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Helmholtz equation

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Proceedings Papers

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

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

Paper presented at the 2017 SEG International Exposition and Annual Meeting, September 24–29, 2017
Paper Number: SEG-2017-17690586
...A 27-point finite difference method using a symmetric perfectly matched layer for the 3d Helmholtz equation Hyunseo Park*, Yoonseo Park, Jaejoon Lee and Changsoo Shin, Seoul National University Summary We present a frequency domain finite difference method using a symmetric form of the Perfectly...
Proceedings Papers

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

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

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

Paper presented at the 2015 SEG Annual Meeting, October 18–23, 2015
Paper Number: SEG-2015-5838886
...A short note on the nested-sweep polarized traces method for the 2D Helmholtz equation Leonardo Zepeda-Nu´n ez and Laurent Demanet Department of Mathematics and Earth Resources Laboratory, Massachusetts Institute of Technology SUMMARY We present a variant of the solver in Zepeda-Nu´n ez and De...
Proceedings Papers

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

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

Paper presented at the 2011 SEG Annual Meeting, September 18–23, 2011
Paper Number: SEG-2011-3158
... ABSTRACT The Helmholtz equation describes wave propagation in the frequency domain and, as such, can be used for seismic imaging and full waveform inversion. We present two novel preconditioners for the efficient solution of the Helmholtz equation in three dimensions. Both methods follow...
Proceedings Papers

Paper presented at the 2010 SEG Annual Meeting, October 17–22, 2010
Paper Number: SEG-2010-3103
... ABSTRACT We study the modelling of time-harmonic seismic data with the Helmholtz equation. We follow a two-step approach. First we discuss conditions on the regularity of the underlying wavespeed model for the direct solution of the Helmholtz equation. Secondly, we extend these conditions...
Proceedings Papers

Paper presented at the 2009 SEG Annual Meeting, October 25–30, 2009
Paper Number: SEG-2009-2557
.... Strictly speaking, in the above mentioned applications, one has to deal with a numerical solution of the wave equation derived for inhomogeneous media, or, in other cases, with the reduced wave equation, which is also known as the Helmholtz equation. Moreover, in Green’s function approximation using travel...
Proceedings Papers

Paper presented at the 2008 SEG Annual Meeting, November 9–14, 2008
Paper Number: SEG-2008-2122
... in the hard 2D synthetic Marmousi model. INTRODUCTION Seismic wavefield modeling is a technique which can be carried out in either the time domain or the frequency domain. When solutions to the Helmholtz equation for all frequencies are available, modeling in the frequency domain is equal to modeling...
Proceedings Papers

Paper presented at the 2002 SEG Annual Meeting, October 6–11, 2002
Paper Number: SEG-2002-1907
... boundary conditions. This article introduces few formulations for the compact scheme for the Helmholtz equation and effective strategy of incorporating absorption boundary conditions. It has been numerically verified that the resulting compact scheme is fourth-order in general heterogeneous media...
Proceedings Papers

Paper presented at the 2011 SEG Annual Meeting, September 18–23, 2011
Paper Number: SEG-2011-0196
... ABSTRACT We consider the discretization and approximate solution of in-homogeneous anisotropic ‘Helmholtzequations in 3D. The anisotropy comprises general (tilted) TI symmetries. In particular, we are concerned with solving these equations on a large domain, for a large number of different...
Proceedings Papers

Paper presented at the 2009 SEG Annual Meeting, October 25–30, 2009
Paper Number: SEG-2009-2531
... SUMMARY We present a joint seismic inverse scattering and finite-frequency (reflection) tomography program, formulated as a coupled set of optimization problems, in terms of inhomogeneous Helmholtz equations. A new structured approximate direct solver for the corresponding linear system...
Proceedings Papers

Paper presented at the 2010 SEG Annual Meeting, October 17–22, 2010
Paper Number: SEG-2010-1039
... SUMMARY We consider the discretization and solution of the 3D inhomogeneous Helmholtz equation on a large domain and for a large number of seismic sources in the context of 3D seismic imaging. We resort to a parsimonious mixed grid finite difference scheme and the perfect matched layer...
Proceedings Papers

Paper presented at the The Seventh International Offshore and Polar Engineering Conference, May 25–30, 1997
Paper Number: ISOPE-I-97-302
..., one can obtain an ordinary Helmholtz equation for constant depth and a corresponding inhomogeneous Helmholtz equation for the variable depth. The ordinary Helmholtz equation is easily solved by a regular BEM. Applying BEM to the inhomogeneous Helmholtz equation, the inhomogeneous part will result...
Proceedings Papers

Paper presented at the SEG International Exposition and Annual Meeting, October 11–16, 2020
Paper Number: SEG-2020-3427351
... the wavefield. A recently introduced machine learning (ML) framework, called physics-informed neural networks (NNs), is used to predict PDE solutions by setting the physical laws as loss functions. These NNs have shown their effectiveness in solving the Helmholtz equation specifically for the scattered...
Proceedings Papers

Paper presented at the 2015 SEG Annual Meeting, October 18–23, 2015
Paper Number: SEG-2015-5796514
... Summary A computational method is presented which enables one to trace exact frequency dependent rays when a solution to the Helmholtz equation is already available. In this paper also is provided the analysis of the properties of exact frequency dependent rays and compare them...

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