Showing papers on "Longitudinal wave published in 2008"

Higher order asymptotic homogenization and wave propagation in periodic composite materials

Abstract: We present an application of the higher order asymptotic homogenization method (AHM) to the study of wave dispersion in periodic composite materials. When the wavelength of a travelling signal becomes comparable with the size of heterogeneities, successive reflections and refractions of the waves at the component interfaces lead to the formation of a complicated sequence of the pass and stop frequency bands. Application of the AHM provides a long-wave approximation valid in the low-frequency range. Solution for the high frequencies is obtained on the basis of the Floquet–Bloch approach by expanding spatially varying properties of a composite medium in a Fourier series and representing unknown displacement fields by infinite plane-wave expansions. Steadystate elastic longitudinal waves in a composite rod (one-dimensional problem allowing the exact analytical solution) and transverse anti-plane shear waves in a fibre-reinforced composite with a square lattice of cylindrical inclusions (two-dimensional problem) are considered. The dispersion curves are obtained, the pass and stop frequency bands are identified.

Algebraic Helmholtz inversion in planar magnetic resonance elastography.

Abstract: Magnetic resonance elastography (MRE) is an increasingly used noninvasive modality for diagnosing diseases using the response of soft tissue to harmonic shear waves. We present a study on the algebraic Helmholtz inversion (AHI) applied to planar MRE, demonstrating that the deduced phase speed of shear waves depends strongly on the relative orientations of actuator polarization, motion encoding direction and image plane as well as on the actuator plate size, signal-to-noise ratio and discretization of the wave image. Results from the numerical calculation of harmonic elastic waves due to different excitation directions and simulated plate sizes are compared to experiments on a gel phantom. The results suggest that correct phase speed can be obtained despite these largely uncontrollable influences, if AHI is based on out-of-plane displacements and the actuator is driven at an optimal frequency yielding an optimal pixel per wavelength resolution in the wave image. Assuming plane waves, the required number of pixels per wavelength depends only on the degree of noise.

Spectral-element simulations of wave propagation in porous media

Abstract: We present a derivation of the equations describing wave propagation in porous media based upon an averaging technique which accommodates the transition from the microscopic to the macroscopic scale. We demonstrate that the governing macroscopic equations determined by Biot remain valid for media with gradients in porosity. In such media, the well-known expression for the change in porosity, or the change in the fluid content of the pores, acquires two extra terms involving the porosity gradient. One fundamental result of Biot's theory is the prediction of a second compressional wave, often referred to as 'type II' or 'Biot's slow compressional wave', in addition to the classical fast compressional and shear waves. We present a numerical implementation of the Biot equations for 2-D problems based upon the spectral-element method (SEM) that clearly illustrates the existence of these three types of waves as well as their interactions at discontinuities. As in the elastic and acoustic cases, poroelastic wave propagation based upon the SEM involves a diagonal mass matrix, which leads to explicit time integration schemes that are well suited to simulations on parallel computers. Effects associated with physical dispersion and attenuation and frequency-dependent viscous resistance are accommodated based upon a memory variable approach. We perform various benchmarks involving poroelastic wave propagation and acoustic–poroelastic and poroelastic–poroelastic discontinuities, and we discuss the boundary conditions used to deal with these discontinuities based upon domain decomposition. We show potential applications of the method related to wave propagation in compacted sediments, as one encounters in the petroleum industry, and to detect the seismic signature of buried landmines and unexploded ordnance.

Background Love and Rayleigh waves simultaneously generated at the Pacific Ocean floors

Abstract: [1] Earth's background free oscillations known as Earth's hum have been interpreted as the Earth response to vertical pressure loads due to atmospheric and/or oceanic disturbances. Such excitation mechanisms, however, can hardly excite Love waves. Here we show clear evidence of background Love waves from 0.01 to 0.1 Hz, based on the array analysis of tiltmeters in the Japanese islands. The observed kinetic energy of Love waves is as large as that of Rayleigh waves through the whole period of analysis. The predominant incident azimuths are common to the Love and Rayleigh waves, the strongest in directions along ocean-continent borders, next from deep ocean floors and the weakest from continents. These observations indicate that background Love and Rayleigh waves are largely generated by the same mechanisms other than vertical pressure loading. We suggest that the most likely excitation source is shear traction acting on a sea-bottom horizon due to linear topographic coupling of infragravity waves.

Dynamics of the Solar Magnetic Network. II. Heating the Magnetized Chromosphere

Abstract: We consider recent observations of the chromospheric network and argue that the bright network grains observed in the Ca II H and K lines are heated by an as-yet-unidentified quasi-steady process. We propose that the heating is caused by dissipation of short-period magnetoacoustic waves in magnetic flux tubes (periods less than 100 s). Magnetohydrodynamic (MHD) models of such waves are presented. We consider wave generation in the network due to two separate processes: (1) transverse motions at the base of the flux tube and (2) the absorption of acoustic waves generated in the ambient medium. We find that the former mechanism leads to efficient heating of the chromosphere by slow magnetoacoustic waves propagating along magnetic field lines. This heating is produced by shock waves with a horizontal size of a few hundred kilometers. In contrast, acoustic waves excited in the ambient medium are converted into transverse fast modes that travel rapidly through the flux tube and do not form shocks, unless the acoustic sources are located within 100 km from the tube axis. We conclude that the magnetic network may be heated by magnetoacoustic waves that are generated in or near the flux tubes.

Variational formulation of pre-stressed solid-fluid mixture theory, with an application to wave phenomena

Abstract: Fluid saturated porous media are modelled by the theory of mixtures and the placement maps of the solid and of the fluid are considered. The momentum balance equations are derived in the framework of a variational approach: We take an action functional and two families of variations and assume that the sum of the virtual work of the external forces and the variation of such an action along each variation are zero. Constitutive equations for the two Cauchy stress tensors and for the interaction force are derived taking into account a general state of pre-stress for the solid and for the fluid species. Governing equations are therefore formulated, however, for the sake of simplicity, only the case of pure initial pressure is further investigated. The propagation of bulk (transversal and longitudinal) waves and the influence of pre-stress are studied: In particular, stability analyses are carried out starting from dispersion relations and the role of pre-stress is investigated. Finally, a numerical example is established for a given state of pre-stress, deriving the phase velocities and the attenuation coefficients of transversal and longitudinal waves.

Large-amplitude steady rotational water waves

Abstract: Two-dimensional, finite-depth periodic water waves with general vorticity and large amplitude are computed The mathematical formulation and numerical method that allow us to compute a continuum of such waves with arbitrary vorticity are described The problems of whether extreme waves exist, where their stagnation points occur, and what qualitative features such waves possess are addressed here with particular emphasis on constant vorticity

Fast wave ultrasonic propagation in trabecular bone: numerical study of the influence of porosity and structural anisotropy.

Abstract: Our goal is to assess the potential of computational methods as an alternative to analytical models to predict the two longitudinal wave modes observed in cancellous bone and predicted by the Biot theory A three-dimensional (3D) finite-difference time-domain method is coupled with 34 human femoral trabecular microstructures measured using microcomputed tomography The main trabecular alignment (MTA) and the degree of anisotropy (DA) were assessed for all samples DA values were comprised between 102 and 19 The influence of bone volume fraction (BV/TV) between 5% and 25% on the properties of the fast and slow waves was studied using a dedicated image processing algorithm to modify the initial 3D microstructures A heuristic method was devised to determine when both wave modes are time separated The simulations (performed in three perpendicular directions) predicted that both waves generally overlap in time for a direction of propagation perpendicular to the MTA When these directions are parallel, both waves are separated in time for samples with high DA and BV/TV values A relationship was found between the least bone volume fraction required for the observation of nonoverlapping waves and the degree of anisotropy: The higher the DA, the lower the least BV/TV

Power Waves and Conjugate Matching

Abstract: The concept of power waves gives more natural relations between incident and reflected power in a microwave network than the typically used traveling waves. The reflection coefficient for power waves directly describes the reflection of power whereas the reflection coefficient of traveling waves describes the reflection of the waves themselves. In this brief, new physical reasoning of power waves is given starting from the principle of conjugate matching. In addition, a new formula for the reference impedances for a two-port system is given such that the system is simultaneously conjugate matched for both ports.

Rotating spherical Couette flow in a dipolar magnetic field: experimental study of magneto-inertial waves

Abstract: The magnetostrophic regime, in which Lorentz and Coriolis forces are in balance, has been investigated in a rapidly rotating spherical Couette flow experiment. The spherical shell is filled with liquid sodium and permeated by a strong imposed dipolar magnetic field. Azimuthally travelling hydromagnetic waves have been put in evidence through a detailed analysis of electric potential differences measured on the outer sphere, and their properties have been determined. Several types of wave have been identified depending on the relative rotation rates of the inner and outer spheres: they differ by their dispersion relation and by their selection of azimuthal wavenumbers. In addition, these waves constitute the largest contribution to the observed fluctuations, and all of them travel in the retrograde direction in the frame of reference bound to the fluid. We identify these waves as magneto-inertial waves by virtue of the close proximity of the magnetic and inertial characteristic time scales of relevance in our experiment.

Formation of undular bores and solitary waves in the Strait of Malacca caused by the 26 December 2004 Indian Ocean tsunami

Abstract: [1] Deformation of the Indian Ocean tsunami moving into the shallow Strait of Malacca and formation of undular bores and solitary waves in the strait are simulated in a model study using the fully nonlinear dispersive method (FNDM) and the Korteweg-deVries (KdV) equation. Two different versions of the incoming wave are studied where the waveshape is the same but the amplitude is varied: full amplitude and half amplitude. While moving across three shallow bottom ridges, the back face of the leading depression wave steepens until the wave slope reaches a level of 0.0036–0.0038, when short waves form, resembling an undular bore for both full and half amplitude. The group of short waves has very small amplitude in the beginning, behaving like a linear dispersive wave train, the front moving with the shallow water speed and the tail moving with the linear group velocity. Energy transfer from long to short modes is similar for the two input waves, indicating the fundamental role of the bottom topography to the formation of short waves. The dominant period becomes about 20 s in both cases. The train of short waves, emerging earlier for the larger input wave than for the smaller one, eventually develops into a sequence of rank-ordered solitary waves moving faster than the leading depression wave and resembles a fission of the mother wave. The KdV equation has limited capacity in resolving dispersion compared to FNDM.

Effects of structural anisotropy of cancellous bone on speed of ultrasonic fast waves in the bovine femur

Abstract: Ultrasonic waves in cancellous bone change dramatically depending on its structural complexity. One good example is the separation of an ultrasonic longitudinal wave into fast and slow waves during propagation. In this study, we examined fast wave propagation in cancellous bone obtained from the head of the bovine femur, taking the bone structure into consideration. We investigated the wave propagation perpendicular to the bone axis and found the two-wave phenomenon. By rotating the cylindrical cancellous bone specimen, changes in the fast wave speed due to the rotation angle then were observed. In addition to the ultrasonic evaluation, the structural anisotropy of each specimen was measured by X-ray micro-computed tomography (CT). From the CT images, we obtained the mean intercept length (MIL), degree of anisotropy (DA), and angle of insonification relative to the trabecular orientation. The ultrasonic and CT results showed that the fast wave speed was dependent on the structural anisotropy, especially on the trabecular orientation and length. The fast wave speeds always were higher for propagation parallel to the trabecular orientation. In addition, there was a strong correlation between the DA and the ratio between maximum and minimum speeds (Vmax/Vmin) (R2 = 0.63).

Reverse wave propagation in the cochlea

Abstract: Otoacoustic emissions, sounds generated by the inner ear, are widely used for diagnosing hearing disorders and studying cochlear mechanics However, it remains unclear how emissions travel from their generation sites to the cochlear base The prevailing view is that emissions reach the cochlear base via a backward-traveling wave, a slow-propagating transverse wave, along the cochlear partition A different view is that emissions propagate to the cochlear base via the cochlear fluids as a compressional wave, a fast longitudinal wave These theories were experimentally tested in this study by measuring basilar membrane (BM) vibrations at the cubic distortion product (DP) frequency from two longitudinal locations with a laser interferometer Generation sites of DPs were varied by changing frequencies of primary tones while keeping the frequency ratio constant Here, we show that BM vibration amplitude and phase at the DP frequency are very similar to responses evoked by external tones Importantly, the BM vibration phase at a basal location leads that at a more apical location, indicating a traveling wave that propagates in the forward direction These data are in conflict with the backward- traveling-wave theory but are consistent with the idea that the emission comes out of the cochlea predominantly through compressional waves in the cochlear fluids

Ultrasonic guided waves for health monitoring of high-pressure composite tanks

Abstract: Ultrasonic guided wave modes are proposed to control the integrity of high-pressure composite tanks produced by EADS-ASTRIUM, France. The purpose is to demonstrate the potentiality of air-coupled transducers to set up a contact-less, single-sided technique for testing the moisture content and/or the micro-cracking of carbon-epoxy composite wound around a Titanium liner. Although guided waves have been experimentally propagated on a real tank, it was not allowed to damage this specimen. Therefore, plates made of similar composite materials than that constituting the tank winding were submitted to water intake or to thermal stresses. After immersing some plates in a humid chamber, it was demonstrated that the attenuation of the A0 guided wave mode is sensitive to the moisture content. Other plate samples were submitted to immersion in liquid nitrogen that induces transversal cracks shown to cause significant drops in the celerity of several guided waves. Inverse problems have been used for quantifying the effects of these damages on the material properties, and they showed that water intake increases the imaginary part of the Coulomb moduli, while micro-cracking decreases all the material stiffness moduli. Such changes in the material properties have then been used as input data for simulating waveforms corresponding to the propagation of circumferential or longitudinal wave modes in the tank. Changes in these waveforms, caused by simulated damages of the composite winding of the tank, have been shown to be quite significant. To conclude the study, an experimental sep-up using air-coupled transducers was employed to generate–detect guided wave modes over large distances in the real tank, with very good signal-to-noise ratios, thus demonstrating the possibility of using such elements for the non-destructive testing of high-pressure composite tanks during their lives.

Viscoelastic true-amplitude prestack reverse-time depth migration

Abstract: A new true-amplitude prestack elastic depth-migration algorithm includes compensation for transmission and anelastic attenuation losses in an isotropic medium. Geometric spreading and its compensation are incorporated by extrapolating up- and downgoing waves using a full two-way wave equation. Intrinsic attenuation is simulated and compensated for using composite memory variables derived from standard linear solid relaxation mechanisms. Zoeppritz equations and their approximations are used to compute and analyze the angle-dependent reflection/transmission coefficients; converted energy is included at each interface. Transmission losses for compressional waves are compensated, based on estimation of angle-dependent elastic reflectivity using a two-pass recursive procedure. The image condition is the ratio of the compressional receiver/source wavefield amplitudes. Application to synthetic data from a dipping-layer model and a salt model accurately extracts P-velocity, S-velocity, density, and P-wave impedance beneath the target reflector, even under a salt overhang. Factors not explicitly considered include building of the smooth background velocity and attenuation models, estimates of the source time function, directivity and coupling, multipathing arrivals, and effects of attenuation and anisotropy on the reflection/transmission coefficients.

Observations on the wavenumber spectrum and evolution of an internal wave attractor

Abstract: Reflecting internal gravity waves in a stratified fluid preserve their frequency and thus their angle with the gravitational direction. At boundaries that are neither horizontal nor vertical, this leads to a focusing or defocusing of the waves. Previous theoretical and experimental work has demonstrated how this can lead to internal wave energy being focused onto ‘wave attractors’ in relatively simple geometries. We present new experimental and theoretical results on the dynamics of wave attractors in a nearly two-dimensional trapezoidal basin. In particular, we demonstrate how a basin-scale mode forced by simple mechanical excitation develops an equilibrium spectrum. We find a balance between focusing of the basin-scale internal wave by reflection from a single sloping boundary and viscous dissipation of the waves with higher wavenumbers. Theoretical predictions using a simple ray-tracing technique are found to agree well with direct experimental observations of the waves. With this we explain the observed behaviour of the wave attractor during the initial development, steady forcing, and the surprising increase of wavenumber during the decay of the wave field after the forcing is terminated.

Particle trajectories in linear deep-water waves

Abstract: Using phase plane analysis we show that within the framework of linear water wave theory the particle paths in a deep-water wave are not closed: there is a forward drift over a period, which decreases with greater depth.

Joint inversion of borehole acoustic radial profiles for in situ stresses as well as third-order nonlinear dynamic moduli, linear dynamic elastic moduli, and static elastic moduli in an isotropically stressed reference state

Abstract: A computer-implemented method of estimating mechanical properties and stresses of rocks around a borehole. In situ stresses and dynamic and static moduli of a rock are jointly inferred from acoustic radial profiles measured with a borehole sonic tool. Inversion is performed on equations that govern the near-borehole distributions of the compressional wave slowness, the fast shear wave slowness, the slow shear wave slowness, and the shear wave modulus in the plane perpendicular to the borehole axis for in situ stresses, the dynamic shear modulus, the dynamic Lame parameter, λ, the static drained Young's modulus, and the static drained Poisson's ratio. Third-order nonlinear dynamic moduli are also inferred by the procedure. Material properties are retrieved in an isotropically stressed reference state. The input data used by the inversion is appropriately prescribed. Methods for constraining the solution in the event of noisy or limited data are demonstrated.

On the Recovery of the Free Surface from the Pressure within Periodic Traveling Water Waves

Abstract: We present a consistent derivation of the pressure transfer function for small amplitude waves within the framework of linear wave theory and discuss some nonlinear aspects.

Ion-acoustic solitary waves and their interaction in a weakly relativistic two- dimensional thermal plasma

Abstract: This paper discusses the existence of ion-acoustic solitary waves and their interaction in a weakly relativistic two-dimensional thermal plasma. Two Korteweg–de Vries equations for small but finite amplitude solitary waves in both ξ and η directions are derived. The phase shifts and trajectories of two solitary waves after the collision with an arbitrary angle α are also obtained. The effects of parameters of the normalized ion temperature σ, the ratio of heat capacity δ, the relativistic factor Fγ, and the colliding angle α on the amplitudes, the widths and the phase shifts of both the colliding solitary waves are studied. The effects of these parameters on the new nonlinear wave created by the collision between two solitary waves are examined as well. The results suggest that these parameters can significantly influence the amplitude, the width of the newly formed nonlinear wave and the colliding solitary waves. The phase shifts of the colliding solitary waves strongly depend on the colliding angle α. M...

Application of low-profile piezoceramic transducers for health monitoring of concrete structures

Abstract: Using piezoceramic patches bonded on concrete beams to perform structural health monitoring is investigated in this paper. To evaluate the performance of piezoceramic sensors and ultrasonic wave methods, two series of tests were carried out on 100×100×500 mm 3 concrete prisms. In the first series of tests, the influence of the frequency of the input signal on the waveforms was investigated and the optimum frequency to generate ultrasonic waves was evaluated. From the velocity of Rayleigh waves and longitudinal waves, the dynamic modulus of elasticity and dynamic Poisson's ratio of the concrete were obtained. In the second series, the effect of uniaxial compressive stress and the resulting internal cracking of the concrete on the amplitude of the waveforms received by piezoceramic sensors was investigated. It is shown that differences in amplitude between two wave packets are sensitive to the cracking process of concrete with externally applied loads. The results confirm that piezoceramic sensors and corresponding ultrasonic waves methods have the potential to monitor cracking and the long-term deterioration of concrete structures.

Effect of phase transitions on compressional-wave velocities in the Earth’s mantle

Abstract: The velocities of seismic waves in the Earth are governed by the response of the constituent mineral assemblage to perturbations in pressure and stress. The effective bulk modulus is significantly lowered if the pressure of the seismic wave drives a volume-reducing phase transformation. A comparison between the amount of time required by phase transitions to reach equilibrium and the sampling period thus becomes crucial in defining the softening and attenuation of compressional waves within such a two-phase zone. These phenomena are difficult to assess experimentally, however, because data at conditions appropriate to the Earth's deep interior are required. Here we present synchrotron-based experimental data that demonstrate softening of the bulk modulus within the two-phase loop of olivine-ringwoodite on a timescale of 100 s. If the amplitude of the pressure perturbation and the grain size are scaled to those expected in the Earth, the compressional-wave velocities within the discontinuities at 410, 520 and, possibly, 660 km are likely to be significantly lower than otherwise expected. The generalization of these observations to aluminium-controlled phase transitions raises the possibility of large velocity perturbations throughout the upper 1,000 km of the mantle.

A Coherence-Based Approach for Tracking Waves in the Solar Corona

Abstract: We consider the problem of automatically (and robustly) isolating and extracting information about waves and oscillations observed in EUV image sequences of the solar corona with a view to near real-time application to data from the Atmospheric Imaging Array (AIA) on the Solar Dynamics Observatory (SDO). We find that a simple coherence/travel-time based approach detects and provides a wealth of information on transverse and longitudinal wave phenomena in the test sequences provided by the Transition Region and Coronal Explorer (TRACE). The results of the search are pruned (based on diagnostic errors) to minimize false-detections such that the remainder provides robust measurements of waves in the solar corona, with the calculated propagation speed allowing automated distinction between various wave modes. In this paper we discuss the technique, present results on the TRACE test sequences, and describe how our method can be used to automatically process the enormous flow of data (≈1 Tb day−1) that will be provided by SDO/AIA.