Showing papers on "Reflection (physics) published in 1982"

Wave propagation and sampling theory—Part I: Complex signal and scattering in multilayered media

Abstract: From experimental studies in digital processing of seismic reflection data, geophysicists know that a seismic signal does vary in amplitude, shape, frequency and phase, versus propagation time To enhance the resolution of the seismic reflection method, we must investigate these variations in more detail. We present quantitative results of theoretical studies on propagation of plane waves for normal incidence, through perfectly elastic multilayered media. As wavelet shapes, we use zero-phase cosine wavelets modulated by a Gaussian envelope and the corresponding complex wavelets. A finite set of such wavelets, for an appropriate sampling of the frequency domain, may be taken as the basic wavelets for a Gabor expansion of any signal or trace in a two-dimensional (2-D) domain (time and frequency). We can then compute the wave propagation using complex functions and thereby obtain quantitative results including energy and phase of the propagating signals. These results appear as complex 2-D functions of time and frequency, i.e., as “instantaneous frequency spectra. ’ ’ Choosing a constant sampling rate on the logarithmic scale in the frequency domain leads to an appropriate sampling method for phase preservation of the complex signals or traces. For this purpose, we developed a Gabor expansion involving basic wavelets with a constant time duration/mean period ratio. For layered media, as found in sedimentary basins,

Fundamentals of ocean acoustics

Abstract: The ocean as an acoustical medium ray theory of the sound field in the ocean reflection of sound from the surface and bottom of the ocean plane waves reflection of sound from the surface and bottom of the ocean point source propagation of sound in shallow water underwater sound channel (USC) range-dependent waveguide antiwave guide sound propagation scattering of sound at rough surfaces sound propagation in the random ocean scattering and absorption of sound by gas bubbles in water.

Self-pumped, continuous-wave phase conjugator using internal reflection

Abstract: Continuous-wave phase conjugation of an image-bearing beam is demonstrated using a single-domain crystal of BaTiO(3) and nothing else. The device operates by four-wave mixing using the photorefractive effect but without any external pumping beams or external mirrors. The customary pumping beams are derived from the incident beam and are internally reflected inside the crystal adjacent to an edge. The device is self-starting and has a phase-conjugate reflectivity of 30%. Imaging applications are discussed.

The Optical Properties of 'Moth Eye' Antireflection Surfaces

Abstract: A ‘moth eye’ antireflection surface is a very fine array of protuberances which behaves as a gradation of refractive index, and which substantially reduces the reflectance. The reflection and transmission properties of such surfaces are described, and are shown to be equal to those of the best multilayer antireflection coatings.

Evidence for specularly reflected ions upstream from the quasi‐parallel bow shock

Abstract: Ion velocity distributions in the form of bunches of gyrating particles traveling along helical paths have been observed moving sunward immediately upstream from quasi-parallel parts of the earth's bow shock using Los Alamos/Garching instruments on ISEE-1 and -2. These distributions have characteristics which indicate that they are produced by the nearly specular reflection at the shock of a portion of the incident solar wind ions. In particular, the guiding center motion and the gyrospeeds of the gyrating ions are quantitatively consistent with simple geometrical considerations for specular reflection. These considerations reveal that specularly reflected ions can escape upstream when the angle between the upstream magnetic field and the local shock normal is less than 45 deg but not when the angle is greater than 45 deg. These upstream gyrating ions are an important signature of one of the processes by which solar wind streaming energy is dissipated into other forms of energy at the shock.

A Fourier method for solving nonlinear water-wave problems: application to solitary-wave interactions

Abstract: A numerical method is developed for solution of the full nonlinear equations governing irrotational flow with a free surface and variable bed topography. It is applied to the unsteady motion of non-breaking water waves of arbitrary magnitude over a horizontal bed. All horizontal variation is approximated by truncated Fourier series. This and finite-difference representation of the time variation are the only necessary approximations. Although the method loses accuracy if the waves become sharp-crested at any stage, when applied to non-breaking waves the method is capable of high accuracy.The interaction of one solitary wave overtaking another was studied using the Fourier method. Results support experimental evidence for the applicability of the Korteweg-de Vries equation to this problem since the waves during interaction are long and low. However, some deviations from the theoretical predictions were observed - the overtaking high wave grew significantly at the expense of the low wave, and the predicted phase shift was found to be only roughly described by theory. A mechanism is suggested for all such solitary-wave interactions during which the high and fast rear wave passes fluid forward to the front wave, exchanging identities while the two waves have only partly coalesced; this explains the observed forward phase shift of the high wave.For solitary waves travelling in opposite directions, the interaction is quite different in that the amplitude of motion during interaction is large. A number of such interactions were studied using the Fourier method, and the waves after interaction were also found to be significantly modified - they were not steady waves of translation. There was a change of wave height and propagation speed, shown by the present results to be proportional to the cube of the initial wave height but not contained in third-order theoretical results. When the interaction is interpreted as a solitary wave being reflected by a wall, third-order theory is shown to provide excellent results for the maximum run-up at the wall, but to be in error in the phase change of the wave after reflection. In fact, it is shown that the spatial phase change depends strongly on the place at which it is measured because the reflected wave travels with a different speed. In view of this, it is suggested that the apparent time phase shift at the wall is the least-ambiguous measure of the change.

A quantum potential description of one-dimensional time-dependent scattering from square barriers and square wells

Abstract: The time-dependent scattering of one-dimensional Gaussian wave packets of various energies incident on(1) a square potential barrier and(2) a square well is examined numerically, using the quantum potential introduced by Bohm. The time-dependent quantum potential is calculated in each case, and the results displayed on three-dimensional computer plots. The particle trajectories from different initial positions within the wave packet are also shown, giving a detailed description of reflection and tunneling in terms of individual processes. The wider implications of this analysis are also briefly considered.

The seismic reflection character of the continental mohorovicic discontinuity

Abstract: The continental Mohorovicic discontinuity is most often interpreted as a step-function velocity boundary. However, on deep crustal seismic reflection profiles, reflections, at depths where refraction data places the Moho, have laminated character and are laterally discontinuous. These observations on continental reflection data point to a model of the Moho that has thin layered rather than block structure. Previous workers, who have synthetically generated seismic responses from various crust-mantle boundary models, have shown that thin layered models of alternating high and low velocity generate responses that best emulate observed Moho arrivals. Geologic interpretations of the thin layering include relatively undeformed metasediments, cumulate layering, tectonic banding, and lenses of partial melt. To obtain more direct geologic evidence, a synthetic seismogram is generated from geologic cross-sections of the Ivrea-Verbano Zone, an exposed section through the lower crust and upper mantle. The synthetic shows laminations similar to those observed on reflection data. Without more direct evidence, no single geologic interpretation of the Moho is reasonable. Indeed, the Moho may be a laterally variable boundary, its composition and structure dependent upon the geologic history of the overlying crust.

Reflection—refraction of general P-and type-I S-waves in elastic and anelastic solids

Abstract: Summary. The reflection and refraction of general (homogeneous or inhomo-geneous) plane P and type-I S(SV) body waves incident on plane boundaries are considered for general linear viscoelastic solids. Reflection—refraction laws, physical characteristics of the waves, and the nature of critical angles are examined in detail at welded boundaries and a free surface. General visco-elasticity with no low-loss approximations predicts that contrasts in intrinsic absorption at boundaries give rise to inhomogeneous reflected and refracted waves with elliptical particle motions, velocities and maximum attenuations that vary with frequency and angle of incidence, energy propagation at speeds and directions different from phase propagation, phase propagation that in general is parallel to the boundary for at most one angle of incidence, and reflection—transmission coefficients dependent on energy flow due to wave interaction. None of these physical characteristics are predicted for waves incident on boundaries that respond instantaneously.

Plane Wave Reflection Coefficients For Gas Sands At Nonnormal Angles of Incidence

Abstract: The P-wave reflection coefficient at an interface separating two media is known to vary with angle of incidence. The manner in which it varies is strongly affected by the relative values of Poisson's ratio in the two media. For moderate angles of incidence, the relative change in reflection coefficient is particularly significant when Poisson's ratio differs greatly between the two media. Theory and laboratory measurements indicate that high-porosity gas sands tend to exhibit abnormally low Poisson's ratios. Embedding these lowvelocity gas sands into sediments having 'normal' Poisson's ratios should result in an increase in reflected P-wave energy with angle of incidence. This phenomenon has been observed on conventional seismic data recorded over known gas sands.

Reflection of a Gaussian beam at a nonlinear interface.

Abstract: By numerical simulations of the reflection of a (2-D) Gaussian beam from a nonlinear interface, we show several new features of the behavior of such an interface and resolve the difference between the results of two previous studies of this type. Newly reported features include a very large nonlinear Goos-Hanchen shift and large variations of the angle of an output beam for small changes in the input intensity. The latter phenomenon has potential applications for a light-controlled angular scanning element. The differences between prior studies of this type are shown to be an artifact of the numerical procedures used.

Hyperbolic heat transfer with reflection

Abstract: The non-Fourier model for heat transfer leads to a hyperbolic evolution problem describing the temperature solution. A one-dimensional case is considered for such a propagating heat wave reflected at a boundary. A primary goal is investigation of the effectiveness of numerical solution techniques for the case of a propagating heat front and the influence of different boundary conditions. Finite elements are employed in space and alternative time integration schemes are studied, including ordinary differential equation system integrators. The effect of solution “roughness” on the error and oscillations before and after reflection is examined and rates of convergence are numerically determined.

Galloping in Crocodylus johnstoni—a reflection of terrestrial activity?

Abstract: Crocodylus johnstoni commonly gallop when released after being caught and handled. Galloping is a bounding gait and, in addition to increased velocities, it allows crocodilians to rapidly negotiate obstacles such as rocks and logs when on land. Bound length and gallop velocity both increase with increasing snout-vent length, but not in the same proportion: small C. johnstoni bound more frequently than larger ones.

Reinterpretation of seismic reflection data over the East Pacific Rise

Abstract: Multichannel seismic reflection data over the axial region of the East Pacific Rise are depth migrated using detailed velocity information from laboratory measurements of ophiolite samples. The data are from the Lamont Doherty Geological Observatory's line 17 shot across the rise at 9/sup 0/N. The migrated data are interpreted to show the structure of the seafloor and what we believe is the magma chamber roof. The polarity and apparent root mean squared velocity of the magma chamber roof are asymmetric with respect to the topographic axis of the ridge. The asymmetry is probably real and not an artifact of data collection. Modeling of the magnetic data gathered along the line shows that spreading has not been proceeding normally. A reasonable explanation for the asymmetry is the possibility that the line intersects a transform fault or an abandoned ridge segment near the ridge axis. The shape of the roof reflection is convex upward with an approximate slope of 10/sup 0/ and a width of 4 km. If extrapolated symmetrically to the other side of the ridge axis, the magma chamber roof event is consistent with the funnel-shaped chamber proposed by Pallister and Hopson (1981) for the Samail ophiolite. If the chambermore » roof steepens rapidly beyond the extent of the reflection, it would be consistent with the mush-filled model of Sleep (1975, 1978) and Dewey and Kidd (1977).« less

Scattering of Rayleigh surface waves by edge cracks: Numerical simulation and experiment

Abstract: Scattering of Rayleigh surface waves by surface edge cracks is numerically simulated in a two‐dimensional geometry, using the finite‐difference method and the FFT algorithm. For shallow cracks, it is revealed that the transmission coefficient decreases with normalized depth h* = hc/λ and the reflection coefficient increases with h*, where hc is the crack depth and λ the wavelength. For relatively deep cracks, these coefficients appear to be independent of h*, while the time‐of‐flight of the transmitted Rayleigh wave linearly increases with h*. The numerical solutions are in good agreement with the experimental observations based on the ultrasonic spectrum analysis and the time‐of‐flight measurements for the artificial cracks in mild‐steel test pieces.

Energy transfer between two beams in writing a reflection volume hologram in a dynamic medium

Abstract: A theoretical study is presented of the stationary energy transfer between two beams in the writing of a reflection hologram in a dynamic medium. The intensities of the two beams both inside the medium and at the surfaces are determined as a function of absorption coefficient, the effective coupling constant, the initial intensity ratio and the thickness of the medium. Numerical results obtained from the computer calculations are presented in graphical form.

Quantifying resolving power of seismic systems

Abstract: A quantitative formulation of vertical resolving power of seismic exploration systems is presented and is offered as a proposed characteristic, or standard, resolving power identified with individual systems. The formulation broadens the classical concept of resolution by taking into account the reflection waveform and the noise, in addition to the classical time variable. The principal feature in the formulation is the stipulation that the intratrace distribution of reflections and of noise be treated as random (Gaussian) distribution, which is regarded as the most general representation for seismic sections as a whole.Through this quantification of vertical resolving power and therefore of intratrace reflection quality, a number of elemental reflection properties that have been described only qualitatively in the past are expressed by simple formulas. The quantification is consistent with the concept that the resolving power of a noise-free zero-phase system with a flat spectral band response is proportional to the bandwidth. The derived basic formula for the proposed characteristic resolving power is a 2 m /E, where a m is the maximum (absolute) amplitude of the signal wavelet of a seismogram interval, E is the energy of the signal wavelet, and noise is neglected. The quantification of the reflection properties, including taking the noise into account, stems from this formula.The classical concept of resolution, which considers only the time variable, such as the dominant period of signal wavelets, is applicable essentially only in cases of two noise-free equal-strength reflections. In contrast, the proposed formulation of resolving power accommodates a wide scope of applications and might be considered basic to seismic systems. I present theoretical material for evaluating the merits of the proposal. Suitable comparisons by seismic modeling would be useful in the overall evaluation.

New formulas for the electromagnetic field of a vertical electric dipole in a dielectric or conducting half‐space near its horizontal interface

Abstract: New formulas are derived for the electromagnetic field of a vertical electric dipole in a conducting or dielectric half‐space. These continuously approximate in accuracy the general complex integrals over the entire practical range, yet are quite simple. They supplement similar formulas for the horizontal electric dipole with which they are compared, and provide the means for studying the interference patterns between the direct and lateral components of the waves and the reflection and transmission of lateral waves at boundaries.

Remote sensing of sea state using laser altimeters

Abstract: The reflection of short laser pulses from the ocean surface is analyzed based on the specular point theory of scattering. The expressions for the averaged received signal, shot noise, and speckle-induced noise are derived for a direct detection receiver system. It is found that the reflected laser pulses have an average shape which is closely related to the probability density function associated with the ocean surface profile. The result is used to estimate the mean sea level and significant wave height from temporal moments of the reflected laser pulse.

Reflection and transmission of bounded sound beams on half‐spaces and through plates

Abstract: Reflection of bounded sound beams incident from a liquid on solid half‐spaces or plates and transmission through plates are described using one new mathematical model. Since the exact expressions for reflection and transmission coefficients are used, reflected and transmitted beam profiles can be predicted at any angle of incidence. Using a simple representation by inhomogeneous infinite waves, it is possible to obtain analytical expressions for reflected and transmitted beams, whatever the form of the incident profile may be. As the bounded beam is built up by inhomogeneous waves, all propagating in the same direction, it can be easily interpreted and it is possible to detect those parts that are generating surface waves.

Reflection and refraction of seismic waves incident obliquely at the boundary of a liquid-saturated porous solid

Abstract: A systematic theory of the propagation of seismic waves in liquid-saturated porous solids was first developed by Biot in 1956. Since then, some theoretical investigations have been carried out on the propagation of body and surface waves in such media. Further studies in this area may be useful in giving greater insight into the propagation of seismic waves in underground layers of porous solids saturated with oil or groundwater. In this connection, the transmission of normally incident seismic waves across the boundary of a liquid-saturated porous solid has been considered earlier. Keeping in view the fact that oblique incidence is more likely than normal incidence for such seismic waves, the authors have investigated the reflection and refraction of P and SV waves, which become obliquely incident at the boundary of a liquid-saturated porous solid, after propagating through an elastic solid. It is found that, corresponding to both P and SV waves obliquely incident at the boundary, there will be two refracted dilatational waves traveling with different velocities, which may be called the Pf and Ps waves, and one refracted SV wave, in the liquid-saturated porous solid, together with reflected P and SV waves in the elastic solid. The amplitude and energy ratios for the different reflected and refracted waves have been calculated theoretically. Numerical values of the amplitude and energy ratios have been computed for different angles of incidence for P and SV waves which propagate through granite, and then become incident at the boundary between the granite and oil-saturated sandstone, using results of laboratory experiments on the elastic behavior of oil-saturated sandstone. It is found that the amplitudes of the reflected and refracted waves depend significantly on the angle of incidence. It is also found that the amplitude of the second refracted P wave is usually much smaller than that of the other reflected and refracted P and SV waves, so that this slower refracted P wave will be difficult to detect. Similar amplitudes and energy ratios are also calculated for P and SV waves incident at the boundary between granite and dry sandstone. Comparison between the cases of dry sandstone and oil-saturated sandstone shows that the presence of oil usually has a significant effect on the amplitudes of the reflected and refracted P and SV waves. It is noted that such theoretical investigations may be useful in utilizing the amplitudes and other characteristics of reflected and refracted seismic waves in the detection and study of underground layers of porous solids saturated with oil or groundwater.

Nonlinear Reflection in Cholesteric Liquid Crystals: Mirrorless Optical Bistability

Abstract: Exact elliptic-function solutions are presented for intense light waves in cholesteric liquid crystals. Light-induced changes in the pitch of the cholesteric helix lead to a bistable reflection characteristic even in the absence of external reflectors.

Reflection of elastic waves under initial stress at a free surface: P and SV motion

Abstract: The phenomenon of reflection of elastic waves at a free surface of an initially stressed sandy medium has been studied here. The reflection coefficients have been computed numerically for both P and SV motion. The variations of reflection coefficients for different values of η, initial stress parameter, and angle of incidence have been represented graphically. The effects of initial stress and sandiness of the layer on surface waves have also been studied. To the best of our knowledge the idea of a sandy medium under initial stress is a new one which is physically possible. Taking into consideration of the theories given by Weiskopf [J. Franklin Inst. 239, 445 (1945)] and Biot [Mechanics of Incremental Deformations (Wiley, New York, 1965)] the equations of motion have been deduced here.

Wave Propagation on Nonuniform Lines

Abstract: The conventional traveling-wave technique is extended to nonuniform lines by attributing distributed reflection and refraction coefficients to each point on the line. Analytical expressions are derived giving the variations in voltage and current wave fronts as they travel along a nonuniform line as well as variations in the voltage and current and their respective ratio Z(t) = E/I at a fixed position of the line caused by the continuous generation of reflections along the line. It is shown that the ratio Z(t), representing the so-called transient surge impedance of a given position of a nonuniform line, depends not only on time and the function expressing the conventional surge impedance of the line but also on the shape of the current wave, a fact which considerably reduces the usefulness of Z(t) in solving nonuniform line problems.