Point-Source Elastic Scattering by a Nested Piecewise Homogeneous Obstacle in an Elastic Environment

Abstract

A nested piecewise homogeneous elastic scatterer is embedded in a homogeneous elastic environment. The scatterer's core may be rigid, cavity, Robin, or lossy penetrable. A 2D or 3D incident elastic field, generated by a point-source located in the homogeneous environment, impinges on the scatterer. The scattering problem is formulated in a dyadic form. The main purpose of this paper is to establish scattering relations for the elastic point-source excitation of a nested piecewise homogeneous scatterer. To this direction, we establish reciprocity principles and general scattering theorems relating the scattered fields with the corresponding far-field patterns. Furthermore, for a scatterer excited by a point-source and a plane wave, mixed scattering relations are derived. The optical theorem, relating the scattering cross-section with the field at the point-source's location a is recovered as a corollary of the general scattering theorem. We present a detailed investigation for the 2D case and summarize the results for the 3D case, pointing out the main differences in the analysis.

Detection and location of cracks using loss of reciprocity in ultrasonic waves propagation

“…4 Although several applications have stemmed from the general reciprocity theorem for elasticity in fields as geophysics, 5 acoustics and ultrasonic waves propagation, 6,7 imaging of scatterers, 8,9 time reversal acoustics, 10,11 etc., questions arise on the validity of the reciprocity principle in nonlinear elastic media. Indeed break of reciprocity was observed in acoustic waves interacting with nonlinear media 12 and due to nonlinear effects in the propagation of waves in water when calibrating hydrophones.…”