Surface and Subsurface Waves

Abstract

Background The existence of surface waves was predicted theoretically over a century ago. Elastic waves propagating along the surface of a half-space were first predicted by Lord Rayleigh in 1885 in his paper “On waves propagating along the plane surface of an elastic bar,” submitted to the Proceedings of the London Mathematical Society. It is telling that this paper was submitted to a mathematical society and not a physical society, as such surface waves were primarily a mathematical concept, although Lord Rayleigh did suspect that they would be relevant to seismology. By the middle of the twentieth century, however, surface waves began to enter into mainstream technological applications. These waves, often referred to as Rayleigh waves or surface acoustic waves (SAW), are now being employed in a number of areas of science and technology, including ultrasonic NDE and SHM, seismology, and electronic circuitry. There is much literature on this subject, including for example Chadwick and Smith (1977), Farnell (1970), Pollard (1977), and Viktorov (1967). Experimental evidence was first obtained in observing wave propagation over the surface of the earth (as a result of earthquakes) and subsequent mode conversion at the earth’s surface. Observations were made regarding the unusual behavior of energy decay with increased depth and the ability of waves to travel along curved surfaces. This chapter examines surface waves on an isotropic, homogeneous, linear elastic semi-space. We take a rather classical approach to-the problem, one that is based on potential functions and boundary conditions for a free surface. Assumptions of isotropy, homogeneity, and linear elastic response will also be made. For more detail, see Auld (1990), Basatskaya and Ermolov (1980), Couchman and Bell (1978), Heelan (1953), Kolsky (1963), Nikiforov and Kharitonov (1981), Pilarski and Rose (1989), Uberall (1973), and Viktorov (1967).