline Brief review of REPSI Data reconstruction
More informationRecent results in curvelet-based primary-multiple separation: application to real data
Recent results in curvelet-based primary-multiple separation: application to real data Deli Wang 1,2, Rayan Saab 3, Ozgur Yilmaz 4, Felix J. Herrmann 2 1.College of Geoexploration Science and Technology,
More informationParallelizing large scale time domain electromagnetic inverse problem
Parallelizing large scale time domain electromagnetic inverse problems Eldad Haber with: D. Oldenburg & R. Shekhtman + Emory University, Atlanta, GA + The University of British Columbia, Vancouver, BC,
More informationStructured tensor missing-trace interpolation in the Hierarchical Tucker format Curt Da Silva and Felix J. Herrmann Sept. 26, 2013
Structured tensor missing-trace interpolation in the Hierarchical Tucker format Curt Da Silva and Felix J. Herrmann Sept. 6, 13 SLIM University of British Columbia Motivation 3D seismic experiments - 5D
More informationUncertainty quantification for Wavefield Reconstruction Inversion
using a PDE free semidefinite Hessian and randomize-then-optimize method Zhilong Fang *, Chia Ying Lee, Curt Da Silva, Tristan van Leeuwen and Felix J. Herrmann Seismic Laboratory for Imaging and Modeling
More informationUncertainty quantification for inverse problems with a weak wave-equation constraint
Uncertainty quantification for inverse problems with a weak wave-equation constraint Zhilong Fang*, Curt Da Silva*, Rachel Kuske** and Felix J. Herrmann* *Seismic Laboratory for Imaging and Modeling (SLIM),
More informationA multigrid method for large scale inverse problems
A multigrid method for large scale inverse problems Eldad Haber Dept. of Computer Science, Dept. of Earth and Ocean Science University of British Columbia haber@cs.ubc.ca July 4, 2003 E.Haber: Multigrid
More informationW011 Full Waveform Inversion for Detailed Velocity Model Building
W011 Full Waveform Inversion for Detailed Velocity Model Building S. Kapoor* (WesternGeco, LLC), D. Vigh (WesternGeco), H. Li (WesternGeco) & D. Derharoutian (WesternGeco) SUMMARY An accurate earth model
More informationSLIM. University of British Columbia
Accelerating an Iterative Helmholtz Solver Using Reconfigurable Hardware Art Petrenko M.Sc. Defence, April 9, 2014 Seismic Laboratory for Imaging and Modelling Department of Earth, Ocean and Atmospheric
More informationSeismic waveform inversion by stochastic optimization
Seismic waveform inversion by stochastic optimization Tristan van Leeuwen, Aleksandr Aravkin and Felix J. Herrmann Dept. of Earth and Ocean sciences University of British Columbia Vancouver, BC, Canada
More informationFull Waveform Inversion (FWI) with wave-equation migration. Gary Margrave Rob Ferguson Chad Hogan Banff, 3 Dec. 2010
Full Waveform Inversion (FWI) with wave-equation migration (WEM) and well control Gary Margrave Rob Ferguson Chad Hogan Banff, 3 Dec. 2010 Outline The FWI cycle The fundamental theorem of FWI Understanding
More informationApproximate- vs. full-hessian in FWI: 1D analytical and numerical experiments
Approximate- vs. full-hessian in FWI: 1D analytical and numerical experiments Raul Cova and Kris Innanen ABSTRACT Feasibility of using Full Waveform Inversion (FWI) to build velocity models has been increasing
More informationAN HELMHOLTZ ITERATIVE SOLVER FOR THE THREE-DIMENSIONAL SEISMIC IMAGING PROBLEMS?
European Conference on Computational Fluid Dynamics ECCOMAS CFD 2006 P. Wesseling, E. Oñate, J. Périaux (Eds) c TU Delft, Delft The Netherlands, 2006 AN HELMHOLTZ ITERATIVE SOLVER FOR THE THREE-DIMENSIONAL
More informationTime domain sparsity promoting LSRTM with source estimation
Time domain sparsity promoting LSRTM with source estimation Mengmeng Yang, Philipp Witte, Zhilong Fang & Felix J. Herrmann SLIM University of British Columbia Motivation Features of RTM: pros - no dip
More informationElastic least-squares migration with two-way wave equation forward and adjoint operators
Elastic least-squares migration with two-way wave equation forward and adjoint operators Ke Chen and Mauricio D. Sacchi, Department of Physics, University of Alberta Summary Time domain elastic least-squares
More informationP016 Toward Gauss-Newton and Exact Newton Optimization for Full Waveform Inversion
P016 Toward Gauss-Newton and Exact Newton Optiization for Full Wavefor Inversion L. Métivier* ISTerre, R. Brossier ISTerre, J. Virieux ISTerre & S. Operto Géoazur SUMMARY Full Wavefor Inversion FWI applications
More informationA decade of fast and robust Helmholtz solvers
A decade of fast and robust Helmholtz solvers Werkgemeenschap Scientific Computing Spring meeting Kees Vuik May 11th, 212 1 Delft University of Technology Contents Introduction Preconditioning (22-28)
More informationA parallel method for large scale time domain electromagnetic inverse problems
A parallel method for large scale time domain electromagnetic inverse problems Eldad Haber July 15, 2005 Abstract In this work we consider the solution of 3D time domain electromagnetic inverse problems
More informationThe truncated Newton method for Full Waveform Inversion
The truncated Newton method for Full Waveform Inversion Ludovic Métivier, Romain Brossier, Jean Virieux, Stéphane Operto To cite this version: Ludovic Métivier, Romain Brossier, Jean Virieux, Stéphane
More informationYouzuo Lin and Lianjie Huang
PROCEEDINGS, Thirty-Ninth Workshop on Geothermal Reservoir Engineering Stanford University, Stanford, California, February 24-26, 2014 SGP-TR-202 Building Subsurface Velocity Models with Sharp Interfaces
More informationOptimization schemes for Full Waveform Inversion: the preconditioned truncated Newton method
Optimization schemes for Full Waveform Inversion: the preconditioned truncated Newton method Ludovic Métivier, Romain Brossier, Jean Virieux, Stéphane Operto To cite this version: Ludovic Métivier, Romain
More informationSpectral analysis of complex shifted-laplace preconditioners for the Helmholtz equation
Spectral analysis of complex shifted-laplace preconditioners for the Helmholtz equation C. Vuik, Y.A. Erlangga, M.B. van Gijzen, and C.W. Oosterlee Delft Institute of Applied Mathematics c.vuik@tudelft.nl
More informationApplication of matrix square root and its inverse to downward wavefield extrapolation
Application of matrix square root and its inverse to downward wavefield extrapolation Polina Zheglova and Felix J. Herrmann Department of Earth and Ocean sciences, University of British Columbia, Vancouver,
More informationFighting the Curse of Dimensionality: Compressive Sensing in Exploration Seismology
Fighting the Curse of Dimensionality: Compressive Sensing in Exploration Seismology Herrmann, F.J.; Friedlander, M.P.; Yilmat, O. Signal Processing Magazine, IEEE, vol.29, no.3, pp.88-100 Andreas Gaich,
More informationSeismic Modeling, Migration and Velocity Inversion
Seismic Modeling, Migration and Velocity Inversion Inverse Scattering Bee Bednar Panorama Technologies, Inc. 14811 St Marys Lane, Suite 150 Houston TX 77079 May 30, 2014 Bee Bednar (Panorama Technologies)
More informationFull waveform inversion and the inverse Hessian
Full waveform inversion and the inverse Hessian Gary Margrave, Matt Yedlin and Kris Innanen ABSTRACT FWI and the inverse Hessian Full waveform inversion involves defining an objective function, and then
More informationComputational methods for large distributed parameter estimation problems with possible discontinuities
Computational methods for large distributed parameter estimation problems with possible discontinuities Uri Ascher Department of Computer Science, University of British Columbia, Vancouver, BC, V6T 1Z4,
More informationWaveform inversion for attenuation estimation in anisotropic media Tong Bai & Ilya Tsvankin Center for Wave Phenomena, Colorado School of Mines
Waveform inversion for attenuation estimation in anisotropic media Tong Bai & Ilya Tsvankin Center for Wave Phenomena, Colorado School of Mines SUMMARY Robust estimation of attenuation coefficients remains
More informationAn Efficient Two-Level Preconditioner for Multi-Frequency Wave Propagation Problems
An Efficient Two-Level Preconditioner for Multi-Frequency Wave Propagation Problems M. Baumann, and M.B. van Gijzen Email: M.M.Baumann@tudelft.nl Delft Institute of Applied Mathematics Delft University
More informationOverview Avoiding Cycle Skipping: Model Extension MSWI: Space-time Extension Numerical Examples
Overview Avoiding Cycle Skipping: Model Extension MSWI: Space-time Extension Numerical Examples Guanghui Huang Education University of Chinese Academy of Sciences, Beijing, China Ph.D. in Computational
More informationarxiv: v1 [math.na] 1 Apr 2015
Nonlinear seismic imaging via reduced order model backprojection Alexander V. Mamonov, University of Houston; Vladimir Druskin and Mikhail Zaslavsky, Schlumberger arxiv:1504.00094v1 [math.na] 1 Apr 2015
More informationOn complex shifted Laplace preconditioners for the vector Helmholtz equation
On complex shifted Laplace preconditioners for the vector Helmholtz equation C. Vuik, Y.A. Erlangga, M.B. van Gijzen, C.W. Oosterlee, D. van der Heul Delft Institute of Applied Mathematics c.vuik@tudelft.nl
More informationNonlinear seismic imaging via reduced order model backprojection
Nonlinear seismic imaging via reduced order model backprojection Alexander V. Mamonov, Vladimir Druskin 2 and Mikhail Zaslavsky 2 University of Houston, 2 Schlumberger-Doll Research Center Mamonov, Druskin,
More informationFull-waveform inversion application in different geological settings Denes Vigh*, Jerry Kapoor and Hongyan Li, WesternGeco
Full-waveform inversion application in different geological settings Denes Vigh*, Jerry Kapoor and Hongyan Li, WesternGeco Summary After the synthetic data inversion examples, real 3D data sets have been
More informationDownloaded 05/27/14 to Redistribution subject to SIAM license or copyright; see
SIAM J. OPTIM. Vol. 22, No. 3, pp. 739 757 c 2012 Society for Industrial and Applied Mathematics AN EFFECTIVE METHOD FOR PARAMETER ESTIMATION WITH PDE CONSTRAINTS WITH MULTIPLE RIGHT-HAND SIDES ELDAD HABER,
More informationPARALLEL LAGRANGE NEWTON KRYLOV SCHUR METHODS FOR PDE-CONSTRAINED OPTIMIZATION. PART I: THE KRYLOV SCHUR SOLVER
SIAM J. SCI. COMPUT. Vol. 27, No. 2, pp. 687 713 c 2005 Society for Industrial and Applied Mathematics PARALLEL LAGRANGE NEWTON KRYLOV SCHUR METHODS FOR PDE-CONSTRAINED OPTIMIZATION. PART I: THE KRYLOV
More informationFighting the curse of dimensionality: compressive sensing in exploration seismology
Fighting the curse of dimensionality: compressive sensing in exploration seismology Felix J. Herrmann, Michael P. Friedlander, Özgür Yılmaz January 2, 202 Abstract Many seismic exploration techniques rely
More information9.1 Preconditioned Krylov Subspace Methods
Chapter 9 PRECONDITIONING 9.1 Preconditioned Krylov Subspace Methods 9.2 Preconditioned Conjugate Gradient 9.3 Preconditioned Generalized Minimal Residual 9.4 Relaxation Method Preconditioners 9.5 Incomplete
More informationWaveform inversion and time-reversal imaging in attenuative TI media
Waveform inversion and time-reversal imaging in attenuative TI media Tong Bai 1, Tieyuan Zhu 2, Ilya Tsvankin 1, Xinming Wu 3 1. Colorado School of Mines 2. Penn State University 3. University of Texas
More informationTrust-Region SQP Methods with Inexact Linear System Solves for Large-Scale Optimization
Trust-Region SQP Methods with Inexact Linear System Solves for Large-Scale Optimization Denis Ridzal Department of Computational and Applied Mathematics Rice University, Houston, Texas dridzal@caam.rice.edu
More informationRegistration-guided least-squares waveform inversion
Registration-guided least-squares waveform inversion Hyoungsu Baek 1, Henri Calandra, Laurent Demanet 1 1 MIT Mathematics department, TOTAL S.A. January 15 013 Abstract Full waveform inversion with frequency
More informationA PRECONDITIONER FOR THE HELMHOLTZ EQUATION WITH PERFECTLY MATCHED LAYER
European Conference on Computational Fluid Dynamics ECCOMAS CFD 2006 P. Wesseling, E. Oñate and J. Périaux (Eds) c TU Delft, The Netherlands, 2006 A PRECONDITIONER FOR THE HELMHOLTZ EQUATION WITH PERFECTLY
More informationEducation Ph.D. Candidate, Rice University, Houston, TX, USA, 08/ Present. M.S, Shanghai Jiao Tong University, Shanghai, China, 09/ /2009
Yin Huang Education Ph.D. Candidate, Rice University, Houston, TX, USA, 08/2010 - Present Dissertation Topic: Nonlinear Extended Waveform Inversion M.A. with Master Thesis: Transparency property of one
More informationPARALLEL LAGRANGE-NEWTON-KRYLOV-SCHUR METHODS FOR PDE-CONSTRAINED OPTIMIZATION. PART I: THE KRYLOV-SCHUR SOLVER
PARALLEL LAGRANGE-NEWTON-KRYLOV-SCHUR METHODS FOR PDE-CONSTRAINED OPTIMIZATION. PART I: THE KRYLOV-SCHUR SOLVER GEORGE BIROS AND OMAR GHATTAS Abstract. Large scale optimization of systems governed by partial
More informationON A ROBUST ITERATIVE METHOD FOR HETEROGENEOUS HELMHOLTZ PROBLEMS FOR GEOPHYSICS APPLICATIONS
INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING Volume 2, Supp, Pages 197 28 c 25 Institute for Scientific Computing and Information ON A ROBUST ITERATIVE METHOD FOR HETEROGENEOUS HELMHOLTZ PROBLEMS
More informationAccelerated large-scale inversion with message passing Felix J. Herrmann, the University of British Columbia, Canada
Accelerated large-scale inversion with message passing Felix J. Herrmann, the University of British Columbia, Canada SUMMARY To meet current-day challenges, exploration seismology increasingly relies on
More informationAlgorithmic strategies for full waveform inversion: 1D experiments
GEOPHYSICS, VOL. 74, NO. 6 NOVEMBER-DECEMBER 2009 ; P. WCC37 WCC46, 7 FIGS., 2 TABLES. 10.1190/1.3237116 Algorithmic strategies for full waveform inversion: 1D experiments Carsten Burstedde 1 and Omar
More informationScalable algorithms for optimal experimental design for infinite-dimensional nonlinear Bayesian inverse problems
Scalable algorithms for optimal experimental design for infinite-dimensional nonlinear Bayesian inverse problems Alen Alexanderian (Math/NC State), Omar Ghattas (ICES/UT-Austin), Noémi Petra (Applied Math/UC
More informationWe E Multiparameter Full-waveform Inversion for Acoustic VTI Medium with Surface Seismic Data
We E16 4 Multiarameter Full-waveform Inversion for Acoustic VI Medium with Surface Seismic Data X. Cheng* (Schlumberger) K. Jiao (Schlumberger) D. Sun (Schlumberger) & D. Vigh (Schlumberger) SUMMARY In
More information2D Laplace-Domain Waveform Inversion of Field Data Using a Power Objective Function
Pure Appl. Geophys. Ó 213 Springer Basel DOI 1.17/s24-13-651-4 Pure and Applied Geophysics 2D Laplace-Domain Waveform Inversion of Field Data Using a Power Objective Function EUNJIN PARK, 1 WANSOO HA,
More informationInversion of 3D electromagnetic data in frequency and time domain using an inexact all-at-once approach
GEOPHYSICS, VOL. 69, NO. 5 (SEPTEMBER-OCTOBER 2004); P. 1216 1228, 9 FIGS., 2 TABLES. 10.1190/1.1801938 Inversion of 3D electromagnetic data in frequency and time domain using an inexact all-at-once approach
More informationShifted Laplace and related preconditioning for the Helmholtz equation
Shifted Laplace and related preconditioning for the Helmholtz equation Ivan Graham and Euan Spence (Bath, UK) Collaborations with: Paul Childs (Schlumberger Gould Research), Martin Gander (Geneva) Douglas
More informationFull waveform inversion with wave equation migration and well control
FWI by WEM Full waveform inversion with wave equation migration and well control Gary F. Margrave, Robert J. Ferguson and Chad M. Hogan ABSTRACT We examine the key concepts in full waveform inversion (FWI)
More informationHigh Performance Nonlinear Solvers
What is a nonlinear system? High Performance Nonlinear Solvers Michael McCourt Division Argonne National Laboratory IIT Meshfree Seminar September 19, 2011 Every nonlinear system of equations can be described
More informationSeismic data interpolation and denoising using SVD-free low-rank matrix factorization
Seismic data interpolation and denoising using SVD-free low-rank matrix factorization R. Kumar, A.Y. Aravkin,, H. Mansour,, B. Recht and F.J. Herrmann Dept. of Earth and Ocean sciences, University of British
More informationNumerical Optimization Professor Horst Cerjak, Horst Bischof, Thomas Pock Mat Vis-Gra SS09
Numerical Optimization 1 Working Horse in Computer Vision Variational Methods Shape Analysis Machine Learning Markov Random Fields Geometry Common denominator: optimization problems 2 Overview of Methods
More informationComputational methods for large distributed parameter estimation problems in 3D
Computational methods for large distributed parameter estimation problems in 3D U. M. Ascher E. Haber March 8, 03 Abstract This paper considers problems of distributed parameter estimation from data measurements
More informationAn introduction to PDE-constrained optimization
An introduction to PDE-constrained optimization Wolfgang Bangerth Department of Mathematics Texas A&M University 1 Overview Why partial differential equations? Why optimization? Examples of PDE optimization
More informationFast algorithms for the inverse medium problem. George Biros University of Pennsylvania
Fast algorithms for the inverse medium problem George Biros University of Pennsylvania Acknowledgments S. Adavani, H. Sundar, S. Rahul (grad students) C. Davatzikos, D. Shen, H. Litt (heart project) Akcelic,
More informationMultigrid based preconditioners for the numerical solution of two-dimensional heterogeneous problems in geophysics
Technical Report RAL-TR-2007-002 Multigrid based preconditioners for the numerical solution of two-dimensional heterogeneous problems in geophysics I. S. Duff, S. Gratton, X. Pinel, and X. Vasseur January
More informationInversion of 3D Electromagnetic Data in frequency and time domain using an inexact all-at-once approach
Inversion of 3D Electromagnetic Data in frequency and time domain using an inexact all-at-once approach Eldad Haber UBC-Geophysical Inversion Facility Department of Earth and Ocean Sciences University
More informationGeophysical Journal International
Geophysical Journal International Geophys. J. Int. (2012) 188, 1221 1242 doi: 10.1111/j.1365-246X.2011.05314.x Full waveform inversion strategy for density in the frequency domain Woodon Jeong, 1 Ho-Yong
More informationLarge-Scale L1-Related Minimization in Compressive Sensing and Beyond
Large-Scale L1-Related Minimization in Compressive Sensing and Beyond Yin Zhang Department of Computational and Applied Mathematics Rice University, Houston, Texas, U.S.A. Arizona State University March
More informationOptimal control problems with PDE constraints
Optimal control problems with PDE constraints Maya Neytcheva CIM, October 2017 General framework Unconstrained optimization problems min f (q) q x R n (real vector) and f : R n R is a smooth function.
More information1.2 Derivation. d p f = d p f(x(p)) = x fd p x (= f x x p ). (1) Second, g x x p + g p = 0. d p f = f x g 1. The expression f x gx
PDE-constrained optimization and the adjoint method Andrew M. Bradley November 16, 21 PDE-constrained optimization and the adjoint method for solving these and related problems appear in a wide range of
More informationMaking Flippy Floppy
Making Flippy Floppy James V. Burke UW Mathematics jvburke@uw.edu Aleksandr Y. Aravkin IBM, T.J.Watson Research sasha.aravkin@gmail.com Michael P. Friedlander UBC Computer Science mpf@cs.ubc.ca Current
More informationOn the interplay between discretization and preconditioning of Krylov subspace methods
On the interplay between discretization and preconditioning of Krylov subspace methods Josef Málek and Zdeněk Strakoš Nečas Center for Mathematical Modeling Charles University in Prague and Czech Academy
More informationSeismic imaging and optimal transport
Seismic imaging and optimal transport Bjorn Engquist In collaboration with Brittany Froese, Sergey Fomel and Yunan Yang Brenier60, Calculus of Variations and Optimal Transportation, Paris, January 10-13,
More informationSimulation based optimization
SimBOpt p.1/52 Simulation based optimization Feb 2005 Eldad Haber haber@mathcs.emory.edu Emory University SimBOpt p.2/52 Outline Introduction A few words about discretization The unconstrained framework
More informationConvex Optimization Algorithms for Machine Learning in 10 Slides
Convex Optimization Algorithms for Machine Learning in 10 Slides Presenter: Jul. 15. 2015 Outline 1 Quadratic Problem Linear System 2 Smooth Problem Newton-CG 3 Composite Problem Proximal-Newton-CD 4 Non-smooth,
More informationAn Efficient Low Memory Implicit DG Algorithm for Time Dependent Problems
An Efficient Low Memory Implicit DG Algorithm for Time Dependent Problems P.-O. Persson and J. Peraire Massachusetts Institute of Technology 2006 AIAA Aerospace Sciences Meeting, Reno, Nevada January 9,
More informationDimension-Independent likelihood-informed (DILI) MCMC
Dimension-Independent likelihood-informed (DILI) MCMC Tiangang Cui, Kody Law 2, Youssef Marzouk Massachusetts Institute of Technology 2 Oak Ridge National Laboratory 2 August 25 TC, KL, YM DILI MCMC USC
More informationTHE RICE INVERSION PROJECT
THE RICE INVERSION PROJECT Mario Bencomo, Lei Fu, Jie Hou, Guanghui Huang, Rami Nammour, and William Symes Annual Report 6 Copyright 5-6 by Rice University i TRIP6 TABLE OF CONTENTS William W. Symes, The
More informationDirect Current Resistivity Inversion using Various Objective Functions
Direct Current Resistivity Inversion using Various Objective Functions Rowan Cockett Department of Earth and Ocean Science University of British Columbia rcockett@eos.ubc.ca Abstract In geophysical applications
More informationLecture 18 Classical Iterative Methods
Lecture 18 Classical Iterative Methods MIT 18.335J / 6.337J Introduction to Numerical Methods Per-Olof Persson November 14, 2006 1 Iterative Methods for Linear Systems Direct methods for solving Ax = b,
More informationNumerical Methods I Non-Square and Sparse Linear Systems
Numerical Methods I Non-Square and Sparse Linear Systems Aleksandar Donev Courant Institute, NYU 1 donev@courant.nyu.edu 1 MATH-GA 2011.003 / CSCI-GA 2945.003, Fall 2014 September 25th, 2014 A. Donev (Courant
More informationSource function estimation in extended full waveform inversion
Source function estimation in extended full waveform inversion Lei Fu The Rice Inversion Project (TRIP) May 6, 2014 Lei Fu (TRIP) Source estimation in EFWI May 6, 2014 1 Overview Objective Recover Earth
More informationIterative methods for positive definite linear systems with a complex shift
Iterative methods for positive definite linear systems with a complex shift William McLean, University of New South Wales Vidar Thomée, Chalmers University November 4, 2011 Outline 1. Numerical solution
More informationAchieving depth resolution with gradient array survey data through transient electromagnetic inversion
Achieving depth resolution with gradient array survey data through transient electromagnetic inversion Downloaded /1/17 to 128.189.118.. Redistribution subject to SEG license or copyright; see Terms of
More informationFast Iterative Solution of Saddle Point Problems
Michele Benzi Department of Mathematics and Computer Science Emory University Atlanta, GA Acknowledgments NSF (Computational Mathematics) Maxim Olshanskii (Mech-Math, Moscow State U.) Zhen Wang (PhD student,
More informationAlvaro F. M. Azevedo A. Adão da Fonseca
SECOND-ORDER SHAPE OPTIMIZATION OF A STEEL BRIDGE Alvaro F. M. Azevedo A. Adão da Fonseca Faculty of Engineering University of Porto Portugal 16-18 March 1999 OPTI 99 Orlando - Florida - USA 1 PROBLEM
More informationLow-rank Promoting Transformations and Tensor Interpolation - Applications to Seismic Data Denoising
Low-rank Promoting Transformations and Tensor Interpolation - Applications to Seismic Data Denoising Curt Da Silva and Felix J. Herrmann 2 Dept. of Mathematics 2 Dept. of Earth and Ocean Sciences, University
More information