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Matrix Approach of Seismic Imaging

Abstract : The project aims at extending to geophysical and seismic imaging a matrix approach of wave propagation in heterogeneous media. The method aims at separating single-scattering from multiple-scatterings contribution in a data set, thus allowing us to improve imaging in heterogeneous media, as if we could see through thick fog. The idea was successfully developed in the ultrasound imaging context at the Langevin Institute, restricted so far to 1-D linear arrays of ultrasonic sources/receivers. It consists in exploiting the set of inter-element impulse responses associated to an array of sensors. This response matrix contains all the information available on the scattering medium under investigation. A set of matrix operations can then be applied whether it be for detection, imaging, characterization or monitoring purposes. The method was tested on actual coarse-grain materials like steel, and was found to improve defect detection very significantly. The adaptability of the method in geophysics (with 2-D unevenly distributed passive sensors as opposed to controllable and periodic 1-D ultrasonic arrays) is to be investigated in this project. On the one hand, iterative time reversal and related techniques can be taken advantage of to overcome aberration effects associated to long-scale inhomogeneities of the superficial layer, leading to a better constrast and resolution of the subsoil image [1-4]. On the other hand, a more sophisticated random matrix approach can be used in areas where short-scale inhomogeneities are strongly scattering and/or concentrated [5-7]. In this regime, conventional imaging methods suffer from the multiple scattering of waves that results in a speckle image, with no direct connection with the medium's reflectivity. In the case of purely passive sensors such as classical geophones, the response matrix will be obtained passively from cross-correlation of ambient noise, as was thoroughly established by pioneer works at ISTERRE [8]. The main objective is to get rid of multiple scattering and push back the imaging-depth limit of existing imaging techniques. In addition, the study of the multiple scattering contribution can also be useful for characterization purposes. Transport parameters such as the scattering or transport mean free paths can actually yield key information about the concentration and the size of the inhomogeneities. References: [1] C. Prada and M. Fink, Wave Motion 20, 151 (1994). [2] C. Prada, S. Manneville, D. Spoliansky, and M. Fink, J. Acoust. Soc. Am. 99, 2067 (1996). [3] J-L. Robert, PhD dissertation on “Evaluation of Green's functions in complex media by decomposition of the Time Reversal Operator: Application to Medical Imaging and aberration correction “, Université Paris VII, 2008. [4] G. Montaldo, M. Tanter, and M. Fink, Phys. Rev. Lett. 106, 054301, 2011. [5] A. Aubry, A. Derode, Phys. Rev. Lett. 102, 084301, 2009. [6] A. Aubry, A. Derode, J. Appl. Phys. 106, 044903, 2009. [7] S. Shahjahan, A. Aubry, F. Rupin, B. Chassignole, and A. Derode, Appl. Phys. Lett. 104, 234105, 2014. [8] Campillo, M., P. Roux, and N.M. Shapiro (2011), Using seismic noise to image and to monitor the Solid Earth, in Encyclopedia of Solid Earth Geophysics, Gupta, Harsh K. (Ed.), 1230-1235, Springer, 2011.
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Thibaud Blondel. Matrix Approach of Seismic Imaging. Physics [physics]. Université Paris sciences et lettres, 2019. English. ⟨NNT : 2019PSLET071⟩. ⟨tel-03174491⟩

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