Reflection Of Surface Waves Research Articles

RESEARCH ON THE GULF STREAM FRONTAL ZONE USING SYNTHETIC-APERTURE RADAR OF THE ALMAZ-1 SPACECRAFT AND CONTACT SHIPBOARD MEASUREMENTS

The results of a joint analysis of data recorded quasisynchronously in the Gulf Stream frontal zone by a radar with a synthetic aperture radar (SAR) carried aboard the Almaz-I spacecraft and the Akademik Vernadskiy research ship (contact measurements) are presented. It is shown that the dark linear structures visible on SAR images are radar images of zones of current convergence, in which surfactants are accumulated, suppressing cm-length ripples. In the case of wave propagation in the same direction as the current, the effects of refraction and reflection of surface waves, leading to the formation of regions of concentration of waves at the current boundaries and in the wave “shadow” region, are detected and investigated.

Depth Measurements of Short Cracks in Perspex with the Scanning Acoustic Microscope

By using a scanning acoustic microscope (SAM) combined with the time-of-flight diffraction technique, the depths of short cracks in perspex have been measured. Perspex was chosen for the work because it is a transparent, isotropic, and acoustically slow material; therefore, it enables one to measure the crack geometry in the light microscope, and it eliminates the involvement of the Rayleigh surface waves and the influence of wave speed anisotropy on the acoustic measurements. Short cracks of different geometries (depth to length ratios of 0.72 and 0.25) were initiated in commercial perspex by bending the specimens slightly and adding a little acetone to the surface bearing a tensile stress while at 20°C and 50°C, respectively. The SAM was operated in a short pulse mode capable of time resolved acoustic measurements. While one scans the lens across a crack, a narrow acoustic pulse (<20ns wide) is sent into the specimen, and the intensities of the signals scattered from the specimen are recorded in a plot of time-of-flight versus lens position, called an s(t,y) plot. Ray theory provides a useful description concerning the significant contributions to the s(t,y) plot from perspex when the lens is scanned across a surface breaking crack. They are (1) specular reflection of incident waves from the specimen surface; (2) diffraction of incident waves at the crack mouth edges; (3) reflection of longitudinal lateral surface waves from the crack mouth; (4) conversion of incident waves into longitudinal lateral surface waves at the crack mouth edges or the other way round; (5) propagation of longitudinal lateral surface waves in the specimen surface; (6) reflection of longitudinal waves from the crack face below the surface, if the crack is oblique; and (7) diffraction of longitudinal waves at the subsurface crack tip. As in the conventional time-of-flight diffraction technique, the crack tip diffracted signals were used to measure the crack depth. In order to enhance the contrast of the crack tip diffracted signals in an s(t,y) plot, the specimens were bent during the acoustic measurements, and a substraction algorithm was used to remove the much stronger specular reflections. The resulting acoustic depth measurements agreed with direct light microscope measurements within 93%, thus demonstrating the ability of the acoustic microscopic to measure the depth of short cracks in perspex. The prospect of using the acoustic microscope to measure the depth of short cracks in opaque materials is apparent.

A roller device to scan for surface-breaking cracks and to determine crack depth by a self-calibrating ultrasonic technique

Abstract A roller device using a square or a rectangular configuration of four roller transducers is used to scan a surface for surface-breaking cracks, by monitoring the reflection and transmission of surface waves. A self-calibrating ultrasonic technique is presented to determine the reflection and transmission coefficients or their ratio. For two configurations, namely, when one or both front rollers have crossed the surface trace of the crack, expressions have been obtained for the reflection and transmission coefficients in terms of measured voltages only, independent of parameters defining the coupling of the transducers to the specimen and the attenuation of surface waves propagating over the specimen. For a two dimensional configuration of a crack normal to the surface, the experimental results for the magnitude of the transmission coefficient show good agreement with theoretical results. For that case, the crack depth can be determined from the measured data.

Surface Waves of Oblique Incidence Across Deep Infilled Trenches

Propagation of surface waves of oblique incidence across infilled trenches is considered. An analytical approach based on the Green's function technique is developed to estimate the reflection and transmission of surface waves across a layer inserted between two homogeneous quarter-spaces. For the transmission of surface waves across the layer, a differential matrix operator is constructed by using Taylor series expansion in order to relate field quantities on each side of the layer. Reflection and transmission coefficients of the Rayleigh wave across the layer are then integrated by using the representation theorem. After validating the method against experimental data, influence of the material contrast and the angle of incidence on the efficiency of an in-filled trench is examined.

Surface wave scattering by a material interphase between two edge bonded plates

Reflection and transmission of surface waves at a material interphase between two edge bonded composite plates have been investigated in this paper. The study is motivated by the need to develop a quantitative ultrasonic technique to characterize properties of joints between two plates which may be laminated and anisotropic. Although there have been some recent studies that have examined the reflection and transmission of surface waves at the interphase between two plates, they consider the plates to be semi-infinite in thickness. Thus the mode conversion of surface waves into higher guided modes of the plates are not taken into account. In this paper we show that at high frequencies when a 0 and S 0 modes tend to become surface waves, the interaction of these waves with the joint interphase gives rise to higher modes, the effect of which is seen as resonant peaks in the reflection and transmission coefficients at the cutoff frequencies of these modes. These peaks become increasingly pronounced as the thickness of the interphase increases. Another interesting feature is that the reflection coefficient becomes minimum at a frequency that depends on the thickness and the properties of the interphase material. These features can be used to determine the relevant properties of the joint.

Reflection and transmission of antiplane surface waves by a surface-breaking crack in a layered elastic solid

The reflection and transmission of antiplane surface waves (Love waves) by a surface-breaking crack in a layered elastic solid is investigated. The crack is normal to the free surface, and breaks into the lower half-space solid. The formulation of the problem is reduced to a singular integral equation of the Cauchy type. In this equation, the unknown function, which is the slope of the crack-face displacement, is discontinuous at the interface between the two solids. It is shown that the magnitude of the discontinuity is related to the ratio of the shear moduli. A Gaussian numerical method is used to obtain the solution of the singular integral equation. At some distance from the plane of the crack, the wave motion is the superposition of a finite number of Love-wave modes. The amplitudes of these modes are readily evaluated in terms of the slope of the crack-face displacement. Curves are presented for the reflection coefficients corresponding to the first three modes and for the transmission coefficient as functions of the dimensionless frequency.

Reflection of Ocean Surface Gravity Waves from a Natural Beach

The energy of seaward and shoreward propagating ocean surface gravity waves on a natural beach was estimated with data from an army of 24 bottom-mounted pressure sensors in 13-m water depth, 2 km from the North Carolina coast. Consistent with a parameterization of surface wave reflection from a plane sloping beach by Miche, the ratio of seaward to shoreward propagating energy in the swell-sea frequency band (0.044–0.20 Hz) decreased with increasing wave frequency and increasing wave height, and increased with increasing beach-face slope. Although most incident swell-sea energy dissipated in the surf zone, reflection was sometimes significant (up to 18% of the incident swell-sea energy) when the beach face was steep (at high tide) and the wave field was dominated by low-energy, low-frequency swell. Frequency-directional spectra show that reflection of swell and sea was approximately specular. The ratio of seaward to shoreward propagating energy in the infragravity frequency band (0.010–0.044 Hz) varied between about 0.5 and 3 and increased with increasing swell energy. This trend suggests that infragravity waves generated in very shallow water, and refractively trapped on the sloping seabed, are significantly dissipated over a 50-km wide shelf during storms.

Reflection and transmission of surface waves at a vertical interface in anisotropic elastic media : Its, E N; Lee, J S Bull Seismol Soc AmV83, N5, Oct 1993, P1355–1372

Reflection and transmission of surface waves at a vertical interface in anisotropic elastic media : Its, E N; Lee, J S Bull Seismol Soc AmV83, N5, Oct 1993, P1355–1372

Guided waves in a jointed composite plate

Reflection of guided waves by a thin region of bonding material at the interface between two composite plates has been investigated in this paper. The study is motivated by the need to develop a quantitative ultrasonic technique to characterize properties of joints between two plates, which may be laminated and anisotropic. Although there have been some recent studies that have examined the reflection and transmission of surface waves at the interface between two plates, they consider the two plates to be semi-infinite in thickness. Thus the mode conversion of waves into higher guided modes of the plates are not taken into account. In this paper, a model study of the interaction of the A0 and S0 guided wave modes with the joint material is presented. It is shown that as the frequency increases the coefficient of reflection shows resonant peaks at the cutoff frequencies of higher guided modes. These peaks become increasingly pronounced as the thickness of the joint increases. Another interesting feature is that the reflection coefficients have minima at a frequency that depends on the thickness and the properties of the joint material. These features can be used to determine the relevant properties of the joint.

Reflection and transmission of surface waves at a vertical interface in anisotropic elastic media

Abstract Propagation of surface waves across a vertical interface between anisotropic blocks is considered in this paper. Dyadic representation of a far field Green's function for an anisotropic half-space is constructed first. An analytical procedure is then developed to determine the reflection and transmission coefficients of surface waves at the vertical interface between two laterally homogeneous anisotropic quarter-spaces. Numerical results of Rayleigh wave reflection at vertical interfaces between dissimilar blocks are presented and the trade-off between anisotropy and inhomogeneity is discussed.

Depth measurements of short cracks in perspex with the scanning acoustic microscope

By using a scanning acoustic microscope (SAM) combined with the time-of-flight diffraction technique, the depths of short cracks in perspex have been measured. Perspex was chosen for the work because it is a transparent, isotropic, and acoustically slow material; therefore, it enables one to measure the crack geometry in the light microscope, and it eliminates the involvement of the Rayleigh surface waves and the influence of wave speed anisotropy on the acoustic measurements. Short cracks of different geometries (depth to length ratios of 0.72 and 0.25) were initiated in commercial perspex by bending the specimens slightly and adding a little acetone to the surface bearing a tensile stress while at 20°C and 50°C, respectively. The SAM was operated in a short pulse mode capable of time resolved acoustic measurements. While one scans the lens across a crack, a narrow acoustic pulse (<20ns wide) is sent into the specimen, and the intensities of the signals scattered from the specimen are recorded in a plot of time-of-flight versus lens position, called an s(t,y) plot. Ray theory provides a useful description concerning the significant contributions to the s(t,y) plot form perspex when the lens is scanned across a surface breaking crack. They are (1) specular reflection of incident waves from the specimen surface; (2) diffraction of incident waves at the crack mouth edges; (3) reflection of longitudinal lateral surface waves from the crack mouth; (4) conversion of incident waves into longitudinal lateral surface waves at the crack mouth edges or the other way round; (5) propagation of longitudinal lateral surface waves in the specimen surface; (6) reflection of longitudinal waves from the crack face below the surface, if the crack is oblique; and (7) diffraction of longitudinal waves at the subsurface crack tip. As in the conventional time-of-flight diffraction technique, the crack tip diffracted signals were used to measure the crack depth. In order to enhance the contrast of the crack tip diffracted signals in an s(t,y) plot, the specimens were bent during the acoustic measurements, and a subtraction algorithm was used to remove the much stronger specular reflections. The resulting acoustic depth measurements agreed with direct light microscope measurements within 93%, thus demonstrating the ability of the acoustic microscopic to measure the depth of short cracks in perspex. The prospect of using the acoustic microscope to measure the depth of short cracks in opaque materials is apparent.

Propagation of surface waves across a vertical layer with non-rigid contacts

Propagation of surface waves across a vertical wave barrier inserted between two laterally homogeneous quarter-spaces is considered in this paper. Based on the Green's function technique, an analytical approach is developed to examine the reflection and transmission of Rayleigh surface waves across a composite barrier. The composite barrier consists of a high velocity layer sandwiched between two thin layers of low shear velocity materials. The high velocity layer is represented by differential matrix operators which relate the wave fields on each side of the layer. The low velocity layers are modeled by non-rigid or “unwelded” contact conditions which allow partial sliding at the interfaces. Screening ratios of barriers with various combinations of material, geometric, and non-rigidness parameters are compared and discussed in some detail.

A note on Bragg scattering of surface waves by sinusoidal bars

The reflection of linear surface waves by sinusoidal bottom undulations is considered in the case where the incident wave is not necessarily close to the resonant frequency. For finite detuning away from the resonant frequency, two previous solutions are shown to give results which are inconsistent with direct numerical solutions, especially when the results are extended to oblique incidence. The correction to the methods is given, and various consequences of the new results are examined.

A comparison of two models for surface-wave propagation over rapidly varying topography

Comparisons are made between the predictions of two models for surface-wave propagation over rapidly-varying bottom topography, one based on the extended-mild-slope equation derived by Kirby (Kirby, J.T. J. Fluid Mechanics, 162 (1986) 171–186), 1 and the other on the successive-application-matrix model described by O'Hare & Davies (O'Hare, T. J. & Davies A. G. Coastal Engineering, 18 (1992) 251–266). 2 The models are applied to two types of undulating topography, namely sinusoidal and doubly-sinusoidal beds, and comparisons are made with existing laboratory data. Both models provide similar, accurate, predictions for the first-order resonant reflection of surface waves having wavelength equal to approximately twice that of the sinusoidal bed components. Agreement between the models and data is less good for higher-order resonances, due to the (different) formulations of the bottom boundary condition used in the models. In particular, some disagreement arises both when the surface wavelength is approximately equal to that of a bed component, and also when it corresponds to the sub-harmonic ‘difference’ wavelength. Generally, the successive-application-matrix model, which provides a more explicit formulation of the wave propagation problem than the extended-mild-slope equation model, gives better predictions of the data, but is computationally more demanding.

Higher-order Bragg reflection of gravity surface waves by periodic beds

Experiments are described which demonstrate higher-order Bragg resonant interactions between linear gravity waves and doubly sinusoidal beds. These higher-order effects, which include harmonic and subharmonic Bragg reflections, have been observed by making very precise measurements in a wave tank. Subharmonic reflection was found to be very large, even for small bottom undulation amplitudes. The experimental data are compared with the predictions of a numerical model based on the full potential theory of linear waves.

Measurement models for quantitative ultrasonics

This paper discusses some important recent developments in quantitative non-destructive evaluation, more specifically in quantitative ultrasonics. The importance of measurement models is emphasized, and the interaction of ultrasound with cracks is discussed in some detail. Three examples are discussed, both from a theoretical and an experimental point of view. These are backscattering of body waves from a surface-breaking crack, reflection and transmission of surface waves by a surface-breaking crack and line-focus acoustic microscopy of a specimen containing a subsurface crack. Mathematical measurement models also play a useful role in the training of neural networks, as discussed by the example of backscattering from a surface-breaking crack.

Application of a diffraction-corrected ray theory to the slot lens in acoustic microscopy

A modified ray approach is used to model the slot lens for determining V(z) and the results are compared with experiment for several materials. The slot lens is also used to obtain V(z) of y-cut quartz for a number of slot orientations relative to the crystalline x axis. The Rayleigh wave velocity as a function of propagation direction is then deduced from these measurements and compared with accepted values. It is shown that although the angular restriction of the slot lens is introduced in the lens aperture plane in contrast to shaped electrodes in the transducer plane, it is still necessary to account for diffraction in the lens rod in order to provide agreement with experiment. The application of the slot lens to crack detection is also examined and an analysis provided that yields substantial agreement with experiment. A simple yet effective method for extracting the surface wave reflection coefficient of a crack from measurements is proposed and demonstrated.

Reflection of axial surface waves from the end of a fluid-loaded cylindrical shell: A Wiener–Hopf analysis

At frequencies somewhat below the ring frequency, a fluid-loaded cylindrical shell supports a surface wave, the energy of which is predominantly in the surrounding fluid. The possible propagation directions are limited to those close to the axial direction. For such waves the inertia of the elastic material is unimportant and the shell behaves nearly as a Winkler foundation, such that the ratio of the external acoustic pressure to the inward displacement is Eh/R2. The present paper seeks to quantify the physical phenomena associated with reflection of such a wave from a free end of a shell, but to make the analysis tractable, the shell is regarded as a semi-infinite locally reacting cylinder extending from −∞ to 0, followed by a rigid cylindrical baffle, also of radius R, extending from 0 to ∞ along the x axis. A known surface wave is incident from x=−∞ and one seeks the amplitude and phase shift of the reflected surface wave along with any acoustic field radiating into the fluid that originates in the vicinity of the shell end at x=0. An exact solution involving contour integrals is derived using the Wiener–Hopf technique and applicable asymptotic results are extracted.

Self-calibrating ultrasonic technique for crack depth measurement

A configuration of transducers together with a self-calibrating measurement technique is proposed to investigate the reflection and transmission of surface waves by a surface-breaking or near surface defect. By means of this technique, the ratio of the reflection and transmission coefficients (R/T and/orT/R) can be obtained in a reliable and accurate manner. The reflection and transmission of surface waves for oblique incidence on a surface breaking crack is investigated in detail. Information onT/R for the latter case can be used to determine the depth of the crack. The experimental measurements ofT/R show excellent agreement with theoretical results.

Reflection and transmission of surface waves in laterally varying media

SUMMARY The T-matrix description of surface wave scattering is viewed in a reflection/transmission context reminiscent of problems involving elastic wave propagation in stratified media. This approach exploits the orthogonality properties of the surface wave basis functions and permits a description of surface wave propagation in environments exhibiting a degree of quasi-concentric multilayering about a vertical axis. In the first case we consider a multilayered environment where the individual layers are laterally homogeneous and where the layer boundaries need not be circularly cylindrical. The reflection/transmission treatment incorporates all higher order scattering processes and may be used to examine both scattering from multilayered obstacles and the outward evolution of a wavefield from a source acting along the vertical coordinate axis. We then examine the form taken by the reflection/transmission matrices where arbitrary lateral variations in material properties are confined to a broad cylindrical band surrounding the vertical axis. The total response is assembled by considering the band as a succession of infinitesimally thin, heterogeneous shells in welded contact. This treatment relies on the use of invariant embedding techniques and the expansion of the Green's function for a stratified medium in terms of surface wave basis functions. It is demonstrated that the theory is the 3-D extension of coupled mode techniques used to model surface wave propagation in strictly 2-D waveguides. The theory is applied to investigate the effect of near-source, continuously varying heterogeneity on surface wave radiation patterns in the far-field. The general character of the transmitted wavefield agrees with that expected from arguments based on geometrical optics. Despite the suggestive behaviour of the surface wave basis functions in the near-field, wavetype coupling by continuously varying heterogeneity is not especially efficient in this regime. This implies that large transverse components of displacement frequently observed on regional seismograms from explosive sources are the result of other mechanisms, for example abrupt changes in structure or anisotropy.