Directional Field of a Point Source for Calculation of Three-Dimensional Harmonic Waves in Layered Media

Abstract

The description of the propagation of elastic waves emitted by a transducer in a solid is of fundamental importance in many applications of ultrasonics. Since there exist many problems with two kinds of geometric dimensions — dimensions much larger than the wavelength and dimensions in the range of the wavelength — the application of the geometric ray theory and the finite element method, resp., is difficult. That’s why semianalytical methods are a good alternative for such problems with a mixed geometry. For a 2-dimensional geometry, such as a half-space, a plate with parallel surfaces or a horizontally layered medium solutions exist in form of Green’s functions^1,2. In ³ the displacement in the interior of a test object for a disk-shaped single-element transducer is obtained by spatial convolution of the solution for a point force with the amplitude distribution of the point sources. This approach, however, is restricted to axisymmetrical sources.