Path-integral analysis of scalar wave propagation in multiple-scattering random media

Samelsohn, Gregory; Mazar, Reuven

doi:10.1103/physreve.54.5697

Cited by 26 publications

(9 citation statements)

References 22 publications

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“…The two methods discussed above, the Born series and Rytov's technique, are the most commonly used techniques dealing with scalar wave propagation through random media. More recently, Samelsohn & Mazar (1996) have treated this problem using a path-integral analysis on the basis of the parabolic wave equation. For a detailed review of stochastic wave propagation and scattering in random media, see e.g.…”

Section: Wav E P R O Pag At I O N T H R O U G H F L U C T Uat I N G Mmentioning

confidence: 99%

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Probing solar convection

Brüggen¹

2000

Monthly Notices of the Royal Astronomical Society

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In the solar convection zone, acoustic waves are scattered by turbulent sound speed fluctuations. In this paper the scattering of waves by convective cells is treated using Rytov’s technique. Particular care is taken to include diffraction effects, which are important, especially for high‐degree modes that are confined to the surface layers of the Sun. The scattering leads to damping of the waves and causes a phase shift. Damping manifests itself in the width of the spectral peak of p‐mode eigenfrequencies. The contribution of scattering to the linewidths is estimated and the sensitivity of the results to the assumed spectrum of the turbulence is studied. Finally, the theoretical predictions are compared with recently measured linewidths of high‐degree modes.

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Section: Wav E P R O Pag At I O N T H R O U G H F L U C T Uat I N G Mmentioning

confidence: 99%

“…More recently, Samelsohn & Mazar (1996) have treated this problem using a path-integral analysis on the basis of the parabolic wave equation. For a detailed review of stochastic wave propagation and scattering in random media, see, e.g.…”

Section: Wave Propagation Through Fluctuating Mediamentioning

confidence: 99%

Probing solar convection

Brüggen¹

2000

Monthly Notices of the Royal Astronomical Society

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“…Path‐integral solutions for the scalar wave equation can also be obtained by introducing a ‘pseudo‐time’ variable that is used to transform the frequency‐domain equation to a parabolic form (e.g. Fishman & McCoy 1983; Samelsohn & Mazar 1996). However, these solutions require integration over the ‘pseudo‐time’ variable and over frequency, in addition to the integral over paths, and consequently it is not apparent that they can be efficiently evaluated in practice for heterogeneous media.…”

Section: Feynman Path Integralsmentioning

confidence: 99%

Path-summation waveforms

Lomax

1999

Geophys. J. Int.

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In this paper, we examine an efficient, practical method to calculate approximate, finite‐frequency waveforms for the early signals from a point source in 3‐D acoustic media with smoothly varying velocity and constant density. In analogy to the use of Feynman path integrals in quantum physics, we obtain an approximate waveform solution for the scalar wave equation by a Monte Carlo summation of elementary signals over a representative sample of all possible paths between a source and observation point. The elementary signal is formed from the convolution of the source time function with a time derivative of the Green’s function for the homogeneous problem. For each path, this elementary signal is summed into a time series at a traveltime obtained from an integral of slowness along the path. The constructive and destructive interference of these signals produces the approximate waveform response for the range of traveltimes covered by the sampled paths. We justify the path‐summation technique for a smooth medium using a heuristic construction involving the Helmholtz–Kirchhoff integral theorem. The technique can be applied to smooth, but strongly varying and complicated velocity structures. The approximate waveform includes geometrical spreading, focusing, defocusing and phase changes, but does not fully account for multiple scattering. We compare path‐summation waveforms with the exact solution for a 3‐D geometry involving a low‐velocity spherical inclusion, and with finite‐difference waveforms for a 2‐D structure with realistic, complicated velocity variations. In contrast to geometrical‐ray methods, the path‐summation approach reproduces finite‐frequency wave phenomena such as diffraction and does not exhibit singular behaviour. Relative to the finite‐difference numerical method, the path‐summation approach requires insignificant computer memory and, depending on the number of waveforms required, up to one to two orders of magnitude less computing time. The sampled paths and associated traveltimes produced by the path summation give a relation between the medium and the signal on the waveform that is not available with finite‐difference and finite‐element methods. Furthermore, the speed and accuracy of the path‐summation method may be sufficient to allow 3‐D waveform inversion using stochastic, non‐linear, global search methods.

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“…works in this spirit have already been presented in the past [3,4,5,6,7], but here we deal with the full vector version. To the best of our knowledge this have not yet been done.…”

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confidence: 99%

Path Integrals for Photonic Crystals

Dimant,

Levit

2009

Preprint

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We develop a path integrals approach for analyzing stationary light propagation appropriate for photonic crystals. The hermitian form of the stationary Maxwell equations is transformed into a quantum mechanical problem of a spin 1 particle with spin-orbit coupling and position dependent mass. After appropriate ordering several path integral representations of a solution are constructed. One leaves the propagation of polarization degrees of freedom in an operator form integrated over paths in coordinate space. The use of spin 1 coherent states allows to represent this part as a path integral over such states. Finally a path integral in transversal momentum space with explicit transversality enforced at every time slice is also given. As an example the geometrical optics limit is discussed and the ray equation is recovered together with the Rytov rotation of the polarization vector.

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Path-integral analysis of scalar wave propagation in multiple-scattering random media

Cited by 26 publications

References 22 publications

Probing solar convection

Probing solar convection

Path-summation waveforms

Path Integrals for Photonic Crystals

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