Some Basic Aspects of Elastic Wave Equation in General Media. Estudiante del Doctorado en Ingeniería Matemática, Universidad EAFIT. Septiembre 7 de 2015.
Abstract: The equation which best describes the propagation of seismic waves in the earth is the elastic wave equation, when neglecting absorption, moreover, to characterize reservoirs, the exploration focus on vertical fractures embedded in a isotropic rock matrix, since these fractures may give rise to increased permeability and are therefore of great interest for production from hydrocarbon reservoirs.
This equation is framed in terms of tensor operators acting on vector quantities, and this is one motivation for considering a general frame in which we can write the elastic wave equation in a covariant manner. In this talk we show some basic aspects of differential geometry applied to propagation in continuous media and give some general forms of the tensors associated to a general and complex media.