An unifying model for spectra of transmitted monochromatic waves

Lacaze, B.

doi:10.1016/j.wavemoti.2006.07.002

Cited by 10 publications

(17 citation statements)

References 19 publications

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“…which satisfies (17) and which then explains (13). In dictionaries of Laplace transforms (of one-sided probability densities), I have found only one law with this property.…”

Section: Appendix 2: the Law Of B(t)mentioning

confidence: 93%

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A stochastic model for acoustic attenuation

Lacaze¹

2007

Waves in Random and Complex Media

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Propagation of waves in gases or liquids has been observed for a long time in homogeneous or nonhomogeneous media. In acoustics, attenuation is a significant problem which is studied mainly through the 'equations of change' of fluid mechanics. These equations are based only on the macroscopic characteristics of the medium. Microscopic variations, related to other phenomena like Brownian motion or critical opalescence, are not taken into account. This paper provides a random one-ray model. This model explains the proportionality between the standard attenuation and the product between length and frequency squared in a logarithmic scale. The wave is shown to be necessarily associated with noise, even if this noise cannot be observed by devices. Furthermore, the 'coefficient of variation' defined in turbulent environments can be explained as a random version of the usual coefficient of attenuation.

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“…which satisfies (17) and which then explains (13). In dictionaries of Laplace transforms (of one-sided probability densities), I have found only one law with this property.…”

Section: Appendix 2: the Law Of B(t)mentioning

confidence: 93%

“…Secondly, we show how to explain the random increase of the attenuation which leads to the coefficient of variation, when inhomogeneities or eddies appear in the fluid. This kind of method was successfully applied to other phenomena [17], like backscattering on trees [18], backscattering on sea of radar waves [19], or HF propagation [20].…”

Section: Introductionmentioning

confidence: 99%

A stochastic model for acoustic attenuation

Lacaze¹

2007

Waves in Random and Complex Media

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“…In the Gaussian case, we can place ourselves in the framework of Gaussian processes where the family of admissible l (, !) is well defined [7]. The main problem for other stable distributions is the fact that second-order moments do not exist.…”

Section: Remarksmentioning

confidence: 99%

“…The model has to be flexible enough to fit a large class of spectra, because we know nothing about the 'noise'. This method was applied successfully to model phenomena in spectral bands from low frequencies up to light frequencies [7][8][9][10]. In these papers, the propagation time is modelled as a Gaussian process.…”

Section: Introductionmentioning

confidence: 99%

Random propagation times in ultrasonics

Lacaze¹

2010

Waves in Random and Complex Media

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The attenuation of acoustic waves is often in the form exp½Àaj!j b with 05b 2. For b ¼ 2, experiments show negligible dispersion. For b ¼ 1, the variation of the velocity is well-fitted by a logarithmic function, and by power functions when b 6 ¼ 1. An explanation of theses results has been provided by T.L. Szabo by extensions of the Kramers-Kronig relations. In this paper, we show that a random propagation time leads to similar results. This model explains the loss of power by the existence of noise which cannot be taken into account by the devices. Also, it explains the redshift linked to the wave bandwidth.

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“…We consider that the random character is summarized by a random propagation time. This process was successfully applied in other domains of propagation like acoustics, ultrasonics, or sea return [6]- [8]. In a first stage, we revisit the paper by Narayanan et al [1].…”

Section: Introductionmentioning

confidence: 99%

Backscattering From Trees Explained by Random Propagation Times

Lacaze¹

2012

IEEE Trans. Geosci. Remote Sensing

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Dealing with radar backscattering from trees, the Wong model is a mixing of Gaussian spectra with parameters deduced from considerations on motions of branches and leaves. Very detailed experiments by Narayanan et al. show gaps with this model. We show that autocorrelation functions by Narayanan et al. are very well fitted by functions in the form exp[−|τ /τ 0 | α ], 0 < α ≤ 2.In this paper, we prove that the random propagation time theory explains this property. I have shown in other papers that this theory is available to study power spectra in acoustics, ultrasonics, and electromagnetics.Index Terms-Radar backscatter, random propagation time, stable probability laws, stationary process.

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An unifying model for spectra of transmitted monochromatic waves

Cited by 10 publications

References 19 publications

A stochastic model for acoustic attenuation

A stochastic model for acoustic attenuation

Random propagation times in ultrasonics

Backscattering From Trees Explained by Random Propagation Times

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