Dispersion of Surface Waves above Time-Varying Reactive Boundaries

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.

The dispersion curves of surface waves have been widely used for the retrieval of subsurface structures. Because the surface-wave dispersion is not sensitive to Vp, classical dispersion inversion can only retrieve Vs structures. To retrieve Vp, the dispersion of guided-P waves, which belong to leaky waves, should be considered. Due to the difficulty in forward modeling, the quantitative analysis of the leaky-wave dispersion curves has been rarely reported. In this study, we first derive the sensitivity analysis method of the leaky-wave dispersion based on previously proposed the semi-analytical spectral element method. Then the quantitative sensitivity analysis of leaky-wave dispersion curves is carried out, which confirms the ability of guided-P wave dispersion to constrain the velocity structures. With the theoretical analysis, we propose a joint inversion method based on surface and guided-P wave dispersion curves, which can simultaneously retrieve Vp and Vs. To verify the effectiveness, the proposed joint inversion has been applied to different kinds of field data including ocean bottom seismometer data with active sources and the seismic data of Nevada in the United States in 2008. Both of the inversion tests show that the joint inversion of surface- and leaky-wave dispersion can effectively constrain the velocity structure of Vp and Vs at the same time, which helps to obtain more complete and accurate models than the traditional surface wave dispersion inversion.

The shallow subsurface can be extremely complex and challenging from a geological and geophysical point of view. Near-surface perturbations impact the imaging of the deeper events and therefore have to be corrected in the seismic reflection information. It is also known that solving the near surface is an important part of any depth imaging velocity modeling. Usually we use refracted waves for P-wave velocity model estimation. Refraction data provide the information about the deeper subsurface and gives directly Vp velocity. In areas with complex near surface estimation of Vp on refracted energy can be challenging: velocity inversions and hidden layers can produce ambiguity in the refraction solution. The near-surface model obtained through surface wave inversion gives geometric information about the near-surface layers, geology, velocity and attenuation distribution down to the investigation depth. Because the propagation properties of the surface waves are directly depend on elastic properties of the near surface, the dispersion of surface waves is the physical property used for its characterization. Presented example of the simultaneous joint inversion successfully shows that resulting compressional and shear depth velocity models provide significant improvement to support refraction statics and shallow velocity model building.

In this paper, a modified laser induced grating technique (LIG) has been utilized to generate narrow band surface waves in an epoxy-bonded copper-aluminum layered structure. A high performance optical interferometer system was utilized to detect the laser-generated surface waves. The dispersion of surface wave in an epoxy-bonded copper-aluminum specimen was measured and compared with the theoretical solution. An inverse algorithm based on the simplex method was then introduced to determine the bonding thickness as well as the elastic properties of the bonding layer. The inversion results demonstrated that the thickness in the microm range or the elastic properties of the bonding layer could be successfully determined.

Surface waves are widely used for determining properties of the subsurface on different scales. In most applications, the dispersion of surface waves is analyzed to yield depthdependent velocity profiles. However, the heterogeneity of the shallow subsurface complicates such an analysis because of the scattering it causes. Here, we use an inverse scattering method to determine the location and properties of the heterogeneity. First, we illustrate this method, using a regular receiver array. A synthetic example shows that the scatterer is imaged at the correct location with good resolution. In practice, we may want to take advantage of existing non-uniform arrays, such as those deployed for global seismic studies. In our next example, we generate scattered data at irregularly spaced locations. By simultaneously inverting the scattered wave field excited by different sources, we observe that the image is well focused on the scatterer. Further work is on the way to better understand the influence of non-uniform (and sparse) sampling on the image quality and what are the sampling requirements.

In this study, we were interested in the dispersion of surface waves caused by the presence of a micrometric field of residual stress on the surface of an amorphous medium. We have shown that in relation to surface waves, a stressed structure like this is comparable to a layer on substrate type structure. The design and implementation of SAW-IDT MEMS sensors enabled quasi-monochromatic Rayleigh-type surface waves to be generated and the dispersion phenomenon to be studied over a wide range of frequencies for different superficial fields of residual stress. The thicknesses of the stressed cortical zones were estimated with good accuracy using an inverse method.

The scattering problem of acoustic plane waves from comb-like impedance gratings on a rigid surface has been investigated in this paper. A rigorous analytic approach for homogeneous plane-wave incidence is presented based on the periodicity of the grating structure, in which the problem was solved as a mixed boundary value problem and the scattered field was represented by the tangent velocity difference across a partition wall of the grating. A singular integral equation has been derived for the tangent velocity difference, which can directly be solved with the Gauss-Chebyshev procedure. The resulting solution consists of a series of Bloch-Floquet waves (plane bulk wave and surface wave modes) with explicit expressions for the expansion coefficients. When the grating period is much less than the incident wavelength (ka << 1), the grating structure is equivalent to a plane impedance surface and no surface waves can be excited with homogeneous plane-wave incidence. When the grating period is comparable to the incident wavelength, resonance phenomena are predicted under certain conditions and surface waves can form, even with homogeneous plane-wave incidence. The dispersion relation for surface waves has also been examined. The impedance effects of the grating on the reflection and diffraction waves as well as on the dispersion and formation of surface waves have been studied, with the acoustically hard grating being the special case of the general impedance grating.

In this review we consider the propagation of nonlinear waves in magnetically structured plasmas. We start from studying nonlinear surface waves on magnetic interfaces and give a derivation of the equation governing propagation of these waves in incompressible plasmas. We present the results of a numerical solution of this equation. Then we discuss various generalizations of this equation.We proceed to study slow nonlinear waves in magnetic slabs. We present the Benjamin-Ono equation describing nonlinear slow sausage surface waves in magnetic slabs, and discuss its solutions in the form of algebraic solitons. Then we consider nonlinear slow body waves and write down the governing equation for these waves. We discuss its numerical solution which shows that the evolution of an initial perturbation results in a gradient catastrophe.After that we consider nonlinear slow sausage surface and slow body waves in magnetic tubes, which are similar to the corresponding counterparts in magnetic slabs. We present a system of two equations describing both types of waves. We briefly discuss the derivation of the Leibovich-Roberts equation for slow sausage surface waves from this system of equations, and present the results of its numerical study. Then we give a brief description of the derivation of the governing equation for slow body waves, which is very similar to its counterpart for slow body waves in magnetic slabs and has very similar properties. We complete this part of the review with presenting the governing equation for non-axisymmetric surface waves in a thin magnetic tube in an incompressible plasma.In the last part of the paper we consider the damping of nonlinear waves in weakly dissipative magnetically structured plasmas. We briefly discuss the application of the obtained results to the problem of heating of the solar corona.KeywordsSurface WaveSolitary WaveSolar PhysMagnetic TubeKink ModeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Potential (electrostatic) surface waves (SWs) in a semi-bounded plasma with degenerate electrons are studied using the quasi-classical mean-field kinetic model. The SW spectrum and the collisionless damping rate are obtained numerically for a wide range of wavelengths. In the limit of long wavelengths, the SW frequency ω approaches the cold-plasma limit ω=ωp/2 with ωp being the plasma frequency, while at short wavelengths, the SW spectrum asymptotically approaches the spectrum of zero-sound mode propagating along the boundary. It is shown that the surface waves in this system remain weakly damped at all wavelengths (in contrast to strongly damped surface waves in Maxwellian electron plasmas), and the damping rate nonmonotonically depends on the wavelength, with the maximum (yet small) damping occurring for surface waves with wavelength of ≈5πλF, where λF is the Thomas-Fermi length. The applicability of the used approximations and of the obtained results is discussed in detail.

Artificial layered materials (composites, superlattices, multifilms etc.) consisting of two or more component phases attract increasing attention in different areas of technology ranging from mechanical structures to electronic devices. Depending on the frequency range under consideration, the study of elastic and electroelastic wave propagation in periodically layered anisotropic media modelling such heterostructures is a subject matter of mechanics, acoustics, surface science, acoustoelectronics etc. (see [1–9] and references there). Within the framework of continuum mechanics ideas, different approaches (the diverse formulations of the transfer matrix method, the Green’s function method, the Stroh formalism etc.) were proposed to construct and analyse the dispersion equations for bulk, surface and plate waves of different polarization, propagating in media with different types of anisotropy. This paper is organized to present the Hamiltonian system formalism which is an effective addition to the above-mentioned approaches. Application of the formalism is illustrated by the procedure of representing the general solution for the periodically layered piezoelectric medium and obtaining the corresponding dispersion equations for three-dimensional electroelastic waves. These equations are valid for any relative value, of the wavelengths compared to the period of the medium. Results are given when the layers are of orthorhombic symmetry belonging to the piezoelectric class mm2, but also can be applied to media, both piezoelectric and pure elastic, with properties of higher symmetry. For example tetragonal 4mm and 422 and hexagonal 6mm layers can be considered as particular cases.

Dispersive surface waves in anisotropic linear electromagnetoelasticity

Nonlinear dispersion shallow water equations are derived, which describe propagation of long surface waves on a spherical surface with allowance for rotation of the Earth and mobility of the ocean bottom. Derivation of these equations is based on expanding the solution of hydrodynamic equations on a sphere in small parameters depending on the relative thickness of the water layer and dispersion of surface waves.

Charged dust grains can have a large effect on the dispersion characteristics of hydromagnetic Alfvén and magnetoacoustic waves propagating at frequencies well below the ion-cyclotron frequency, even if the proportion of the total charge on the dust (usually negative) is quite small in space and astrophysical plasmas, such as cometary atmospheres and interstellar molecular clouds. The dust introduces a cutoff-resonance pair. A number of effects of the dust are considered here. Wave energy propagating at oblique angles to the magnetic field in an increasing density gradient can be very efficiently damped by resonance absorption processes in a dusty plasma. It is shown that, as well as the usual Alfvén resonance, a low frequency dust-ion hybrid resonance also occurs. The effects of dust on the dispersion of surface waves in highly structured plasmas and damping due to dust charging may also play roles in such plasmas.

The self-organization process in a Dicke model is studied with taking into account electromagnetic field states. The interaction between two-level emitters provided by the field results in generating field waves of increasing amplitudes. The picture of superradiance development in a prolonged system can be described in terms of electromagnetic field in continuous medium formed by emitters. The generalized induction in the Dicke system is introduced on the basis of the material equation for charge current obtained using the Bogolyubov reduced description method. The dispersion equation for waves and its solutions are derived and analyzed. Non-singular expressions for material coefficients are proposed and used for calculating the wave characteristics.

Measurements of the Doppler spectra of airborne ultrasound backscattered by the rough dynamic surface of a shallow turbulent flow are presented in this paper. The interpretation of the observed acoustic signal behavior is provided by means of a Monte Carlo simulation based on the Kirchhoff approximation and on a linear random-phase model of the water surface elevation. Results suggest that the main scattering mechanism is from capillary waves with small amplitude. Waves that travel at the same velocity of the flow, as well as dispersive waves that travel at a range of velocities, are detected, studied, and used in the acoustic Doppler analysis. The dispersive surface waves are not observed when the flow velocity is slow compared to their characteristic velocity. Relatively wide peaks in the experimental spectra also suggest the existence of nonlinear modulations of the short capillary waves, or their propagation in a wide range of directions. The variability of the Doppler spectra with the conditions of the flow can affect the accuracy of the flow velocity estimations based on backscattering Doppler. A set of different methods to estimate this velocity accurately and remotely at different ranges of flow conditions is suggested.