Horizontal Rays Research Articles

Comparison of hybrid three-dimensional modeling with measurements on the continental shelf

During the CALOPS 2007 experiment, off the coast of Fort Lauderdale, Florida, three-dimensional (3D) multipath was observed using a bottom mounted horizontal line array during source tows along the 200 m isobath [Kevin D. Heaney and James J. Murray, J. Acoust. Soc. Am. 125(4), 1394-1402 (2008)]. In this paper a hybrid modeling approach is presented to model the 3D sound on the Florida shelf, nearly shaped like the canonical wedge. The hybrid approach combines vertical acoustic normal modes with the parabolic equation solution (in range/cross-range). The approach is shown to satisfy the 3D Cartesian-coordinate wave equation in the limit of adiabatic mode propagation. In the adiabatic mode parabolic equation (AMPE) approach modal phase speeds vs position are used as the input to the parabolic equation computation with dimensions of easting (km) and northing (km). Vertical adiabatic modes and horizontal rays are also computed to illustrate the 3D multipath arrival. The AMPE field is computed for all the modes for each element of the horizontal array. Beamforming vs source range is then conducted and excellent agreement with data is achieved.

Analysis of Polarization Properties of Optical Isolator for Fiber Laser

An isolator transmits light in the forward direction and blocks light from passing in the reverse direction. It is regarded an essential optical component in medical, industrial, and research lasers for blocking reflection beams that cause optical damage and noise. It is also used as a communicative light intensifier to expand the lifespan of devices and enhance transmission quality. This study analyzed the characteristics of the core components in the construction of a polarization-independent isolator, namely, the walk-off polarizer and the Faraday rotator. Measurement of the extinction ratio of the resultant walk-off polarizer revealed that the ratio between the vertical and horizontal rays was 1,050:1 with a laser output of 0.032 W and 1,010:1 with a laser output of 2.68 W, thus presenting ratios similar to 1,000:1. In addition, the walk-off polarizer and Faraday rotator constructed in this study were used to compare output changes according to changes in power of input light and to check the penetration ratio. Results from the study presented variations in output value according to changes in power of input light. However, the average penetration ratio remained relatively consistent (~81.4%).

Refraction of horizontal rays and vertical modes from receding solitary internal wave front in shallow water

Previously, it was shown that on the approach of an internal wave to an acoustic source-receiver track in shallow water, interference between a direct and a horizontally refracted acoustic path can occur (J. Acoust. Soc. Am. 129(4), EL141, 2011). This phenomenon that is dependent on the angular geometry between the solitary internal wave (IW) front and the acoustic track is similar to the well known Lloyd mirror interference phenomenon in optics. In particular, for a specific time during the SW06 experiment, it was shown that the refracted pulse propagating along horizontal ray, corresponding to the fourth vertical mode arrives with temporal delay relative to the direct horizontal ray. In this paper, we show this phenomenon occurring on the back front of the solitary IW. On the receding front, the forth mode of the refracted signal occurs with an increasing delay in the modal arrival time as the IW leaves the acoustic track. This separation between the direct and the refracted path continues while it gets larger until the IW is far enough from the track for refraction not to occur. A theoretical description of this phenomenon in support of the experimental observation is also presented. [Work supported by ONR.]

Equation, describing temporal evolution of the sound pulse in horizontal plane in shallow water

It is shown that for comparatively narrow-band pulses in shallow water sound propagation, it is possible to introduce modal pulses, corresponding to variation (or evolution) of space-time dependence of the amplitude of separate waveguide modes. In ray approximation, in the presence of perturbation depending on horizontal coordinates, these signals propagate along different trajectories in horizontal plane (space-time horizontal rays) depending on mode number and frequency. In the paper equation, describing evolution of amplitude of modal pulses as a function of time in horizontal plane outside the ray approximation is obtained. This equation can be considered as extension of well-known parabolic equation in horizontal plane. Examples of solutions for some shallow water models are shown; applicability of this equation is discussed.

Cycad Wood from the Lopingian (Late Permian) of Southern China:Shuichengoxylon tianiigen. et sp. nov.

AbstractAnatomically preserved wood collected from coal seam no. 1 of the Naluozhai coal mine in the Lopingian (Late Permian) Wangjiazhai Formation in western Guizhou Province, China, is documented and interpreted. The wood belonged to a trunk with an inferred diameter of 25 cm or more and consists of axial tracheids and horizontal rays. Tracheids vary greatly in size, and small ones are usually irregularly arranged. Tracheid walls are 5–10 μm thick and usually bilayered. There are usually biseriate araucarioides-type bordered pits on the radial tracheid walls. Two to five oval bordered pits are in each cross-field. Ray cells are thin walled, although thick-walled cells exist in some rays. Rays are quite variable in width and height. Uni- and partly biseriate rays are usually 2–20 cells high, while bi- and partly tri- to tetraseriate ones are 5–79 cells high. The cell size of rays is also quite variable and is usually larger than that of tracheids in the tangential direction. There are numerous leaf trace...

Rearrangement of the horizontal space-time structure of the sound field in shallow water in the presence of moving internal waves

The rearrangement of the space-time structure of the sound field in a shallow-water waveguide with a moving intense internal wave packet is considered. The analysis is performed in terms of an approach characterized by space-time horizontal rays and vertical modes. It is shown that, within the time the packet travels over the acoustic track (about an hour), considerable spatial and temporal fluctuations occur in the field intensity and interference structure.

Nonlinear internal wave parameter influences on energy propagation using radiative transport theory.

When two trains of nonlinear internal waves roughly align, their lead waves form effective boundaries of an acoustic duct in which energy is trapped. This type of propagation may be considered a scattering process resulting from the broken internal wave fronts between the lead waves. A traditional approach uses adiabatic normal modes and sound speed perturbations to calculate energy propagation along horizontal rays. An alternate is a radiative transport method in which acoustic vertical modes carry energy and a two-dimensional (2D) transport equation describes horizontal propagation. This model has parameters that are related to waveguide properties and are found from physical internal wave features. One parameter incorporates the significant curvature observed in many internal wave fronts. The two solution approaches are compared and contrasted. Data from the Shallow Water ‘06 Experiment are used to specify internal wave parameters and to compare with model calculations. [Work supported by the ONR.]

On the interaction between acoustic waves and an approaching solitary wave front in waveguides.

Existence of temperature or density solitary wave fronts in waveguides can change the modal behavior of acoustic wave propagation. When a sound signal travels in horizontal distances, certain source-receiver geometries with respect to the front of a soliton cause multipath intensity interference fringes that are related to the generation of rays in the horizontal plane. Intensity fringes registered at the receiver during these events are due to the interaction of various vertical modes and horizontal rays. The fringe patterns and time-frequency structure, before and after a solitary wave crosses an acoustic track, are shown. Analysis of these fringe structures is discussed using normal mode and PE models. [Work supported by the ONR].

Influence of Rays at Low Elevation Angles on the Ionospheric CT Imaging

电离层层析成像(Computerized Tomography, CT)是一个有限视角问题, 水平射线的缺失造成CT结果垂直分辨率的严重下降. 很多人直观地认为低仰角射线可以弥补水平射线的缺失, 然而本文的理论分析和数值模拟研究结果表明, 低仰角射线对CT结果的影响十分微小, 其无法弥补水平射线缺失所带来的垂直分辨率的下降. 模拟结果显示, 增加低仰角射线前后CT反演结果几乎没有变化; 而去掉680条低仰角射线和高仰角射线后, CT反演结果差别巨大; 去掉680条低仰角射线的CT结果与模型吻合很好; 去掉680条高仰角射线的CT反演结果失真严重, 几乎无法恢复模型的扰动特征.

Space‐time parabolic equation in horizontal plane for description of non‐stationary horizontal refraction in shallow water.

Propagation of the sound signals in inhomogeneous anisotropic shallow water environment is studied. Because the waveguide dispersion shape of the radiated pulse is being changed, waveguide modes have different group velocities and, generally speaking, propagate along different ray paths in the horizontal plane. It can lead to simultaneous redistribution of the sound pulse intensity in the horizontal plane and compression/decompression in time. For a description of the spatial and temporal variation of the traveling pulse, space‐time horizontal rays and space‐time parabolic equation in the horizontal plane are derived using a standard approach used in electrodynamics based on integral non‐local connection between field and response. Non‐stationary parabolic equation (PE) is an extension of the well known approach of vertical modes and PE in the horizontal plane. This equation is analyzed and its solutions are constructed for different models of perturbation: nonlinear internal waves, coastal slope, etc.

On orthogonal ray graphs

An orthogonal ray graph is an intersection graph of horizontal and vertical rays (half-lines) in the x y -plane. An orthogonal ray graph is a 2-directional orthogonal ray graph if all the horizontal rays extend in the positive x -direction and all the vertical rays extend in the positive y -direction. We first show that the class of orthogonal ray graphs is a proper subset of the class of unit grid intersection graphs. We next provide several characterizations of 2-directional orthogonal ray graphs. Our first characterization is based on forbidden submatrices. A characterization in terms of a vertex ordering follows immediately. Next, we show that 2-directional orthogonal ray graphs are exactly those bipartite graphs whose complements are circular arc graphs. This characterization implies polynomial-time recognition and isomorphism algorithms for 2-directional orthogonal ray graphs. It also leads to a characterization of 2-directional orthogonal ray graphs by a list of forbidden induced subgraphs. We also show a characterization of 2-directional orthogonal ray trees, which implies a linear-time algorithm to recognize such trees. Our results settle an open question of deciding whether a ( 0 , 1 ) -matrix can be permuted to avoid the submatrices [ 1 0 0 1 ] and [ 1 0 1 1 ] .

Spatial and temporal sound fluctuations in shallow water in presence of internal soliton in transition areas.

Behavior of the sound field is considered in a 1–2‐h time interval in presence of train of internal soliton (IS) crossing an acoustic track. During this period moving ISs pass through several stages: approaching an acoustic track, consequent covering source (receiver) only, both source and receiver, receiver (source) only, and receding from an acoustic track. Correspondingly there are different regimes of interaction of the sound field with IS: horizontal reflection, capture of signals in horizontal waveguide, adiabatic variations, and transition areas between these regimes. So, rather complex spatial and temporal structure of the sound field takes place, including frequency and modal dependence of its parameters. Theoretical analysis of variations in the sound field on the basis of techniques of vertical modes and horizontal rays (PE in horizontal plane) is carried out, and estimation of feasibility of an experimental setup is presented. [Work was supported by CRDF.]

High-speed spectral domain polarization- sensitive optical coherence tomography using a single camera and an optical switch at 1.3 µm

We propose high-speed spectral domain polarization-sensitive optical coherence tomography (SD-PS-OCT) using a single camera and a 1x2 optical switch at the 1.3-microm region. The PS-low coherence interferometer used in the system is constructed using free-space optics. The reflected horizontal and vertical polarization light rays are delivered via an optical switch to a single spectrometer by turns. Therefore, our system costs less to build than those that use dual spectrometers, and the processes of timing and triggering are simpler from the viewpoints of both hardware and software. Our SD-PS-OCT has a sensitivity of 101.5 dB, an axial resolution of 8.2 microm, and an acquisition speed of 23,496 A-scans per second. We obtain the intensity, phase retardation, and fast axis orientation images of a rat tail tendon ex vivo.

Stability of Acoustic Wave Fronts Propagating in Anisotropic Three-Dimensional Environments

Extensive numerical modeling of long-range propagation of sound and seismic waves as well as observations of underwater acoustic fields with line arrays reveal that wave fronts are often much more stable and predictable than the rays comprising these wave fronts. This paper considers multiple scattering of sound by environmental inhomogeneities with spatial scales that are small compared to the propagation range but large compared to the wavelength. These inhomogeneities include 3-D variations in sound speed and current velocity that are small compared to the average sound speed, can be either random or deterministic, and are superimposed on an arbitrary slowly varying background. A theoretical explanation of wave-front stability in highly structured environments is achieved by demonstrating that end points of rays launched from a point source and having a given eikonal (phase) are scattered primarily along the wave front corresponding to the same eikonal in an unperturbed environment. The ratio of displacements of the ray end points along and across the unperturbed wave front is proportional to the number of uncorrelated scattering events. The results apply to conventional rays and to horizontal rays describing propagation of adiabatic normal modes in almost-layered media. The origin of relative stability of wave fronts compared to rays is traced back to Fermat's principle.

Acoustic ducting, refracting, and shadowing by curved nonlinear internal waves in shallow water.

Nonlinear internal waves are common on continental shelves and have been shown to have strong effects on acoustic propagation and scattering. Transmissions from previous field work performed in an along‐shelf geometry show very strong ducting of low‐frequency (50–500 Hz) sound between nonlinear waves. This strong ducting effect is acoustically important. Most all of the acoustic propagation studies of internal waves have used straight line internal wave fronts for individual waves or packets. In our work, we implement a theoretical analysis using the Weinberg‐Burridge horizontal rays and vertical modes formalism to study the acoustic ducting, refracting and shadowing of low‐frequency sound due to curved internal waves, which seem to dominate in shelf break regions. A three‐dimensional parabolic‐approximation sound propagation model is also used with consideration of realistic environmental conditions, and the modeling results provide a clear depiction of the underlying physical processes. The oceanographic origin of the internal wave curvature is discussed, as this affects the predictability of the sound speed field. [This work is sponsored by the Office of Naval Research.]

Sound field phase front variations in shallow water in the presence of intense internal waves

The method of vertical modes and horizontal rays and the method of parabolic equation in the horizontal plane are used to study space-time fluctuations of the phase front of the sound field in the presence of a train of internal waves passing through the acoustic path. The possibility of measuring the distortions of the phase front with a simultaneous filtering of modes by a horizontal array is analyzed. A numerical simulation is carried out for the conditions corresponding to the Eastern coast of United States and the Barents Sea.

Stability of wavefronts at sound propagation in highly structured three-dimensional environments

Extensive numerical modeling of long-range propagation of sound and seismic waves as well as observations of underwater acoustic fields with line arrays reveal that wavefronts are often much more stable and predictable than the rays comprising these wavefronts. This paper considers multiple scattering of sound by environmental inhomogeneities with spatial scales small compared to the propagation range but large compared to the wavelength. These inhomogeneities include 3D variations in sound speed and current velocity that are small compared to the average sound speed, can be either random or deterministic, and are superimposed on an arbitrary slowly-varying background. A theoretical explanation of wavefront stability in highly-structured environments is achieved by demonstrating that end points of rays launched from a point source and having a given eikonal (phase) are scattered primarily along the wavefront corresponding to the same eikonal in the unperturbed environment. The ratio of displacements of the ray end points along and across the unperturbed wavefront is proportional to the number of uncorrelated scattering events. The results apply to conventional rays and to horizontal rays describing propagation of adiabatic normal modes in almost-layered media. The origin of relative stability of wavefronts compared to rays is traced back to Fermat's principle.

Frequency dependence and intensity fluctuations due to shallow water internal waves

A theory and experimental results for sound propagation through an anisotropic shallow water environment are presented to examine the frequency dependence of the scintillation index in the presence of internal waves. The theory of horizontal rays and vertical modes is used to establish the azimutal and frequency behavior of the sound intensity fluctuations, specifically for shallow water broadband acoustic signals propagating through internal waves. This theory is then used to examine the frequency dependent, anisotropic acoustic field measured during the SWARM'95 experiment. The frequency dependent modal scintillation index is described for the frequency range of 30-200 Hz on the New Jersey continental shelf.

Air-shower spectroscopy at horizons

Downward cosmic rays are mostly revealed on the ground by their air-showers diluted and filtered secondary μ + μ − traces and/or by their (Cerenkov - Fluorescent) light because of the high altitude numerous and luminous electromagnetic e + e − , γ shower component. Horizontal and upward air-showers are even more suppressed by deeper atmosphere opacity and by the Earth shadows. In such noise-free horizontal and upward directions rare Ultra High Cosmic rays and rarer neutrino induced air-showers may shine, mostly mediated by resonant PeV ν e ̄ + e − → W − interactions in air or by higher energy tau air-showers originated by ν τ skimming the Earth. At high altitude (mountains, planes, balloons) the air density is so rarefied that nearly all common air-showers might be observed at their maximal growth at a tuned altitude and direction. The arrival angle samples different distances and the corresponding most probable primary cosmic ray energy. The larger and larger distances (between observer and C.R. interaction) make wider and wider the shower area and it enlarges the probability of being observed (up to three orders of magnitude more than vertical showers); the observation of a maximal electromagnetic shower development may amplify the signal by two–three orders of magnitude (with respect to a suppressed shower at sea level); the peculiar altitude–angle range (ten–twenty km height and ≃ 8 0 ∘ – 9 0 ∘ zenith angle) may disentangle at best the primary cosmic ray energy and composition. Even from existing mountain observatories the up-going air-showers may trace, above the horizons, PeV–EeV high energy cosmic rays and, below the horizons, PeV–EeV neutrino astronomy: their early signals may be captured in already existing gamma telescopes such as Magic at Canarie, while facing the Earth edges during (useless) cloudy nights.

Measurement and modeling of three-dimensional sound intensity variations due to shallow-water internal waves

Broadband acoustic data (30-160 Hz) from the SWARM'95 experiment are analyzed to investigate acoustic signal variability in the presence of ocean internal waves. Temporal variations in the intensity of the received signals were observed over periods of 10 to 15 min. These fluctuations are synchronous in depth and are dependent upon the water column variability. They can be explained by significant horizontal refraction taking place when the orientation of the acoustic track is nearly parallel to the fronts of the internal waves. Analyses based on the equations of vertical modes and horizontal rays and on a parabolic equation in the horizontal plane are carried out and show interesting frequency-dependent behavior of the intensity. Good agreement is obtained between theoretical calculations and experimental data.