Showing papers on "Reflection (physics) published in 1983"

Scattering and absorption of turbid materials determined from reflection measurements. 1: theory.

Abstract: To allow the determination of scattering and absorption parameters of a turbid material from reflection measurements the relation of these parameters to the reflection has been described by two theoretical approaches. One approach is based on the diffusion theory which has been extended to include anisotropic scattering. This results in a reflection formula in which the scattering and absorption are described by one parameter each. As a second more general approach a Monte Carlo model is applied. Comparison of the results indicates the range of values of the scattering and absorption parameters where the computationally fast diffusion approach is applicable.

Sampling Theory and Wave Propagation

Abstract: In the seismic reflection method, the seismic signal does vary in amplitude, shape, frequency and phase versus the propagation time

Damped oscillations in reflection high energy electron diffraction during GaAs MBE

Abstract: Oscillations in the time evolution of electron diffraction during MBE growth of GaAs are shown to be related to periodic variations in the step distributions on GaAs surfaces during epitaxial growth. Unintentionally doped GaAs surfaces were first prepared by MBE. Then the Ga flux is interrupted until an instrument limited diffraction pattern was obtained. During this process the angular width of the specular beam was measured versus time. When the Ga flux there are intensity oscillations that are weak near the Bragg angle. At the Bragg angle, where the diffraction is insensitive to surface steps, the length of the specular RHEED streak does not change. At angles between the Bragg angles, where steps lengthen the streaks, there are periodic variations in the streak length. We interpret the results in terms of a model in which a partially completed surface has a step distribution with smaller average terrace lengths than a completed surface.

Computing true amplitude reflections in a laterally inhomogeneous earth

Abstract: Recently Bortfeld (1982) gave a cursory nonmathematical introduction to a procedure for computing the geometrical spreading factor of a primary zero‐offset reflection from the common datum point traveltime measurements of the event. To underline the significance and consequences of this method, a derivation and discussion of geometrical spreading factors is now given for two‐ and three‐dimensional earth models with curved reflecting boundaries. The spreading factors can be used easily to transform primary reflections in a zero‐offset seismic section to true amplitude reflections. These permit an estimation of interface reflection coefficients, either directly or in connection with a true amplitude migration. A seismic section with true amplitude reflections can be described by one physical experiment: the tuned reflector model. Hence the application of the wave equation (in connection with a migration after stack) is justified on such a seismic section. Also the geometrical spreading factors that are deri...

Enhanced light reflection by dye monolayers at the air–water interface

Abstract: The reflection of light from an air–water interface is enhanced by dye containing monolayers in the spectral region of the dye absorption. The intensity of the reflected light depends linearly on the density of chromophores in the mixed monolayer. From the measurement of both absorption and reflection spectra of a dye containing monolayer the damping constant of coherent light scattering can be estimated. The value of the reflection measurement for the investigation of adsorption processes and the control of monolayer organization is demonstrated.

Propagation of obliquely incident water waves over a trench

Abstract: The diffraction of obliquely incident surface waves by an asymmetric trench is investigated using linearized potential theory. A numerical solution is constructed by matching particular solutions for each subregion of constant depth along vertical boundaries ; the resulting matrix equation is solved numerically. Several cases where the trench-parallel wavenumber component in the incident-wave region exceeds the wavenumber for freely propagating waves in the trench are investigated and are found to result in large reductions in wave transmission ; however, reflection is not total owing to the finiteness of the obstacle. Results for one case are compared with data obtained from a small-scale wave-tank experiment. An approximate solution based on plane-wave modes is derived and compared with the numerical solution and, in the long-wave limit, with a previous analytic solution. 1. Introduction The problem of the diffraction of incident waves by a finite obstacle in an otherwise infinite and uniform domain remains of general interest in linear wave theory. Several geometries of interest can be schematized by domains divided into separate regions by vertical geometrical boundaries, with the fluid depth being constant in each subdomain. Representative two-dimensional problems, with the boundary geometry uniform in the direction normal to the plane of interest, include those of elevated rectangular sills, fixed or floating rectangular obstacles at the water surface, and submerged trenches. The approach to the solution of problems of this type has typically been to construct solutions for each constant-depth subdomain in terms of eigenfunction expansions of the velocity potential ; the solutions are then matched at the vertical boundaries, resulting in sets of linear integral equations which must be truncated to a finite number of terms and solved numerically. One of the earliest solutions of this type was given by Takano (1960), who studied the cases of normal wave incidence on an elevated sill and fixed obstacle at the surface. In this study, we employ a modification of Takano’s method, discussed in $3. Newman (19653) also employed an integral-equation approach to study reflection and transmission of waves normally incident on a single step between finite- and infinite-depth regions. A variational approach, developed by Schwinger to study discontinuitiesin waveguides (see Schwinger & Saxon 1968) has been used by Miles (1967), to study Newman’s single-step problem, and by Mei & Black (1969), who studied the symmetric elevated sill and a floating rectangular cylinder. Lassiter (1 972), using the variational approach, studied waves normally incident on a rectangular trench where the water depths before and after the trench are constant but not necessarily equal, referred to here as the asymmetric case. Lee &

Theory of a self-pumped phase conjugator with two coupled interaction regions

Abstract: We present a plane-wave analysis of a recently demonstrated self-pumped phase conjugator. This device uses four-wave mixing to produce the phase-conjugate replica of an incident optical wave. All the waves are derived from the single incident wave: there are no externally supplied pumping beams. We consider the case of four-wave mixing in two interaction regions coupled by simple reflection. We calculate the phase-conjugate reflectivity as a function of coupling strength, taking into account imperfect coupling between the two interaction regions, and show that there is a threshold coupling strength below which the reflectivity is zero and above which the reflectivity is multiple valued. We also compute the coupling strength per unit length for a photorefractive crystal of barium titanate.

Effect of wind-generated waves on the transfer of solar radiation in the atmosphere-ocean system

Abstract: Transfer of solar radiation in the combined atmosphere and ocean system is evaluated by the matrix operator method. Derivation of the reflection and transmission matrices required for applying the matrix method is discussed introducing the shadowing effect of light by the ocean waves. Spectral and total radiation fields just above and below the ocean surface, as well as the top of the atmosphere, are numerically calculated using several optical models of the atmosphere, ocean, and wind roughened ocean surface. Dependencies of radiance and flux reflectivity on the wind velocity and optical property of the ocean body are discussed in detail.

Scattering and absorption of turbid materials determined from reflection measurements. 2: measuring method and calibration.

Abstract: A new experimental method has been developed to determine the scattering and absorption characteristics of a turbid material. Existing methods usually require transmission and reflection measurements carried out on a thin slab of the material under study; this method is based on reflection measurements carried out on bulk material. This will be of great advantage in many applications. This paper describes the measuring system and indicates the area of application of the method. Calibration measurements have been carried out to substantiate the approach.

On the origin of plasmaspheric hiss: Ray path integrated amplification

Abstract: An investigation has been made of processes responsible for the growth, damping, and propagation characteristics of whistler mode emissions within the earth's plasmasphere. Three-dimensional ray path calculations of the integrated wave gain in a realistic model plasmasphere have provided an explicit confirmation of the anisotropic electron cyclotron resonant generation mechanism for the maintenance of plasmaspheric hiss. Peak wave amplification occurs for field-aligned waves in the outer plasmasphere. The majority of unstable low-frequency waves follow ray trajectories that internally reflect at the plasmapause and are thus trapped within the plasmasphere. This reflection allows waves to subsequently propagate into the locally stable inner and middle plasmasphere and also migrate substantially in longitude. The combination of internal reflection at the plasmapause and magnetospheric reflection at high latitude provide an important class of wave trajectories that are recycled back to the equatorial growth region with sufficiently small wave normal angles to allow further cyclotron resonant amplification. It is unlikely that wave growth can occur from the natural incoherent emissivity level within the plasmasphere since the required gains (≈100 dB) would mandate unreasonably high energetic electron flux. An alternate, as yet unidentified, embryonic source is therefore required to initiate the growth process. But once established the observed spectrum of broad band plasmaspheric hiss can be maintained by the modest net gains anticipated along ray trajectories that are recycled back to the favorable equatorial growth region. A simulation of the spectral properties of waves arriving at selected observation points following several equatorial transits shows that the largest accumulated gain occurs for recycled waves that reflect from the plasmapause following each equatorial crossing. Furthermore, the peak gain is relatively insensitive to the location of the observation point, and waves are expected to arrive over a broad solid angle in k space consistant with observations. The ability of waves to gain access to regions far from the source is a direct result of the relatively weaker Landau damping of oblique waves along the high latitude portion of the recycled ray path in comparison to the equatorial cyclotron resonant growth. The hiss upper frequency cutoff can result from the limited anisotropy of the cyclotron resonant electrons, the more severe Landau damping at higher frequencies, or in part, from the decreased ability of the higher frequency waves to recycle and thus experience multitransit growth. The characteristic lower frequency cutoff can be due to either the decrease in flux of energetic electrons that cyclotron resonate with the lower frequency waves or from thermal electron Landau damping should the plasmaspheric electron temperature exceed several electron volts.

Seismic reflections from a gas‐water contact

Abstract: Using the Biot theory, we have performed calculations to show that viscous fluid flow affects seismic wave amplitudes and reflection coefficients at a gas‐water boundary in a porous sand reservoir. Our formulation of the boundary value problem for fluid‐filled porous rocks is applicable at all angles and follows parallel to the classical reflection and transmission problem solved by Knott, Zoeppritz, and others for two elastic media in perfect contact. It is pointed out that there are two major differences between the two: (1) in the present case, we deal with the propagation of inhomogeneous waves, and (2) there are interference fluxes of energy between various types of waves. The latter exists only at an oblique incidence. In our model, loss of seismic energy is mainly due to mode converted type II waves of Biot at the gas‐water contact which propagate away from the boundary in the manner of a diffusion process at low frequencies. Both seismic energy loss and reflection coefficients are studied over a w...

Properties of a periodically stratified acoustic half‐space and its relation to a Biot fluid

Abstract: The problem of the reflection of acoustic waves from a periodically layered acoustic half‐space is solved exactly at all frequencies. Pass and stop bands and the associated complex slowness surfaces of propagation through the periodic medium are found. In the low‐frequency limit, when the wavelength normal to the layering is much greater than one period, it is shown that there always exists a homogeneous ideal fluid with the same reflection properties as the layered medium. However, the effective acoustic medium that models transmission as well as reflection at low frequencies has a bulk modulus Keff given by 〈K−1〉−1 where the brackets denote a volume weighted average, and, for the inertial density appearing in the equations of motion, the effective medium has a transverse isotropic density tensor with ρ∥, the density component parallel to the layering, given by 〈1/ρ〉−1, and ρ⊥, the density component perpendicular to the layering given by 〈ρ〉. The range of wavespeeds speeds as a function of angle is shown...

The Reflection of Equatorial Waves from Oceanic Boundaries

Abstract: Theory is developed to discuss the reflection of long equatorial waves from ocean boundaries. The main results are as follows: 1) Energy flux reflection coefficients for the reflection of equatorial waves from meridional eastern and western ocean boundaries have been plotted as a function of frequency. The coefficients enable one to determine, for example, how much energy of an incoming equatorial wave of frequency ω is transmitted along an eastern oceanic boundary as poleward propagating Kelvin waves. The coefficients are useful for, both modal and vertically propagating descriptions of equatorial waves. As an example, the reflection of the Yanai wave observed in the equatorial Pacific is discussed in connection with poleward propagating sea levels along the South American coast. 2) Moore (1968) showed that the reflection of an incoming equatorial wave to an eastern meridional boundary consists, in part, of poleward propagating Kelvin waves. Here the same result is generalized to non-meridional ...

Reflection and transmission of obliquely incident Rayleigh waves by a surface‐breaking crack

Abstract: Reflection, transmission, and scattering of Rayleigh waves that are obliquely incident on a surface‐breaking crack are investigated. The formulation of the problem has been reduced to two systems of singular integral equations of the first kind for the dislocation densities across the crack faces. The systems of integral equations are solved numerically. Substitution of the dislocation densities into appropriate representation integrals yields the reflected and transmitted surface waves. Reflection and transmission coefficients are plotted versus the angle of incidence for various values of the frequency and versus the frequency for various values of the angle of incidence. A critical angle of incidence, which depends on the material properties of the solid, has been observed. Beyond this angle no mechanical energy is radiated into the solid by body waves.

The anisotropic reflectivity technique: theory

Abstract: Summary. The reflectivity technique for the calculation of synthetic seismograms from a point source in a horizontally stratified isotropic structure is extended to include weakly anisotropic layers. The formulation is in terms of displacement excitation factors rather than potential functions, which have not yet been specified for wave propagation in anisotropic media. Coupling between vertical, radial and transverse components of motion increases the number of plane-wave reflection and transmission coefficients which must be computed for any problem. These coefficients are calculated by extending Kennett’s iterative scheme for the computation of isotropic coefficients to

Influence of the atmosphere on space measurements of directional properties.

Abstract: To compare measurements performed in different geometrical conditions, one must take into account the angular anisotropy of the reflection properties of natural surfaces. As use of the exact boundary conditions in the radiative transfer codes seems prohibitive, a simple but accurate formulation of the problem has been sought. In this paper, two average angular reflectances are defined from which the reflected radiance may be deduced for any distribution of the downward radiance. Calculations made for different atmospheric models show that the solar directionality is partly preserved in the downward radiation field, so that the average reflectances can be written as a linear combination of actual reflectance and spherical albedo of the surface. Finally, the feasibility of detecting directional properties from space measurements is discussed.

Reflection from a periodically perforated plane using a subsectional current approximation

Abstract: The scattering from a zero thickness plane having finite sheet resistance and perforated periodically with apertures is calculated for arbitrary plane wave illumination. The surface current density within the unit cell is approximated by a finite number of current elements having rooftop spatial dependence. The transverse electric field is expressed in terms of the current, and the electric field boundary condition is satisfied in an integral sense over the conductor, generating a finite dimension matrix equation whose solution is the current density. Since the conductor shape is defined through the locations of subsectional current elements, arbitrary shaped apertures can be handled. The reflection coefficient and current distribution are calculated for square apertures in both perfectly conducting and resistive sheets, and for cross-shaped apertures. Finite resistivity is shown to cause the magnitude of the transverse magnetic (TM) reflection coefficient to decrease more rapidly and its phase to decrease less rapidly, as the angle of incidence approaches glancing. Through detailed plots of the current density, the current crowding around the apertures is made clearly evident.

A new evaluation of the Goos–Hänchen shift and associated time delay

Abstract: A wave packet reflected totally at an interface between two media may undergo the Goos–Hanchen shift and associated time delay. Two different theoretical approaches have been presented so far to evaluate this phenomenon. One is the stationary‐phase method and the other is the conventional energy‐flux method. In this paper, a certain deficiency existing in the conventional energy‐flux method is pointed out and a new energy‐flux method is derived based on an accurate argument of the conservation of energy flux. The new energy‐flux method confirms the consistency of the predictions by the stationary‐phase method from the point of view of the conservation of energy.

Spurious reflection of elastic waves due to gradually changing finite element size

Abstract: SUMMARY When a homogeneous elastic continuum is modelled by a non-uniform finite element grid. the differences in the size of adjacent finite elements can cause a spurious wave reflection which does not exist in the continuum. Extending previous studies in which the spurious wave reflection was investigated for the case of two uniform grids with a sudden element size change from one grid to the other, the present study deals with the case when the two uniform grids of different element sizes are separated by a transition zone through which the element size varies gradually, either by a geometric progression or by an arithmetic progression. The solution is carried out in complex variables and numerical plots of the results are given. When the ratio of wavelength to the largest element size is as low as 4: 1, the spurious wave reflection is very significant, while for the ratios over 10: 1 it is insignificant. Inserting a transition zone with gradually varying element size between the two uniform parts of the grid somewhat mitigates the phenomenon of spurious reflection, but this is significant only when the ratio of element sizes in the uniform grids is small (less than about 1· 5: 1). Varying the element size throughout the transition zone in an arithmetic progression seems slightly better than in a geometric progression. The spurious wave reflection is less pronounced for higher-order elements, in particular for linear strain elements as compared to constant strain elements. The spurious reflection is also less severe for consistent mass than for lumped mass.

Scattering of electromagnetic waves from a half space of densely distributed dielectric scatterers

Abstract: The scattering of a plane wave obliquely incident on a half space of densely distributed spherical dielectric scatterers is studied. The quasi-crystalline approximation is applied to truncate the hierarchy of multiple scattering equations, and the Percus-Yevick and the Verlet-Weis results are used to represent the pair distribution function. The coherent reflected wave is studied with these approximations. The incoherent scattered wave is calculated with the distorted Born approximation. In the low-frequency limit, closed-form expressions are obtained for the effective propagation constants, the coherent reflected wave, and the bistatic scattering coeficients. Results at higher frequencies are calculated numerically. The advantage of the present approach is that, in the low-frequency limit, it reproduces the effects of specular reflection, Fresnel reflection coefficient, Brewster angle, and Clausius-Mosotti relation. In addition to the classical results, the bistatic scattering coefficients are also calculated. The theory is also applied to match backscattering data from dry snow at microwave frequencies.

Wave reflection from a sediment layer with depth-dependent properties

Abstract: The reflection of plane acoustic waves at the water–sediment interface is analyzed. The sediments are modeled using Biot’s equations with depth‐dependent coefficients. Computations are made of the reflection coefficient as a function of the incident wave frequency and angle for representative sediment properties. The results are compared to those obtained by modeling the sediments as a homogeneous viscoelastic material and as a viscoelastic material with depth‐dependent properties. It is shown that both of these models yield predictions of the reflection coefficient that can differ substantially from the Biot model.

Reflection of MHD-waves in the Pc4-5 period range at ionospheres with non-uniform conductivity distributions

Abstract: A theoretical model is proposed which describes the influence of non-uniform ionospheric conductivity distributions on ULF-pulsations. The assumption is made that the field-aligned currents carried by the wave-field are closed by polarisation currents in the magnetosphere and by the irrotational part of the ionospheric currents. Current continuity at the magnetosphere-ionosphere boundary provides for a differential equation for the reflected electric field for arbitrary non-uniform conductivity distributions. A solution of the equation for two simple but realistic conductivity and electric field distributions shows that anomalies in the reflected electric field can occur which are confined to the conductivity gradient region. Under certain conditions also double peak electric field disturbances have been obtained.

An update on non-stationary oblique shock-wave reflections: actual isopycnics and numerical experiments

Abstract: Nonstationary oblique shock-wave reflections over compressive wedges in air and argon were investigated using infinite-fringe interferometric techniques. These allowed direct, continuous and accurate observations of the isopycnics (lines of constant density) of the flow field. The initial pressures for these experiments were made as high as possible (15 to 250 torr) in order to increase the number of isopycnics and to enhance their details and distribution along the wedge surface over a shock-Mach-number range 2.0 < Ms [les ] 8.7. Included in the study were two cases of regular reflection (RR) and one of each single Mach reflection (SMR), complex Mach reflection (CMR) and double-Mach reflection (DMR) for air, and one RR, SMR, CMR and DMR for argon. These particular cases, which we investigated previously in N2 and Ar using a finite-fringe technique, have been used by computational fluid dynamicists to check their finite-difference results against our experimental data. It will be shown that the isopycnic structure previously reported by us differs in detail, in most cases, from that of the present study. The major difference arises from the fact that it was only possible previously to obtain discrete points on isopycnics and along the wedge surface. Consequently, the results obtained before were not as accurate. Comparisons were made of actual wall-density distributions with numerical simulations of the density contours of the various flows obtained by a number of authors. Each numerical method displays its advantages and disadvantages in describing the details of the flow fields. The present experimental results for air are new. They are of great interest from a practical viewpoint. The experiments in argon were redone to provide better data for a gas free from real-gas effects in the range of initial conditions considered, in order to simplify the computations in the numerical simulations. Although the recent numerical simulations are better than those reported previously, additional efforts are required to improve the predictions of the shape, location and values of the isopycnics and other flow isolines in the various regions and along the wall, and to render the predictions free of computer ‘noise’. It is worth noting that real-gas effects did not play any significant role in determining the various wave systems in RR, SMR, CMR and DMR; a different claim was made in our previous work. Relaxation of nitrogen in air can be seen however, at the highest shock Mach numbers (Ms = 7.19 and 8.70), with relaxation lengths in good agreement with accepted predictions.

High‐frequency acoustic properties of a fluid/porous solid interface. II. The 2D reflection Green’s function

Abstract: A 2‐D space–time reflection Green’s function is developed using the Cagniard–de Hoop technique for a fluid/lossless porous media planar interface configuration. It is then used to study the effects of the various surface waves whose velocities were calculated in the previous article. The time‐dependent pressure response to a modeling source signal (Blackman–Harris pulse) for certain simulated experimental configurations is also presented. It is concluded that the amplitudes with which the new surface modes are generated are large enough to enable their detection.

Studies of the self‐focusing instability at Arecibo

Abstract: Precisely simultaneous radar and satellite measurements at the altitude of reflection of a strong HF heating wave above the Arecibo Observatory were made on June 7, 1977. Parametric instabilities produce strong enhancements in the plasma line and ion line incoherent scatter radar echoes. These echoes also exhibit periodic deep fading that is attributed to a self-focusing instability. This explanation was confirmed by the in situ observation of electron density fluctuations with peak-to-peak amplitudes reaching at least 3% and a spatial dependence that corresponded closely to the radar fading pattern, at least for irregularity wavelengths ranging from a few hundred meters to a few kilometers. The correspondence implies that the radar fading is associated with the convection of the density irregularities through the radar beam. The radar and satellite observations also provided values for the important parameters of the ambient ionosphere, making possible a quantitative comparison of the data with existing theories of the self-focusing instability. In particular, the agreement with the theory of Cragin et al. (1977) is fairly good.