Showing papers on "Wave propagation published in 1988"

Fourth-order finite-difference P-SV seismograms

Abstract: I describe the properties of a fourth-order accurate space, second-order accurate time two-dimensional P-Sk’ finite-difference scheme based on the MadariagaVirieux staggered-grid formulation. The numerical scheme is developed from the first-order system of hyperbolic elastic equations of motion and constitutive laws expressed in particle velocities and stresses. The Madariaga-Virieux staggered-grid scheme has the desirable quality that it can correctly model any variation in material properties, including both large and small Poisson’s ratio materials, with minimal numerical dispersion and numerical anisotropy. Dispersion analysis indicates that the shortest wavelengths in the model need to be sampled at 5 gridpoints/wavelength. The scheme can be used to accurately simulate wave propagation in mixed acoustic-elastic media, making it ideal for modeling marine problems. Explicitly calculating both velocities and stresses makes it relatively simple to initiate a source at the free-surface or within a layer and to satisfy free-surface boundary conditions. Benchmark comparisons of finite-difference and analytical solutions to Lamb’s problem are almost identical, as are comparisons of finite-difference and reflectivity solutions for elastic-elastic and acoustic-elastic layered models.

Acoustics of Porous Media

Abstract: This book contains all that is currently known about the propagation of acoustic waves in porous media. Emphasis is on the physical aspects of wave propagation in porous media. Theory is developed rigorously, but it is supported with detailed descriptions of the texture of porous media, by an explanation of measurements, and by a review of experimental techniques and field applications. It discusses the following Contents: Porous media. Wave propagation in saturated porous media. Wave propagation and vibration in viscoelastic media (unidimensional). Experimental techniques for measuring velocities and attenuations. Wave propagation in porous media - results and mechanisms. Waves and interfaces. Some applications in petroleum geophysics and Bibliography.

Correlations and fluctuations of coherent wave transmission through disordered media.

Abstract: The correlation functions of the transmission coefficients for scalar wave propagation through disordered media are calculated by use of both diagrammatic techniques and numerical simulations. The calculation is valid in the diffusive regime: multiple elastic scattering with negligible absorption or inelastic scattering and a scattering length much longer than the wavelength. In addition to the familiar large local intensity fluctuations we find a novel memory effect and long-range correlations in the transmission coefficients which decay to a positive background value. Implications for light-scattering experiments are discussed.

Intensity images and statistics from numerical simulation of wave propagation in 3-D random media

Abstract: An extended random medium is modeled by a set of 2-D thin Gaussian phase-changing screens with phase power spectral densities appropriate to the natural medium being modeled. Details of the algorithm and limitations on its application to experimental conditions are discussed, concentrating on power-law spectra describing refractive-index fluctuations of the neutral atmosphere. Inner and outer scale effects on intensity scintillation spectra and intensity variance are also included. Images of single realizations of the intensity field at the observing plane are presented, showing that under weak scattering the small-scale Fresnel length structure of the medium dominates the intensity scattering pattern. As the strength of scattering increases, caustics and interference fringes around focal regions begin to form. Finally, in still stronger scatter, the clustering of bright regions begins to reflect the large-scale structure of the medium. For plane waves incident on the medium, physically reasonable inner scales do not produce the large values of intensity variance observed in the focusing region during laser propagation experiments over kilometer paths in the atmosphere. Values as large as experimental observations have been produced in the simulations, but they require inner scales of the order of 10 cm. Inclusion of an outer scale depresses the low-frequency end of the intensity spectrum and reduces the maximum of the intensity variance. Increasing the steepness of the power law also slightly increases the maximum value of intensity variance.

Wave propagation simulation in a linear viscoacoustic medium

Abstract: SUMMARY A new approach for viscoacoustic wave propagation is developed. The Boltzmann’s superposition principle based on the general standard linear solid rheology is implemented in the equation of motion by the introduction of memory variables. This approach replaces the conventional convolutional rheological relation, and thus the complete time history of the material is no longer required, and the equations of motion become a coupled first-order linear system in time. The propagation in time is done by a direct expansion of the evolution operator by a Chebycheff polynomial series. The resulting method is highly accurate and effects such as the numerical dispersion often encountered in time-stepping methods are avoided. The numerical algorithm is tested in the problem of wave propagation in a homogeneous viscoacoustic medium. For this purpose the l-D and 2-D viscoacoustic analytical solutions were derived using the correspondence principle.

Electromagnetic wave propagation through a dielectric–chiral interface and through a chiral slab

Abstract: The reflection from and transmission through a semi-infinite chiral medium are analyzed by obtaining the Fresnel equations in terms of parallel- and perpendicular-polarized modes, and a comparison is made with results reported previously. The chiral medium is described electromagnetically by the constitutive relations D = ∊E + iγB and H = iγE + (1/μ)B. The constants ∊, μ, and γ are real and have values that are fixed by the size, the shape, and the spatial distribution of the elements that collectively compose the medium. The conditions are obtained for the total internal reflection of the incident wave from the interface and for the existence of the Brewster angle. The effects of the chirality on the polarization and the intensity of the reflected wave from the chiral half-space are discussed and illustrated by using the Stokes parameters. The propagation of electromagnetic waves through an infinite slab of chiral medium is formulated for oblique incidence and solved analytically for the case of normal incidence.

Steep, steady surface waves on water of finite depth with constant vorticity

Abstract: Two-dimensional steady surface waves on a shearing flow are computed for the special case where the flow has uniform vorticity, i.e. in the absence of waves the velocity varies linearly with height. A boundary-integral method is used in the computation which is similar to that of Simmen & Saffman (1985) who describe such waves on deep water. Particular attention is given to the effects of finite depth with descriptions of waves of limiting steepness, waves with eddies beneath their crests and extremely high waves on high-speed flows.Many qualitative features of these waves are relevant to steep waves propagating in shallow water, or on a strong wind-induced drift current. An important practical point in the interpretation of wave measurements of wind driven waves is that mean kinetic energy and potential energy densities are unequal even for infinitesimal waves. This may mean that wave energy spectra deduced from surface-elevation measurements in the conventional way may sometimes be misleading.

Boundary element methods in elastodynamics

Abstract: Governing equations of motions boundary integral formulation in elastodynamics numerical treatment of boundary equations other boundary methods wave propagation analysis soil structure interaction vibrations of structures other linear material models computer implementation aspects.

Resonance absorption of compressible magnetohydrodynamic waves at thin “surfaces”

Abstract: The behavior of plasma and fields in the transition layer supporting MHD surface waves is analyzed, assuming that the total pressure fluctuations, delta-P(tot), can be taken to be nearly constant across this thin transition layer, with a value nearly the same as would be obtained if the MHD wave were supported by a truly discontinuous surface Regarding therefore delta-P(tot) as known, the plasma and field equations in the transition layer were cast into a form in which delta-P(tot) appeared as a driving term Among the two resonances that appear (the cusp resonance and the Alfven resonance) special attention is given to the Alfven resonance, which affects the velocity and magnetic field components normal to the background magnetic field The effects of three types of viscosity on the Alfven resonance are considered, and it is shown that energy is pumped out of the surface wave into thin layers surrounding the resonant field lines

Modeling electromagnetic wave propagation in the troposphere using the parabolic equation

Abstract: A computational method is described for predicting electromagnetic wave propagation in the troposphere using the parabolic approximation of the Helmholtz wave equation. The model represents propagation over a spherical, finitely conducting Earth and allows specification of frequency, polarization, antenna pattern, antenna altitude, and elevation angle. The method enables calculations to be performed using either ideal or measured refractivity profiles that vary in both altitude and range. A brief discussion of the theoretical formulation and computational implementation of the propagation model is presented, followed by examples that demonstrate various features. Example calculations include 3-GHz propagation over a calm sea in the presence of both range-dependent and range-independent surface-based ducts as well as in standard atmosphere conditions. Comparisons with two other propagation models are also discussed. >

Velocity and attenuation of ultrasound in suspensions of particles in fluids

Abstract: The theory of the scattering of compression waves in viscous fluids is examined. The effects of fluid viscosity, of differences in density and in elastic modulus between the particles and the fluid, of heat transfer and of concentration are considered. Ultrasonic phase velocity and attenuation are derived. Results for the phase velocity are compared with several other formulations. The feasibility of using ultrasound to characterise suspensions is discussed.

Wave Propagation in a Solid Ice Pack

Abstract: The analysis presented in this paper was inspired by the report that the R/V Polarstern has encountered surface waves of large amplitude hundreds of kilometers inside the ice pack in the Weddell Sea. This paper presents analysis of processes that affect waves in an ice pack, namely the refraction of waves at the pack edge, the effects of pack compression on wave propagation, wave train stability and buckling stability in the ice pack. Sources of pack compression and interaction between wave momentum and pack compression are discussed. Viscous damping of propagating waves are also studied. Significant results include the conditions for total reflection of waves at the pack edge, the strong effect of pack compressive stress on wave group speed, with the concomitant possibility of extreme local concentration of wave energy. The result that compressive stress in the pack leads to very rapid development of wave packets, through changes in the parameters for weakly nonlinear modulational instability of...

Scattering matrix method for propagation of radiation in stratified media: attenuated total reflection studies of liquid crystals

Abstract: We present a new scattering matrix formalism for the modeling of electromagnetic wave propagation in stratified media. It is computationally efficient and stable and is well suited to the layer geometry that is characteristic of stratified materials. It is applied successfully to the modeling of total attenuated reflection in nematic liquid crystals with beyond-critical-angle incidence when the conventional transfer matrix methods normally fail.

Magnetic field and density fluctuations at perpendicular supercritical collisionless shocks

Abstract: Perpendicular collisionless shocks are studied by means of two-dimensional hybrid (particle ion, fluid electron) simulations, with emphasis on the relaxation of the highly anisotropic ion distribution that arises primarily from reflection of some of the incident ions but also adiabatic compression of the other, directly transmitted ions and the related growth of low frequency electromagnetic waves. It is commonly assumed that the waves are due to Alfven ion cyclotron instability that propagate parallel to the ambient magnetic field (k/sub perpendicular/ = 0) and that the isotropization of the ions due to pitch angle scattering by the waves and the corresponding modification of the wave spectrum is quasi-linear. It is shown that this is indeed a reasonably good description downstream of the shock front, behind the magnetic overshoot. However, at the shock ramp there is a large discrepancy between the wavelengths measured in the simulations and those predicted by linear theory, and large density and magnetic field oscillations parallel to the ambient magnetic field are also seen. By comparing results for both high and low ion beta cases, it is shown that these effects can be understood in terms of obliquely propagating (k/sub perpendicular/not =0) modes, more likely due to themore » Alfven ion cyclotron instability instead of the (drift) mirror instability, although a more complete explanation awaits the derivation and analysis of an appropriate dispersion relation describing the growth and coupling of low-frequency modes in the inhomogeneous high beta environment of the shock. The observational consequences of these results and their application to improving nonlocal leakage models for the ion foreshock are also discussed. copyright American Geophysical Union 1988« less

Propagation and optical interaction of guided acoustic waves in two-mode optical fibers

Abstract: Acoustic modes propagating in cylindrical solid rods are considered. A review of the properties of several mode groups is given, and computed results are shown for a wide range of material properties. The lower mode of each group is relevant for an all-fiber-optic frequency shifter recently demonstrated. For these modes, dispersion relations, mode patterns, power relations, and acoustooptic coupling strength are calculated. Some experimental results are compared with the calculations, and alterations to improve the frequency shifter are proposed. >

Frequency up-conversion of electromagnetic radiation with use of an overdense plasma.

Abstract: We investigate the effects of quickly creating a plasma around a monochromatic electromagnetic source wave, on time scales on the order of a cycle of the wave. It is found that this results in an upward shifting of the wave frequency, which can be varied by changing of the plasma density. It is also found that a substantial fraction of the magnetic field associated with the initial wave can be sustained in the plasma as a time-independent magnetic field. Computer simulations have been used to study this process in detail, including the effects of finite ionization time. For long ionization times, strong plasma heating results.

Wave propagation in laminated composite plates

Abstract: A stiffness method has been used in this article to study dispersive wave propagation in a laminated anisotropic plate. The advantage of this method is in its usefulness in obtaining numerical results for the dispersion characteristics of waves propagating in a plate with an arbitrary number of arbitrarily anisotropic laminae. This method has been applied here, as a way of illustration, to a plate made up of transversely isotropic laminae with the axis of isotropy of each lamina lying in the plane of the lamina. Results thus obtained are shown to agree well with the exact solutions for isotropic and transversely isotropic single layered plates. Numerical results are presented for cross‐ply (0°/90°/0°) laminated composite plates and show that the frequency spectrum in this case differs considerably from that for a single layered (0°) plate.

Observational evidence of a saturated gravity wave spectrum in the troposphere and lower stratosphere

Abstract: Radial velocity and temperature data obtained at the MU Radar Observatory during October and November 1986 are used to examine the character of the motion spectrum in the troposphere and lower stratosphere. It is found that the spectrum is dominated by low-frequency gravity waves with an upward sense of propagation in the lower stratosphere and both upward and downward propagation in the troposphere. Vertical wavenumber spectra of velocity and temperature are used to examine the consistency of the motion spectrum with the saturated spectrum of gravity waves proposed by Smith et al. Results indicate excellent agreement of the observed and predicted velocity and temperature spectra in both amplitude and slope. Vertical wavenumber spectra in area-preserving form reveal a dominant vertical wavelength of ∼2.5 km, systematic variations in energy density and the dominant vertical scale with time, and consistency between the temporal variations of velocity and temperature variance. Taken together, our re...

Weak nonlinear electromagnetic waves and low-frequency magnetic-field generation in electron-positron-ion plasmas

Abstract: The weakly nonlinear localization of obliquely modulated high-frequency electromagnetic waves in an electron-positron-ion plasma is considered. It is shown that the amplitude of the wave turns out to be a strongly dependent function of the angle between the slow modulations and the fast spatial variations and that the possibility appears of spontaneous generation of low-frequency magnetic fields. These magnetic fields are also functions of this angle and of the high-frequency wave polarization. The analysis of colinear modulation in electron-positron plasmas shows that some restriction must be made regarding the validity of previous calculations.

Scattering from black holes

Abstract: This book investigates the propagation of waves in the presence of black holes Astrophysical black holes may eventually be probed by these techniques The authors emphasise intuitive physical thinking in their treatment of the techniques of analysis of scattering, but alternate this with chapters on the rigourous mathematical development of the subject High and low energy limiting cases are treated extensively and semi-classical results are also obtained The analogy between Newtonian gravitational scattering and Coulomb quantum mechanical scattering is fully exploited The book introduces the concepts of scattering by considering the simplest, scalar wave case of scattering by a spherical black hole It then develops the formalism of spin-weighted spheroidal harmonics and of plane wave representations for neutrino, electromagnetic and gravitational scattering Research workers and graduate and advanced undergraduate students in scattering theory, wave propagation and relativity will find this a comprehensive treatment of the topic

Optical solitary waves induced by cross-phase modulation.

Abstract: We show that an optical pulse can propagate undistorted as a bright solitary wave in the normal dispersion regime when it couples through cross-phase modulation to a dark pulse in the anomalous dispersion regime.

Wide‐angle one‐way wave equations

Abstract: A one‐way wave equation, also known as a paraxial or parabolic wave equation, is a differential equation that permits wave propagation in certain directions only. Such equations are used regularly in underwater acoustics, in geophysics, and as energy‐absorbing numerical boundary conditions. The design of a one‐way wave equation is connected with the approximation of (1−s2)1/2 on [−1,1] by a rational function, which has usually been carried out by Pade approximation. This article presents coefficients for L2, L∞, and other alternative classes of approximants that have better wide‐angle behavior. For theoretical results establishing the well posedness of these wide‐angle equations, see the work of Trefethen and Halpern [‘‘Well‐posedness of one‐way wave equations and absorbing boundary conditions,’’ Math. Comput. 47, 421–435 (1986)].

Bound solitary waves in a birefringent optical fiber.

Abstract: We present the first mixed-type solutions to the coupled nonlinear Schr\"odinger equations which govern optical pulse propagation in a birefringent fiber. These represent polarization-modulated pulses which, apart from the absolute phase, propagate unchanged in form. It is shown they are bound states of two solitary waves which separately have constant and uniform orthogonal linear polarizations. Furthermore, there exists a minimum-energy threshold for the formation of these bound states.

Estimation of the Kelvin Wave Contribution to the Semiannual oscillation.

Abstract: Daily temperature data acquired during the Limb Infrared Monitor of the Stratosphere experiment are used to study the behavior of Kelvin waves in the equatorial middle atmosphere. It is suggested that Kelvin wave packets of different zonal wave numbers propagate separately and may be forced separately. Two Kelvin wave regimes were identified during the October 1978 to May 1979 data period. Most of the properties of the observed waves are shown to be consistent with slowly-varying theory. Results suggest that gravity waves may contribute significantly to the equatorial stratopause semiannual oscillation.

Introduction: Seismic wave scattering in three-dimensionally heterogeneous earth

Abstract: The classical earth model of spherical symmetry (or layered structure) is undergoing a revolution. The earth has been revealed to be laterally heterogeneous everywhere from the crust, mantle to the core with scale from the grain size of rocks to the lowest orders of global spherical harmonics. Figure 1 shows the strength and scale length of heterogeneities in the crust and mantle of the earth, in terms of v, the perturbation index of seismic (P or S) wave speed, defined as the r.m.s. fractional variations of wave speed over the measured region. The scale length of heterogeneities revealed by seismic waves, not including the laboratory measurements of rock samples, spans 8 orders of magnitude. These heterogeneities with different scales have different effects to seismic waves. The velocity and density heterogeneities can cause the change in waveform, phase (or travel-time) and amplitude fluctuation, as well as apparent attenuation of the direct arrivals. They can also generate coda waves such as the P-coda, S-coda, and Lg-coda caused by the lithospheric heterogeneities and precursory waves such as the scattered PKP waves as the precursors to PKIKP caused by the heterogeneities near the core-mantle boundary. The near-source or near-receiver structures can modify the seismic waveforms by resonance and other effect. Rough topography or rough interface can cause the coupling between body wave and surface wave. Aligned cracks in the crust can produce the effective anisotrophy. A great complexity arises when heterogeneities have interaction with anisotrophy and nonlinearity.