Journal ArticleDOI
Numerical modeling of Gaussian beam propagation and diffraction in inhomogeneous media based on the complex eikonal equation
Xingguo Huang,Hui Sun +1 more
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TLDR
In this article, a modified fast marching method was proposed to address the irregular boundary near the curved central ray in Gaussian beam wave propagation and diffraction in the subsurface with complex geological structure.Abstract:
Gaussian beam is an important complex geometrical optical technology for modeling seismic wave propagation and diffraction in the subsurface with complex geological structure. Current methods for Gaussian beam modeling rely on the dynamic ray tracing and the evanescent wave tracking. However, the dynamic ray tracing method is based on the paraxial ray approximation and the evanescent wave tracking method cannot describe strongly evanescent fields. This leads to inaccuracy of the computed wave fields in the region with a strong inhomogeneous medium. To address this problem, we compute Gaussian beam wave fields using the complex phase by directly solving the complex eikonal equation. In this method, the fast marching method, which is widely used for phase calculation, is combined with Gauss–Newton optimization algorithm to obtain the complex phase at the regular grid points. The main theoretical challenge in combination of this method with Gaussian beam modeling is to address the irregular boundary near the curved central ray. To cope with this challenge, we present the non-uniform finite difference operator and a modified fast marching method. The numerical results confirm the proposed approach.read more
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Journal ArticleDOI
Target-Oriented Inversion of Time-Lapse Seismic Waveform Data
TL;DR: In this article, an efficient target-oriented inversion scheme for time-lapse seismic data using an integral equation formulation with Gaussian beam based Green's function approach is presented.
Journal ArticleDOI
Traveltime approximation for strongly anisotropic media using the homotopy analysis method
Xingguo Huang,Stewart Greenhalgh +1 more
TL;DR: In this article, the authors presented a retrieved zero-order deformation equation that creates a map from the anisotropic eikonal equation to a linearized partial differential equation system based on the homotopy analysis method.
Journal ArticleDOI
Extended Beam Approximation for High-Frequency Wave Propagation
TL;DR: The author presents an extension of the Airybeam, referred to as the Gaussian Airy beam, to simulate high-frequency wave propagation in inhomogeneous media and examines the effectiveness of the method for high- frequencies wavefields by performing numerical simulations for models exhibiting pronounced heterogeneity.
Journal ArticleDOI
High-precision Joint 2D Traveltime Calculation for Seismic Processing
TL;DR: A joint traveltime calculation method is put forward to address the problem of poor calculation precision of Fast Marching Method when it is applied to the largescale model, which is an essential reason for the low accuracy of the whole algorithm.
References
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Book
Principles of Optics
TL;DR: In this paper, the authors discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals, including interference, interferometers, and diffraction.
Principles of Optics
TL;DR: In this article, the authors discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals, including interference, interferometers, and diffraction.
Journal ArticleDOI
Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science (2nd edition)
Journal ArticleDOI
A fast marching level set method for monotonically advancing fronts
TL;DR: A fast marching level set method is presented for monotonically advancing fronts, which leads to an extremely fast scheme for solving the Eikonal equation.
Book
Level set methods and fast marching methods : evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science
TL;DR: In this paper, the Hamilton-Jacobi equations and associated theory are used to formulate the interface propagation problem and then algorithms for the initial and boundary value formulations are proposed for semi-conductor manufacturing.