Showing papers on "Wave propagation published in 1986"

P-SV wave propagation in heterogeneous media: Velocity‐stress finite‐difference method

Abstract: I present a finite-difference method for modeling P-SV wave propagation in heterogeneous media This is an extension of the method I previously proposed for modeling SH-wave propagation by using velocity and stress in a discrete grid The two components of the velocity cannot be defined at the same node for a complete staggered grid: the stability condition and the P-wave phase velocity dispersion curve do not depend on the Poisson's ratio, while the S-wave phase velocity dispersion curve behavior is rather insensitive to the Poisson's ratio Therefore, the same code used for elastic media can be used for liquid media, where S-wave velocity goes to zero, and no special treatment is needed for a liquid-solid interface Typical physical phenomena arising with P-SV modeling, such as surface waves, are in agreement with analytical results The weathered-layer and corner-edge models show in seismograms the same converted phases obtained by previous authors This method gives stable results for step discontinuities, as shown for a liquid layer above an elastic half-space The head wave preserves the correct amplitude Finally, the corner-edge model illustrates a more complex geometry for the liquid-solid interface As the Poisson's ratio v increases from 025 to 05, the shear converted phases are removed from seismograms and from the time section of the wave field

The statistical performance of the MUSIC and the minimum-norm algorithms in resolving plane waves in noise

Abstract: This paper presents an asymptotic statistical analysis of the null-spectra of two eigen-assisted methods, MUSIC [1] and Minimum-Norm [2], for resolving independent closely spaced plane waves in noise. Particular attention is paid to the average deviation of the null-spectra from zero at the true angles of arrival for the plane waves. These deviations are expressed as functions of signal-to-noise ratios, number of array elements, angular separation of emitters, and the number of snapshots. In the case of MUSIC. an approximate expression is derived for the resolution threshold of two plane waves with equal power in noise. This result is validated by Monte Carlo simulations.

Wave Interactions and Fluid Flows

Abstract: Part I. Introduction: 1. Introduction Part II. Linear Wave Interactions: 2. Flows with piecewise-constant density and velocity 3. Flows with constant density and continuous velocity profile 4. Flows with density stratification and piecewise-constant velocity 5. Flows with continuous profiles of density and velocity 6. Models of mode coupling 7. Eigenvalue spectra and localized disturbances Part III. Introduction to Nonlinear Theory: 8. Introduction to nonlinear theory Part IV. Waves and Mean Flows: 9. Spatially-periodic waves in channel flows 10. Spatially-periodic waves on deformable boundaries 11. Modulated wave-packets 12. Generalized Lagrangian mean (GLM) formulation 13. Spatially-periodic means flows Part V. Three-wave Resonance: 14. Conservative wave interactions 15. Solutions of the conservative interaction equations 16. Linearly damped waves 17. Non-conservative wave interactions Part VI. Evolution of a Nonlinear Wave-Train: 18. Heuristic derivation of the evolution equations 19. Weakly nonlinear waves in inviscid fluids 20. Weakly nonlinear waves in shear flows 21. Properties of the evolution equations 22. Waves of larger amplitude Part VII. Cubic Three- and Four-wave Interactions: 23. Conservative four-wave interactions 24. Mode interactions in Taylor-Couette flow 25. Rayleigh-Benard convection 26. Wave interactions in planar shear flows Part VIII. Strong Interactions, Local Instabilities and Turbulence: A Postscript: 27. Strong interactions, local instabilities and turbulence: A postscript References Index.

Nonlinear pulse propagation in the neighborhood of the zero-dispersion wavelength of monomode optical fibers

Abstract: Nonlinear pulse propagation is investigated in the neighborhood of the zero-dispersion wavelength in monomode fibers. When the amplitude is sufficiently large to generate breathers (N > 1 solitons), it is found that the pulses break apart if λ – λ0 is sufficiently small, owing to the third-order dispersion. Here λ0 denotes the zero-dispersion wavelength. By contrast, the solitary-wave (N = 1) solution appears well behaved for arbitrary λ – λ0. Implications for communication systems and pulse compression are discussed.

Acoustic and Electromagnetic Waves

Abstract: The representation of acoustic and electromagnetic fields the special theory of relativity radiation resonators the theory of waveguides refraction surface waves scattering by smooth objects diffraction by edges transient waves. Appendices: Bessel functions Legendre functions Mathieu functions parabolic cylinder functions spheroidal functions tensor calculus asymptotic evaluation of integrals.

Resonant flow of a stratified fluid over topography

Abstract: The flow of a stratified fluid over topography is considered in the long-wavelength weakly nonlinear limit for the case when the flow is near resonance; that is, the basic flow speed is close to a linear long-wave phase speed for one of the long-wave modes. It is shown that the amplitude of this mode is governed by a forced Korteweg-de Vries equation. This equation is discussed both analytically and numerically for a variety of different cases, covering subcritical and supercritical flow, resonant or non-resonant, and for localized forcing that has either the same, or opposite, polarity to the solitary waves that would exist in the absence of forcing. In many cases a significant upstream disturbance is generated which consists of a train of solitary waves. The usefulness of internal hydraulic theory in interpreting the results is also demonstrated.

Decay instability of finite-amplitude circularly polarized Alfven waves - A numerical simulation of stimulated Brillouin scattering

Abstract: By means of a numerical simulation, nonlinear evolution of large amplitude dispersive Alfven waves is studied. An energy transfer from the parent wave to two daughter Alfven-like waves and a soundlike wave is observed (a stimulated Brillouin scattering process). The observed growth rates and propagation characteristics of these daughter waves agree with the analytical results, which we obtain by extending the previous treatments by Goldstein, Derby, Sakai, and Sonnerup. Ions are first trapped by the electrostatic potential of the daughter soundlike waves. Along with the eventual decay (ion Landau damping) of the soundlike waves, ions are phase-mixed and left heated in the parallel direction. The increased parallel energy of ions is transferred to the perpendicular thermal energy through the nonresonant scattering process in the colliding Alfven waves (parent and daughter waves). We further observe that the daughter Alfven waves, which still have a large amplitude, are also unstable for further decay, and that the wave energy is continuously transferred to the longer wavelength regime (inverse cascading process).

A geometrical theory for spiral waves in excitable media

Abstract: In this paper, we develop a geometrical theory for waves in excitable reacting media. Using singular perturbation arguments and dispersion of traveling plane wave trains, we derive an approximate theory of wave front propagation which has strong resemblance to the geometrical diffraction theory of high frequency waves in hyperbolic systems, governed by the eikonal equation. Using this theory, we study the effect of curvature on waves in excitable media, specifically, rotating spiral patterns in planar regions. From this theory we are able to determine the frequency and wavelength for spiral patterns in excitable, nonoscillatory media.

Large intensity fluctuations for wave propagation in random media.

Abstract: The intensity pattern generated by a monochromatic point source in a random medium is studied. The intensity-intensity correlation function is calculated and it is shown that the intensity, as a function of coordinate, exhibits large fluctuations (the speckle pattern). The sensitivity of this speckle pattern to small changes in the source frequency is also studied.

Leaky and non-leaky oscillations in magnetic flux tubes

Abstract: An extensive analysis, both analytic and numerical, of waves in flux tubes imbedded in (possibly) magnetic surroundings is given. It is shown that any wave confined to the tube and its neighbourhood can be put into one of seven categories. Simple criteria for deciding the existence of each type in any particular case are derived. Many other (leaky) modes are found which excite waves in the external medium and thereby lose energy to the surroundings. A number of asymptotic analyses allow much information to be gained about these without the need for numerical solution of the complicated equations involved. Three particular cases, pertaining to photospheric flux tubes, Hα fibrils, and coronal loops, are considered in detail.

Southern hemisphere medium-scale waves and total ozone disturbances in a spectral general circulation model

Abstract: The ozone distribution and its variability is simulated with a general circulation model (GCM), which includes self-consistent representation of the physical processes and an accurate parameterization of the ozone photochemical sources and sinks. Emphasis is placed on analysis of the action of atmospheric waves on the O3 distribution. In particular, the model generates the medium-scale waves which are often observed in the southern hemisphere. These waves tend to form quasi-regular O3 patterns with zonal wave numbers 4, 5, and 6, in fairly good agreement with the observations. Baroclinic instability generates the waves in the lower troposphere, but it is their equivalent barotropic structure in the upper troposphere-lower stratosphere which produces the signal on the total ozone column, since O3 disturbances are nearly in phase in this altitude range. Episodes of large amplitude of the medium-scale waves occur when the transient waves interact with a stationary wave. This standing wave has a zonal wave number close to 4 and appears to result from the large convective activity within the South Pacific Convergence Zone and its southward extension at mid-latitudes. This study gives a good illustration of the important role played by GCMs in understanding the interactions between dynamical and physical processes in the troposphere and wave activity and O3 distribution in the lower stratosphere.

Pore fluids and frequency-dependent wave propagation in rocks

Abstract: Attenuation is the anelastic process which dissipates seismic energy by conversion to heat, thus decreasing the amplitude and modifying the frequency and phase content of a propagating wavelet. Laboratory measurements show seismic phase velocity and attenuation are dependent upon the fluid saturation and the product of frequency and pore‐fluid viscosity, with a peak in attenuation between the seismic and sonic bands. The dominant mechanism by which seismic energy is dissipated in the upper crust is local viscous fluid flow in pores of small aspect ratio. Phenomenologically, this behavior is modeled as a series of linear viscoelastic elements with a narrow distribution of relaxation times, where velocity and attenuation are related through the Hilbert transform. This model may be generalized to include constant-Q behavior, as observed in dry rocks. Solutions to the wave equation may be generated for an arbitrary frequency dependence of phase velocity and Q. When Q is nearly independent of frequency, the im...

Time delay spread and signal level measurements of 850 MHz radio waves in building environments

Abstract: Time delay spread and signal level measurements of 850 MHz radio signals were made over inside-to-outside radio paths at two residential locations and an office building. Root mean square time delay spreads of up to 420 ns were encountered in residential environments. However, when a direct path was present, this improved to less than 325 ns overall, and even to 100 ns at one residence. Received power levels were around -40 dB, with respect to levels received at 0.3 m antenna separation, Under favorable conditions. In other cases, these relative levels varied from - 40 to - 80 dB. Median signal levels agreed well with continuous wave measurements made earlier at one site. No significant polarization dependence or floor level dependence were seen in these data.

Finite-Difference Analysis of Rectangular Dielectric Waveguide Structures

Abstract: A class of dielectric waveguide structures using a rectangular dielectric strip in conjunction with one or more layered dielectrics is analyzed with a finite-difference method formulated directly in terms of the wave equation for the transverse components of the magnetic field. This leads to an eigenvalue problem where the nonphysical, spurious modes do not appear. Moreover, the analysis inclndes hybrid-mode conversion effects, such as complex waves, at frequencies where the modes are not yet completely bound to the core of the highest dielectric constant, as well as at frequencies below cutoff. Dispersion characteristic examples are calculated for structures suitable for millimeter-wave and optical integrated circuits, such as dielectric image lines, shielded dielectric waveguides, insulated image guides, ridge guides, and inverted strip, channel, strip-slab, and indiffused inverted ridge guides. The numerical examples are verified by results available from other methods.

Upper mantle velocity structure estimated from PS- converted wave beneath the north-eastern Japan Arc

Abstract: Summary. The upper boundary of the descending oceanic plate is located by using PS-waves (converted from P to S at the boundary) in the Tohoku District, the north-eastern part of Honshu, Japan. The observed PS-P time data are well explained by a two-layered oceanic plate model composed of a thin low-velocity upper layer whose thickness is less than 10 km and a thick high-velocity lower layer; the upper and lower layers respectively have 6 per cent lower and 6 per cent higher velocity than the overriding mantle. The estimated location of the upper boundary is just above the upper seismic plane of the double-planed deep seismic zone. This result indicates that events in the upper seismic plane, at least in the depth range from 60 to 150 km, occur within the thin low-velocity layer on the surface of the oceanic plate.

Direct and inverse scattering in the time domain for a dissipative wave equation. Part 1: Scattering operators

Abstract: This is the first part of a series of papers devoted to direct and inverse scattering of transient waves in lossy inhomogeneous media The medium is assumed to be stratified, ie, it varies only with depth The wave propagation is modeled in an electromagnetic case with spatially varying permittivity and conductivity The objective in this first paper is to analyze properties of the scattering operators (impulse responses) for the medium and to introduce the reader to the inverse problem, which is the subject of the second paper in this series In particular, imbedding equations for the propagation operators are derived and the corresponding equations for the scattering operators are reviewed The kernel representations of the propagation operators are shown to have compact support in the time variable This property implies that transmission and reflection data can be extended from one round trip to arbitrary time intervals The compact support of the propagator kernels also restricts the admissible set of transmission kernels consistent with the model employed in this paper Special cases of scattering and propagation kernels that can be expressed in closed form are presented

Optically nonlinear waves in thin films

Abstract: A new treatment of the behavior of TE nonlinear waves in an optically nonlinear film is given. The new mathematical results are expressed in terms of the physical parameters of the system and represent a straightforward way to introduce the necessary Jacobian elliptic functions. The optical nonlinearity is of the Kerr type and the numerical calculations are performed for a self-focusing medium. Dispersion curves labeled with optical power density at the lower film boundary, detailed plots of the variation of electric field amplitude as the wave number changes, and details of the power distribution across the guide are given. Since two values of a wave number can exist for the same power level and power thresholds exist, the system is of device interest in the area of optical switching.

Physics of shock waves in gases and plasmas

Abstract: 1. Introduction to the Theory of Gasdynamic Shock Waves.- 1.1 Equations of Motion.- 1.1.1 Conservation Laws and the Euler Equation.- 1.1.2 Viscosity and Heat Transfer in a Fluid. The Navier-Stokes Equation.- 1.2 Kinetic Theory and Gasdynamic Equations.- 1.2.1 Kinetic Equations for a Gas.- 1.2.2 Obtaining the Gasdynamic Equations.- 1.3 Limits of Applicability of the Gasdynamic Equations in Studying Shock-Wave Structure.- 1.4 Linear and Nonlinear Waves.- 1.4.1 Linear and Sonic Waves.- 1.4.2 Nonlinear Plane Waves.- 1.4.3 The Riemann Invariants.- 1.4.4 Simple Waves.- 1.4.5 Expansion Waves.- 1.5 Origins of Discontinuities.- 1.5.1 Profile Distortion of a Running Wave.- 1.5.2 Breakdown of the Sonic Wave Front.- 1.5.3 Burgers' Equation. Evolution of Spectral Composition of the Sonic Wave.- 1.6 Discontinuities and Shocks.- 1.6.1 Discontinuous Solutions.- 1.6.2 The Solution of Burgers' Equation for the Profile of a Weak Shock Wave.- 1.6.3 The Shock Adiabat.- 1.6.4 Production of Shock Waves. Elementary Theory of a Shock Tube.- 1.7 Criteria of Stability and Evolutionarity of Discontinuities.- 1.7.1 Evolutionarity.- 1.7.2 Evolutionarily Condition and Existence of the Shock Structure. Basic and Additional Relations on the Front.- 1.7.3 Spectra of Dissipative Waves, Corresponding to Shock-Wave Structure Described by Burgers' Equation for the Profile of a Weak Shock Wave.- 1.6.3 The Shock Adiabat.- 1.6.4 Production of Shock Waves. Elementary Theory of a Shock Tube.- 1.7 Criteria of Stability and Evolutionarity of Discontinuities.- 1.7.1 Evolutionarity.- 1.7.2 Evolutionarily Condition and Existence of the Shock Structure. Basic and Additional Relations on the Front.- 1.7.3 Spectra of Dissipative Waves, Corresponding to Shock-Wave Structure Described by Burgers' Equation.- 1.7.4 Stability and Evolutionarity of Plane Discontinuities in Three Dimensions.- 1.8 Structures of Gasdynamic Shock Waves.- 1.8.1 Equations of the Shock Layer.- 1.8.2 Shock Structure Shaped by Viscosity Alone.- 1.8.3 Shock-Front Structure in a Gas with High Heat Conductivity.- 1.9 Detonation and Deflagration.- 1.9.1 Propagation of an Exothermal Reaction. Equations of Structure of the Reaction Zone.- 1.9.2 Structures of the Detonation and Deflagration Fronts.- 1.9.3 Realization of Different Propagation Regimes of the Reaction. The Piston Problem.- 2. Gas Shock Ionization and Shock-Wave Structures in Plasmas.- 2.1 Shock Structures in a Completely Ionized Plasma.- 2.1.1 Equations for the Shock Layer and Boundary Conditions.- 2.1.2 Structure of a Weak Shock Wave.- 2.1.3 Structure of a Strong Shock Wave.- 2.1.4 Polarization of Plasma in Shock Waves.- 2.2 Shock Structure in a Plasma with Ionization.- 2.2.1 Shock-Layer Equations and Boundary Conditions.- 2.2.2 Shock Structure Associated with Multiple Ionization.- 2.2.3 Shock Structure in Partially Ionized Argon.- 2.3 Structure of an Ionizing Shock Wave.- 2.3.1 Morphology.- 2.3.2 Structure of the Precursor Region.- 2.3.3 Precursor Ionization in Electromagnetic Shock Tubes.- 2.3.4 Structure of the Ionization-Relaxation and Radiative Cooling Regions.- 2.4 Effects of Plasma Flow Nonunidimensionality in Ionizing Shock Waves.- 2.4.1 Effects of the Wall Boundary Layer in a Shock Tube on the Structure of the Relaxation Region.- 2.4.2 Instability of Ionizing Shock Waves.- 3. Magnetohydrodynamic Shock Waves in Plasmas.- 3.1 Basic Equations.- 3.1.1 Magnetohydrodynamic Equations.- 3.1.2 Two-Fluid Transfer Equations for a Plasma.- 3.2 Magnetohydrodynamic Waves.- 3.2.1 Linear MHD Waves.- 3.2.2 Damping and Dispersion of Linear MHD Waves.- 3.2.3 Nonlinear Simple MHD Waves.- 3.3 Discontinuities and Shock Waves in Magnetohydrodynamics.- 3.3.1 Classification of Discontinuities.- 3.3.2 Boundary Conditions and the Shock Adiabat in Magnetohydrodynamics.- 3.3.3 Evolutionarity Conditions for MHD Shock Waves.- 3.3.4 Shock Structures in the MHD Approximation.- 3.3.5 Evolutionarity of Singular MHD Shock Waves.- 3.4 Structures of Transverse Shocks.- 3.4.1 Boundary Conditions and the Shock Adiabat.- 3.4.2 Structure of Transverse Shock Waves in Magnetized Plasmas.- 3.4.3 Structures of Transverse Shock Waves in Nonmagnetized and Partly Magnetized Plasmas.- 3.4.4 Plasma Polarization in Transverse Shock Waves.- 3.4.5 Experimental Investigations of Transverse Shock Waves in Plasma.- 3.5 Structures of Switch-On Shock Waves.- 3.5.1 Boundary Conditions and the Shock Adiabat.- 3.5.2 Switch-On Shock-Wave Structures in Nonmagnetized Plasma.- 3.5.3 Switch-On Shock-Wave Structure in Magnetized Plasma.- 3.6 Structures of Switch-Off Shock Waves.- 4. Ionizing Shock Waves in Magnetic Fields: Structures and Stability.- 4.1 Classification and the Problem of Boundary Conditions.- 4.1.1 The Basic Boundary Conditions.- 4.1.2 Evolutionarity Conditions.- 4.2 Shock Structures and Additional Boundary Conditions.- 4.2.1 Magnetic Structures of Ionizing Shocks as Pm? 0.- 4.2.2 The Criterion for Distinguishing Between Ionizing and MHD Shock Propagation Regimes.- 4.2.3 Precursor Ionization in a Magnetic Field. Conditions for the Ionization Stability of the Upstream Flow.- 4.2.4 Additional Boundary Conditions and the Magnetic Structures of Ionizing Shocks.- 4.2.5 Limiting Regimes.- 4.3 Transverse Ionizing Shock Waves.- 4.3.1 Magnetic Structures.- 4.3.2 Additional Boundary Conditions and Structures of Transverse Ionizing Shocks.- 4.3.3 Structure of Transverse MHD Shocks in Partially Ionized Plasma.- 4.4 Normal Ionizing Shock Waves.- 4.4.1 Magnetic Structures.- 4.4.2 Tensor Conductivity and Joule Heating of Plasmas in Normal Ionizing Shocks.- 4.4.3 Switch-On MHD Shocks in Partially Ionized Plasmas.- 4.5 Switch-Off Ionizing Shock Waves.- 5. Dynamics of Shock Waves in Magnetic Fields.- 5.1 Electromagnetic Shock Tubes.- 5.1.1 Design and Operation of Electromagnetic Shock Tubes.- 5.1.2 Elementary Theory of Electromagnetic Shock Tubes: The Snowplow Model.- 5.1.3 Effects of Nonunidimensionality of the Plasma Flow in Coaxial Electromagnetic Shock Tubes.- 5.2 Piston Problem.- 5.2.1 Self-Similar Magnetic Piston Problem in Magnetohydrodynamics.- 5.2.2 Self-Similar Piston Problem for Flows with Ionizing Shock Waves.- 5.3 Dynamics of Transverse Shocks in Magnetized Plasma.- 5.4 Evolution of the Initial Ionizing Discontinuity in the Transverse Magnetic Field.- 5.5 Shaping the Structure of the Normal Ionizing Shock.- References.

Nonlinear waves in compacting media

Abstract: An investigation of the mathematical model of a compacting medium proposed by McKenzie (1984) for the purpose of understanding the migration and segregation of melts in the Earth is presented. The numerical observation that the governing equations admit solutions in the form of nonlinear one-dimensional waves of permanent shape is confirmed analytically. The properties of these solitary waves are presented, namely phase speed as a function of melt content, nonlinear interaction and conservation quantities. The information at hand suggests that these waves are not solitons.

On the Behavior of Hydromagnetic Surface Waves

Abstract: The behavior of velocity, magnetic field, and pressure perturbations about a continuously varying interface in pressure equilibrium is investigated in detail within ideal incompressible magnetohydrodynamics. A specific initial value problem is solved in quadrature for a thin interface and compared with the solution for a discontinuous interface. The unattenuated surface wave about a discontinuous interface is replaced at a thin interface by a collective surface disturbance which decays, with the associated energy density flowing into local oscillations within the interface. At long times the envelope of the local oscillations is concentrated within a small fraction of the thin interface (gradients within the envelope increase linearly with time, eventually resulting in a breakdown of the linearized ideal theory). Thus, the derived decay rate of the surface disturbance gives a mode-conversion rate rather than a heating rate. In applications to the propagation and dissipation of surface waves in the solar corona, this rate cannot in general be interpreted as a coronal heating rate.

Analytical Studies of Body Wave Propagation and Attenuation

Abstract: : In situ crosshole and downhole seismic methods are becoming widely used as a means of nondestructively evaluating the elastic properties of geotechnical systems. The elastic constants are calculated from the records of body waves (longitudinal and transverse waves) traveling through the media. Measurements are made by generating a seismic disturbance at one point and measuring the time required for the disturbance to travel to one or more seismic receivers. Several simplifying assumptions are made in traditional analysis of seismic measurements for engineering purposes. These include assuming plane wave propagation, measurement of only far-field waves, and independence of the measurements on the source-receiver configuration and on the amount of material damping. An analytical study of the effects and the validity of the different assumptions is presented. It is found that, for the range of distances and frequencies typically used in engineering applications: body wave fronts generated by point source cannot be considered plane; and near-field effects associated with spherical wave fronts can be very important. The near-field effects are caused by coupling between waves which exhibit the same particle motion but which propagate at different velocities and attenuate at different rates. To minimize the detrimental effects of near-field waves in those methods based on spectral analysis techniques, it is recommended that, in the field setup, the ratio of distances from the source to the second and first receivers be of the order of two or greater.

Two-and-One-Half Dimensional In-Plane Wave Propagation.

Abstract: : The purpose of this paper is to collect certain wave propagation results in two-and-one-half dimensions -- defined as three dimensional propagation in a medium that has variations in two dimensions only. The results of interest are for sources and receivers in the plane determined by the two directions of parameter variation. The objective of this work is to reduce the analysis of the in-plane propagation to two dimensional analysis while retaining -- at least asymptotically -- the proper three dimensional geometrical spreading. We do this for the free space Green's function and for the Kirchhoff approximate upward scattered field from a single reflector. In both cases, we carry out a derivation under the assumption of a background velocity with two dimensional -- c(x,z) -- variation; we specialize the results to a constant background velocity and a depth dependent background velocity. For the convenience of the user we have included a glossary and two tables of equation numbers to help in finding specific results. Keywords include: Ray method; Geometrical optics; Wave propagation; Green's function; Jacobian; Travel time; and WKB.