William W. Symes

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All published works

Action	Title	Year	Authors
+ PDF Chat	A numerical investigation of Matched Source Waveform Inversion applied to acoustic transmission data	2024	William W. Symes Huiyi Chen Susan E. Minkoff
+ PDF Chat	Adaptive waveform inversion for transmitted wave data	2024	William W. Symes
+ PDF Chat	Efficient computation of extended surface sources	2023	William W. Symes
+ PDF Chat	Corrigendum: Solution of an acoustic transmission inverse problem by extended inversion (2022 Inverse Problems 38 115003)	2022	William W. Symes Huiyi Chen Susan E. Minkoff
+ PDF Chat	Solution of an acoustic transmission inverse problem by extended inversion	2022	William W. Symes Huiyi Chen Susan E. Minkoff
+ PDF Chat	Error bounds for extended source inversion applied to an acoustic transmission inverse problem	2022	William W. Symes
+	Efficient Computation of Extended Surface Sources	2022	William W. Symes
+	Solution of an Acoustic Transmission Inverse Problem by Extended Inversion	2022	William W. Symes Huiyi Chen Susan E. Minkoff
+	Solution of an Acoustic Transmission Inverse Problem by Extended Inversion: Theory	2021	William W. Symes
+ PDF Chat	Error Bounds for Extended Source Inversion applied to an Acoustic Transmission Inverse Problem	2021	William W. Symes
+ PDF Chat	Full-waveform inversion by source extension: Why it works	2020	William W. Symes Huiyi Chen Susan E. Minkoff
+ PDF Chat	Wavefield reconstruction inversion: an example	2020	William W. Symes
+	Full Waveform Inversion by Source Extension: Why it works	2020	William W. Symes
+	Full Waveform Inversion by Source Extension: Why it works	2020	William W. Symes
+	A mathematical framework for inverse wave problems in heterogeneous media	2013	Kirk Blazek Christiaan C. Stolk William W. Symes
+	SOURCE SYNTHESIS FOR INVERSE PROBLEMS IN WAVE PROPAGATION	2011	William W. Symes
+	Methods for Optimal Control Problems	2010	Marco U. Enriquez William W. Symes
+ PDF Chat	A software framework for abstract expression of coordinate-free linear algebra and optimization algorithms	2009	Anthony D. Padula Shannon D. Scott William W. Symes
+	The Acoustic Radiation Solution	2008	William W. Symes Tetyana Vdovina
+	Guest Editors' introduction to the special section on statistical and computational issues in inverse problems	2008	Luis Tenorio Eldad Haber William W. Symes Philip B. Stark Dennis D. Cox Omar Ghattas
+	Regularity of an inverse problem in wave propagation	2007	Gang Bao William W. Symes
+	A paraxial formulation for the viscosity solution of quasi-P eikonal equations	2003	Jianliang Qian William W. Symes
+	Adaptive Simulation, the Adjoint State Method, and Optimization	2003	Mark S. Cockenbach William W. Symes
+ PDF Chat	Smooth objective functionals for seismic velocity inversion	2002	Christiaan C. Stolk William W. Symes
+	Efficient and automatic implementation of the adjoint state method	2002	Mark S. Gockenbach Daniel R. Reynolds Peng Shen William W. Symes
+	Automatic Differentiation and the Adjoint State Method	2002	Mark S. Gockenbach Daniel R. Reynolds William W. Symes
+	Paraxial Eikonal Solvers for Anisotropic Quasi-P Travel Times	2001	Jianliang Qian William W. Symes
+	Upwind finite difference traveltime for anisotropic media	1999	Jianliang Qian William W. Symes
+	A slowness matching finite difference method for traveltimes beyond transmission caustics	1998	William W. Symes
+ PDF Chat	Anomalous reflections near a caustic	1997	Clifford J. Nolan William W. Symes
+	Global solution of a linearized inverse problem for the wave equation	1997	Clifford J. Nolan William W. Symes
+ PDF Chat	An Infeasible Point Method for Minimizing the Lennard-Jones Potential	1997	Mark S. Gockenbach Anthony J. Kearsley William W. Symes
+	Inverse Problems in Wave Propagation	1997	Guy Chavent Paul Sacks George Papanicolaou William W. Symes
+ PDF Chat	Computation of Pseudo-Differential Operators	1996	Gang Bao William W. Symes
+	A note on consistency and adjointness for numerical schemes	1995	Alain Sei William W. Symes
+ PDF Chat	Time-Like Trace Regularity of the Wave Equation with a Nonsmooth Principal Part	1995	Gang Bao William W. Symes
+ PDF Chat	Stability Analysis of Finite-Difference Schemes for the Viscoelastic Wave Equation	1994	Joakim O. Blanch William W. Symes
+	Trace Regularity for a Second Order Hyperbolic Equation with Nonsmooth Coefficients	1993	Gang Bao William W. Symes
+	Integrated Approaches to Parallelism in Optimization and Solution of Inverse Problems	1993	William W. Symes
+ PDF Chat	Computation of Pseudo-Differential Operators	1992	Gang Bao William W. Symes
+ PDF Chat	Conjugate residual methods for almost symmetric linear systems	1992	Juan Meza William W. Symes
+ PDF Chat	Deflated Krylov subspace methods for nearly singular linear systems	1992	Juan Meza William W. Symes
+ PDF Chat	A trace theorem for solutions of linear partial differential equations	1991	Gang Bao William W. Symes
+ PDF Chat	An Upper Bound for the Linearized Map of an Inverse Problem for the Wave Equation	1991	Gang Bao William W. Symes
+ PDF Chat	The Reflection Inverse Problem for Acoustic Waves	1990	William W. Symes
+ PDF Chat	A Trace Theorem for Solutions of Linear Partial Differential Equations	1989	Gang Bao William W. Symes
+	Velocity inversion from common offset data	1989	Paul Sacks William W. Symes
+ PDF Chat	Propagation of Singularities and Some Inverse Problems in Wave Propagation	1989	William W. Symes
+	9. Computing the Least-Squares Solution	1989	Fadil Santosa William W. Symes Raymon L. Brown
+	8. Implications for the Solution of the Least-Squares Inverse Problem	1989	Fadil Santosa William W. Symes Raymon L. Brown
+	6. Perturbations about a Slowly Varying Reference Velocity	1989	Fadil Santosa William W. Symes Raymon L. Brown
+	Appendix A: Least-Squares and the Velocity Spectrum	1989	Fadil Santosa William W. Symes Raymon L. Brown
+	Reconstruction of blocky impedence profiles from normal-incidence reflection seismograms which are band-limited and miscalibrated	1988	Fadil Santosa William W. Symes
+	Uniqueness for an inverse problem for the wave equation	1988	Rakesh Rakesh William W. Symes
+	Inversion of band-limited reflection seismograms using stacking velocities as constraints	1987	Fadil Santosa William W. Symes G. Raggio
+	Domain Decomposition Algorithms for Linear Hyperbolic Equations	1987	Juan Meza William W. Symes
+	On the Relation between Coefficient and Boundary Values for Solutions of Webster’s Horn Equation	1986	William W. Symes
+	Linearization Stability for an Inverse Problem in Several-Dimensional Wave Propagation	1986	William W. Symes
+	ON THE RELATIONBETWEEN COEFFICIENTANDBOUNDARY VALUESFOR SOLUTIONS OF WEBSTER'SHORN EQUATION*	1986	William W. Symes
+	Uniqueness and continuous dependence for a multidimensional hyperbolic inverse problem	1985	Paul Sacks William W. Symes
+ PDF Chat	Stability considerations for one-dimensional inverse problems	1985	Samuel H. Gray William W. Symes
+	Impedance profile inversion via the first transport equation	1983	William W. Symes
+	A trace theorem for solutions of the wave equation, and the remote determination of acoustic sources	1983	William W. Symes L. E. Payne
+ PDF Chat	Systems of Toda type, inverse spectral problems, and representation theory	1981	William W. Symes
+	Erratum: Numerical Stability in an Inverse Scattering Problem	1981	William W. Symes
+	Stable Solution of the Inverse Reflection Problem for a Smoothly Stratified Elastic Medium	1981	William W. Symes
+	Hamiltonian group actions and integrable systems	1980	William W. Symes
+	Numerical Stability in an Inverse Scattering Problem	1980	William W. Symes
+	Inverse boundary value problems and a theorem of Gel'fand and Levitan	1979	William W. Symes
+	The Inverse Reflection Problem for a Smoothly Stratified Elastic Medium.	1979	William W. Symes
+	An integral representation for eigenfunctions of linear ordinary differential operators	1979	William W. Symes

Common Coauthors

Coauthor	Papers Together
Fadil Santosa	6
Susan E. Minkoff	5
Huiyi Chen	5
Gang Bao	4
Raymon L. Brown	4
Juan Meza	3
Mark S. Gockenbach	3
Jianliang Qian	3
Gang Bao	3
Paul Sacks	3
Daniel R. Reynolds	2
Clifford J. Nolan	2
Christiaan C. Stolk	2
Shannon D. Scott	1
Samuel H. Gray	1
Alain Sei	1
Anthony D. Padula	1
Omar Ghattas	1
Marco U. Enriquez	1
Dennis D. Cox	1
George Papanicolaou	1
Joakim O. Blanch	1
L. E. Payne	1
Gang Bao	1
Rakesh Rakesh	1
Anthony J. Kearsley	1
Peng Shen	1
Tetyana Vdovina	1
Eldad Haber	1
G. Raggio	1
Guy Chavent	1
Luis Tenorio	1
Kirk Blazek	1
Mark S. Cockenbach	1
Philip B. Stark	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	About the stability of the inverse problem in 1-D wave equations?application to the interpretation of seismic profiles	1979	A. Bamberger Guy Chavent Patrick Lailly	10
+	Impedance profile inversion via the first transport equation	1983	William W. Symes	8
+	A trace theorem for solutions of the wave equation, and the remote determination of acoustic sources	1983	William W. Symes L. E. Payne	7
+ PDF Chat	Inverse Problem for the One-dimensional Wave Equation	1970	M. L. Gerver	6
+	On the Relation between Coefficient and Boundary Values for Solutions of Webster’s Horn Equation	1986	William W. Symes	6
+	Propagation of singularities for hyperbolic pseudo differential operators with non‐smooth coefficients	1982	Michael Beals Michael C. Reed	5
+	The One-Dimensional Inverse Problem of Reflection Seismology	1983	Kenneth P. Bube Robert Burridge	5
+ PDF Chat	Fourier integral operators. I	1971	Lars Hörmander	5
+	On the determination of a differential equation from its spectral function	1987	I. M. Gel'fand	5
+	On the determination of a differential equation from its spectral function	1955	I. M. Ge′lfand B. M. Levitan	5
+	Continuous and Discrete Inverse-Scattering Problems in a Stratified Elastic Medium. I. Plane Waves at Normal Incidence	1969	Jerry A. Ware K. Aki	5
+	Stable Solution of the Inverse Reflection Problem for a Smoothly Stratified Elastic Medium	1981	William W. Symes	5
+	Uniqueness and continuous dependence for a multidimensional hyperbolic inverse problem	1985	Paul Sacks William W. Symes	4
+ PDF Chat	Microlocal regularity theorems for nonsmooth pseudodifferential operators and applications to nonlinear problems	1984	Michael Beals Michael C. Reed	4
+	Linearization Stability for an Inverse Problem in Several-Dimensional Wave Propagation	1986	William W. Symes	4
+ PDF Chat	Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations	1988	Stanley Osher James A. Sethian	4
+ PDF Chat	A trace theorem for solutions of linear partial differential equations	1991	Gang Bao William W. Symes	4
+ PDF Chat	A penalty method for PDE-constrained optimization in inverse problems	2015	Tristan van Leeuwen Felix J. Herrmann	4
+ PDF Chat	Wavefield reconstruction inversion: an example	2020	William W. Symes	4
+	The Inverse Problem in the Quantum Theory of Scattering	1963	L. D. Faddeyev Bernard D. Seckler	4
+	Trace regularity of the solutions of the wave equation with homogeneous Neumann boundary conditions and data supported away from the boundary	1989	Irena Lasiecka Roberto Triggiani	4
+	The inversion of acoustical impedance profile by methods of characteristics	1982	Fadil Santosa Horst Schwetlick	4
+	Pseudodifferential Operators (PMS-34)	1981	Michael E. Taylor	4
+	Linear Partial Differential Operators	1964	Lars Hörmander	4
+ PDF Chat	Full-waveform inversion by source extension: Why it works	2020	William W. Symes Huiyi Chen Susan E. Minkoff	4
+	Lectures on Linear Partial Differential Equations	1973	Louis Nirenberg	4
+	The Gelfand-Levitan, the Marchenko, and the Gopinath-Sondhi integral equations of inverse scattering theory, regarded in the context of inverse impulse-response problems	1980	Robert Burridge	3
+	An Inverse Method for Determining Small Variations in Propagation Speed	1977	Jack K. Cohen Norman Bleistein	3
+	Numerical Methods for Unconstrained Optimization and Nonlinear Equations	1996	J. E. Dennis Robert B. Schnabel	3
+	Inverse boundary value problems and a theorem of Gel'fand and Levitan	1979	William W. Symes	3
+ PDF Chat	Smooth objective functionals for seismic velocity inversion	2002	Christiaan C. Stolk William W. Symes	3
+ PDF Chat	Methods of Mathematical Physics, vol. II. Partial Differential Equations	1963	Courant Hilbert	3
+	Linear Partial Differential Operators	1963	Lars Hörmander	3
+	Optimal Control of Systems Governed by Partial Differential Equations	1971	J. L. Lions	3
+	A Linearised inverse problem for the wave equation	1988	Rakesh Rakesh	3
+	Hyperbolic Partial Differential Equations	2006	Peter D. Lax	3
+ PDF Chat	The inverse Sturm-Liouville problem with symmetric potentials	1978	Ole H. Hald	3
+	Trace Regularity for a Second Order Hyperbolic Equation with Nonsmooth Coefficients	1993	Gang Bao William W. Symes	3
+ PDF Chat	Improving full-waveform inversion by wavefield reconstruction with the alternating direction method of multipliers	2018	Hossein S. Aghamiry Ali Gholami S. Operto	3
+	Pseudodifferential Operators	2010	Michael E. Taylor	3
+	Stability for the one dimensional inverse problem via the gel’fand-levitan equation	1982	Robert Carroll Fadil Santosa Jaime H. Ortega	3
+ PDF Chat	Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion	2017	Yunan Yang Björn Engquist Junzhe Sun Brittany Froese Hamfeldt	3
+	High-Order Essentially Nonoscillatory Schemes for Hamilton–Jacobi Equations	1991	Stanley Osher Chi‐Wang Shu	3
+ PDF Chat	Reflection of singularities of solutions to systems of differential equations	1975	Michael E. Taylor	3
+	Pseudodifferential Operators and Nonlinear PDE	1991	Michael E. Taylor	2
+	Integrals of nonlinear equations of evolution and solitary waves	1968	Peter D. Lax	2
+	Introduction to Pseudodifferential and Fourier Integral Operators	1980	François Trèves	2
+	Inverse scattering on the line	1979	Percy Deift Eugene Trubowitz	2
+	Least Squares Methods for Ill-Posed Problems with a Prescribed Bound	1970	Keith Miller	2
+	A discrete version of the inverse scattering problem	1973	K. M. Case Mark Kac	2