Generalized optical theorems for the reconstruction of Green's function of an inhomogeneous elastic medium

This paper investigates the reconstruction of elastic Green's function from the cross-correlation of waves excited by random noise in the context of scattering theory. Using a general operator equation, -the resolvent formula-, Green's function reconstruction is established when the noise sources satisfy an equipartition condition. In an inhomogeneous medium, the operator formalism leads to generalized forms of optical theorem involving the off-shell $T$-matrix of elastic waves, which describes scattering in the near-field. The role of temporal absorption in the formulation of the theorem is discussed. Previously established symmetry and reciprocity relations involving the on-shell $T$-matrix are recovered in the usual far-field and infinitesimal absorption limits. The theory is applied to a point scattering model for elastic waves. The $T$-matrix of the point scatterer incorporating all recurrent scattering loops is obtained by a regularization procedure. The physical significance of the point scatterer is discussed. In particular this model satisfies the off-shell version of the generalized optical theorem. The link between equipartition and Green's function reconstruction in a scattering medium is discussed

Measurements of Thermodynamic Data of Water in Ca-Bentonite by Relative Humidity Method

Buffer material (compacted bentonite), one of the engineered barrier elements in the geological disposal of a high-level radioactive waste, develops swelling stress due to groundwater penetration from the surrounding rock mass. Montmorillonite is the major clay mineral component of bentonite. Even previous studies provide few mechanical and thermodynamic data on Ca-montmorillonite. In this study, thermodynamic data on Ca-montmorillonite were obtained as a function of water content by measuring relative humidity (RH) and temperature. The activities of water and the relative partial molar Gibbs free energies of water were determined from the experimental results, and the swelling stress of Ca-bentonite was calculated using the thermodynamic model and compared with measured data. The activities of water and the relative partial molar Gibbs free energies obtained in the experiments decreased with decreasing water content in water contents lower than about 25%. This trend was similar to that of Na-montmorillonite. The swelling stress calculated based on the thermodynamic model was approximately 200 MPa at a montmorillonite partial density of 2.0 Mg/m3 and approximately 10 MPa at a montmorillonite partial density of 1.4 Mg/m3. The swelling stresses in the high-density region (around 2.0 Mg/m3) were higher than that of Na-montmorillonite and were similar levels in the low-density region (around 1.5 Mg/m3). Comparison with measured data showed the practicality of the thermodynamic model

Changes of Temperature and Moisture Distribution over Time by Thermo-Hydro-Chemical (T-H-C)-Coupled Analysis in Buffer Material Focusing on Montmorillonite Content

Bentonite is used as a buffer material in engineered barriers for the geological disposal of high-level radioactive waste. The buffer material will be made of bentonite, a natural clay, mixed with silica sand. The buffer material is affected by decay heat from high-level radioactive waste, infiltration of groundwater, and swelling of the buffer material. The analysis of these factors requires coupled analysis of heat transfer, moisture transfer, and groundwater chemistry. The purpose of this study is to develop a model to evaluate bentonite types and silica sand content in a unified manner for thermo-hydro-chemical (T-H-C)-coupled analysis in buffer materials. We focused on the content of the clay mineral montmorillonite, which is the main component of bentonite, and developed a model to derive the moisture diffusion coefficient of liquid water and water vapor based on Philip and de Vries, and Kozeny-Carman. The evolutions of the temperature and moisture distribution in the buffer material were analyzed, and the validity of each distribution was confirmed by comparison with the measured data obtained from an in situ experiment at 350 m in depth at the Horonobe Underground Research Center, Hokkaido, Japan

A Semi-classical calculus of correlations

The method of passive imaging in seismology has been developped recently in order to image the earth crust from recordings of the seismic noise. This method is founded on the computation of correlations of the seismic noise. In this paper, we give an explicit formula for this correlation in the "semi-classical" regime. In order to do that, we define the power spectrum of a random field as the ensemble average of its Wigner measure, this allows phase-space computations: the pseudo-differential calculus and the ray theory. This way, we get a formula for the correlation of the seismic noise in the semi-classcial regime with a source noise which can be localized and non homogeneous. After that, we show how the use of surface guided waves allows to image the earth crust.Comment: To appear in a special issue "Imaging and Monitoring with Seismic Noise" of the series "Comptes Rendus G\'eosciences", from the French "Acad\'emie des sciences