Relevant bibliographies by topics / Eikonal equation

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Eikonal equation'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Eikonal equation"

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Hu, Jiangtao, Jianliang Qian, Jian Song, Min Ouyang, Junxing Cao, and Shingyu Leung. "Eulerian partial-differential-equation methods for complex-valued eikonals in attenuating media." GEOPHYSICS 86, no. 4 (2021): T179—T192. http://dx.doi.org/10.1190/geo2020-0659.1.

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Seismic waves in earth media usually undergo attenuation, causing energy losses and phase distortions. In the regime of high-frequency asymptotics, a complex-valued eikonal is an essential ingredient for describing wave propagation in attenuating media, where the real and imaginary parts of the eikonal function capture dispersion effects and amplitude attenuation of seismic waves, respectively. Conventionally, such a complex-valued eikonal is mainly computed either by tracing rays exactly in complex space or by tracing rays approximately in real space so that the resulting eikonal is distribut
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Fedorov, Arseny V., Christina A. Stepa, Anna V. Korolkova, Migran N. Gevorkyan, and Dmitry S. Kulyabov. "Methodological derivation of the eikonal equation." Discrete and Continuous Models and Applied Computational Science 31, no. 4 (2023): 399–418. http://dx.doi.org/10.22363/2658-4670-2023-31-4-399-418.

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Usually, when working with the eikonal equation, reference is made to its derivation in the monograph by Born and Wolf. The derivation of this equation was done rather carelessly. Understanding this derivation requires a certain number of implicit assumptions. For a better understanding of the eikonal approximation and for methodological purposes, the authors decided to repeat the derivation of the eikonal equation, explicating all possible assumptions. Methodically, the following algorithm for deriving the eikonal equation is proposed. The wave equation is derived from Maxwell’s equation. In
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Leung, Shingyu, Jiangtao Hu, and Jianliang Qian. "Liouville partial-differential-equation methods for computing 2D complex multivalued eikonals in attenuating media." GEOPHYSICS 87, no. 2 (2021): T71—T84. http://dx.doi.org/10.1190/geo2021-0113.1.

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We have developed a Liouville partial-differential-equation (PDE)-based method for computing complex-valued eikonals in real phase space in the multivalued sense in attenuating media with frequency-independent qualify factors, where the new method computes the real and imaginary parts of the complex-valued eikonal in two steps by solving Liouville equations in real phase space. Because the earth is composed of attenuating materials, seismic waves usually attenuate so that seismic data processing calls for properly treating the resulting energy losses and phase distortions of wave propagation.
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Meher, Mehrollah, and Davood Rostamy. "Hybrid of differential quadrature and sub-gradients methods for solving the system of Eikonal equations." Nonlinear Engineering 10, no. 1 (2021): 436–49. http://dx.doi.org/10.1515/nleng-2021-0035.

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Abstract Many important natural phenomena of wave propagations are modeled by Eikonal equations and a variety of new methods are needed to solve them. The differential quadrature method (DQM) is an effective numerical method for solving the system of differential equations that can achieve accurate numerical results using fewer grid points and therefore requires relatively little computational effort. In this paper, we focus on the implementation of the non-smooth Eikonal optimization by using a hybrid of polynomial differential quadrature (PDQ) or Fourier differential quadrature (FDQ) method
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Liner, Christopher L. "Some analytic aspects of a 2.5-D wave equation." GEOPHYSICS 60, no. 5 (1995): 1536–40. http://dx.doi.org/10.1190/1.1443886.

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A recently proposed 2.5-D wave equation is transformed to the frequency domain where WKBJ analysis is applied. This analysis assumes a general c(x, z) velocity field. Eikonal and transport equations are derived and compared to their 2-D and in‐plane 3-D counterparts. The implied eikonal equation is shown to be identical to the 2-D and in‐plane 3-D eikonal. This assures traveltime accuracy of the 2.5-D wave equation for any velocity model. The implied transport equation is shown to be consistent with 3-D theory in a constant velocity region containing a point source.
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Gudynas, Gintautas. "Representation Formula for Solutions of Eikonal Type Equations." Nonlinear Analysis: Modelling and Control 6, no. 1 (2001): 57–65. http://dx.doi.org/10.15388/na.2001.6.1.15225.

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Equations of an eikonal type ones arise in many areas of applications, including optics, fluid mechanics, material sciences, and control theory. This article investigates the representation formula for semiconcave solutions of the boundary problem for eikonal type equation. The formula is given by forming envelope of some fundamental solutions of the equation. Using these fundamental solutions we obtain the representation formula for solutions of Cauchy problem for appropriate Hamilton – Jacobi equation.
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Bekar, Ali Can, Erdogan Madenci, Ehsan Haghighat, Umair bin Waheed, and Tariq Alkhalifah. "Solving the eikonal equation for compressional and shear waves in anisotropic media using peridynamic differential operator." Geophysical Journal International 229, no. 3 (2022): 1942–63. http://dx.doi.org/10.1093/gji/ggac037.

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SUMMARY Traveltimes of compressional (P) and shear (S) waves have proven essential in many earthquake and exploration seismology applications. An accurate and efficient traveltime computation for P and S waves is crucial for the success of these applications. However, solving the eikonal equation with a complex phase velocity field in anisotropic media is challenging. The eikonal equation is a first-order nonlinear hyperbolic partial differential equation. It represents the high-frequency asymptotic approximation of the wave equation. The fast marching and sweeping methods are commonly used du
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Sava, Paul, and Sergey Fomel. "3-D traveltime computation using Huygens wavefront tracing." GEOPHYSICS 66, no. 3 (2001): 883–89. http://dx.doi.org/10.1190/1.1444977.

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Traveltime computation is widely used in seismic modeling, imaging, and velocity analysis. The two most commonly used methods are ray tracing and numerical solutions to the eikonal equation. Eikonal solvers are fast and robust but are limited to computing only the first‐arrival traveltimes. Ray tracing can compute multiple arrivals but lacks the robustness of eikonal solvers. We propose a robust and complete method of traveltime computation. It is based on a system of partial differential equations, which is equivalent to the eikonal equation but formulated in the ray‐coordinates system. We us
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Bouin, Emeric, and Vincent Calvez. "A kinetic eikonal equation." Comptes Rendus Mathematique 350, no. 5-6 (2012): 243–48. http://dx.doi.org/10.1016/j.crma.2012.03.009.

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Li, Siwei, Alexander Vladimirsky, and Sergey Fomel. "First-break traveltime tomography with the double-square-root eikonal equation." GEOPHYSICS 78, no. 6 (2013): U89—U101. http://dx.doi.org/10.1190/geo2013-0058.1.

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First-break traveltime tomography is based on the eikonal equation. Because the eikonal equation is solved at fixed-shot positions and only receiver positions can move along the raypath, the adjoint-state tomography relies on inversion to resolve possible contradicting information between independent shots. The double-square-root (DSR) eikonal equation allows not only the receivers but also the shots to change position, and thus describes the prestack survey as a whole. Consequently, its linearized tomographic operator naturally handles all shots together, in contrast with the shotwise approac
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Dissertations / Theses on the topic "Eikonal equation"

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Covello, Paul Eugene. "Solving the eikonal equation on an adaptive mesh /." For electronic version search Digital dissertations database. Restricted to UC campuses. Access is free to UC campus dissertations, 2003. http://uclibs.org/PID/11984.

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Wojcik, Stefanie E. "Effects of internal waves and turbulent fluctuations on underwater acoustic propagation." Link to electronic thesis, 2006. http://www.wpi.edu/Pubs/ETD/Available/etd-030906-152505/.

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Gibbs, Simon Paul. "Solutions of the reaction-diffusion eikonal equation on closed two-dimensional manifolds." Thesis, Glasgow Caledonian University, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.357134.

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Chang, Kaiwen. "Apprentissage artificiel pour la segmentation d'image." Thesis, Paris Sciences et Lettres (ComUE), 2019. http://www.theses.fr/2019PSLEM058.

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La présente thèse vise à développer une méthodologie générale basée sur des méthodes d’apprentissage pour effectuer la segmentation d’une base de données constituée d’images similaires, à partir d’un nombre limité d’exemples d’entraînement. Cette méthodologie est destinée à être appliquée à des images recueillies dans le cadre d’observations de la terre ou lors d’expériences menées en science des matériaux, pour lesquelles il n’y a pas suffisamment d’exemples d’entraînement pour appliquer des méthodes basées sur des techniques d’apprentissage profond. La méthodologie proposée commence par cons
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Pila, Matheus Fabiano 1979. "Modelamento sismico assintotico utilizando diferenças finitas." [s.n.], 2005. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307616.

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Orientadores: Lucio Tunes dos Santos, Maria Amélia Novais Schleicher<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-04T04:00:54Z (GMT). No. of bitstreams: 1 Pila_MatheusFabiano_M.pdf: 955722 bytes, checksum: adb4b488d6a2e8995d1f8985186d2693 (MD5) Previous issue date: 2005<br>Mestrado<br>Geofisica Computacional<br>Mestre em Matemática Aplicada
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GIORGIERI, ELENA. "A boundary value problem for a PDE model in mass transfer theory: representations of solutions and regularity results." Doctoral thesis, Università degli Studi di Roma "Tor Vergata", 2006. http://hdl.handle.net/2108/211.

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Goldstein, Gérald. "Description de la dissociation de noyaux à halo par l'approximation eikonale dynamique." Doctoral thesis, Universite Libre de Bruxelles, 2007. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210667.

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Depuis leur découverte au milieu des années quatre-vingt, les noyaux à halo n'ont cessé d'intriguer et de fasciner. Cette découverte a été rendue possible par le développement de faisceaux d'ions radioactifs au cours des années septante. Cette performance a ouvert le champ de l'exploration des propriétés des noyaux atomiques aux frontières de la stabilité.<p><p>Les noyaux à halo présentent une taille beaucoup plus grande que prévue par l'hypothèse communément adoptée du noyau sphérique et seraient constitués d'un coeur, qui a les propriétés d'un noyau normal, auquel un ou deux neutrons qui for
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Belayouni, Nidhal. "Nouveaux algorithmes efficaces de modélisation 2D et 3D : Temps des premières arrivées, angles à la source et amplitudes." Phd thesis, Ecole Nationale Supérieure des Mines de Paris, 2013. http://pastel.archives-ouvertes.fr/pastel-00871200.

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Les temps de trajet, amplitudes et angles à la source des ondes sismiques sont utilisés dans de nombreuses applications telles que la migration, la tomographie, l'estimation de la sensibilité de détection et la localisation des microséismes. Dans le contexte de la microsismicité, il est nécessaire de calculer en quasi temps réel ces attributs avec précision. Nous avons développé ici un ensemble d'algorithmes rapides et précis en 3D pour des modèles à fort contraste de vitesse.Nous présentons une nouvelle méthode pour calculer les temps de trajet, les amplitudes et les angles à la source des on
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Belayouni, Nidhal. "Nouveaux algorithmes efficaces de modélisation 2D et 3D : Temps des premières arrivées, angles à la source et amplitudes." Electronic Thesis or Diss., Paris, ENMP, 2013. http://www.theses.fr/2013ENMP0012.

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Les temps de trajet, amplitudes et angles à la source des ondes sismiques sont utilisés dans de nombreuses applications telles que la migration, la tomographie, l'estimation de la sensibilité de détection et la localisation des microséismes. Dans le contexte de la microsismicité, il est nécessaire de calculer en quasi temps réel ces attributs avec précision. Nous avons développé ici un ensemble d'algorithmes rapides et précis en 3D pour des modèles à fort contraste de vitesse.Nous présentons une nouvelle méthode pour calculer les temps de trajet, les amplitudes et les angles à la source des on
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Fontaine, Adrien. "Relations de dispersion dans les plasmas magnétisés." Thesis, Rennes 1, 2017. http://www.theses.fr/2017REN1S029/document.

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Cette thèse décrit comment les ondes électromagnétiques se propagent dans les plasmas magnétisés, lorsque les fréquences sollicitées sont proches de la fréquence électron cyclotron. Elle porte sur l’analyse mathématique des variétés caractéristiques qui sont associées à des systèmes de type Vlasov-Maxwell relativiste avec paramètres rapides.La première partie s’intéresse aux plasmas froids des magnétosphères planétaires. On explique comment obtenir les relations de dispersion dans le cas d’un dipôle magnétique. Cela conduit à l’étude détaillée de certaines variéte
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Books on the topic "Eikonal equation"

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United States. National Aeronautics and Space Administration. Scientific and Technical Information Division., ed. Eikonal solutions to optical model coupled-channel equations. National Aeronautics and Space Administration, Scientific and Technical Information Division, 1988.

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United States. National Aeronautics and Space Administration. Scientific and Technical Information Division., ed. Eikonal solutions to optical model coupled-channel equations. National Aeronautics and Space Administration, Scientific and Technical Information Division, 1988.

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Cotaras, Frederick D. Nonlinear effects in long range underwater acoustic propagation. Applied Research Laboratories, University of Texas at Austin, 1985.

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A, Walther. The ray and wave theory of lenses. Cambridge University Press, 2006.

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A, Walther. The ray and wave theory of lenses. Cambridge University Press, 1995.

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Basics of Functional Methods and Eikonal Models. World Scientific Publishing Co Pte Ltd, 1990.

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A, Walther. Ray and Wave Theory of Lenses. Cambridge University Press, 2011.

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Mann, Peter. Canonical & Gauge Transformations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0018.

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In this chapter, the Hamilton–Jacobi formulation is discussed in two parts: from a generating function perspective and as a variational principle. The Poincaré–Cartan 1-form is derived and solutions to the Hamilton–Jacobi equations are discussed. The canonical action is examined in a fashion similar to that used for analysis in previous chapters. The Hamilton–Jacobi equation is then shown to parallel the eikonal equation of wave mechanics. The chapter discusses Hamilton’s principal function, the time-independent Hamilton–Jacobi equation, Hamilton’s characteristic function, the rectification th
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Sharma, Subodh K., and David J. Sommerford. Light Scattering by Optically Soft Particles: Theory and Applications. Springer, 2006.

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Sharma, Subodh K., and David J. Sommerford. Light Scattering by Optically Soft Particles: Theory and Applications. Springer Berlin / Heidelberg, 2014.

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Book chapters on the topic "Eikonal equation"

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Jacquemet, Vincent. "Eikonal Equation: Computation." In Encyclopedia of Applied and Computational Mathematics. Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-540-70529-1_297.

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Dacorogna, Bernard, and Paolo Marcellini. "The Complex Eikonal Equation." In Implicit Partial Differential Equations. Birkhäuser Boston, 1999. http://dx.doi.org/10.1007/978-1-4612-1562-2_9.

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Bellman, Richard, and Ramabhadra Vasudevan. "Eikonal Equation and the WKB Approximation." In Wave Propagation. Springer Netherlands, 1986. http://dx.doi.org/10.1007/978-94-009-5227-0_2.

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Ta, Vinh-Thong, Abderrahim Elmoataz, and Olivier Lézoray. "Adaptation of Eikonal Equation over Weighted Graph." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02256-2_16.

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Angenent, S. B., and D. G. Aronson. "The focusing problem for the Eikonal equation." In Nonlinear Evolution Equations and Related Topics. Birkhäuser Basel, 2003. http://dx.doi.org/10.1007/978-3-0348-7924-8_7.

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Siddiqi, Kaleem, Allen Tannenbaum, and Steven W. Zucker. "A Hamiltonian Approach to the Eikonal Equation." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/3-540-48432-9_1.

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Rangarajan, Anand, and Karthik S. Gurumoorthy. "A Schrödinger Wave Equation Approach to the Eikonal Equation: Application to Image Analysis." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-03641-5_11.

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Churbanov, Alexander G., and Petr N. Vabishchevich. "Numerical Solving a Boundary Value Problem for the Eikonal Equation." In Finite Difference Methods. Theory and Applications. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11539-5_3.

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Albano, Paolo. "Some Remarks on the Dirichlet Problem for the Degenerate Eikonal Equation." In Trends in Control Theory and Partial Differential Equations. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-17949-6_1.

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Bagnerini, P., P. Hoch, and M. Rascle. "The Eikonal Equation on a Manifold. Applications to Grid Generation or Refinement." In Hyperbolic Problems: Theory, Numerics, Applications. Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8370-2_12.

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Conference papers on the topic "Eikonal equation"

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Capozzoli, A., C. Curcio, A. Liseno, and S. Savarese. "Numerical Solution of the 3D Eikonal Equation by the Fast Marching Method for Electromagnetic Problems." In 2024 IEEE International Symposium on Antennas and Propagation and INC/USNC‐URSI Radio Science Meeting (AP-S/INC-USNC-URSI). IEEE, 2024. http://dx.doi.org/10.1109/ap-s/inc-usnc-ursi52054.2024.10687016.

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Chiri, Maria Teresa, Kenneth D. Czuprynski, and Ludmil T. Zikatanov. "Weakly Coupled Systems of Eikonal Equations in Path-Planning Problems." In 2024 American Control Conference (ACC). IEEE, 2024. http://dx.doi.org/10.23919/acc60939.2024.10644838.

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Kulyabov, Dmitry S., Anna V. Korolkova, Tatiana R. Velieva, and Migran N. Gevorkyan. "Numerical analysis of eikonal equation." In Saratov Fall Meeting 2018: Laser Physics, Photonic Technologies, and Molecular Modeling, edited by Vladimir L. Derbov. SPIE, 2019. http://dx.doi.org/10.1117/12.2525142.

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Cunha*, Carlos A., Claudio Guerra, and Jessé Costa. "Robust Picking with the Eikonal Equation." In 14th International Congress of the Brazilian Geophysical Society & EXPOGEF, Rio de Janeiro, Brazil, 3-6 August 2015. Brazilian Geophysical Society, 2015. http://dx.doi.org/10.1190/sbgf2015-257.

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Biondi, B. "Solving the frequency‐dependent eikonal equation." In SEG Technical Program Expanded Abstracts 1992. Society of Exploration Geophysicists, 1992. http://dx.doi.org/10.1190/1.1821982.

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Le Bouteiller, P., M. Ben Jemaa, H. Chauris, et al. "Discontinuous Galerkin Method for TTI Eikonal Equation." In 79th EAGE Conference and Exhibition 2017. EAGE Publications BV, 2017. http://dx.doi.org/10.3997/2214-4609.201701253.

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Hasanov, Elman. "On Complex Solutions of the Eikonal Equation." In 2007 International Conference on Electromagnetics in Advanced Applications. IEEE, 2007. http://dx.doi.org/10.1109/iceaa.2007.4387383.

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Mokrý, Pavel. "Iterative method for solving the eikonal equation." In Optics and Measurement 2016 International Conference, edited by Jana Kovacicinova. SPIE, 2016. http://dx.doi.org/10.1117/12.2257326.

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Waheed, U., and T. Alkhalifah. "Fast Sweeping Methods for Factored TTI Eikonal Equation." In 77th EAGE Conference and Exhibition 2015. EAGE Publications BV, 2015. http://dx.doi.org/10.3997/2214-4609.201412998.

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Murman, Scott M., and Laslo T. Diosady. "A Spectral-Element Approach for the Eikonal Equation." In 22nd AIAA Computational Fluid Dynamics Conference. American Institute of Aeronautics and Astronautics, 2015. http://dx.doi.org/10.2514/6.2015-2285.

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Reports on the topic "Eikonal equation"

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Cornea, Emil, Ralph Howard, and Per-Gunnar Martinsson. Solutions Near Singular Points to the Eikonal and Related First Order Non-linear Partial Differential Equations in Two Independent Variables. Defense Technical Information Center, 2000. http://dx.doi.org/10.21236/ada640692.

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