Scattering of elastic waves by periodic arrays of spherical bodies

We develop a formalism for the calculation of the frequency band structure of a phononic crystal consisting of non-overlapping elastic spheres, characterized by Lam\'e coefficients which may be complex and frequency dependent, arranged periodically in a host medium with different mass density and Lam\'e coefficients. We view the crystal as a sequence of planes of spheres, parallel to and having the two dimensional periodicity of a given crystallographic plane, and obtain the complex band structure of the infinite crystal associated with this plane. The method allows one to calculate, also, the transmission, reflection, and absorption coefficients for an elastic wave (longitudinal or transverse) incident, at any angle, on a slab of the crystal of finite thickness. We demonstrate the efficiency of the method by applying it to a specific example.Comment: 19 pages, 5 figures, Phys. Rev. B (in press

3-D wave propagation in fluid-filled irregular boreholes in elastic formations

Different seismic testing techniques rely on the propagation of acoustic waves in fluid-filled boreholes from sources placed within the borehole and in the solid media. The interpretation of the signals recorded relies on understanding how waves propagate in the borehole and its immediate vicinity. It is known that very complex wave patterns can arise, depending on the distance between the source and the receiver, and their placement and orientation relative to the axis of a circular borehole. The problem becomes more complex if the cross-section is not circular, conditions for which analytical solutions are not known. In this work, the Boundary Element Method (BEM) is used to evaluate the three-dimensional wave field elicited by monopole sources in the vicinity of a fluid-filled borehole. This model is used to assess the effects of the receiver position on the propagation of both axisymmetric and non-axisymmetric wave modes when different borehole cross-sections are used. Both frequency vs. axial-wave number responses and time-domain responses are calculated.http://www.sciencedirect.com/science/article/B6V4Y-43439WJ-3/1/ad2294f2c7bbe37aedf40218044930f