Correlation based passive imaging with a white noise source

Passive imaging refers to problems where waves generated by unknown sources are recorded and used to image the medium through which they travel. The sources are typically modelled as a random variable and it is assumed that some statistical information is available. In this paper we study the stochastic wave equation partial derivative(2)(t)u- Delta(g)u = chi W, where W is a random variable with the white noise statistics on R1+n, n >= 3, chi is a smooth function vanishing for negative times and outside a compact set in space, and Delta(g) is the Laplace Beltrami operator associated to a smooth non-trapping Riemannian metric tensor g on R-n. The metric tensor g models the medium to be imaged, and we assume that it coincides with the Euclidean metric outside a compact set. We consider the empirical correlations on an open set chi subset of R-n, C-T(t(1), x(1), t(2), x(2)) = 1/T integral(T)(0) u(t(1) s, x(1))u(t(2) s, x(2))ds, t(1), t(2) > 0, x(1), x(2) is an element of chi, for T > 0. Supposing that chi is non-zero on chi and constant in time after t > 1, we show that in the limit T -> infinity, the data C-T becomes statistically stable, that is, independent of the realization of W. Our main result is that, with probability one, this limit determines the Riemannian manifold (R-n, g) up to an isometry. (C) 2018 Elsevier Masson SAS. All rights reserved.Peer reviewe

Numerical modeling of the tool-rock penetration process using FEM coupled with SPH technique

The numerical simulation of penetration into rock is an important tool to gain insights into rock drilling mechanisms, since it can be exploited as an alternative to the expensive field testing. This research aims to present an innovative computer simulation of rock penetration process on the basis of the finite element method (FEM) coupled with smoothed particle hydrodynamics (SPH). An advanced material model, namely the Karagozian and Case Concrete (KCC) model, was employed for this purpose. The Punch Penetration test (PPT) was carried out on a medium strength sandstone for validating the numerical method. The comparison of the numerical and experimental results obtained concluded that the FEM coupled with SPH method in conjunction with the fully calibrated KCC material model is a reliable method for the study of rock penetration due to its ability to deal with large deformations and its realistic constitutive modeling. The modeling approach was finally applied to estimate the required force to penetrate an offshore reservoir rock block under the in-situ confining pressure with a double conical tool up to 5 mm depth. The effective stresses in sedimentary basins of Agosta and Dosso Campus at a depth of 3000 m below the seabed are considered as the confining pressures of this study