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Keywords: helmholtz equation
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Proceedings Papers
Kronecker neural networks for the win: Overcoming spectral bias for PINN-based wavefield computation
Publisher: Society of Exploration Geophysicists
Paper presented at the SEG/AAPG International Meeting for Applied Geoscience & Energy, August 28–September 1, 2022
Paper Number: SEG-2022-3747298
... Wavefield computation constitutes the majority of the computational cost for seismic applications, including reverse-time migration and full waveform inversion (FWI). One of the popular approaches is to solve for the wavefields in the frequency domain by using the Helmholtz equation. However...
Proceedings Papers
Publisher: Society of Exploration Geophysicists
Paper presented at the SEG/AAPG/SEPM First International Meeting for Applied Geoscience & Energy, September 26–October 1, 2021
Paper Number: SEG-2021-3584030
... solutions to partial differential equations (PDEs) offers the opportunity to solve the Helmholtz equation with a neural network (NN) model. The input to such an NN is a location in space and the output are the real and imaginary parts of the scattered wavefield at that location, thus, acting like a function...
Proceedings Papers
Publisher: Society of Exploration Geophysicists
Paper presented at the SEG International Exposition and Annual Meeting, October 11–16, 2020
Paper Number: SEG-2020-3421468
... Type: Oral neural network simple layered model wavefield machine learning upstream oil & gas wave equation singularity artificial intelligence background model source location reservoir characterization frequency point source helmholtz equation hz frequency seg international...
Proceedings Papers
Publisher: Society of Exploration Geophysicists
Paper presented at the SEG International Exposition and Annual Meeting, September 15–20, 2019
Paper Number: SEG-2019-3216730
... ABSTRACT We introduce a novel idea, the WaveHoltz iteration, for solving the Helmholtz equation inspired by recent work on exact controllability (EC) methods. As in EC methods our method make use of time domain methods for wave equations to design frequency domain Helmholtz solvers but unlike...
Proceedings Papers
Publisher: Society of Exploration Geophysicists
Paper presented at the SEG International Exposition and Annual Meeting, September 15–20, 2019
Paper Number: SEG-2019-3214907
... equation equation helmholtz equation solver memory consumption annual meeting upstream oil & gas direct solver requirement reservoir characterization Amestoy , P. R. , C. , Ashcraft , O. , Boiteau , A. , Buttari , J.-Y. , L’Excellent , and C...
Proceedings Papers
Publisher: Society of Exploration Geophysicists
Paper presented at the 2018 SEG International Exposition and Annual Meeting, October 14–19, 2018
Paper Number: SEG-2018-2998004
... ABSTRACT Solving elastic-wave equation in the frequency domain for highly heterogeneous and complex anisotropic media is computationally challenging. Conventional methods for solving the elastic-wave Helmholtz equation usually lead to largedimensional linear system that is difficult to solve...
Proceedings Papers
Publisher: Society of Exploration Geophysicists
Paper presented at the 2018 SEG International Exposition and Annual Meeting, October 14–19, 2018
Paper Number: SEG-2018-2996158
... ABSTRACT We propose a virtual element method for the numerical simulation of time-harmonic wave propagation, here in the simplest form of the Helmholtz equation. As opposed to classical finite elements, the shape functions are defined only implicitly (virtually), in such a way that numerical...
Proceedings Papers
Publisher: Society of Exploration Geophysicists
Paper presented at the 2017 SEG International Exposition and Annual Meeting, September 24–29, 2017
Paper Number: SEG-2017-17728116
... ABSTRACT In this work we propose a hybridizable discontinuous Galerkin (hdG) discretization of the high-frequency Helmholtz equation in the presence of point sources and highly heterogeneous and discontinuous wave speed models. We show that it delivers solutions that are provably second-order...
Proceedings Papers
Publisher: Society of Exploration Geophysicists
Paper presented at the 2017 SEG International Exposition and Annual Meeting, September 24–29, 2017
Paper Number: SEG-2017-17690586
...: Exhibit Hall C/D Presentation Type: POSTER operator annual meeting wave equation finite difference operator discretization coefficient geophysics reservoir characterization equation pml decomposition helmholtz equation inversion upstream oil & gas matrix finite difference method...
Proceedings Papers
Publisher: Society of Exploration Geophysicists
Paper presented at the 2016 SEG International Exposition and Annual Meeting, October 16–21, 2016
Paper Number: SEG-2016-13869051
... , An optimal 9-point finite difference scheme for the helmholtz equation with PML : International Journal of Numerical Analysis and Modeling , 10 , 389 – 410 . van den Berg , E., M. P. F. , 2014 , Spot — a linear-operator toolbox , http://www.cs.ubc.ca/labs/scl/spot/ Lago , R...
Proceedings Papers
Publisher: Society of Exploration Geophysicists
Paper presented at the 2016 SEG International Exposition and Annual Meeting, October 16–21, 2016
Paper Number: SEG-2016-13848017
... ABSTRACT The method of polarized traces provides the first documented algorithm with truly scalable complexity for the high-frequency Helmholtz equation, i.e., with a runtime sublinear in the number of volume unknowns in a parallel environment. However, previous versions of this method were...
Proceedings Papers
Publisher: Society of Exploration Geophysicists
Paper presented at the 2016 SEG International Exposition and Annual Meeting, October 16–21, 2016
Paper Number: SEG-2016-13867211
... ABSTRACT We present a fast solver for the 3D high-frequency Helmholtz equation in heterogeneous, constant density, acoustic media. The solver is based on the method of polarized traces, coupled with distributed linear algebra libraries and pipelining to obtain a solver with online runtime (max...
Proceedings Papers
Publisher: Society of Exploration Geophysicists
Paper presented at the 2015 SEG Annual Meeting, October 18–23, 2015
Paper Number: SEG-2015-5796514
...Exact Frequency Dependent Rays on the Basis of Helmholtz Solver Maxim Protasov* and Kirill Gadylshin, Institute of Petroleum Geology and Geophysics, SB RAS Summary A computational method is presented which enables one to trace exact frequency dependent rays when a solution to the Helmholtz equation...
Proceedings Papers
Publisher: Society of Exploration Geophysicists
Paper presented at the 2015 SEG Annual Meeting, October 18–23, 2015
Paper Number: SEG-2015-5827540
... the effectiveness of our OFD scheme by computing solutions to the Helmholtz equation below 3.5 points-per-wavelength (ppw). Introduction Finite-difference methods remain popular for solving numerically the wave and Helmholtz equations for seismic modeling, imaging, and inversion. To minimize the impacts...
Proceedings Papers
Publisher: Society of Exploration Geophysicists
Paper presented at the 2015 SEG Annual Meeting, October 18–23, 2015
Paper Number: SEG-2015-5840170
... Summary Conventional finite-element method for solving Helmholtz equation on highly heterogeneous media usually require very finely discretized mesh to accurately represent the medium property variations, and therefore is computationally expensive. We present a continuous Galerkin generalized...
Proceedings Papers
Publisher: Society of Exploration Geophysicists
Paper presented at the 2015 SEG Annual Meeting, October 18–23, 2015
Paper Number: SEG-2015-5838886
... propagation, where offline precomputations are often amortized over the large number of system solves with the same matrix H . application helmholtz equation integral system upstream oil & gas preconditioner decomposition precomputation iterative method helmholtz problem local solve...
Proceedings Papers
Publisher: Society of Exploration Geophysicists
Paper presented at the 2014 SEG Annual Meeting, October 26–31, 2014
Paper Number: SEG-2014-1275
... Summary We present a domain decomposition solver for the 2D Helmholtz equation, with a special choice of integral transmission condition that involves polarizing the waves into one-way components. This refinement of the transmission condition is the key to combining local direct solves...
Proceedings Papers
Publisher: Society of Exploration Geophysicists
Paper presented at the 2014 SEG Annual Meeting, October 26–31, 2014
Paper Number: SEG-2014-1412
... ,Novosibirsk ,Russia Summary We propose an iterative method for solving the Helmholtz equation in heterogeneous 3D media based on the usage of a Krylov-type technique with a semi-analytical preconditioner. The distinctive feature of our method is the use of the preconditioner, obtained as the solution...
Proceedings Papers
Publisher: Society of Exploration Geophysicists
Paper presented at the 2014 SEG Annual Meeting, October 26–31, 2014
Paper Number: SEG-2014-1566
... samples can be made according to the frequency spectrum of the source wavelet and/or data. Several synthetic examples demonstrate the validity of the proposed approach. helmholtz equation reservoir characterization coefficient frequency frequency-domain reverse-time migration regularized...
Proceedings Papers
Publisher: Society of Exploration Geophysicists
Paper presented at the 2014 SEG Annual Meeting, October 26–31, 2014
Paper Number: SEG-2014-0795
... Summary Seismic modeling in the frequency domain results in a Helmholtz equation. A Krylov-based iterative solver is commonly used for the solution of large-size inhomogeneous problems. However, it suffers from slow iterative convergence or even divergence. In this paper, we develop...
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