A compressively strained elastic film bonded to a viscous layer can form wrinkles. The present study provides a theoretical model for the wrinkling process. The elastic film is modeled with the nonlinear theory of a thin plate subject to in-plane and out-of-plane loads. The flow of the viscous layer is modeled with the theory of lubrication. The interface between the elastic film and the viscou...

Seismic waves propagate through the earth as a superposition of different wave modes. Seismic imaging in areas characterized by complex geology requires techniques based on accurate reconstruction of the seismic wavefields. A crucial component of the methods in this category, collectively known as wave-equation migration, is the imaging condition that extracts information about the discontinuit...

From the elastic-wave equation and the energy conservation principle, we have derived an energy norm that is applicable to imaging with elastic wavefields. Extending the concept of the norm to an inner product enables us to compare two related wavefields. For example, the inner product of source and receiver wavefields at each spatial location leads to an imaging condition. This new imaging con...

The relation between the elastic wave equation for plane, isotropic bodies and an underlying classical ray dynamics is investigated. We study, in particular, the eigenfrequencies of an elastic disk with free boundaries and their connection to periodic rays inside the circular domain. Even though the problem is separable, wave mixing between the shear and pressure component of the wave field at ...

Résumé: Le but de ce projet est une investigation des techniques d’amortissement pour l’équation d’onde. Cette étude est intéressante tant du point de vue de la physique et que de l’analyse numérique. En effet l’amortissement apparâıt fréquemment dans les systèmes avec friction. Du point de vue mathématique, l’amortissement donne une meilleure régularité de l’équation élastique qui est importan...

Time-reversal (TR) methods provide a simple and robust solution to source imaging problems. However, for recovering a well resolved image of the source, TR requires a balanced illumination of the target from all angles. When acquisition is incomplete and a balanced illumination is not possible, the TR solution may not be adequate. In a previous paper, by formulating source imaging as an optimiz...

Upon invoking Huygen's principle, matrix equations are obtained describing the scattering of waves by an obstacle of arbitrary shape immersed in an elastic medium. New relations are found connecting surface tractions with the divergence and curl of the displacement, and conservation laws are discussed. When mode conversion effects are arbitrarily suppressed by resetting appropriate matrix eleme...

The theory of Gaussian wave packet (GWP) propagation in elastic materials is developed. The GWP solutions are in the form of localized disturbances with Gaussian spatial envelopes at any instant in time. The method is explicitly time dependent, but is conceptually no more difficult than time halmonic ray theory. The equations of propagation and evolution are very similar to those of standard, e...

The theory of elastic wave emission (i.e., acoustic emission; AE) from damage processes such as slip and microcracking is discussed. Analogous developments in the literature on earthquake seismology and dynamic dislocation theory are noted and utilized. A general representation of the displacement field of an AE event is given in terms of the double-couple response to a distribution of "moment ...