Rayleigh-type Surface Waves Research Articles

GeneralP, type-IS, and type-IISwaves in anelastic solids; inhomogeneous wave fields in low-loss solids

AbstractThe physical characteristics for general plane-wave radiation fields in an arbitrary linear viscoelastic solid are derived. Expressions for the characteristics of inhomogeneous wave fields, derived in terms of those for homogeneous fields, are utilized to specify the characteristics and a set of reference curves for general P and S wave fields in arbitrary viscoelastic solids as a function of wave inhomogeneity and intrinsic material absorption. The expressions show that an increase in inhomogeneity of the wave fields causes the velocity to decrease, the fractional-energy loss (Q−1) to increase, the deviation of maximum energy flow with respect to phase propagation to increase, and the elliptical particle motions for P and type-I S waves to approach circularity. Q−1 for inhomogeneous type-I S waves is shown to be greater than that for type-II S waves, with the deviation first increasing then decreasing with inhomogeneity. The mean energy densities (kinetic, potential, and total), the mean rate of energy dissipation, the mean energy flux, and Q−1 for inhomogeneous waves are shown to be greater than corresponding characteristics for homogeneous waves, with the deviations increasing as the inhomogeneity is increased for waves of fixed maximum displacement amplitude. For inhomogeneous wave fields in low-loss solids, only the tilt of the particle motion ellipse for P and type-I S waves is independent to first order of the degree of inhomogeneity. Quantitative estimates for the characteristics of inhomogeneous plane body waves in layered low-loss solids are derived and guidelines established for estimating the effect of inhomogeneity on seismic body waves and a Rayleigh-type surface wave in low-loss media.

Surface and interface acoustic waves in SiO2/Y X-LiNbO3

For Y-cut lithium niobate, a leaky shear horizontal (SH) surface wave is known to propagate along the X axis. When an SiO2 film is deposited on the LiNbO3 surface, the SH wave is found experimentally to have low loss and theoretical calculations show the wave to be closely confined to the surface. Two additional acoustic modes are observed in the SiO2/YX-LiNbO3 configuration. One mode is a Rayleigh-type surface wave and the other a generalized Stoneley wave. Experimental measurements and theoretical predictions of the wave velocities versus film thickness to wavelength ratio (h/λ) are presented. Measurements of the temperature coefficient of time delay are given for the SH wave showing a zero first order coefficient at h=0.42λ. The sensitivity of this wave to bending strains is also presented.

Surface Waves in Viscoelastic Media Under the Influence of Gravity

In this paper formulae are derived for surface waves in a viscoelastic medium of Voigt type under the influence of gravity. The wave velocity equations are deduced from Biot's theory of stress by assuming that the effects of gravity are equivalent to a type of initial stress of a hydrostatic nature. The resulting equations are used to briefly investigate the particular surface waves of Rayleigh, Love and Stoneley type. In all cases the final results are in agreement with the corresponding classical results when the effects of gravity and viscosity are neglected.

Rayleigh-type surface wave on a linear viscoelastic half-space

The analytic solution for a Rayleigh-type surface wave on a linear viscoelastic half-space is obtained. The general viscoelastic solution predicts several properties of the surface wave distinct from those predicted by elasticity. The velocity, absorption coefficient, and displacement field are described theoretically.

The Theory of Stress Wave Radiation from Explosions in Prestressed Media

Stress wave radiation from underground explosions has been observed to contain an anomalous shear wave contribution which is most likely of tectonic origin. In this paper the theoretical radiation field to be expected from an explosion in a prestressed medium is given under the assumption that no secondary low symmetry faulting on a large scale occurs and that the total tectonic component of the field is due to stress relaxation around the roughly spherical fracture zone created by the explosive shock wave. Evidence for the occurrence of this simple kind of tectonic source is considered, and it is concluded that this model is appropriate in many, if not most, instances involving underground explosions. Expressions for the spectrum of the radiation field and its spatial radiation pattern are given in terms of multipole expansions for the components of the rotation potential and the dilatation potential. Several possible rupture formation models are treated. All models show that the tectonic radiation is of simple quadrupole form, as has been observed. The energy radiated due to stress relaxation is considered in detail, and it is also shown that, in terms of the energy released, a dislocation source can be used as an equivalent for the stress relaxation effects. The theoretical energy partition between compressional and shear waves for the tectonic field is in the ratio of (approximately) 1 to 10, so that tectonic stress release does not affect the direct compressional body wave particularly, but gives rise to totally anomalous SH polarized waves (e. g. Love waves) and affects Rayleigh type surface waves significantly, as is also observed. The theory can be applied to obtain estimates of source dimensions and the orientation and magnitude of the initial prestress field in the region of the explosion. In addition, application of this particular form of the general tectonic source theory to deep earthquakes and volcanic earthquakes also appears to be reasonable in view of the probable high symmetry of the failure or phase transition regions for such events.

Magnetoelastic Rayleigh-Type Surface Wave on a Tangentially Magnetized YIG Substrate

The propagation characteristics of an exchange-free magnetoelastic Rayleigh-type surface wave propagating on a YIG substrate in the direction of a tangentially applied bias field are treated. The surface wave is found to be of the leaky-wave variety within a band of frequencies given approximately by the magnetostatic bulk-wave spectrum, rather than of the bound surface-wave variety occurring outside this frequency band.

The effect of boundaries on wave propagation in a liquid-filled porous solid: IV. Surface waves in a half-space

abstract Dispersion and dissipation of Rayleigh-type surface waves in a porous, elastic half-space filled with a viscous liquid are studied within the framework of Biot's field equations. The algebraic secular equation turns out to be of the seventh degree, its (complex) coefficients being functions of a dimensionless frequency parameter. It is shown that for small and for large values of this parameter the wave is essentially non-dissipative. A numerical analysis of the secular equation pertaining to a kerosene-saturated sandstone reveals the existence of several extremal values of the phase velocity, a skewed bell-shaped variation of the dissipation per cycle, and a high-frequency cutoff for the surface wave for certain values of the dynamical coefficients.

Surface Elastic Waves in Cubic Crystals

A theoretical investigation of surface elastic waves in cubic crystals has been carried out using a theory developed by Stoneley. The range of elastic constants for which Rayleigh type surface waves exist on a (100) free surface has been determined. For other allowed values of the elastic constants generalized Rayleigh waves exist which are characterized by complex attenuation constants. In either case waves may not be propagated in certain directions parallel to the surface depending on the values of the elastic constants. A lattice dynamical theory of surface waves has been developed for a monatomic simple cubic lattice with nearest and next nearest neighbor central forces and angle-bending forces involving successive nearest neighbors. The surface waves exhibit dispersion when the wavelength is comparable to the lattice spacing. In the case of Rayleigh waves a critical wavelength exists, in general, such that for shorter wavelengths the atomic displacements show a reversal in phase between successive layers parallel to the surface.

The dispersion of surface waves on multilayered media*

abstract A matrix formalism developed by W. T. Thomson is used to obtain the phase velocity dispersion equations for elastic surface waves of Rayleigh and Love type on multilayered solid media. The method is used to compute phase and group velocities of Rayleigh waves for two assumed three-layer models and one two-layer model of the earth's crust in the continents. The computed group velocity curves are compared with published values of the group velocities at various frequencies of Rayleigh waves over continental paths. The scatter of the observed values is larger than the difference between the three computed curves. It is believed that not all of this scatter is due to observational errors, but probably represents a real horizontal heterogeneity of the continental crusts.