Showing papers on "Reflection (physics) published in 2003"

Reflection phase characterizations of the EBG ground plane for low profile wire antenna applications

Abstract: Mushroom-like electromagnetic band-gap (EBG) structures exhibit unique electromagnetic properties that have led to a wide range of electromagnetic device applications. This paper focuses on the reflection phase feature of EBG surfaces: when plane waves normally illuminate an EBG structure, the phase of the reflected field changes continuously from 180/spl deg/ to -180/spl deg/ versus frequency. One important application of this feature is that one can replace a conventional perfect electric conductor (PEC) ground plane with an EBG ground plane for a low profile wire antenna design. For this design, the operational frequency band of an EBG structure is defined as the frequency region within which a low profile wire antenna radiates efficiently, namely, having a good return loss and radiation patterns. The operational frequency band is the overlap of the input-match frequency band and the surface-wave frequency bandgap. It is revealed that the reflection phase curve can be used to identify the input-match frequency band inside of which a low profile wire antenna exhibits a good return loss. The surface-wave frequency bandgap of the EBG surface that helps improve radiation patterns is very close to its input-match frequency band, resulting in an effective operational frequency band. In contrast, a thin grounded slab cannot work efficiently as a ground plane for low profile wire antennas because its surface-wave frequency bandgap and input-match frequency band do not overlap. Parametric studies have been performed to obtain design guidelines for EBG ground planes. Two novel EBG ground planes with interesting electromagnetic features are also presented. The rectangular patch EBG ground plane has a polarization dependent reflection phase and the slotted patch EBG ground plane shows a compact size.

Angle-domain common-image gathers by wavefield continuation methods

Abstract: Migration in the angle domain creates seismic images for different reflection angles. We present a method for computing angle-domain common-image gathers from seismic images obtained by depth migration using wavefield continuation. Our method operates on prestack migrated images and produces the output as a function of the reflection angle, not as a function of offset ray parameter as in other alternative approaches. The method amounts to a radial-trace transform in the Fourier domain and is equivalent to a slant stack in the space domain. We obtain the angle gathers using a stretch technique that enables us to impose smoothness through regularization. Several examples show that our method is accurate, fast, robust, and easy to implement. The main anticipated applications of our method are in the areas of migration-velocity analysis and amplitude-versus-angle analysis.

Observation of the inverse Doppler effect

Abstract: We report experimental observation of an inverse Doppler shift, in which the frequency of a wave is increased on reflection from a receding boundary. This counterintuitive effect has been produced by reflecting a wave from a moving discontinuity in an electrical transmission line. Doppler shifts produced by this system can be varied in a reproducible manner by electronic control of the transmission line and are typically five orders of magnitude greater than those produced by solid objects with kinematic velocities. Potential applications include the development of tunable and multifrequency radiation sources.

The reflection of the fundamental torsional mode from cracks and notches in pipes

Abstract: A quantitative study of the reflection of the T(0,1) mode from defects in pipes in the frequency range 10-300 kHz has been carried out, finite element predictions being validated by experiments on selected cases. Both cracklike defects with zero axial extent and notches with varying axial extents have been considered. The results show that the reflection coefficient from axisymmetric cracks increases monotonically with depth at all frequencies and increases with frequency at any given depth. In the frequency range of interest there is no mode conversion at axisymmetric defects. With nonaxisymmetric cracks, the reflection coefficient is a roughly linear function of the circumferential extent of the defect at relatively high frequencies, the reflection coefficient at low circumferential extents falling below the linear prediction at lower frequencies. With nonaxisymmetric defects, mode conversion to the F(1,2) mode is generally seen, and at lower frequencies the F(1,3) mode is also produced. The depth and circumferential extent are the parameters controlling the reflection from cracks; when notches having finite axial extent, rather than cracks, are considered, interference between the reflections from the start and the end of the notch causes a periodic variation of the reflection coefficient as a function of the axial extent of the notch. The results have been explained in terms of the wave-number-defect size product, ka. Low frequency scattering behavior is seen when ka 1.

Giant Goos-Hänchen effect at the reflection from left-handed metamaterials

Abstract: We study the beam reflection from a layered structure with a left-handed metamaterial. We predict a giant lateral (Goos-Hanchen) shift and splitting of the beam due to the resonant excitation of surface polaritons with a vortexlike energy flow between the right- and left-handed materials.

The measurement of lubricant–film thickness using ultrasound

Abstract: Ultrasound is reflected from a liquid layer between two solid bodies. This reflection depends on the ultrasonic frequency, the acoustic properties of the liquid and solid, and the layer thickness. ...

Reflection of generalized thermoelastic waves from the boundary of a half-space

Abstract: We investigated the problem of thermoelastic wave reflection from the insulated and isothermal stress-free as well as rigidly fixed boundaries of homogeneous isotropic solid half-spaces in the context of various linear theories of thermoelasticity, namely, Lord-Shulman, Green-Lindsay, Green-Nagdhi, coupled thermoelasticity, and uncoupled thermoelasticity. The ratios of reflection coefficients to that of incident coefficients are obtained for P- and SV-wave incidence cases. The results for partition of the energy for various values of the angle of incidence are computed numerically and presented graphically for aluminum-epoxy composite material in case of incident P- and SV-waves from the stress-free and rigidly fixed thermally insulated boundaries. The results obtained are discussed and compared in various models of thermoelasticity.

Internal Wave Breaking at Concave and Convex Continental Slopes

Abstract: Internal wave reflection from a sloping topographic boundary may lead to enhanced shear if the topographic angle to the horizontal is close to that of the internal wave group velocity vector. Previous analytic studies have suggested that shear enhancement is reduced at concave slopes as compared with convex and planar slopes near the critical angle. Here the internal wave reflection from concave and convex slopes that pass through the critical angle is investigated numerically using the nonhydrostatic Massachusetts Institute of Technology General Circulation Model (MITgcm). Overturning, shear instability, and resultant mixing are examined. Results are compared with simulations of wave reflection from planar slopes with angles greater than, less than, and equal to the critical angle. In contrast to the analytic predictions, no reduction in mixing is found for the concave slope as compared with the other slopes. In all cases, stratification is eroded in a band above the slope, bounded at its outer ...

Light emitting apparatus

Abstract: A light emitting apparatus has: a light emitting element of nitride semiconductor; a phosphor that absorbs light emitted from the light emitting element and emits light with a wavelength different from that of the absorbed light; a first reflection mirror that reflects the light emitted from the light emitting element to converge the light; a second reflection mirror that has a light passing hole at a position on which the light reflected on the first reflection mirror is converged and that has a reflection surface on the side opposite to the side facing the first reflection mirror; and a phosphor layer that includes the phosphor, the phosphor layer being placed over the light passing hole and at a specific region in transparent resin that part of light passing through the light passing hole is radiated.

Generation of internal tides in an ocean of finite depth: analytical and numerical calculations

Abstract: Mixing in the abyssal ocean is known to play an important role in controlling the large-scale ocean circulation. In the search for sources of mechanical energy for mixing, internal tides generated by the interaction of the barotropic tide with bottom topography (mode conversion) have been implicated. However, estimates of the rate at which barotropic tidal energy is converted into the internal wave field are quite uncertain. Here, I present analytical and numerical calculations of internal tide generation in a fluid layer of finite depth to better understand the energetics of the wave generation process. Previous theoretical models of wave generation have assumed an upper radiation boundary condition (BC) appropriate for an ocean of infinite depth. But recent observations of internal tides at significant distances from their generation region indicate that this BC is not always valid, and that reflection from the upper surface is important. I show that the presence of an upper free-surface reduces the rate at which energy is fed into the internal wave field (the power) and thus the energy available for mixing. This reduction increases with the horizontal extent of the topography (relative to the wavelength of a mode-1 internal wave). Fully nonhydrostatic, nonlinear numerical calculations are used to both test the theory and to explore more realistic parameters for which linear theories are formally invalid. As bottom topography becomes steeper, linear theory underestimates mode conversion by an increasing amount, although even at critical slope the difference is quite small (O(20%)). An important finding of this study is that for certain topographic shapes the power input into the wave field can saturate as the topography becomes supercritical. A comparison of model results with a recent finite amplitude theory suggests that even though finite depth effects may be negligible in the linear regime, they may become important when the topography is of finite amplitude. The results of process studies such as this should lead to improved estimates of mode conversion in the ocean.

Optical near-field distributions of surface plasmon waveguide modes

Abstract: Thin gold stripes, featuring various widths in the micrometer range, were microfabricated to obtain surface-plasmon guides on a glass substrate. Each metal stripe (MS) was excited by an incident surface-plasmon polariton which was itself launched on an extended thin gold film by the total internal reflection of a focused beam coming through the substrate. The optical near-field distributions of the surface-plasmon (sp) modes sustained by the stripes were then recorded using a photon scanning tunneling microscope (PSTM). For a fixed frequency of the incident light, these field distributions are found to depend on the widths of the stripes. We first provide an experimental study of the various order modes which arise as a function of the decreasing width. Specifically, we show that the lateral confinement of a MS surface-plasmon mode is not related to a reflection of the SP on the edges of the stripe. On the basis of PSTM images recorded over a gold thin-film step discontinuity, we show that the metal stripe plasmon modes are hybrid modes created by the coupling of interface and boundary modes. Using MSs of various thicknesses, we finally demonstrate that, similarly to the symmetric mode of an extended metal thin film bounded by different dielectric media, the field of the MS modes is mostly localized at the interface between the metal and the dielectric medium with the lowest refractive index.

Total negative refraction in real crystals for ballistic electrons and light.

Abstract: It is found that there exists a category of material interfaces, readily available, that not only can provide total refraction (i.e., zero reflection) but can also give rise to amphoteric refraction (i.e., both positive and negative refraction) for electromagnetic waves in any frequency domain as well as for ballistic electron waves. These two unusual phenomena are demonstrated experimentally for the propagation of light through such an interface.

P wave seismic velocity structure derived from sonic logs and industry reflection data in the Los Angeles basin, California

Abstract: [1] We present a new three-dimensional seismic P wave velocity model of the Los Angeles basin that is based on more than 150 sonic logs and 7000 stacking velocities from industry reflection profiles. The model was developed using kriging techniques implemented in GoCAD (a commercial application specializing in the construction of surfaces, the analysis of spatially distributed data, and the modeling or simulation of properties) and is characterized by a heterogeneous, spatial varying velocity gradient with maximum velocities of ∼5000 m/s in the sedimentary section. Variability of the observed P wave velocities increases with depth, reflecting complex structural and sedimentological controls. The model contains a new representation of the basin shape as defined by the sediment-basement interface, which was mapped using well control and seismic reflection profiles. Our model differs substantially in approach and outcome from previous representations of crustal velocity structure in southern California.

Wave scattering by narrow cracks in ice sheets floating on water of finite depth

Abstract: An explicit solution is provided for the scattering of an obliquely incident flexural-gravity wave by a narrow straight-line crack separating two semi-infinite thin elastic plates floating on water of finite depth. By first separating the solution into the sum of symmetric and antisymmetric parts it is shown that a simple form for each part can be derived in terms of a rapidly convergent infinite series multiplied by a fundamental constant of the problem. This constant is simply determined by applying an appropriate edge condition. Curves of reflection and transmission coefficients are presented, showing how they vary with plate properties and angle of incidence. It is also shown that in the absence of incident waves and for certain relations between their wavelength and frequency, symmetric edge waves exist which travel along the crack and decay in a direction normal to the crack.

Synthesis of an inhomogeneous medium from its acoustic transmission response

Abstract: In 1968 Claerbout showed that the reflection response of a horizontally layered medium can be synthesized from the autocorrelation of its transmission response. During a workshop on passive imaging methods at the 2002 SEG conference, Claerbout showed that this result can be obtained straightforwardly from the principle of conservation of acoustic power. In this paper I briefly review this derivation and show that the 3D generalization can be obtained along the same lines using a power reciprocity theorem. The resulting expression confirms Claerbout9s conjecture that “by crosscorrelating noise traces recorded at two locations on the surface, we can construct the wave field that would be recorded at one of the locations if there was a source at the other.”

Polarized Light, Revised and Expanded

Abstract: Polarized Light, Second Edition explores polarized light, its production, and its use, facilitating self-study without prior knowledge of Maxwell's equations. This comprehensive second edition includes more than 2500 thoroughly updated figures and equations for easier understanding and application across various industries. It features new chapters on polarization by refraction and reflection, polarization elements, anisotropic materials, Stokes polarimetry, Mueller matrix polarimetry, the mathematics of the Mueller matrix. This edition also offers updated and expanded material on the derivation of the Fresnel equations with plots of the magnitude and phase of the reflection coefficients.

Total external reflection from metamaterials with ultralow refractive index

Abstract: Metamaterials composed of metal-dielectric nanostructures are engineered to have an effective refractive index less than unity at optical wavelengths. The effect of total external reflection is demonstrated when light from vacuum is incident onto these materials at an angle exceeding the critical angle defined by Snell’s law. Novel approaches are discussed to derive the effective index of refraction from the reflection and refraction properties of finite slabs. The effect of losses and dispersion are analyzed in the visible range of frequencies by consideration of the measured properties of silver. The differences among ultralow refractive-index metamaterials, photonic bandgap materials, and metals are discussed. Remarkably, a bandgap is not required to obtain total external reflection.

Casimir force and the quantum theory of lossy optical cavities

Abstract: We present a derivation of the Casimir force between two parallel plane mirrors at zero temperature. The two mirrors and the cavity they enclose are treated as quantum optical networks. They are, in general, lossy and characterized by frequency-dependent reflection amplitudes. The additional fluctuations accompanying losses are deduced from expressions of the optical theorem. A general proof is given for the theorem relating the spectral density inside the cavity to the reflection amplitudes seen by the inner fields. This density determines the vacuum radiation pressure and, therefore, the Casimir force. The force is obtained as an integral over the real frequencies, including the contribution of evanescent waves besides that of ordinary waves, and then as an integral over imaginary frequencies. The demonstration relies only on general properties obeyed by real mirrors which also enforce general constraints for the variation of the Casimir force.

Measuring the porosity and the tortuosity of porous materials via reflected waves at oblique incidence.

Abstract: An ultrasonic reflectivity method is proposed for measuring porosity and tortuosity of porous materials having a rigid frame. Porosity is the relative fraction by volume of the air contained within a material. Tortuosity is a geometrical parameter which intervenes in the description of the inertial effects between the fluid filled the porous material and its structure at high frequency range. It is generally easy to evaluate the tortuosity from transmitted waves, this is not the case for porosity because of its weak sensitivity in transmitted mode. The proposed method is based on measurement of reflected wave by the first interface of a slab of rigid porous material. This method is obtained from a temporal model of the direct and inverse scattering problems for the propagation of transient ultrasonic waves in a homogeneous isotropic slab of porous material having a rigid frame [Z. E. A. Fellah, M. Fellah, W. Lauriks, and C. Depollier, J. Acoust. Soc. Am. 113, 61 (2003)]. Reflection and transmission scattering operators for a slab of porous material are derived from the responses of the medium to an incident acoustic pulse at oblique incidence. The porosity and tortuosity are determined simultaneously from the measurements of reflected waves at two oblique incidence angles. Experimental and numerical validation results of this method are presented.

Use of low frequencies for sub‐basalt imaging

Abstract: Many prospective passive ocean margins are covered by large areas of basalts. These basalts are often extremely heterogeneous and scatter the seismic energy of the conventional seismic reflection system so that it becomes difficult to obtain information on deeper reflectors. Since high frequencies are scattered more than low frequencies, we argue that the acquisition system for sub-basalt targets should be modified to emphasize the low frequencies, using much larger airguns, and towing the source and receivers at about 20 m depth. In the summer of 2001 we obtained seismic reflection data over basalt in the northeast Atlantic using a system modified to enhance the low-frequency energy. These new data show deep reflections that are not visible on lines shot in the same places with a conventional system.

Reflectance and albedo, surface

Abstract: ‘Albedo’ is Latin, meaning whiteness. The albedo of a surface is the fraction of the incident sunlight that the surface reflects. Radiation that is not reflected is absorbed by the surface. The absorbed energy raises the surface temperature, evaporates water, melts and sublimates snow and ice, and energizes the turbulent heat exchange between the surface and the lowest layer of the atmosphere. The surface albedo is a key ingredient in the remote sensing of surface and atmospheric properties from space. The spectral and angular dependence of reflected sunlight is used to infer surface properties such as the extent and nature of vegetation cover. It must also be allowed for when determining atmospheric composition such as the amount, size, and optical properties of haze particles. Over continents, the largest component of the reflected sunlight under cloud-free conditions is due to reflection by the surface. Consequently, the determination of atmospheric composition from reflected sunlight requires accurate knowledge of the contribution made by the reflecting surface. Different surfaces have different albedos. Oceans, lakes, and forests reflect relatively small fractions of the incident sunlight and have low albedos. Snow, sea ice, and deserts reflect relatively large fractions of the incident sunlight and have large albedos. While estimates of albedos for various surfaces are presented later (Table 3), it should be recognized that an albedo is not an intrinsic property of a surface. Instead, for any surface, the albedo depends on the spectral and angular distributions of the incident light, which in turn are governed by atmospheric composition and the direction of the beam of light from the sun. Ideally, surfaces may be broken into components, each component reflecting light following its own intrinsic optical rules for the wavelength and angular dependence of reflection. In practice, however, when viewed at the few-meters to several-kilometers resolution typical of spaceborne sensors, surfaces exhibit complex mixtures of components and geometric structures. At such scales, surfaces can contain any mixture of soil, vegetation, twigs, branches, rocks, snow, ice, water, and so on. The list is seemingly endless. Even if the scene is spatially uniform, reflection by the individual surface elements, such as grains of sand in a desert, or snowflakes in a drift, can be so difficult to treat according to the principles of optics as to render predictions of reflectance futile. In addition, topography and the consequent shading add further to the complexity. Thus, for practical treatments, surfaces are reduced to having few components, even as few as one or two, and both the spectral and angular distributions of the reflectances for the individual components are highly simplified. Simplifications of the spectral dependence of surface reflection are often dealt with through use of wavelength intervals over which the reflectivity of the surface remains reasonably constant. Simplifications of the angular dependence of surface reflection are often dealt with through the separation of the incident light into two components: one for the direct beam of incident light, which is the sunlight that has not been absorbed or scattered in the atmosphere; and one for incident sunlight that has been scattered into directions that differmarkedly from that of the direct beam. These simplifications are used below in combination with a global inventory of surface types to produce global maps of surface albedos. These maps, however, should be taken as providing only rudimentary estimates. Because of the complexities noted earlier, systematic attempts to construct global maps of surface albedos from satellite observations are just now being undertaken.

PML Absorbing Boundaries

Abstract: It has been previously demonstrated that no reflection is generated when elastic (or electromagnetic) waves enter a region with Perfectly Matching Layer (PML) absorbing conditions in a continuous medium. The practical application of PMLs, however, is in numerical modeling, where the medium is discretized by either a finite-element or a finite-difference scheme thus introducing a reduced amount of reflection. In such a case what is the practical and quantitative efficiency of PML absorbing boundaries? Assuming a regular spatial mesh, we start by evaluating analytically the reflection of body waves introduced by the discrete transition toward PML properties, under variable angle of incidence and wavelength. We then extend our evaluation with numerical tests for both body and Rayleigh waves. Surprisingly enough, the absorption remains equally efficient at wavelengths far larger than the PML thickness itself. As a consequence, the PML thickness can be kept minimal even for studies involving relatively low frequencies, and no rescaling with model size is required. Another pleasant feature is that it is all the more efficient at shallow angles of incidence. Finally, we show through numerical examples that a major advantage of using PMLs is their efficiency in absorbing Rayleigh waves at the free surface, a point where more classical methods perform rather poorly. Although previous authors essentially limited the description of their discrete implementation to 2D, we develop to some level of detail a 3D finite-difference scheme for PMLs and provide numerical examples.

Reflection signature of seismic and aseismic slip on the northern Cascadia subduction interface

Abstract: At the northern Cascadia margin, the Juan de Fuca plate is underthrusting North America at about 45 mm yr-1 (ref. 1), resulting in the potential for destructive great earthquakes2,3. The downdip extent of coupling between the two plates is difficult to determine because the most recent such earthquake (thought to have been in 1700)4 occurred before instrumental recording. Thermal and deformation studies5 indicate that, off southern Vancouver Island, the interplate interface is presently fully locked for a distance of ∼60 km downdip from the deformation front. Great thrust earthquakes on this section of the interface (with magnitudes of up to 9)4,5 have been estimated to occur at an average interval of about 590 yr (ref. 3). Further downdip there is a transition from fully locked behaviour to aseismic sliding (where high temperatures allow ductile deformation), with the deep aseismic zone exhibiting slow-slip thrust events6. Here we show that there is a change in the reflection character on seismic images from a thin sharp reflection where the subduction thrust is inferred to be locked, to a broad reflection band at greater depth where aseismic slip is thought to be occurring. This change in reflection character may provide a new technique to map the landward extent of rupture in great earthquakes and improve the characterization of seismic hazards in subduction zones.

The properties and causes of rippling in quasi-perpendicular collisionless shock fronts

Abstract: . The overall structure of quasi-perpendicular, high Mach number collisionless shocks is controlled to a large extent by ion reflection at the shock ramp. Departure from a strictly one-dimensional structure is indicated by simulation results showing that the surface of such shocks is rippled, with variations in the density and all field components. We present a detailed analysis of these shock ripples, using results from a two-dimensional hybrid (particle ions, electron fluid) simulation. The process that generates the ripples is poorly understood, because the large gradients at the shock ramp make it difficult to identify instabilities. Our analysis reveals new features of the shock ripples, which suggest the presence of a surface wave mode dominating the shock normal magnetic field component of the ripples, as well as whistler waves excited by reflected ions. Key words. Space plasma physics (numerical simulation studies; shock waves; waves and instabilities)

Multipass cavity for illumination and excitation of moving objects

Abstract: An illumination system for increasing a light signal from an object passing through a reflection cavity. The reflection cavity is disposed between spaced-apart, opposed first and second surfaces disposed on opposite sides of a moving stream of objects. A light collection system is disposed substantially orthogonal to a plane passing through the surfaces and the stream so as to collect light that is scattered from or emitted by the objects as they pass through a field of view disposed between the first and second surfaces. A beam of light from a laser source is directed through the stream of moving objects in a direction nearly orthogonal to the stream (but slightly inclined) and lying in the plane that extends through the surfaces and the stream. Due to the reflection angle and the distance between the stream and the first surface, the point at which the light reflected from the first surface intersects the stream on a second pass is displaced from where it passed though the stream on its initial pass. The light is reflected back and forth between the surfaces a plurality of times, illuminating a different portion of the field of view with each pass until, having ranged over the field of view, the light exits the reflection cavity. The “recycling” of the light beam in this manner substantially improves the SNR of the detection system by increasing an average illumination intensity experienced by the objects in the stream.

Closed-form expressions for ocean reverberation and signal excess with mode stripping and Lambert’s law

Abstract: Closed-form expressions for two-way propagation and reverberation in variable depth ducts are derived for isovelocity water by using ray invariants and acoustic flux. These expressions include the transition to single mode propagation at long range. Three surface scattering laws are considered: Lambert, Lommel-Seeliger, and angle independent, and these are compared with a point target to give explicit signal-to-reverberation ratios. In particular, there is interesting and sometimes surprising behavior when the propagation obeys mode-stripping (the high angles are preferentially attenuated by bottom losses) whilst the scattering obeys Lambert’s law (high angles are preferentially back-scattered). There may be conditions where the signal-to-reverberation ratio is independent of range so that there is no reverberation range limit. Bottom slope dependence of both target echo and reverberation is surprisingly weak. The implications of refraction are discussed. The angle dependence for a point or surface scatterer at a given range can be translated into arrival time, so it is possible to calculate the received pulse shape for one-way or two-way paths. Because the tail is exponential with a range-independent half-life that only depends on bottom reflection properties there is scope for extracting geoacoustic information from the pulse shape alone. This environmental time spread is also of use to sonar designers.

Scattering of the fundamental shear horizontal mode from steps and notches in plates

Abstract: The scattering of the SH0 mode from discontinuities in the geometry of a plate has been studied. Both finite element and modal decomposition methods have been used to study the reflection and transmission characteristics from a thickness step in a plate, obtaining very good agreement. The significance of nonpropagating modes in the scattering from steps in plates has been specifically investigated. A method to approximate the reflection from rectangular notches by superimposing the reflection from a step down (start of the notch) and a step up (end of the notch) has been proposed. It is demonstrated that it is possible to use this method to obtain the reflection from a notch of any depth and at any frequency. The effect of frequency on the reflection from notches has been examined. The limits of this method in approximating cracklike defects have also been studied.

Reflection and transmission responses of layered transversely isotropic viscoelastic media

Abstract: We consider a layered heterogeneous viscoelastic transversely isotropic medium with a vertical symmetry axis (a viscoelastic TIV medium) and parameters that depend on depth only. This takes into account intrinsic attenuation, anisotropy and thin layering. The seismic wavefield is decomposed into up‐ and downgoing waves scaled by the vertical energy flux. This scaling gives important symmetry relationships for both reflection and transmission (R/T) responses. For a stack of homogeneous layers, the exact reflection response can be computed in a numerically stable way by a simple layer‐recursive algorithm. We derive exact plane‐wave R/T coefficients and several linear and quadratic approximations between two viscoelastic TIV media, as functions of the real‐valued horizontal slowness. The approximations are valid for pre‐ and post‐critical values of horizontal slowness provided that the proper complex square roots are used when computing the vertical slowness. Numerical examples demonstrate that the quadratic approximations can be used for large differences in medium parameters, while the linear approximations can be used for small differences. For weak anisotropy it is sufficient to use an isotropic background medium, while for strong anisotropy it is necessary to use a weak TIV or TIV background medium. We also extend the O'Doherty–Anstey formula to the P‐ and SV‐wave transmission responses of a stack of viscoelastic TIV layers, taking into account intrinsic attenuation, anisotropy and thin layering.

Lamb wave reflection at the free edge of a plate.

Abstract: This study concentrates on the reflection of Lamb waves at the free end of a plate. The conversion phenomena are examined in detail over a large frequency range and the energy conversion coefficients are obtained by three different ways: theoretically, numerically (finite element method) and experimentally. The experimental energy determination is obtained from the measurement of the plate normal displacements, by mean of a laser interferometer. All results are in relatively good agreement and the energy balance between incident and reflected waves is discussed in each case.