Shahram Khazaie, Régis Cottereau. Influence of local cubic anisotropy on the transition towards an equipartition regime in a 3D texture-less random elastic medium. Wave Motion, Elsevier, 2020, 96, pp.102574. ⟨10.1016/j.wavemoti.2020.102574⟩. ⟨hal-02566857⟩ Plus de détails...
At long lapse times in randomly fluctuating media with macroscopic isotropy (texture-less media), the energy of elastic waves is equipartitioned between compressional (P) and shear (S) waves. This property is independent of the local isotropy or anisotropy of the heterogeneous constitutive tensor and of the type of source. However the local symmetry of the constitutive tensor does influence the rate of convergence to equipartition and this paper discusses the precise influence of local anisotropy on the time required to reach equipartition. More particularly, a randomly-fluctuating medium is considered, whose behavior is statistically isotropic, and locally cubic. After calculating all the differential and total scattering cross-sections in that case, an analytical formula is derived for the rate of convergence to the equipartition regime, function of the second-order statistics of the mechanical parameter fields (bulk and shear moduli and anisotropy parameter). The local anisotropy is shown to influence strongly that transition rate, with a faster transition when the fluctuations of the anisotropy parameter are positively correlated to those of the shear modulus. A numerical model is constructed to illustrate numerically these results. Since the asymptotic regime of equipartition cannot be simulated directly because it would require too large a computational domain, boundaries are introduced and mechanical properties are chosen so as to minimize their influence on equipartition.
Shahram Khazaie, Régis Cottereau. Influence of local cubic anisotropy on the transition towards an equipartition regime in a 3D texture-less random elastic medium. Wave Motion, Elsevier, 2020, 96, pp.102574. ⟨10.1016/j.wavemoti.2020.102574⟩. ⟨hal-02566857⟩
Xun Wang, Shahram Khazaie, Dimitri Komatitsch, Pierre Sagaut. Sound-Source Localization in Range-Dependent Shallow-Water Environments Using a Four-Layer Model. IEEE Journal of Oceanic Engineering, Institute of Electrical and Electronics Engineers, 2017, pp.1 - 9. ⟨10.1109/JOE.2017.2775978⟩. ⟨hal-01702364⟩ Plus de détails...
Sound-source localization in shallow water is a difficult task due to the complicated environment, e.g., complex sound-speed profile and irregular water bottom reflections. Full-wave numerical techniques are currently able to accurately simulate the propagation of sound waves in such complex environments. However, the source localization problem, which generally involves a large number of sound propagation calculations, still requires a fast computation of the wave equation, and thus a simplified model is well advised. In this paper, a four-layer model is considered, which is able to approximate a wide range of shallow-water environments, particularly those in summer conditions. More specifically, the medium is assumed to be horizontally stratified and vertically divided into four layers, and the sound speed in each layer is assumed to be constant or varying linearly. Under this assumption, the wave propagation can be rapidly computed via a classical wave number integration method. The main contribution of this paper is to show the suitability of the four-layer model in terms of source localization in a complex (range-dependent) environment. The sound-speed profile is assumed to be vertically irregular and horizontally slowly varying and the bottom is nonflat. In the forward problem, sound propagation in complex underwater environments is simulated via a time-domain full-wave simulation approach called the spectral-element method. The source localization error due to model imprecision is analyzed.
Xun Wang, Shahram Khazaie, Dimitri Komatitsch, Pierre Sagaut. Sound-Source Localization in Range-Dependent Shallow-Water Environments Using a Four-Layer Model. IEEE Journal of Oceanic Engineering, Institute of Electrical and Electronics Engineers, 2017, pp.1 - 9. ⟨10.1109/JOE.2017.2775978⟩. ⟨hal-01702364⟩
Xun Wang, Shahram Khazaie, Luca Margheri, Pierre Sagaut. Shallow water sound source localization using the iterative beamforming method in an image framework. Journal of Sound and Vibration, Elsevier, 2017, 395, pp.354 - 370. ⟨10.1016/j.jsv.2017.02.032⟩. ⟨hal-01527615⟩ Plus de détails...
Shallow water is a complicated sound propagation medium due to multiple reflections by water surface and bottom, imprecisely measured sound speed, noisy environment, etc. Therefore, in order to localize a shallow water sound source, classical signal processing techniques must be improved by taking these complexities into account. In this work, the multiple reflections and uncertain reflectivity of water bottom are explicitly modeled. In the proposed model, a measured signal is a mixture of the direct propagation from the source and the multiple reflections. Instead of solving the Helmholtz equation with boundary conditions of reflections, each signal is interpreted as a superposition of signals emitting from the physical source and its image sources in a free space, which results in a fast computation of sound propagation. Then, the source location, along with its amplitude, reflection paths and power loss of bottom reflection, is estimated via the iterative beamforming (IB) method, which alternatively estimates the source contributions and performs beamforming on these estimates until convergence. This approach does not need to compute the sound propagation for all the possible source locations in a large space, which thus leads to a low computational cost. Finally, numerical simulations are introduced to illustrate the advantage of the proposed model and the source estimation method. The sensitivity of the proposed method with respect to model parameter uncertainties is also investigated via a full uncertainty quantification analysis. The localization error of IB is proved to be acceptable in the given error range of sound speed and water depth. Besides, the IB source estimate is more sensitive to the sound speed while the matched-field processing methods have a stronger sensitivity to the water depth: this result can guide the choice of source localization method in different cases of model parameter uncertainties.
Xun Wang, Shahram Khazaie, Luca Margheri, Pierre Sagaut. Shallow water sound source localization using the iterative beamforming method in an image framework. Journal of Sound and Vibration, Elsevier, 2017, 395, pp.354 - 370. ⟨10.1016/j.jsv.2017.02.032⟩. ⟨hal-01527615⟩
Shahram Khazaie, Régis Cottereau, Didier Clouteau. Numerical observation of the equipartition regime in a 3D random elastic medium, and discussion of the limiting parameters. Computers & Geosciences, Elsevier, 2017, 102, pp.56-67. ⟨10.1016/j.cageo.2017.02.007⟩. ⟨hal-01473195⟩ Plus de détails...
At long lapse times in the weakly scattering regime, the energy of the coda in a randomly fluctuating isotropic medium is equipartitioned between P and S modes. This behavior is well understood mathematically and physically for full spaces. For realistic domains, analytical results are more scarce and numerical simulations become a valuable tool. This paper discusses, based on numerical simulations of wave propagation in a 3D randomly heterogeneous elastic medium, the transition to an equipartitioned regime of the wave field. Both the time to transition and the value of the ratio of energies after transition are evaluated. Several influencing parameters are discussed, either physical (ratio of background P-and S-velocities, propagation length, variance of the heterogeneities) or numerical (influence of Perfectly Matched Layers). Setting up of a localization regime, inefficient mixture of body waves and small propagation length compared to the transport mean free paths are identified as constraining for the transition toward an equipartition regime.
Shahram Khazaie, Régis Cottereau, Didier Clouteau. Numerical observation of the equipartition regime in a 3D random elastic medium, and discussion of the limiting parameters. Computers & Geosciences, Elsevier, 2017, 102, pp.56-67. ⟨10.1016/j.cageo.2017.02.007⟩. ⟨hal-01473195⟩
Shahram Khazaie, Régis Cottereau, D Clouteau. Influence of the spatial correlation structure of an elastic random medium on its scattering properties. Journal of Sound and Vibration, Elsevier, 2016, 370, pp.132-148. ⟨10.1016/j.jsv.2016.01.012⟩. ⟨hal-01281405⟩ Plus de détails...
In the weakly heterogeneous regime of elastic wave propagation through a random medium, transport and diffusion models for the energy densities can be set up. In the isotropic case, the scattering cross sections are explicitly known as a function of the wave number and the correlations of the Lamé parameters and density. In this paper, we discuss the precise influence of the correlation structure on the scattering cross sections, mean free paths and diffusion parameter, and separate that influence from that of the correlation length and variance. We also analyze the convergence rates towards the low-and high-frequency ranges. For all analyses, we consider five different correlation structures, that allow us to explore a wide range of behaviors. We identify that the controlling factors for the low-frequency behavior are the value of the Power Spectral Density Function (PSDF) and its first non-vanishing derivative at the origin. In the high frequency range, the controlling factor is the third moment of the PSDF (which may be unbounded).
Shahram Khazaie, Régis Cottereau, D Clouteau. Influence of the spatial correlation structure of an elastic random medium on its scattering properties. Journal of Sound and Vibration, Elsevier, 2016, 370, pp.132-148. ⟨10.1016/j.jsv.2016.01.012⟩. ⟨hal-01281405⟩
Shahram Khazaie, Xun Wang, Pierre Sagaut. Localization of random acoustic sources in an inhomogeneous medium. Journal of Sound and Vibration, Elsevier, 2016, 384, pp.75 - 93. ⟨10.1016/j.jsv.2016.08.004⟩. ⟨hal-01375680⟩ Plus de détails...
In this paper, the localization of a random sound source via different source localization methods is considered, the emphasis being put on the robustness and the accuracy of classical methods in the presence of uncertainties. The sound source position is described by a random variable and the sound propagation medium is assumed to have spatially varying parameters with known values. Two approaches are used for the source identification: time reversal and beamforming. The probability density functions of the random source position are estimated using both methods. The focal spot resolutions of the time reversal estimates are also evaluated. In the numerical simulations, two media with different correlation lengths are investigated to account for two different scattering regimes: one has a correlation length relatively larger than the wavelength and the other has a correlation length comparable to the wavelength. The results show that the required sound propagation time and source estimation robustness highly depend on the ratio between the correlation length and the wavelength. It is observed that source identification methods have different robustness in the presence of uncertainties. Advantages and weaknesses of each method are discussed.
Shahram Khazaie, Xun Wang, Pierre Sagaut. Localization of random acoustic sources in an inhomogeneous medium. Journal of Sound and Vibration, Elsevier, 2016, 384, pp.75 - 93. ⟨10.1016/j.jsv.2016.08.004⟩. ⟨hal-01375680⟩