Rayleigh surface waves

Rayleigh waves

Rayleigh waves, also known as the Rayleigh-Lamb Wave or "ground roll", are a type of surface waves.They are associated on the Earth with earthquakes and subterranean movement of magma, or with any other source of seismic energy, such as an explosion or even a sledgehammer impact, and are also the form of ocean waves. .
From a condensed matter physicspoint of view Rayleigh waves are surface acounting waves and associated with a huge number of electronic components, the SAW devices, which employ them. SAW devices are mainly used in cellular phones and wireless technology, and their worldwide yearly production is approximated to lie over 1000 million


Abstract

Rayleigh surface waves were discovered theoretically as a solution of wave equation. Their physical existence was confirmed later thanks to numerous experimental investigations and practical applications in acoustics, geophysics, electronics, etc. Conditions of Rayleigh surface waves propagation are defined by one of the real roots of Rayleigh equation. The other real roots of the equation were assumed to be extraneous and were not taken into account. This paper is considering possibility to use additional (extraneous) real roots of Rayleigh equation for explanation of existence of a special type of leaky waves, which propagate on the border of half-space solid and vacuum. Conditionally these waves could be referred to as Rayleigh transformed sub-surface waves as they propagate along the surface, their main energy concentrates in a local zone under the surface, and below this zone they transform into bulk waves taking away the wave energy. Some computer simulations and calculations are presented as a theoretical explanation of conditions of Rayleigh transformed sub-surface waves propagation. Keywords: acoustics, Rayleigh equation, surface waves, ultrasonics, phase velocity.


Introduction

Physical Acoustics as fundamental science was born about two hundred years ago thanks to monumental works of great scholars: Rayleigh, Lamb, and Love [1, 2, 3]. The second part of the 20th century demonstrated high performance acoustic applications in several fields of science and technology. Ultrasonics as a branch of acoustics is one of the main consumers of physical acoustics fundamentals. The latest advances of electrical and electronic engineering gave opportunity to build a wide class of ultrasonic equipment allowing verification of basic acoustic concepts. Some recent experimental results cannot be explained unambiguously by existing basic theories especially in the field of acoustic surface waves classification. Depending on classification of the wave type testing results may be interpreted differently. In spite of the fact that a lot of basic and experimental works are published on the problem of analysis and classification of Rayleigh type surface waves, distance between theoretical models and real materials is hard to come by.


Theoretical Background

Transformed surface (TS) waves are a recently discovered [4,5] special class of elastic waves in solids. This class of waves is intermediate between bulk and surface waves, which propagate along the border of solid medium and transform acoustic energy from surface co-boundary space or into the solid depth. Their characteristic behavior may be described as follows: they appear in a local area near the energy source, propagate further with splitting into bulk and surface wave components, have limited zone of propagation because of fast energy transformation from surface to bulk component and absorption and dissipation of energy in solid.
It is possible to distinguish a sub-class of TS waves, which have got a name of "leaky surface waves" (LSW). At present two types of the LSW have been investigated: waves on the border of two solid half-spaces with different physical properties and on the border of solid half-space and liquid. The first type of the LSW could be presented by Stoneley waves [6]. In the case of Stoneley waves acoustic energy is leaking from one solid half-space to the other, and the wave propagates on the border between them. The second type of the LSW could be presented by Rayleigh type of waves: on the border between solid half-space and liquid [7]; and Lamb type of waves in plates immersed into liquid [8]. In this case acoustic energy is leaking from half-space solid or plate to liquid [9].