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Journal articles on the topic 'Wave refraction'

Author: Grafiati

Published: 4 June 2021

Last updated: 12 February 2022

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1

Nemat-Nasser, Sia. "Anti-plane shear waves in periodic elastic composites: band structure and anomalous wave refraction." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2180 (August 2015): 20150152. http://dx.doi.org/10.1098/rspa.2015.0152.

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For anti-plane shear waves in periodic elastic composites, it is shown that negative energy refraction can be accompanied by positive phase-velocity refraction and positive energy refraction can be accompanied by negative phase-velocity refraction , and that this can happen over a broad range of frequencies. Hence, in general, negative refraction does not necessarily require antiparallel group and phase-velocity vectors. Details are given for layered composites and the results are extended to, and illustrated for, two-dimensional periodic composites, revealing a wealth of information about the refractive characteristics of this class of composites. The composite's unit cell may consist of any number of constituents of any variable mass density and elastic modulus, admitting large discontinuities . A powerful variational-based solution method is used that applies to one-, two- and three-dimensional composites, irrespective of their constituents being homogeneous or heterogeneous. The calculations are direct, accurate and efficient, yielding the band structure, group-velocity, energy-flux and phase-velocity vectors as functions of the frequency and wavevector components, over an entire frequency band.

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2

FENG, LIANG, XIAO-PING LIU, JIE REN, YAN-FENG CHEN, and YONG-YUAN ZHU. "COMPARISONS OF NEGATIVE REFRACTION IN LEFT-HANDED MATERIALS AND PHOTONIC CRYSTALS." International Journal of Modern Physics B 19, no. 23 (September 20, 2005): 3547–61. http://dx.doi.org/10.1142/s0217979205032371.

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Using the equifrequency surfaces (EFS) to describe negative refractions in left-handed materials (LHMs) and photonic crystals (PCs), negative phase and negative group refractive indexes in LHMs were compared with positive phase and negative group refractive indexes in PCs. The refractive indexes in PCs were dependent on frequencies and incident angles of electromagnetic wave, while indexes in LHMs were constant in the left-handed region. Furthermore, the phase compensating effect resulting from the negative phase refractive index was addressed to distinguish the perfect lens made of LHMs from the superlens realized in the all angle negative refraction (AANR) region of PCs.

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3

Ivanov, Julian, Richard D. Miller, Jianghai Xia, Don Steeples, and Choon B. Park. "Joint analysis of refractions with surface waves: An inverse solution to the refraction-traveltime problem." GEOPHYSICS 71, no. 6 (November 2006): R131—R138. http://dx.doi.org/10.1190/1.2360226.

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We describe a possible solution to the inverse refraction-traveltime problem (IRTP) that reduces the range of possible solutions (nonuniqueness). This approach uses a reference model, derived from surface-wave shear-wave velocity estimates, as a constraint. The application of the joint analysis of refractions with surface waves (JARS) method provided a more realistic solution than the conventional refraction/tomography methods, which did not benefit from a reference model derived from real data. This confirmed our conclusion that the proposed method is an advancement in the IRTP analysis. The unique basic principles of the JARS method might be applicable to other inverse geophysical problems.

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4

Tleukenov, S. K., K. N. Balabekov, and Z. K. Zhalgasbekova. "Laws of reflection and refraction of TE and TM polarization waves on the border of rhombic crystals." Bulletin of the Karaganda University. "Physics" Series 97, no. 1 (March 30, 2020): 70–81. http://dx.doi.org/10.31489/2020ph1/70-81.

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The article analytically solves the problem of reflection and refraction of electromagnetic plane waves of different polarization at the boundary of anisotropic half-spaces of rhombic symmetry. Based on the matrix method, the angles of refraction of electromagnetic waves of different polarization, the amplitudes of the reflected and refracted waves, the angles that determine the direction of the group velocities and vectors of the flow of electromagnetic energy, the magnitudes of the flows of electromagnetic energy and their components depending on the direction of the wave vector of the incident wave are determined. The determination of the angles of total internal reflection and the refractive index of electromagnetic waves of different polarization is considered. A significantly different dependence of the kinematic and energy characteristics of electromagnetic waves of different polarization on the anisotropy of the magnetic and dielectric tensors is shown. For electromagnetic waves, the polarization of which is determined by the component of the electric tension vector perpendicular to the wave propagation plane (TE wave), the characteristics of the reflected and refracted waves, the velocity indicatrix, the propagation angles, etc. determined primarily by the components of the magnetic permeability tensor. In the case of electromagnetic waves, when the polarization is determined by the component of the magnetic field (TM wave), perpendicular to the plane of wave propagation, all characteristics depend mainly on the components of the dielectric constant. The validity of the Fresnel formulas for determining the coefficients of reflected and refracted waves at the boundary of anisotropic media of rhombic symmetry is shown. However, in this case, the components of the wave vectors included in the Fresnel formulas are determined by their indicatrices. In addition, it is necessary to take into account the dependence of these components on the angle of refraction in the second medium

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5

Jiang, Ping, Kang Xie, Huajun Yang, and Zhenhai Wu. "Negative Propagation Effects in Two-Dimensional Silicon Photonic Crystals." International Journal of Photoenergy 2012 (2012): 1–7. http://dx.doi.org/10.1155/2012/702637.

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We demonstrated negative refraction effects of light propagating in two-dimensional square and hexagonal-lattice silicon photonic crystals (PhCs). The plane wave expansion method was used to solve the complex eigenvalue problems, as well as to find dispersion curves and equal-frequency contour (EFC). The finite-difference time-domain (FDTD) method was used to simulate and visualize electromagnetic wave propagation and scattering in the PhCs. Theoretical analyses and numerical simulations are presented. Two different kinds of negative refractions, namely, all-angle negative refraction (AANR) without a negative index and negative refraction with effective negative index, have been verified and compared.

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6

Salim, Ashadi. "Analisis Data Seismik Refraksi dengan Metode Generalized-Reciprocal." ComTech: Computer, Mathematics and Engineering Applications 3, no. 1 (June 1, 2012): 162. http://dx.doi.org/10.21512/comtech.v3i1.2397.

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The analysis of seismic refraction data by the generalized reciprocal method can be used for delineating undulating refractors. The forward and reverse times of arrival at different geophones with XY distance along a refraction profile, are used for calculating time depth. The seismic wave velocity in refractor may be obtained from velocity analysis function, and the depth of refractor under each geophone is obtained from time-depths function. This method has been applied at one line of seismic refraction measurement that was 440 m long with 45 geophone positions. The measurement obtained 20 m as the optimum XY-value and 2250 m/s as the velocity of seismic wave in refractor, and the undulating refractor topography with the depths varies 10.4 – 22.1 m. The optimum XY-value was obtained from approximate calculation derived from the observation, that was indicated the absent of undetected layer.

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7

Li, Jing. "Tunable Multimode Filtering of Solid Acoustic Waves in a Three-Component Phononic Crystal Slab." Advanced Materials Research 150-151 (October 2010): 1625–39. http://dx.doi.org/10.4028/www.scientific.net/amr.150-151.1625.

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Using of the multiple scattering methods, we characterize the positive and negative multi-refraction and transmission properties of a solid-based phononic crystal composed of coated solid inclusions in view of its applications in tunable multimode filtering. The geometrical parameters are chosen so that a left-handed longitudinal wave mode and a right-handed transverse wave mode, are simultaneously obtained in this three-component phononic crystal. When multimode Gaussian beams are placed transmitting through the phononic crystal slab, both positive and negative refractions are observed. We then study the individual propagation behavior of different modes. The angle dependent transmission beams with different energy distributions are found at the other side of the slab. Transmitted transverse waves coming from different directions incidence finally walk together into four oriented beams. Meanwhile, longitudinal wave incidence with different directions behaves simply as negative refraction in the slab. A far-field longitudinal wave image can be achieved being excited by a longitudinal wave point source. The three-component phononic crystal slab thus can be served as an alternate in tunable multimode filtering devices.

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8

Hwang, Sin-Chun, and Timothy Halpin-Healy. "Chemical wave refraction phenomena." Physical Review E 54, no. 3 (September 1, 1996): 3009–12. http://dx.doi.org/10.1103/physreve.54.3009.

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9

Janssen, T. T., and T. H. C. Herbers. "Nonlinear Wave Statistics in a Focal Zone." Journal of Physical Oceanography 39, no. 8 (August 1, 2009): 1948–64. http://dx.doi.org/10.1175/2009jpo4124.1.

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Abstract In this paper, the combined effects of refraction and nonlinearity on the evolution of ocean surface wave statistics are considered and possible implications for the likelihood of extreme waves, also known as freak or rogue waves, are examined. A frequency-angular spectrum model is derived that accounts for cubic nonlinear dynamics and weak lateral homogeneity of the medium. Through Monte Carlo simulations, the evolution of wave statistics in freely developing waves, waves over an opposing shearing current, and waves refracted over an isolated topographical feature is modeled. The simulations show that freely developing, directionally spread wave fields generally maintain near-Gaussian statistics, which was also found in earlier model studies. However, the enhanced nonlinearity caused by the refractive focusing of narrowband wave fields can result locally in strongly non-Gaussian statistics and an associated increased likelihood of extreme wave events.

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10

Henderson, L. F., P. Colella, and E. G. Puckett. "On the refraction of shock waves at a slow–fast gas interface." Journal of Fluid Mechanics 224 (March 1991): 1–27. http://dx.doi.org/10.1017/s0022112091001623.

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We present the results of numerical computations of the refraction of a plane shock wave at a CO2/CH4 gas interface. The numerical method was an operator split version of a second-order Godunov method, with adaptive grid refinement. We solved the unsteady, two-dimensional, compressible, Euler equations numerically, assuming perfect gas equations of state, and compared our results with the experiments of Abd-El-Fattah & Henderson. Good agreement was usually obtained, especially when the contamination of the CH4 by the CO2 was taken into account. Remaining discrepancies were ascribed to the uncertainties in measuring certain wave angles, due to sharp curvature, poor definition, or short length of the waves at large angles of incidence. All the main features of the regular and irregular refractions were resolved numerically for shock strengths that were weak, intermediate, or strong. These include free precursor shock waves in the intermediate and strong cases, evanescent (smeared out) compressions in the weak case, and the appearance of an extra expansion wave in the bound precursor refraction (BPR). The structure of a BPR was elucidated for the first time.

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11

KIM, JEONG-HOON. "REFRACTION AND DIFFUSION OF ACOUSTIC WAVES IN A RANDOM FLUID MEDIUM." Journal of Computational Acoustics 10, no. 02 (June 2002): 265–74. http://dx.doi.org/10.1142/s0218396x02001632.

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Based upon the asymptotic and stochastic formulation of the acoustic wave equations, this article considers a stochastic wave propagation problem in a random multilayer which is totally refracting. Both the WKB analysis and the diffusion limit theory of stochastic differential equations are used to analyze the interplay of refraction (macrostructure) and diffusion (microstructure) of the propagating waves. The probabilistic distribution of solutions to the resultant Kolmogorov–Fokker–Planck equation is given as a computable form from the pseudodifferential operator theory and Wiener's path integral theory.

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12

Hasha, Alexander, Oliver Bühler, and John Scinocca. "Gravity Wave Refraction by Three-Dimensionally Varying Winds and the Global Transport of Angular Momentum." Journal of the Atmospheric Sciences 65, no. 9 (September 1, 2008): 2892–906. http://dx.doi.org/10.1175/2007jas2561.1.

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Abstract Operational gravity wave parameterization schemes in GCMs are columnar; that is, they are based on a ray-tracing model for gravity wave propagation that neglects horizontal propagation as well as refraction by horizontally inhomogeneous basic flows. Despite the enormous conceptual and numerical simplifications that these approximations provide, it has never been clearly established whether horizontal propagation and refraction are indeed negligible for atmospheric climate dynamics. In this study, a three-dimensional ray-tracing scheme for internal gravity waves that allows wave refraction and horizontal propagation in spherical geometry is formulated. Various issues to do with three-dimensional wave dynamics and wave–mean interactions are discussed, and then the scheme is applied to offline computations using GCM data and launch spectra provided by an operational columnar gravity wave parameterization scheme for topographic waves. This allows for side-by-side testing and evaluation of momentum fluxes in the new scheme against those of the parameterization scheme. In particular, the wave-induced vertical flux of angular momentum is computed and compared with the predictions of the columnar parameterization scheme. Consistent with a scaling argument, significant changes in the angular momentum flux due to three-dimensional refraction and horizontal propagation are confined to waves near the inertial frequency.

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13

Dalrymple, Robert A., James T. Kirby, and Daniel J. Seli. "WAVE TRAPPING BY BREAKWATERS." Coastal Engineering Proceedings 1, no. 20 (January 29, 1986): 133. http://dx.doi.org/10.9753/icce.v20.133.

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The refraction of water waves around the heads of breakwaters can lead to large wave heights along the sheltered side of the structure. These waves are shown to be edge waves, trapped on the breakwater, based on the comparison of laboratory data and linear edge wave theory.

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14

Winbow, Graham A. "Compressional and shear arrivals in a multipole sonic log." GEOPHYSICS 50, no. 7 (July 1985): 1119–26. http://dx.doi.org/10.1190/1.1441985.

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A sound source in a liquid‐filled borehole generates, among other excitations, compressional and shear waves in the rock which are detected in the fluid as refractions. It is practical to be able to separate the latter components. I show that this can always be achieved in principle by appropriately choosing the properties of the source. Solutions of the acoustic wave equation in the “far field” of the source are analyzed in detail. Suppose the source radiation depends upon the azimuthal angle η through some function F(η). The refracted waves are analyzed conveniently in terms of Fourier components [Formula: see text], where n and η are Fourier conjugates. For a source symmetrical about the axis of the borehole, as conventional sources are, [Formula: see text] vanishes except for n = 0. Our principal results concern the z dependence of the pressure radiation field in the drilling mud p (r, η, z) (using cylindrical polar coordinates). For a fixed n, as z → ∞, the refracted P‐wave is proportional to [Formula: see text] for n = 0, 1, … . The refracted S‐wave signal is proportional to [Formula: see text]. Thus, for an axially symmetric source, the P‐wave refraction generally dominates the S‐wave refraction as z → ∞. For an axially asymmetric source the S‐wave dominates the P‐wave. An example of an n = 1 source is a horizontally pointing dipole on the borehole axis. Higher order multipole sources also effectively produce nearly pure S‐wave signals in a borehole.

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15

O'Reilly, W. C., and R. T. Guza. "Comparison of Spectral Refraction and Refraction‐Diffraction Wave Models." Journal of Waterway, Port, Coastal, and Ocean Engineering 117, no. 3 (May 1991): 199–215. http://dx.doi.org/10.1061/(asce)0733-950x(1991)117:3(199).

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16

Deck-Léger, Zoé-Lise, Xuezhi Zheng, and Christophe Caloz. "Electromagnetic Wave Scattering from a Moving Medium with Stationary Interface across the Interluminal Regime." Photonics 8, no. 6 (June 5, 2021): 202. http://dx.doi.org/10.3390/photonics8060202.

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This paper extends current knowledge on electromagnetic wave scattering from bounded moving media in several regards. First, it complements the usual dispersion relation of moving media, ω(θk) (θk: phase velocity direction, associated with the wave vector, k), with the equally important impedance relation, η(θS) (θS: group velocity direction, associated with the Poynting vector, S). Second, it explains the interluminal-regime phenomenon of double-downstream wave transmission across a stationary interface between a regular medium and the moving medium, assuming motion perpendicular to the interface, and shows that the related waves are symmetric in terms of the energy refraction angle, while being asymmetric in terms of the phase refraction angle, with one of the waves subject to negative refraction, and shows that the wave impedances of the two transmitted waves are equal. Third, it generalizes the problem to the case where the medium moves obliquely with respect to the interface. Finally, it highlights the connection between this problem and a spacetime modulated medium.

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17

Sadin, D. V., B. V. Belyaev, and V. A. Davidchuk. "EFFECT OF RELAXATION PROCESSES ON THE SHOCK WAVE FOCUSING IN A GAS SUSPENSION CLOUD." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 66 (2020): 121–31. http://dx.doi.org/10.17223/19988621/66/10.

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In this paper, the interaction of a plane shock wave in air with a cylindrical region of a gas suspension and the effect of relaxation processes for various particle sizes on the refraction and focusing of the shock wave are studied. In the course of numerical modeling, the Euler approach is used to describe non-equilibrium motion of the gas and dispersed phases. A second order accuracy method in space and time is used. Verification of the method through test problems by comparing with exact solutions and calculations of other authors confirms a capability of detecting shock wave refraction effects and wave focusing with the appearance of peak profiles in a distribution of parameters. With an increase in particle sizes, the relaxation zones behind the shock wave and secondary waves, which propagate through a gas suspension cloud, have a significant impact on the shock wave refraction, focusing of transverse shock waves, and interface instability evolution. A focus point is shifted towards suspension cloud boundaries, while for sufficiently large particles, it moves beyond the boundaries (external focus mode). Thus, the reflection pressure of transverse waves and intensity of the instability at the interface reduce.

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18

HJELMERVIK, KARINA B., and KARSTEN TRULSEN. "Freak wave statistics on collinear currents." Journal of Fluid Mechanics 637 (September 17, 2009): 267–84. http://dx.doi.org/10.1017/s0022112009990607.

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Linear refraction of waves on inhomogeneous current is known to provoke extreme waves. We investigate the effect of nonlinearity on this phenomenon, with respect to the variation of significant wave height, kurtosis and occurrence of freak waves. Monte Carlo simulations are performed employing a modified nonlinear Schrödinger equation that includes the effects of a prescribed non-potential current. We recommend that freak waves should be defined by a local criterion according to the wave distribution at each location of constant current, not by a global criterion that is either averaged over, or insensitive to, inhomogeneities of the current. Nonlinearity can reduce the modulation of significant wave height. Depending on the configuration of current and waves, the kurtosis and probability of freak waves can either grow or decrease when the wave height increases due to linear refraction. At the centre of an opposing current jet where waves are known to become large, we find that freak waves should be more rare than in the open ocean away from currents. The largest amount of freak waves on an opposing current jet is found at the jet sides where the significant wave height is small.

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19

Mai, Yanbo, Zheng Sheng, Hanqing Shi, and Qixiang Liao. "Using Improved XGBoost Algorithm to Obtain Modified Atmospheric Refractive Index." International Journal of Antennas and Propagation 2021 (September 23, 2021): 1–11. http://dx.doi.org/10.1155/2021/5506599.

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Atmospheric refraction is a special meteorological phenomenon mainly caused by gas molecules and aerosol particles in the atmosphere, which can change the propagation direction of electromagnetic waves in the atmospheric environment. Atmospheric refractive index, an index to measure atmospheric refraction, is an important parameter for electromagnetic wave. Given that it is difficult to obtain the atmospheric refractive index of 100 meters (m)–3000°m over the ocean, this paper proposes an improved extreme gradient boosting (XGBoost) algorithm based on comprehensive learning particle swarm optimization (CLPSO) operator to obtain them. Finally, the mean absolute percentage error (MAPE) and root mean-squared error (RMSE) are used as evaluation criteria to compare the prediction results of improved XGBoost algorithm with backpropagation (BP) neural network and traditional XGBoost algorithm. The results show that the MAPE and RMSE of the improved XGBoost algorithm are 39% less than those of BP neural network and 32% less than those of the traditional XGBoost. Besides, the improved XGBoost algorithm has the strongest learning and generalization capability to calculate missing values of atmospheric refractive index among the three algorithms. The results of this paper provide a new method to obtain atmospheric refractive index, which will be of great reference significance to further study the atmospheric refraction.

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20

Lee, Dong-Woo, Young-Hoon Kang, and Sang-Hoon Kim. "Seismic Surface Wave Cloaking by Acoustic Wave Refraction." Journal of the Earthquake Engineering Society of Korea 19, no. 6 (November 1, 2015): 257–63. http://dx.doi.org/10.5000/eesk.2015.19.6.257.

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21

Arnaud, Gwendoline, Vincent Rey, Julien Touboul, and Damien Sous. "Wave Propagation Through Dense Vertical Cylinder Arrays: 3D Experimental Study." International Journal of Ocean and Coastal Engineering 02, no. 01n02 (March 2019): 1950001. http://dx.doi.org/10.1142/s2529807019500015.

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The purpose of this research work is to study the diffraction of surface gravity waves propagating through rectangular porous medium in three dimensions. The considered porous structure consists of dense arrays of surface piercing vertical cylinders. Experiments for different regular wave conditions have been carried out, especially for three-wave frequencies. The experimental data of wave refraction–diffraction and reflection have been compared to computed results from potential linear theory solved with an integral matching method. Comparison with a previous 2D study about wave propagation through porous medium in a 10 m long wave flume is also discussed in order to highlight the refraction–diffraction effect due to the porous structure.

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22

Jones, Glyn M., and D. B. Jovanovich. "A ray inversion method for refraction analysis." GEOPHYSICS 50, no. 11 (November 1985): 1701–20. http://dx.doi.org/10.1190/1.1441861.

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A new technique is presented for the inversion of head‐wave traveltimes to infer near‐surface structure. Traveltimes computed along intersecting pairs of refracted rays are used to reconstruct the shape of the first refracting horizon beneath the surface and variations in refractor velocity along this boundary. The information derived can be used as the basis for further processing, such as the calculation of near‐surface static delays. One advantage of the method is that the shape of the refractor is determined independently of the refractor velocity. With multifold coverage, rapid lateral changes in refractor geometry or velocity can be mapped. Two examples of the inversion technique are presented: one uses a synthetic data set; the other is drawn from field data shot over a deep graben filled with sediment. The results obtained using the synthetic data validate the method and support the conclusions of an error analysis, in which errors in the refractor velocity determined using receivers to the left and right of the shots are of opposite sign. The true refractor velocity therefore falls between the two sets of estimates. The refraction image obtained by inversion of the set of field data is in good agreement with a constant‐velocity reflection stack and illustrates that the ray inversion method can handle large lateral changes in refractor velocity or relief.

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23

Bulat, Pavel, Anzhelika Melnikova, Vladimir Upyrev, and Konstantin Volkov. "Refraction of Oblique Shock Wave on a Tangential Discontinuity." Fluids 6, no. 9 (August 24, 2021): 301. http://dx.doi.org/10.3390/fluids6090301.

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The refraction of an oblique shock wave on a tangential discontinuity dividing two gas flows with different properties is considered. It is shown that its partial reflection occurs with the exception of the geometrical diffraction of an oblique shock. Another oblique shock, expansion wave or weak discontinuity that coincides with the Mach line can act as a reflected disturbance. This study focuses on the relationships that define the type of reflected discontinuity and its parameters. The domains of shock wave configurations with various types of reflected discontinuities, including characteristic refraction and refraction patterns with a reflected shock and a reflected rarefaction wave, are analyzed. The domains of existence of various shock wave structures with two types of reflected disturbance, and the boundaries between them, are defined. The domains of parameters with one or two solutions exist for the characteristic refraction. Each domain is mapped by the type of refraction with regard to the Mach number, the ratio of the specific heat capacities of the two flows and the intensity of a refracted oblique shock wave. The conditions of the regular refraction and the Mach refraction are formulated, and the boundaries between the two refraction types are defined for various types of gases. Refraction phenomena in various engineering problems (hydrocarbon gaseous fuel and its combustion products, diatomic gas, fuel mixture of oxygen and hydrogen, etc.) are discussed. The result can be applied to the modeling of the shock wave processes that occur in supersonic intakes and in rotating and stationary detonation engines. The solutions derived can be used by other researchers to check the quality of numerical methods and the correctness of experimental results.

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24

Sarrikostis, E., and J. McManus. "Potential longshore transports on the coasts north and south of the Tay Estuary." Proceedings of the Royal Society of Edinburgh. Section B. Biological Sciences 92, no. 3-4 (1987): 297–310. http://dx.doi.org/10.1017/s0269727000004723.

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SynopsisA method of predicting coastal changes north and south of the Tay Estuary, due to the action of waves and wave-generated nearshore currents using computer simulation techniques, is described. The computation is based upon a wave refraction procedure, using as input data the deep-water wave climate (height, period and direction of approach) and the bathymetric characteristics of the sea area from Montrose to Fife Ness. The technique provides a prediction of the longshore component of wave energy flux at breaking, by computing the wave energy dissipation through shoaling, refraction and friction of the waves, for a number of points along the 70 km of shoreline. Potential patterns of longshore sediment transport are then derived in order to establish zones of potential erosion, transport and deposition between Boddin Point and Fife Ness.

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25

Wang, An Ling, and Fu Ping Liu. "The Phase Shift of Reflection and Refraction of SH-Wave at an Interface of Two Media ." Advanced Materials Research 983 (June 2014): 388–91. http://dx.doi.org/10.4028/www.scientific.net/amr.983.388.

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Using the reflection and refraction coefficient of SH wave at the interface of strata, we derived the phase shift of total reflection and refraction SH-wave, The results show that, the phase shift reflection than the phase shift refraction, phase shift of reflection 2 times the phase shift of refraction.

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26

Fu, Lei, Sherif M. Hanafy, and Gerard T. Schuster. "Parsimonious wave-equation travel-time inversion for refraction waves." Geophysical Prospecting 65, no. 6 (February 14, 2017): 1452–61. http://dx.doi.org/10.1111/1365-2478.12488.

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27

Tang, Frederick L. W., and C. F. Lin. "PRACTICAL METHOD FOR EVALUATION DIRECTIONAL SPECTRA AFTER SHOALING AND REFRACTION." Coastal Engineering Proceedings 1, no. 20 (January 29, 1986): 59. http://dx.doi.org/10.9753/icce.v20.59.

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Different Methods have been developed to calculate the deformation of spectrum as waves advance to the shallow water. Wave ray method is a traditional way to compute the change of wave ray after refraction. It is restricted to the regular wave. After slicing the linear spectrum, a lot of components of spectrum can be gained, and each component can be considered as a monochromatic wave. And then after the deformed components are worked out at the same point in sea, a deformed spectrum in shallow water is gained by summing up them. Therefore the wave ray method could be extended to the irregular wave in ocean. In real bathymetry, the difficulty in applying such method is to solve the wave ray which must pass through the assigned point. In this paper, calculation approach as well as computer program are contrived to adopted in real bathymetry. The results of computation reveal some significant characteristics of directional spectra in shallow water. Furthermore, the statistical features of waves at the point of interest are to be evaluated.

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28

Ci, Long Sheng, and Gui Lan Yu. "Propagation of SH Waves through an Interface between a Phononic Crystal and a Uniform Solid." Materials Science Forum 675-677 (February 2011): 1061–64. http://dx.doi.org/10.4028/www.scientific.net/msf.675-677.1061.

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The reflection and refraction of harmonic SH waves at the interface between a homogeneous solid and a one-dimensional phononic crystal is studied. The effects of wave frequencies on the refraction coefficients are investigated. The results show that for lower frequencies, most part of the energy is reflected into the homogeneous solid and that the frequency has little effects on the energy distribution at the interface. While for higher frequencies, SH waves cannot propagate in some directions because of the existence of the directional band gaps, which results in the discontinuity in the refraction coefficient curve. For waves passing through the interface, the higher the frequency is, the smaller the refraction coefficient is.

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29

Dementiev, D. V. "Analysis of methods for determining the refraction coefficient in the atmospheric surface layer." Geodesy and Cartography 947, no. 5 (June 20, 2019): 2–11. http://dx.doi.org/10.22389/0016-7126-2019-947-5-2-11.

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In the instructions for modern geodetic instruments, it is recommended to introduce an amendment for the refraction, taking into account the “standard” refraction coefficient k = 0,13÷0,2. In fact, in the surface layer of the atmosphere, the refractive index can range from –6 to 6. Various classical methods of determining refraction are analyzed. Conclusions based on experimental work made by various researchers are presented. Using the results of numerous studies of various methods for determining vertical refraction, it can be concluded that all classical (static) methods do not provide a high degree of reliability to determine the refraction. An exception is the method of determining refraction at a neutral temperature stratification of the atmosphere, when the time interval is not very long. For this reason, their practical application is extremely limited. To improve the accuracy of determining refraction, it is necessary to take into account the turbulence of the atmosphere, that is, to use dynamic measurement methods that take the fluctuations of the electromagnetic wave passing through the path into account.

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30

SINGH, S. S. "TRANSMISSION OF ELASTIC WAVES IN ANISOTROPIC NEMATIC ELASTOMERS." ANZIAM Journal 56, no. 4 (April 2015): 381–96. http://dx.doi.org/10.1017/s1446181115000061.

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The problem of reflection and refraction of elastic waves due to an incident quasi-primary $(qP)$ wave at a plane interface between two dissimilar nematic elastomer half-spaces has been investigated. The expressions for the phase velocities corresponding to primary and secondary waves are given. It is observed that these phase velocities depend on the angle of propagation of the elastic waves. The reflection and refraction coefficients corresponding to the reflected and refracted waves, respectively, are derived by using appropriate boundary conditions. The energy transmission of the reflected and refracted waves is obtained, and the energy ratios and the reflection and refraction coefficients are computed numerically.

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31

Mapp, George R., Christopher S. Welch, and John C. Munday. "Wave refraction by warm core rings." Journal of Geophysical Research 90, no. C4 (1985): 7153. http://dx.doi.org/10.1029/jc090ic04p07153.

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32

McLeish, William, and Duncan B. Ross. "Wave refraction in an ocean front." Journal of Geophysical Research 90, no. C6 (1985): 11929. http://dx.doi.org/10.1029/jc090ic06p11929.

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33

Mathiesen, Martin. "Wave refraction by a current whirl." Journal of Geophysical Research 92, no. C4 (1987): 3905. http://dx.doi.org/10.1029/jc092ic04p03905.

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34

Cao, Zhoujian, Hong Zhang, and Gang Hu. "Negative refraction in nonlinear wave systems." Europhysics Letters (EPL) 79, no. 3 (July 17, 2007): 34002. http://dx.doi.org/10.1209/0295-5075/79/34002.

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35

Huang, Hao, and Zhongxiang Shen. "Brewster Lens With Perfect Wave Refraction." IEEE Transactions on Antennas and Propagation 68, no. 8 (August 2020): 6204–13. http://dx.doi.org/10.1109/tap.2020.2990232.

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36

Nourgaliev, R. R., S. Y. Sushchikh, T. N. Dinh, and T. G. Theofanous. "Shock wave refraction patterns at interfaces." International Journal of Multiphase Flow 31, no. 9 (September 2005): 969–95. http://dx.doi.org/10.1016/j.ijmultiphaseflow.2005.04.001.

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37

Liu, Kun, Zhigang Yuan, Chen Zhou, Qinglin Zhu, Haining Wang, Dongsheng Sheng, and Xiang Dong. "Integrated High-Accuracy Correction Technology of Radio-Wave Refraction for Deep-Space (High-Orbit) Targets." Atmosphere 12, no. 9 (September 7, 2021): 1151. http://dx.doi.org/10.3390/atmos12091151.

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The radio-wave refraction error caused by the troposphere and ionosphere badly affects accuracy in terms of the navigation, positioning, measurement, and control of a target; it is the main source of errors in high-accuracy measurement and control systems. The high-accuracy technology needed for radio-wave refraction error correction (mainly in the troposphere and ionosphere) has been the focus of research for a long time. At present, the correction methods used for radio-wave refraction errors have a low accuracy. For an S-band radio-wave signal, the accuracy of refraction error correction can generally only reach m-level (elevation angle of 15° and above), and thus has difficulty meeting the requirements of dm-level accuracy refraction error correction for deep-space and high-orbit targets. To improve the accuracy of radio-wave refraction error correction for deep-space and high-orbit targets, a novel correction method for tropospheric and ionospheric range error due to refraction is proposed in this study, on the basis of the measured data from a water vapor radiometer and dual-frequency Global Navigation Satellite System (GNSS). The comprehensive calibration test is conducted in combination with the Chinese Area Positioning System (CAPS) in Kunming. Results show that this method can effectively correct the range error due to refraction that is caused by the troposphere and ionosphere. For an S-band radio-wave signal, the accuracy of refraction error correction can reach dm-level accuracy (elevation angle of 15° and above), which is 50% higher than that achieved with traditional methods. This work provides an effective support system for major projects, such as lunar exploration and Mars exploration.

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38

Jiang, Qingfang, James D. Doyle, Stephen D. Eckermann, and Bifford P. Williams. "Stratospheric Trailing Gravity Waves from New Zealand." Journal of the Atmospheric Sciences 76, no. 6 (May 22, 2019): 1565–86. http://dx.doi.org/10.1175/jas-d-18-0290.1.

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Abstract Gravity waves are frequently observed in the stratosphere, trailing long distances from mid- to high-latitude topography. Two such trailing-wave events documented over New Zealand are examined using observations, numerical simulations, and ray-tracing analysis to explore and document stratospheric trailing-wave characteristics and formation mechanisms. We find that the trailing waves over New Zealand are orographically generated and regulated by several processes, including interaction between terrain and mountaintop winds, critical-level absorption, and lateral wave refraction. Among these, the interaction between topography and low-level winds determines the perturbation energy distribution over horizontal scales and directions near the wave source, and accordingly, trailing waves are sensitive to terrain features and low-level winds. Terrain-forced wave modes are filtered by absorption associated with directional wind shear and Jones critical levels. The former plays a role in defining wave-beam orientation, and the latter sets an upper limit for the permissible horizontal wavelength of trailing waves. On propagating into the stratosphere, these orographic gravity waves are subject to horizontal refraction associated with the meridional shear in the stratospheric westerlies, which tends to elongate the wave beams pointing toward stronger westerlies and shorten the wave beams on the opposite side.

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39

Hardy, Thomas A., and Nicholas C. Kraus. "COUPLING STOKES AND CNOIDAL WAVE THEORIES IN A NONLINEAR REFRACTION MODEL." Coastal Engineering Proceedings 1, no. 21 (January 29, 1988): 42. http://dx.doi.org/10.9753/icce.v21.42.

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An efficient numerical model is presented for calculating the refraction and shoaling of finite-amplitude waves over an irregular sea bottom. The model uses third-order Stokes wave theory in relatively deep water and second-order cnoidal wave theory in relatively shallow water. It can also be run using combinations of lower-order wave theories, including a pure linear wave mode. The problem of the connection of Stokes and cnoidal theories is investigated, and it is found that the use of second-order rather than first-order cnoidal theory greatly reduces the connection discontinuity. Calculations are compared with physical model measurements of the height and direction of waves passing over an elliptical shoal. The finite-amplitude wave model gives better qualitative and quantitative agreement with the measurements than the linear model.

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40

Fassieh, K. M., O. Fahmy, M. M. El-Shabrawy, and M. A. Zaki. "Modeling of on Shore Propagation of Random Water Waves." ISRN Civil Engineering 2011 (October 19, 2011): 1–7. http://dx.doi.org/10.5402/2011/132769.

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Two numerical models are investigated to model random water waves (RWWs) transformation due to mild depth variation. Modelling of steady on-shore propagation of small-amplitude RWWs is based on superposition principle of waves of different heights and directions. Each component is simulated through either the parabolic model (PM) or the elliptic model (EM). PM simulates weak refraction, diffraction, shoaling, and wave breaking. EM simulates strong refraction, diffraction, and shoaling. Both models neglect wave reflection. Comparison between PM and EM, in test cases that are experimentally measured, proved that both models give good results for unidirectional and narrow-directional RWW. However, EM is more accurate in modelling broad-directional RWWs.

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41

Jordà, G., R. Bolaños, M. Espino, and A. Sánchez-Arcilla. "Assessment of the importance of the current-wave coupling in the shelf ocean forecasts." Ocean Science 3, no. 3 (July 11, 2007): 345–62. http://dx.doi.org/10.5194/os-3-345-2007.

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Abstract. The effects of wave-current interactions on shelf ocean forecasts is investigated in the framework of the MFSTEP (Mediterranean Forecasting System Project Towards Enviromental Predictions) project. A one way sequential coupling approach is adopted to link the wave model (WAM) to the circulation model (SYMPHONIE). The coupling of waves and currents has been done considering four main processes: wave refraction due to currents, surface wind drag and bottom drag modifications due to waves, and the wave induced mass flux. The coupled modelling system is implemented in the southern Catalan shelf (NW Mediterranean), a region with characteristics similar to most of the Mediterranean shelves. The sensitivity experiments are run in a typical operational configuration. The wave refraction by currents seems to be not very relevant in a microtidal context such as the western Mediterranean. The main effect of waves on current forecasts is through the modification of the wind drag. The Stokes drift also plays a significant role due to its spatial and temporal characteristics. Finally, the enhanced bottom friction is just noticeable in the inner shelf.

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42

Jordà, G., R. Bolaños, M. Espino, and A. Sánchez-Arcilla. "Assessment of the importance of the current-wave coupling in the shelf ocean forecasts." Ocean Science Discussions 3, no. 5 (October 25, 2006): 1825–70. http://dx.doi.org/10.5194/osd-3-1825-2006.

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Abstract. The effects of wave-current interactions on shelf ocean forecasts is investigated in the framework of the MFSTEP (Mediterranean Forecasting System Project Towards Enviromental Predictions) project. A one way sequential coupling approach is adopted to link the wave model (WAM) to the circulation model (SYMPHONIE). The coupling of waves and currents has been done considering four main processes: wave refraction due to currents, surface wind drag and bo€ttom drag modifications due to waves, and the wave induced mass flux. The coupled modelling system is implemented in the southern Catalan shelf (NW Mediterranean), a region with characteristics similar to most of the Mediterranean shelves. The sensitivity experiments are run in a typical operational configuration. The wave refraction by currents seems to be not very relevant in a microtidal context such as the western Mediterranean. The main effect of waves on current forecasts is through the modification of the wind drag. The Stokes drift also plays a significant role due to its spatial and temporal characteristics. Finally, the enhanced bottom friction is just noticeable in the inner shelf.

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43

Kim, D. Ch, E. T. Ageeva, N. T. Afanasiev, S. O. Chudaev, I. G. Makhro, and O. I. Medvedeva. "Numerical-analytical method for calculating the refraction of radio waves in a chaotic upper atmosphere." Canadian Journal of Physics 99, no. 9 (September 2021): 772–77. http://dx.doi.org/10.1139/cjp-2020-0334.

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An operational method is proposed for calculating the refraction of decameter radio waves in a randomly-inhomogeneous upper atmosphere. The method is based on the numerical-analytical solution of stochastic equations of geometric optics. An integral expression is obtained for the dispersion of the refraction angle of a radio wave on the atmospheric path using the approximation of the perturbation method. For a quick calculation of the statistical moment of the refraction angle, the integral expression is reduced to an ordinary first-order differential equation. Joint numerical solution of the unperturbed ray equations and the equations for the statistical moment allows an operational estimate of beam width of radio waves arriving at the observation point. The results of numerical calculations of the standard deviations of the refraction angles of radio waves on paths of various lengths are presented.

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44

Liu, Bin, Quan Yong Shen, Jian Mei Ye, Zi Qing Xie, and Min Yan Xu. "Characteristics of the Lateral Shift at the Surface of the Metamaterial." Applied Mechanics and Materials 201-202 (October 2012): 238–41. http://dx.doi.org/10.4028/www.scientific.net/amm.201-202.238.

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In some metamaterial such as the chiral negative refraction medium, the lateral shift is analyzed in theory. When total internal reflection occurs, the lateral shift curves as the incident angle have been figured out for a linearly polarized incident wave. The shift directions of the TM and TE components in the reflected wave are opposite when the incident angle is between the two critical angles of the eigen-waves. Both TM and TE waves will have positive lateral shift once the incident angle is larger than the total internal reflection angle. By contrast with the common medium and normal chiral medium, we have found that the lateral shift character in the chiral negative refraction medium is distinctive.

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45

Hirosue, F., and T. Sakai. "DIRECTIONAL SPECTRA IN CURRENT-DEPTH REFRACTION." Coastal Engineering Proceedings 1, no. 20 (January 29, 1986): 19. http://dx.doi.org/10.9753/icce.v20.19.

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According to Brink-Kjaer et al.'s discussion(1984), the expression of the wave direction change velocity is modified in our numerical model for the directional wave spectra change due to current-depth refraction (Sakai et al., 1983). The wave reflection and breaking conditions due to current are discussed from a view point of numerical analysis. Effects of the refraction term in the modified wave action equation on the directional spectra change are examined. The relative importance of current and water depth change in the directional spectra change is also examined.

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46

Holzschuh, Josef. "Low‐cost geophysical investigations of a paleochannel aquifer in the Eastern Goldfields, Western Australia." GEOPHYSICS 67, no. 3 (May 2002): 690–700. http://dx.doi.org/10.1190/1.1484512.

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Compressional (P) wave and shear (S) wave seismic reflection techniques were used to delineate the sand and gravel aquifer within a highly saline clay‐filled paleochannel in the Eastern Goldfields of Western Australia. The seismic refraction and gravity methods were also used to investigate the paleochannel. The unsaturated loose fine‐grained sand up to 10 m in depth at the surface is a major factor in degrading subsurface imaging. The seismic processing needed to be precise, with accurate static corrections and normal moveout corrections. Deconvolution enhanced the aquifer and other paleochannel reflectors. P‐wave reflection and refraction layer depths had good correlation and showed a total of six boundaries: (1) water table, (2) change in velocity (compaction) in the paleochannel sediments, (3) sand and gravel aquifer, (4) red‐brown saprolite and green saprolite boundary, (5) weathered bedrock, and (6) unweathered bedrock. P‐wave explosive and hammer sources were found to have similar signal characteristics, and the aquifer and bedrock were both imaged using the hammer source. The deep shots below the water table have the most broadband frequency response for reflections, but stacking clear reflections was difficult. The S‐wave reflection results showed high lateral and vertical resolution of the basal saprolite clay, the sand and gravel aquifer, and very shallow clays above the aquifer. The S‐wave reflection stacking velocities were 10–20% of the P‐waves, increasing the resolution of the S‐wave section. The gravity data were modelled to fit the known drilling and P‐wave seismic reflection depths. The refraction results did not identify the top of bedrock, so refraction depths were not used for the gravity modeling in this highly weathered environment. The final gravity model mapped the bedrock topography beyond the lateral extent of the seismic and drilling data.

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47

Dang, Song Yang, Hong Yu Xu, Qing Yong Sun, and Bin Liang. "Propagation Characteristics of Coupled Wave through Micropolar Fluid Interlayer in Micropolar Elastic Solid." Advanced Materials Research 721 (July 2013): 729–32. http://dx.doi.org/10.4028/www.scientific.net/amr.721.729.

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Based on micropolar fluid theory and micropolar solid elasticity theory, reflection and transmission characteristics of longitudinal displacement wave and two coupled waves were studied when incident coupled wave propagated through micropolar fluid interlayer in micropolar elastic solid. Using numerical example, the rules of the reflection waves and refraction waves amplitudes varied with incident angle are also discussed. Results show that there exist extremum values of reflection and transmission coefficient for coupled wave. There are two peaks and one zero value of transmission coefficient for longitudinal displacement wave.

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48

Diephuis, J. G. H. R., and J. G. Gerritze. "DETERMINATION OF THE WAVE HEIGHT IN NATURE FROM MODEL TESTS SUPPLEMENTED BY CALCULATION." Coastal Engineering Proceedings 1, no. 6 (January 29, 2011): 12. http://dx.doi.org/10.9753/icce.v6.12.

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This paper deals with the problem of determining the wave characteristics in shallow water from those in deep water. In general this can be done by means of a refraction calculation. If the sea bottom topography is too irregular the height of the waves can be determined by means of a small-scale refraction model. In both cases, however, some additional effects have to be taken into account, viz. the influence of the bottom friction and the influence of the wind.

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49

Liau, Jian-Ming, Aaron Roland, Tai-Wen Hsu, Shan-Hwei Ou, and Yi-Ting Li. "Wave refraction–diffraction effect in the wind wave model WWM." Coastal Engineering 58, no. 5 (May 2011): 429–43. http://dx.doi.org/10.1016/j.coastaleng.2011.01.002.

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50

Rahnema, Hossein, Sohrab Mirassi, and Giancarlo Dal Moro. "Cavity effect on Rayleigh wave dispersion and P-wave refraction." Earthquake Engineering and Engineering Vibration 20, no. 1 (January 2021): 79–88. http://dx.doi.org/10.1007/s11803-021-2006-y.

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