The Green's function of acoustic or elastic wave propagation can, for loss-less media, be retrieved by correlating the wave field that is excited by random sources and is recorded at two locations. Here the generalization of this idea to attenuating acoustic waves in an inhomogeneous medium is addressed, and it is shown that the Green's function can be retrieved from waves that are excited thro...

We present a multi-scale solution scheme for hyperbolic evolution equations with curvelets. We assume, essentially, that the second-order derivatives of the symbol of the evolution operator are uniformly Lipschitz. The scheme is based on a solution construction introduced by Smith [19] and is composed of generating an approximate solution following a paradifferential decomposition of the mentio...

In this paper we present an analytical approach to pilot-based synchronization algorithms for data hiding in still images. A representative algorithm belonging to the family of those exploiting a regular structure in the spreading sequence is chosen for study. We improve it by proposing the use of the Levenberg–Marquardt’s method for nonlinear least-squares estimation, and show how an estimate ...

Non-linear sound propagation is investigated computationally by simulating compressible time-developing mixing layers using the Large Eddy Simulation (LES) approach and solving the viscous Burgers Equation. The mixing layers are of convective Mach numbers of 0.4, 0.8 and 1.2. The LES results agree qualitatively with known flow behavior. Mach waves are observed in the near sound field of the sup...

This article aims at studying one dimensional unsteady planar and cylindrically symmetric flow involving shocks under the influence of magnetic field. The method of generalized wavefront expansion (GWE) is employed to derive a coupled system of nonlinear transport equations for the jump of field variables and of its spatial derivatives across the shock, which, in turn determine the evolution of...

Offset continuation (OC) is the operator that transforms common-offset seismic reflection data from one offset to another. Earlier papers by the first author presented a partial differential equation in midpoint and offset to achieve this transformation. The equation was derived from the kinematics of the continuation process with no reference to amplitudes. We present here a proof that the sol...