Gaussian beam decomposition of high frequency wave fields using expectation–maximization

Ariel, Gil; Engquist, Björn; Tanushev, Nicolay M.; Tsai, Richard

doi:10.1016/j.jcp.2010.12.018

Cited by 21 publications

(20 citation statements)

References 28 publications

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“…A recent survey of Gaussian beam methods can be found in [27]. Numerical approaches for treating general high frequency initial data for superposition over physical space were considered in [28,29] for the wave equation.…”

Section: Introductionmentioning

confidence: 99%

A wavefront-based Gaussian beam method for computing high frequency wave propagation problems

Motamed

Runborg

2015

Computers & Mathematics with Applications

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a b s t r a c tWe present a novel wavefront method based on Gaussian beams for computing high frequency wave propagation problems. Unlike standard geometrical optics, Gaussian beams compute the correct solution of the wave field also at caustics. The method tracks a front of two canonical beams with two particular initial values for width and curvature. In a fast post-processing step, from the canonical solutions we recreate any other Gaussian beam with arbitrary initial data on the initial front. This provides a simple mechanism to include a variety of optimization processes, including error minimization and beam width minimization, for a posteriori selection of optimal beam initial parameters. The performance of the method is illustrated with two numerical examples.Published by Elsevier Ltd.

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Section: Introductionmentioning

confidence: 99%

A wavefront-based Gaussian beam method for computing high frequency wave propagation problems

Motamed

Runborg

2015

Computers & Mathematics with Applications

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“…Specifically, one decomposes the initial wave function into localized wave packets (Gaussian beams) which are then evolved individually along particle trajectories and finally summed up to construct the solution at a later time. It was first studied rigorously in [25], and has seen many recent developments in both Eulerian and Lagrangian frameworks [13,14,15,17,20,21], error estimates [2,19], and fast Gaussian wave decompositions [1,24]. A related approach, known as the Hagedorn wave packet method, was studied in [8,6].…”

Section: Introductionmentioning

confidence: 99%

A Gaussian Beam Method for High Frequency Solution of Symmetric Hyperbolic Systems with Polarized Waves

Jefferis¹,

Jin²

2015

Multiscale Model. Simul.

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Symmetric hyperbolic systems include many physically relevant systems of partial differential equations (PDEs) such as Maxwell's equations, the elastic wave equations and the acoustic equations [26]. In this paper we extend the Gaussian beam method to efficiently compute the high frequency solutions to such systems with constant degeneracy that corresponds to polarized waves, in which the dispersion matrix of the hyperbolic system has eigenvalues with constant degeneracy over the domain of computation. The new results in this paper include new Gaussian beam equations in the presence of eigenvalue degeneracy, improved error estimates for Gaussian beam summation and a new multi-directional Eulerian summation formula which maintains accuracy after the formation of caustics.

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“…Wavefield decompositions using Gaussian beam/wave packets were also discussed by other authors in the space domain (Tanushev ; Tanushev, Engquist, and Tsai ; Qian and Ying ,; Ariel et al . ; Tanushev et al . ).…”

Section: Introductionmentioning

confidence: 99%

Gabor‐frame‐based Gaussian packet migration

Geng

Gao

2014

Geophysical Prospecting

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We present a Gaussian packet migration method based on Gabor frame decomposition and asymptotic propagation of Gaussian packets. A Gaussian packet has both Gaussian‐shaped time–frequency localization and space–direction localization. Its evolution can be obtained by ray tracing and dynamic ray tracing. In this paper, we first briefly review the concept of Gaussian packets. After discussing how initial parameters affect the shape of a Gaussian packet, we then propose two Gabor‐frame‐based Gaussian packet decomposition methods that can sparsely and accurately represent seismic data. One method is the dreamlet–Gaussian packet method. Dreamlets are physical wavelets defined on an observation plane and can represent seismic data efficiently in the local time–frequency space–wavenumber domain. After decomposition, dreamlet coefficients can be easily converted to the corresponding Gaussian packet coefficients. The other method is the Gabor‐frame Gaussian beam method. In this method, a local slant stack, which is widely used in Gaussian beam migration, is combined with the Gabor frame decomposition to obtain uniform sampled horizontal slowness for each local frequency. Based on these decomposition methods, we derive a poststack depth migration method through the summation of the backpropagated Gaussian packets and the application of the imaging condition. To demonstrate the Gaussian packet evolution and migration/imaging in complex models, we show several numerical examples. We first use the evolution of a single Gaussian packet in media with different complexities to show the accuracy of Gaussian packet propagation. Then we test the point source responses in smoothed varying velocity models to show the accuracy of Gaussian packet summation. Finally, using poststack synthetic data sets of a four‐layer model and the two‐dimensional SEG/EAGE model, we demonstrate the validity and accuracy of the migration method. Compared with the more accurate but more time‐consuming one‐way wave‐equation‐based migration, such as beamlet migration, the Gaussian packet method proposed in this paper can correctly image the major structures of the complex model, especially in subsalt areas, with much higher efficiency. This shows the application potential of Gaussian packet migration in complicated areas.

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Gaussian beam decomposition of high frequency wave fields using expectation–maximization

Cited by 21 publications

References 28 publications

A wavefront-based Gaussian beam method for computing high frequency wave propagation problems

A wavefront-based Gaussian beam method for computing high frequency wave propagation problems

A Gaussian Beam Method for High Frequency Solution of Symmetric Hyperbolic Systems with Polarized Waves

Gabor‐frame‐based Gaussian packet migration

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