Showing papers on "Reflection (physics) published in 1981"

Bidirectional reflectance spectroscopy: 1. Theory

Abstract: An approximate analytic solution is derived for the radiative transfer equation describing particulate surface light scattering, taking into account multiple scattering and mutual shadowing. Analytical expressions for the following quantities are found: bidirectional reflectance, radiance coefficient and factor, the normal, Bond, hemispherical, and physical albedos, integral phase function and phase integral, and limb-darkening profile. Scattering functions for mixtures can be calculated, as well as corrections for comparisons of experimental transmission or reflection spectra with observational planetary spectra. The theory should be useful for the interpretation of reflectance spectroscopy of laboratory surfaces and the photometry of solar system objects.

Seismic waves and sources

Abstract: 1 Classical Continuum Dynamics.- 1.1. The Stress Dyadic and Its Properties.- 1.2. Geometry of Small Deformations.- 1.3. Linear Elastic Solid.- 1.4. The Field Equations.- 1.5. Lagrangian Formulation.- 1.6. One-Dimensional Approximations.- 1.7. Two-Dimensional Approximations.- 1.8. Representation of Finite Strains.- 2 Waves in Infinite Media.- 2.1. Elementary Solutions of the Wave Equation.- 2.2. Separability of the Scalar Helmholtz Equation.- 2.3. Separability of the Vector Helmholtz Equation.- 2.4. Eigenvector Solutions of the Navier Equation.- 2.5. Plane Waves.- 2.6. Interrelations Among Plane, Cylindrical, and Spherical Waves.- 2.7. Dyadic Plane Waves.- 3 Seismic Plane Waves in a Layered Half-Space.- 3.1. Reflection and Refraction of Plane Waves- General Considerations.- 3.2. Reflection at a Free Surface.- 3.3. Reflection and Refraction at a Solid-Solid Interface.- 3.4. Reflection and Refraction at a Solid-Liquid Interface.- 3.5. Reflection and Refraction at a Liquid-Solid Interface.- 3.6. Surface Waves.- 3.7. Spectral Response of a Multilayered Crust.- 3.8. Generalization of the Matrix Method-the Matrix Propagator.- 3.9. The Inverse Surface-Wave Problem.- 4 Representation of Seismic Sources.- 4.1. A Concentrated Force in a Homogeneous Medium.- 4.2. Dipolar Point Sources.- 4.3. Relations of Betti, Somigliana, and Volterra.- 4.4. Fault-Plane Geometry.- 4.5. Dipolar Sources in a Homogeneous Medium.- 4.6. Stress Distributions on a Spherical Cavity and Their Equivalent Sources.- 4.7. Radiations from a Finite Moving Source.- 4.8. Radiation of Elastic Waves by Volume Sources.- 5 Surface-Wave Amplitude Theory.- 5.1. Surface-Wave Amplitudes in Simple Configurations.- 5.2. Generalization to a Vertically Inhomogeneous Half-space.- 5.3. Surface Waves from a Finite Moving Source.- 6 Normal-Mode Solution for Spherical Earth Models.- 6.1. Introduction.- 6.2. Oscillations of a Homogeneous Sphere.- 6.3. Oscillations of a Radially Inhomogeneous Self-Gravitating Earth Model.- 6.4. Effect of the Rotation of the Earth.- 6.5. Energy Integrals.- 6.6. Source Effects.- 6.7. Numerical Procedures.- 7 Geometric Elastodynamics: Rays and Generalized Rays.- 7.1. Asymptotic Body Wave Theory.- 7.2. Ray-Amplitude Theory.- 7.3. Ray Theory in Vertically Inhomogeneous Media.- 7.4. Asymptotic-Wave Theory in Vertically Inhomogeneous Media.- 7.5. Breakdown of the GEA: Caustics.- 7.6. Theoretical Seismograms.- 7.7. Spectral Asymptotic Approximations.- 7.8. Initial Motions.- 7.9. Normal-Mode versus Ray Solutions for Vertically Inhomogeneous Media.- 8 Asymptotic Theory of the Earth's Normal Modes.- 8.1. Jeans' Formula.- 8.2. Watson's Transformation of the Spectral Field.- 8.3. Surface Waves on a Sphere.- 8.4. Mode-Ray Duality.- 8.5. Ray Analysis in a Homogeneous Sphere.- 8.6. SH-Fild Analysis in a Uniform Shell Overlying a Fluid Core.- 8.7. Generalized Rays in Spherical-Earth Models.- 9 Atmospheric and Water Waves and Companion Seismic Phenomena.- 9.1. The Navier-Stokes Equation.- 9.2. Sound Waves.- 9.3. Gravity Waves in Liquids.- 9.4. Acoustic-Gravity Waves in the Atmosphere.- 9.5. Waves Generated by Atmospheric Explosions.- 9.6. Coupled Air-Sea Waves.- 9.7. Rayleigh Waves from Atmospheric Explosions.- 10 Seismic Wave Motion in Anelastic Media.- 10.1. The Specific Dissipation Parameter.- 10.2. Linear Viscoelastic Solid.- 10.3. Pulse Propagation in Unbounded Anelastic Media.- 10.4. Attenuation of Seismic Waves in the Earth.- Appendices.- A. Algebra and Calculus of Dyadics.- B. Orthogonal Curvilinear Coordinates.- C. The Material Derivative.- D. Bessel and Legendre Functions.- E. Asymptotic Evaluation of Special Integrals.- F. Generalized Functions.- G. The Airy Integral.- H. Asymptotic Solutions of Second-Order Linear Differential Equations.- I. Generalized Spherical Harmonics.- J. Transformation of Wave Functions under Translation and Rotation of the Coordinate Axes.- K. The Mathematics of Causality.- L. Models of the Earth and the Atmosphere.- List of Symbols.- Author Index.

Reflection of an open-ended coaxial line and application to nondestructive measurement of materials

Abstract: Reflection measurement techniques require a way to correlate measured reflection factors with the permittivity of the materials. This relationship is derived for the open-ended coaxial line propagating the TEM mode.

Reflection of acoustic waves at a water–sediment interface

Abstract: Reflection and refraction of plane acoustic waves are studied for the case where the sediment is modeled as a porous viscoelastic medium. The model is based on the classical work of Biot which predicts that three different kinds of attenuating body waves may propagate in the sediment. As a consequence when homogeneous plane waves in water are incident to a water‐sediment interface, three nonhomogeneous waves are generated in the sediment. In these waves the direction of phase propagation and the direction of maximum attenuation are not the same and particle motion follows an elliptic path. Moreover, the velocity and attenuation of the refracted waves become dependent on the angle of incidence and no “critical” angle occurs. Numerical examples show that the reflectivity of a porous viscoelastic model differs significantly from the case where the sediment is modeled as a viscoelastic solid with constant complex modulus. Finally, because of the frequency dependence of reflectivity in the porous model, it is ...

Seismic wave attenuation

Abstract: Seismic waves propagating through the earth are attenuated by the conversion of some fraction of the elastic energy to heat. Using terminology analogous to that used for the elastic properties that control seismic velocities, attenuation properties are characterized as anelastic properties. Attenuation data complement other physical measurements for characterizing rock properties. In seismic studies, attenuation data can at least double the information obtained from velocities alone. An understanding of the attenuative properties of the earth has two major motivations. First, seismic wave amplitudes are reduced as waves propagate through an anelastic medium, and this reduction is generally frequency dependent. Second, attenuation characteristics reveal much information, such as lithology, physical state, and degree of saturation of rocks. The phenomenon of attenuation is much more complex than the elastic aspects of seismic wave propagation, Both laboratory and field measurements are difficult to make. The mechanisms contributing to attenuation are numerous, and small changes in some conditions can affect attenuation significantly. However, sensitivities to some parameters, su ch as fluid saturation, make the measurement and understanding of attenuation highly important for many applications. The realization of the need and promise for specific data and models has prompted astrong resurgence of interest and research concerning attenuation in the fields of both seismology and rock physics. Laboratory measurements of attenuation in rock samples under varying pressures, temperatures, strain amplitudes, frequencies, and saturation conditions are presently being carried out. Detailed theoretical modeling of processes that may be responsible for attenuation is being undertaken. Measurements of attenuation in the earth using direct and refracted compressional and shear waves, surface waves, reflection seismograms, vertical seismic profiling, and full-wave acoustic well logs are being explored intensively. The net result of these field, laboratory, and theoretical studies will be a rapid expansion of our knowledge concerning the attenuation of seismic waves in the earths crust. We have undertaken the editing of this volume to help the broad-range research effort gain abetter understanding of attenuation and its applications to seismic exploration problems.

A theory of rheed

Abstract: Elastic Reflection High Energy Electron Diffraction (RHEED) by solid surfaces is studied theoretically. First, the problem of finding the electron reflection and transmission coefficients of a crystal slab is formally solved. Following this, it is shown how the formal solution may be used in a practical computation of the diffracted beam intensities. These two results are applied to a study of high energy (20 keV) electron diffraction by the Ag(001) surface. Rocking curves are computed to illustrate the dependence of the reflection coefficients on the glancing angle of the incident beam, the incident beam azimuth being in the [110] direction. The curves are shown to have several features in common with a typical set of LEED I - V plots: primary Bragg peaks, secondary Bragg peaks and resonance peaks are all present. The dependence of the reflection coefficients on the deviation of the incident beam azimuth from the [110] direction is also described. Additional computations are made to illustrate the sensitivity of the RHEED pattern to the details of the surface structure: the relative heights of the peaks in the rocking curves are shown to be quite sensitive to the spacing of the topmost atomic layers.

Amplified reflection, transmission, and self-oscillation in real-time holography

Abstract: A theory of phase conjugation in asymmetric materials that allow a phase shift between the grating and the light-interference pattern is developed. We find that when this phase is nonzero, maximum phase-conjugate reflectivity occurs for unequal pump intensities. The conditions for self-oscillation are studied.

Optical Properties of Direct Restorative Materials

Abstract: The contrast ratio, light reflectivity, scattering coefficient, and absorption coefficient of four composites and an unfilled resin were calculated algebraically from reflection spectrophotometric data using Kubelka's equations The correlation coefficient between calculated and experimental values of contrast ratio was 09996 Values of infinite optical thickness ranged from 419 to 670 mm

A Note on Low-Frequency Equatorial Basin Modes

Abstract: A new low-frequency standing equatorial wave mode is described. It is composed solely of long Kelvin and Rossby waves, whereas previously described low-frequency modes involved short, eastward propagating Rossby waves. It is argued that these short waves travel too slowly to allow such modes to set up. A simple closed form expression is given for the new basin mode; this is also a new form for the sum of a Kelvin wave and its eastern boundary reflection.

Photoelectric plethysmography-some fundamental aspects of the reflection and transmission methods

Abstract: In photoelectric plethysmography a distinction is made between the reflection and transmission methods. Uncertainties still exist, especially regarding the origin of the reflected signal: some investigators attach quantitative value to the amplitude of the plethysmogram. These various findings are reconsidered. Various fluids are pulsatilely pumped through an in vitro circuit. Flow, pressure and volume pulsations are measured, as is the total light intensity detected by a photoelectric plethysmograph with the small variations caused in it by the pulsations in flow. Both phase and amplitude of the resulting plethysmogram are studied and the results compared with those found in vivo at the fingers and auricles. In vitro, the variations in light reflection are in phase with the volume pulsations: this can only be ascribed to reflection by orienting erythrocytes. In vivo, however, the light reflection, like the light transmission, is in anti-phase with the volume excursions, thus eliminating the determinative effect of light reflection by orienting erythrocytes-the strong reflection from surrounding tissues completely dominates reflection from erythrocytes. Since erythrocytes also have absorptive properties, and the light reflection is in anti-phase with the volume excursions, it is concluded that this absorptivity can manifest itself over the strong reflection from surrounding tissue. In vivo, therefore, the reflection plethysmogram is, in principle, an absorption measurement.

Neutron reflection as a probe of surface magnetism

Abstract: Polarized neutrons reflected from the surface of a ferromagnet are sensitive to the magnetization close to the surface as well as to the bulk magnetization. In a calculation using parameters appropriate to nickel it is shown how the two contributions can be separated. Neutron measurements can determine the first moment of the magnetic disturbances at the surface, with a sensitivity corresponding to one magnetic dead layer.

Depth-dependent eigenenergies and damping of excitonic polaritons near a semiconductor surface

Abstract: This paper reports the experimentally observed change of exciton-polariton eigenenergies near the surface of a semiconductor. Normal-incidence-reflection spectra and attenuated-total-reflection (ATR) spectra are measured in the $n=1$ exciton-polariton energy region. It is shown that ATR spectra probe regions near the surface whereas reflection spectra probe more deeply into the crystal bulk. Model calculations, which include spatial dispersion and depth-dependent eigenenergies and damping of excitonic polaritons, yield excellent agreement with experiments for various semiconductors. This agreement proves that reflection spectra are determined not only by bulk properties of excitonic polaritons, but reveal also the properties of the transition region at the crystal surface. Therefore, information extracted so far from reflection spectra about additional boundary conditions of excitons and exciton-free surface layers may have to be revised.

Transformation and analysis of record sections

Abstract: Slant stacking is used to transform an observed record section Φ(x,t) into its plane wave decomposition Ψ(p,τ). The invertible transformation untangles travel time triplications and removes focusing and defocusing effects, yielding signals with the plane wave amplitudes and phases. The principal arrival, composed of refraction and wide angle reflections, appears in these coordinates as a display of the intercept time function τ(p), which may be inverted by any of several currently popular methods. The transformation into the (p,τ) domain; is an objective procedure which removes many of the interpreter's difficulties by casting the picking process into much simpler variables. Moreover, the decomposition into plane waves directly yields the transient reflectivity matrix of the (one dimensional) medium. Several lines of argument lead us to conclude that the comparison of data and synthetic data should be done in the (p,τ) domain. The use of these techniques requires that the wave field be sampled with sufficient spatial density of receivers to avoid wave number aliasing. We show examples of plane wave decomposition for shallow data from the COCORP deep crustal reflection program.

Thin-skinned tectonics in the northern Rhenish Massif, Germany

Abstract: A network of profiles in the Hercynian mountain system (Geo-traverse Rhenoherzynikum) is needed to determine details of the geological structure and find the reasons for tectonic movements. Outstanding features within the mountain system such as the large fault zone along the southern boundary of the Hunsruck1 and the left flank of the Rhinegraben have already been investigated by reflection seismology2,3 We describe here a new reflection–refraction experiment carried out in 1978 in the most northern part of the Rhenish Massif, across the Stavelot–Venn Massif near Aachen (Fig. 1). While layers in the lower crust dip to the NNW, a strong upper reflector at 3–4 km depth shows a slight dip to the SSE and indicates a prominent fault zone near Aachen, known in Belgium as the Faille du Midi. Here, a comparable and apparently identical reflector was found some 100 and 175 km to the west of our profile. We interpreted this reflector as a prominent and well lubricated thrust fault along which a huge horizontal nappe displacement took place during the last stages of the Variscan orogeny.

Pressure and velocity detectors for seismic exploration

Abstract: Pressure and velocity detectors produce outputs which are combined to substantially cancel ghost reflections. The pressure detector produces a positive output in response to upwardly travelling compressional waves and a negative output in response to downwardly travelling rarefaction waves. The velocity detector for this is a positive output in response to upwardly travelling compressional waves and a positive output in response to downwardly travelling rarefaction waves. These outputs are filtered so that the impulse response of the rarefaction waves cancels. The filtered outputs are combined to produce an output in which the ghost reflection is substantially suppressed.

A method for calculating synthetic seismograms which include the effects of absorption and dispersion

Abstract: A method is outlined for the calculation of synthetic seismograms which include the effects of absorption and dispersion. The absorption model used is the usual model of exponential decay of amplitude with distance given by A=A0e-αz, where α is a linear function of frequency. This attenuation is accounted for mathematically by allowing the elastic modulus to be a complex function of frequency. This results in a complex velocity and wavenumber, and the reflection and transmission coefficients also become complex functions of frequency. The method is based upon the communication theory approach and is applicable to plane waves in a flat layered model. The source can be placed at an arbitrary depth. The equations are outlined in detail for a particular absorption‐dispersion pair taken from Futterman (1962). An example with a surface synthetic seismogram and synthetic traces at several depths is presented.

Picosecond microwave pulse generation

Abstract: Picosecond duration X‐band microwave pulses have been generated using a laser‐activated photoconductive switch. These pulses have been used to observe the microwave reflection from optically excited germanium. The reflection measurements indicate that the microwave pulse has a full width at half‐maximum of 50 ps and is synchronized with picosecond precision to the laser pulse. A high‐resolution radar experiment is also reported.

A Simple Derivation of the Surface Contribution to the Reflectivity of a Metal, and its Use in the Van der Waals Interaction

Abstract: The reflection coefficients for light, polarized parallel and perpendicular to the plane of incidence, incident on a translationally invariant jellium surface are derived. The derivation is based on a form of pillbox integration of the two Maxwell equations which normally give the continuity of the parallel field components. In this manner we derive the corrections to the usual Fresnel result due to a varying electron density profile in the surface region. To illustrate the usefulness of these reflection coefficients explicit examples are given for the Van der Waals interaction between an adatom and a solid. The local field at the adatom, the lifetime of an excited adatom and the general form for the Van der Waals interaction incorporating the effects of non-locality in the solid.

Wave propagation over a rectangular trench

Abstract: An analysis is presented for the propagation of water waves past a rectangular submarine trench. Two-dimensional, linearized potential flow is assumed. The fluid domain is divided into two regions along the mouth of the trench. Solutions in each region are expressed in terms of the unknown normal derivative of the potential function along this common boundary with the final solution obtained by matching. Reflection and transmission coefficients are found for various submarine geometries. The result shows that, for a particular flow configuration, thereexists an infinite number of discrete wave frequencies at which waves are completely transmitted. The validity of the solution in the infinite constant-water-depth region is shown by comparing with the results using the boundary integral method for given velocity distributions along the mouth of the trench. The accuracy of the matching procedure is also demonstrated through the results of the boundary integral technique. In addition, laboratory experiments were performed and are compared with the theory for two of the cases considered.

Fresnel scattering model for the specular echoes observed by VHF radar

Abstract: In recent years several groups using VHF radars have reported highly anisotropic echoes originating from stable regions of the troposphere and stratosphere The echoes are most intense looking vertically, and their occurrence is well correlated with regions of hydrostatic stability Observations also show that the echoes are usually much stronger when observed with coarse spatial resolution There is no commonly used scattering or reflection model that can account for these features In this paper we present a new model to explain the enhanced vertical echoes The model pertains to scattering from the half-wavelength Fourier component of horizontally coherent fine structure in the radio refractive index within a region of finite vertical extent We refer to this echoing mechanism as ‘Fresnel scattering’ The new model is applied to simulate the magnitude of VHF radar echoes by using radiosonde temperature soundings as input Good agreement is found between these simulations and observations at the Sunset VHF radar in Colorado

Optical bistability with surface plasmons.

Abstract: We theoretically examine bistable operation in reflection with simultaneous excitation of the surface-plasmon mode at the interface with a nonlinear Kerr medium. Bistability may occur for an incident power an order of magnitude below that reported previously for a grazing-incidence geometry.

Umbral oscillations as resonant modes of magneto-atmospheric waves

Abstract: Umbral oscillations in sunspots are identified as a resonant response of the umbral atmosphere to forcing by oscillatory convection in the subphotosphere. The full, linearized equations for magnetoatmospheric waves are solved numerically for a detailed model of the umbral atmosphere, for both forced and free oscillations. Resonant 'fast' modes are found, the lowest mode having a period of 153 s, typical of umbral oscillations. A comparison is made with a similar analysis by Uchida and Sakurai (1975), who calculated resonant modes using an approximate ('quasi-Alfven') form of the wave equations. Whereas both analyses give an appropriate value for the period of oscillation, several new features of the motion follow from the full equations. The resonant modes are due to upward reflection in the subphotosphere (due to increasing sound speed) and downward reflection in the photosphere and low chromosphere (due to increasing Alfven speed); downward reflection at the chromosphere-corona transition is unimportant for these modes.

Diffracted fields in the focal volume of a converging wave

Abstract: Expressions for the scalar field in the focal volume are derived for the case of a uniform, converging, spherical wave incident upon a circular aperture. The intensity exhibits a reflection asymmetry with respect to the focal plane.

Rigorous Analysis of the Scattering of Surface Waves in an Abruptly Ended Slab Dielectric Waveguide

Abstract: The reflection and the scattering properties of even TE and TM surface waves incident in an abruptly ended dielectric slab waveguide are analyzed. The discontinuity is regarded as a junction between two open waveguides namely the dielectric slab waveguide and the free space waveguide. The boundary conditions acting together with the orthogonality provide singular coupled integral equations on the discrete and the continuous wave amplitudes at the discontinuity. These singular coupled intergral equations with Cauchy kernels and infinite limits of integration are solved by iteration via the Neuman series. Numerical results are presented for the reflectivity of the even TE/sub 0/ and TM/sub 0/ fundamental modes, together with their mode conversion on even TE/sub 2/ and TM/sub 2/ in a slab where two guided modes can propagate. Reflectivity and mode conversion of higher order excitations are also investigated

Total and partial reflection from the end of a parallel‐plate waveguide with an extended dielectric slab

Abstract: This investigation concerns a TEM wave obliquely incident onto the open end of a parallel plate wave guide with a truncated upper plate. The lower plate as well as the dielectric slab between the two plates is assumed to extend out indefinitely in order to support the propagation of at least one surface wave mode. Reflection from the wave guide opening is determined as a function of incident angle via a dual Wiener-Hopf formulation. It is found that total reflection, i.e., a reflection coefficient with magnitude equal to unity, is possible for incident angles greater than the critical angle associated with the lowest-order surface wave mode of the grounded dielectric slab. The field external to the parallel plate wave guide in this case becomes completely evanescent in the cross-sectional plane perpendicular to the plane of incidence, which is determined by the propagation direction of the incident wave and the edge of the upper plate. It is shown that the phase of the reflection coefficient thus obtained can be used to construct the modal equation for the fundamental mode(s) of a wide microstrip.

Coupled-Wave Analysis of Reflection Gratings,

Abstract: Diffraction of electromagnetic waves by longitudinally periodic media (reflection gratings) is rigorously analyzed using an exact coupled-wave approach. The analysis is formulated in a simple matrix form easily implemented on a digital computer. The intensities of the two waves, the diffracted (reflected) and transmitted waves, are calculated for a wide range of parameters. These exact results are then compared to results obtained with approximate two-wave modal, and with multiwave and two-wave coupled-wave analyses. The applicability of these approximate theories is discussed. The case of other than first-order Bragg incidence is also included.

Stable Solution of the Inverse Reflection Problem for a Smoothly Stratified Elastic Medium

Abstract: The subject of this paper is a version of the inverse reflection problem for a smoothly stratified elastic medium. The same mathematics describes the inverse problem of the vibrating string. This problem is solved in a constructive way. Also, a priori estimates are derived which exhibit the continuous dependence of the solution (index of refraction, relative sound speed) on the data (scattering or reflection measurements).

Anisotropy detection in sapphire by acoustic microscope using line-focus beam

Abstract: Nonscanning reflection acoustic microscopes can be satisfactorily applied to detect the anisotropy of acoustic properties of solid materials using a line-focus beam. As a demonstration, the anisotropic dependence of leaky surfac-acoustic-wave velocities on the propagation directions are measured on the water/Z-cut-sapphire boundary at a frequency of 200 MHz. The measured values are in good agreement with the calculated results within a difference of about 1%.