Reflection coefficients of P-SV waves in weak anisotropic media

We introduce the Thomsen anisotropic parameters into the approximate linear reflection coefficient equation for P-SV wave in weakly anisotropic HTI media. From this we get a new, more effective, and practical reflection coefficient equation. We performed forward modeling to AVO attributes, obtaining excellent results. The combined AVO attribute analysis of PP and PS reflection data can greatly reduce ambiguity, obtain better petrophysical parameters, and improve parameter accuracy.

Wave Reflection by Rectangular Breakwaters for Coastal Protection

In this study,we focus on the numerical modelling of the interaction between waves and submerged structures in the presence of a uniform flow current.Both the same and opposite senses of wave propagation are considered.The main objective is an understanding of the effect of the current and various geometrical parameters on the reflection coefficient.The wave used in the study is based on potential theory,and the submerged structures consist of two rectangular breakwaters positioned at a fixed distance from each other and attached to the bottom of a wave flume.The numerical modeling approach employed in this work relies on the Boundary Element Method(BEM).The results are compared with experimental data to validate the approach.The findings of the study demonstrate that the double rectangular breakwater configuration exhibits superior wave attenuation abilities if compared to a single rectangular breakwater,particularly at low wavenumbers.Furthermore,the study reveals that wave mitigation is more pronounced when the current and wave propagation are coplanar,whereas it is less effective in the case of opposing current.

Reflection and refraction of attenuated waves at boundary of elastic solid and porous solid saturated with two immiscible viscous fluids

The propagation of elastic waves is studied in a porous solid saturated with two immiscible viscous fluids. The propagation of three longitudinal waves is represented through three scalar potential functions. The lone transverse wave is presented by a vector potential function. The displacements of particles in different phases of the aggregate are defined in terms of these potential functions. It is shown that there exist three longitudinal waves and one transverse wave. The phenomena of reflection and refraction due to longitudinal and transverse waves at a plane interface between an elastic solid half-space and a porous solid half-space saturated with two immiscible viscous fluids are investigated. For the presence of viscosity in pore-fluids, the waves refracted to the porous medium attenuate in the direction normal to the interface. The ratios of the amplitudes of the reflected and refracted waves to that of the incident wave are calculated as a non- singular system of linear algebraic equations. These amplitude ratios are used to further calculate the shares of different scattered waves in the energy of the incident wave. The modulus of the amplitude and the energy ratios with the angle of incidence are computed for a particular numerical model. The conservation of the energy across the interface is verified. The effects of variations in non-wet saturation of pores and frequencies on the energy partition are depicted graphically and discussed,

Reflection and refraction of plane waves at the boundary of an elastic solid and double-porosity dual-permeability materials

Phenomena of reflection and refraction of plane harmonic waves at a plane interface between an elastic solid and doubleporosity dual-permeability material are investigated. The elastic solid behaves non-dissipatively, while double-porosity dual-permeability materials behave dissipatively to wave propagation due to the presence of viscosity in pore fluids. All the waves(i.e., incident and reflected) in an elastic medium are considered as homogeneous(i.e., having the same directions of propagation and attenuation), while all the refracted waves in double-porosity dual-permeability materials are inhomogeneous(i.e., having different directions of propagation and attenuation). The coefficients of reflection and refraction for a given incident wave are obtained as a non-singular system of linear equations. The energy shares of reflected and refracted waves are obtained in the form of an energy matrix. A numerical example is considered to calculate the partition of incident energy among various reflected and refracted waves. The effect of incident direction on the partition of the incident energy is analyzed with a change in wave frequency, wave-induced fluid-flow, pore-fluid viscosity and double-porosity structure.It has been confirmed from numerical interpretation that during the reflection/refraction process, conservation of incident energy is obtained at each angle of incidence.

Seismic reflection and transmission coefficients of a single layer sandwiched between two dissimilar poroelastic solids

The seismic reflection and transmission characteristics of a single layer sandwiched between two dissimilar poroelastic solids saturated with two immiscible viscous fluids are investigated. The sandwiched layer is modeled as a porous solid with finite thickness. The propagation of waves is represented with potential functions. The displacements of particles in different phases of the aggregate are defined in terms of these potential functions. Due to the presence of viscosity in pore fluids, the reflected and transmitted waves are inhomogeneous in nature, i.e., with different directions of propagation and attenuation. The closed-form analytical expressions for reflection and transmission coefficients are derived theoretically for appropriate boundary conditions. These expressions are calculated as a non-singular system of linear algebraic equations and depend on the various parameters involved in this non-singular system. Hence,numerical examples are studied to determine the effects of various properties of the sandwich layer on reflection and transmission coefficients. The essential features of layer thickness, incident direction, wave frequency, liquidsaturation and capillary pressure of the porous layer on reflection and transmission coefficients are depicted graphically and discussed. The analysis shows that reflection and transmission coefficients are strongly associated with incident direction and various properties of the porous layer.

Structural Characteristics of the Basement beneath Qiangtang Basin in Qinghai-Tibet Plateau: Results of Interaction Interpretation from Seismic Reflection/Refraction Data

The studies on configuration, character/property of the basement of Qiangtang basin is helpful for evaluating petroleum and nature gas resources as well as understanding the basin evolvement. Recently a moderate to high-grade metamorphic gneiss rock was found underlying beneath very low metamorphic Ordovician strata in Mayer Kangri to the north of the central uplift. That fact actually proved existence of the crystalline basement just the distribution and structures of pre-Paleozoic crystalline basement still remain puzzle. In recent years a number of active sources deep seismic profiling, to aim at lithospheric structure of northern Tibet and petroleum resources of the Qiangtang basin, had been conducted that make it possible to image the structure of the basement of the Qiangtang. Near vertical reflection profiles, included those acquired previously and those during 2004 to 2008, have been utilized in this study. By through the interaction process and interpretation between the reflection profiles and the wide-angle profile, a model with the detailed structure and velocity distribution from surface to the depth of 20 km of Qiangtang basin has been imaged.Based on the results and discussions of this study, the preliminary conclusions are as follows： （1） The velocity structure section （~20 kin） that is interactively constrained by the refraction and reflection seismic data reveals that the sedimentary stratum gently lie until 10 km in the south Qiangtang basin. （2） The basement consists of fold basement （the upper） and crystalline basement （the lower）.The fold basement buried at the average depth of 6 km with a velocity of 5.2-5.8 km/s. The shallowest appear at range of the central uplift. The crystalline basement is underlying beneath the fold basement at the average depth of 10 km with a velocity of 5.9-6.0 km/s except near Bangong-Nujiang suture. （3） The high-velocity body at the depth range of 3-6 km of the central uplift is considered as a fragment of the crystalline basement that perhaps was raised by Thermal or deformation. （4） The lower-consolidated fold basement show more affinity of Yangtze block but the crystalline basement seems more approximate to Lhasa terrene in geophysical nature. We have attempted to improve the resolution and reliability by interaction of the active seismic data and prove it effective to image complex basement structure. It will be a potential to process the piggy-back acquisition data and has wide prospects.

Reflection and refraction of waves in oscillatory media

This paper uses the two-dimensional Brusselator model to study reflection and refraction of chemical waves. It presents some boundary conditions of chemical waves, with which occurence of observed phenomena at interface as refraction and reflection of chemical waves can be interpreted. Moreover, the angle of reflection may be calculated by using the boundary conditions. It finds that reflection and refraction of chemical waves can occur simultaneously even if plane wave goes from a medium with higher speed to a medium with lower speed, provided the incident angle is larger than the critical angle.

Reflection and Refraction of Gaussian Beam on Wavy Surface in Airborne Ocean Lidar

According to the statistical description of direction distribution on wavy surface by Cox, we have set up a physical model of reflection and refraction of Gaussian beam on wavy surface, derived that a beam reflected and refracted by wavy surface is also a Gaussian beam when the incident beam is a Gaussian beam, and set up the relationship between Gaussian beam's light spot size and wind speed over sea surface.

Electromagnetic chirality-induced negative refraction with the same amplitude and anti-phase of the two chirality coefficients

This paper suggests a scheme of electromagnetic chirality-induced negative refraction utilizing magneto-lectric cross coupling in a four-level atomic system. The negative refraction can be achieved with the two chirality coefficients having the same amplitude but the opposite phase, without requiring the simultaneous presence of an electric-dipole and a magnetic-dipole transition near the same transition frequency.

The Mathematical Modelling for Studying the Influence of the Initial Stresses and Relaxation Times on Reflection and Refraction Waves in Piezothermoelastic Half-Space

The present paper concentrates on the study of reflection and refraction phenomena of waves in pyroelectric and piezo-electric media under initial stresses and two relaxation times influence by apply suitable conditions. The generalized theories of linear piezo-thermoelasticity have been employed to investigate the problem. In two-dimensional model of transversely isotropic piezothermoelastic medium, there are four types of plane waves quasi-longitudinal (qP), quasi-transverse (qSV), thermal wave (T-mode), and potential electric waves (φ-mode) The amplitude ratios of reflection and refraction waves have been obtained. Finally, the results in each case are presented graphically.

Analysis of Directional Spectra and Reflection Coefficients in Incident and Reflected Wave Field

In this paper, the modified Bayesian method for the analysis of directional wave spectra and reflection coefficients is verified by numerical and physical simulation of waves. The results show that the method can basically separate the incident and reflected directional spectra. In addition, the effect of the type of wave gage arrays, the number of measured wave properties, and the distance between the wave gage array and the reflection line on the resolution of the method are investigated. Some suggestions are proposed for practical application.

Light Refraction and Reflection near a Black Hole

In this paper, we have calculated the angle of refraction that light travels approaching to the strong gravitational field like a black hole by combining the general relativity and the classical Snell’s law, assuming that the gravitational field can act as a non-vacuum filled with medium of some coefficients. We have found that the value of refracted angle exactly coincides with the value from the Einstein’s relativity theory in a weak gravitational field. From this optical interpretation of the traveling of light near a black hole, we have suggested that there might have the reflection phenomenon and investigated that the total reflection occurs at the surface of a black hole. Regardless this might cause controversy, we can explain the recent observation that light reflects from a black hole.

Improving seismic interpretation: a high-contrast approximation to the reflection coefficient of a plane longitudinal wave

Linearized approximations of reflection and transmission coefficients set a foundation for amplitude versus offset（AVO） analysis and inversion in exploration geophysics.However,the weak properties contrast hypothesis of those linearized approximate equations leads to big errors when the two media across the interface vary dramatically.To extend the application of AVO analysis and inversion to high contrast between the properties of the two layers,we derive a novel nonlinearized high-contrast approximation of the PP-wave reflection coefficient,which establishes the direct relationship between PPwave reflection coefficient and P-wave velocities,S-wave velocities and densities across the interface.（A PP wave is a reflected compressional wave from an incident compressional wave（P-wave）.） This novel approximation is derived from the exact reflection coefficient equation with Taylor expansion for the incident angle.Model tests demonstrate that,compared with the reflection coefficients of the linearized approximations,the reflection coefficients of the novel nonlinearized approximate equation agree with those of the exact PP equation better for a high contrast interface with a moderate incident angle.Furthermore,we introduce a nonlinear direct inversion method utilizing the novel reflection coefficient equation as forward solver,to implement the direct inversion for the six parameters including P-wave velocities,S-wave velocities,and densities in the upper and lower layers across the interface.This nonlinear inversion algorithm is able to estimate the inverse of the nonlinear function in terms of model parameters directly rather than in a conventional optimization way.Three examples verified the feasibility and suitability of this novel approximation for a high contrast interface,and we still could estimate the six parameters across the interface reasonably when the parameters in both media across the interface vary about 50%.

Experimental study of reflection coefficient and wave forces acting on perforated caisson

The reflection coefficient and the total horizontal forces of regular waves acting on theperforated caisson are experimentally investigated. The empirical relationship between reflection coefficient and the ratio of the total horizontal forces acting on the perforated caisson to those on solid vertical walls with the relative chamber width, relative water depth and porosity of perforated wall, etc. are given. Moreover, the results of the ratio of the total horizontal forces are also compared with formulas given by Chinese Harbour Design Criteria and Takahashi, which may be useful for the practical engineering application.

Ultrasonic characterization of modified Cr_2O_3 coatings by reflection coefficient spectroscopy

Pores,microcracks and density of plasma sprayed Cr2O3 coatings before and after high-intensity pulsed ion beam(HIPIB) irradiation were investigated using the ultrasonic reflection coefficient spectroscopy(URCS).The URCS was analyzed based on an acoustic transmission model for the multi-layered structure.The longitudinal velocity in the coatings was calculated from the experimental URCS,and the attenuation coefficient expression was deduced by comparing the experimental and numerical fitting amplitude spectral lines.The longitudinal velocity of as-sprayed Cr2O3 coating is 2 002 m/s,and increases to 2 099 and 2 148 m/s after being irradiated by HIPIB with 1 and 5 shots.Correspondingly,the factor A changes from 0.046 to 0.026 and 0.020 and n from 1.702 to 1.658 and 1.649 in the attenuation coefficient expression of α=Af n.It is observed that the surface morphology of Cr2O3 coatings changes from rough and porous to smooth and uniform with the increase of shot number,which accords with the ultrasonic analyses reasonably.The URCS seems to provide a convenient and nondestructive method to characterize surface modification of the plasma sprayed coatings.

Forward Modeling of the Relationship Between Reflection Coefficient and Incident Angle of the P Wave in a Coal Seam

Although the Zoeppritz equation is suitable for a single interface in a thick deposit, it has some limitations for composite reflection waves from both the floor and the roof of coal seams. Based on the ray model, the relationship of the overall reflection coefficient of composite reflection P waves, from coal seam versus incidence angle (AVO), is dis- cussed. The result shows that: 1) the overall reflection coefficient of composite reflection waves from coal seams is a negative value and is determined mainly by the lithology of roof and floor, which is different from the reflection coeffi- cient of a single interface; 2) if the incidence angle ranges from 0° to 6°, the reflection coefficient of composite waves of a coal seam does not change with the incidence angle and 3) if the incidence angle ranges from 6–60° , the reflection coefficient increases monotonically.

Calculation of Wave Reflection Coefficient for Perforated-Pipe Breakwater

The hollow-pipe perforated breakwater is of low reflection. In this paper the functions of reflection coefficients of both regular and random waves are theoretically derived, based on the concept of linear superimposition of reflected and incident waves and with the total flow rate continuity of integral form instead of the non-continuity of the boundary condition, and based on the concept of linear wave spectrum theory. Comparisons between theoretical results presented here and measurements of model tests show reasonable agreement.

A NOVEL METHOD FOR MEASURING COMPLEX REFLECTION COEFFICIENT USING A FOUR-PORT REFLECTOMETER

A novel method for precise measurement of complex reflection coeffcient using a four-port reflectometer is presented. First, three new complex system constants are introduced,which depend only on the scattering parameters of the four-port reflectometer. Therefore, the stability of the reflectometer is greatly improved. Then, these complex system constants are used to determine the complex reflection coeffcient F of the device under test by calibrating the reflectometer. Finally, a four-port reflectometer comprising a magic tee and a power detector is constructed and excellent experimental results are obtained.

The Approach of Compensation of Air Refractive Index in Thermal Expansion Coefficients Measurement Based on Laser Feedback Interferometry

We present the thermal expansion coefficient （TEC） measurement technology of compensating for the effect of variations in the refractive index based on a Nd： YA G laser feedback system, the beam frequency is shifted by a pair of aeousto-optic modulators and then the heterodyne phase measurement technique is used. The sample measured is placed in a muffle furnace with two coaxial holes opened on the opposite furnace walls. The measurement beams hit perpendicularly and coaxially on each surface of the sample. The reference beams hit on the reference mirror and the high-refiectivity mirror, respectively. By the heterodyne configuration and computing, the influences of the vibration, distortion of the sample supporter and the effect of variations in the refractive index are measured and largely minimized. For validation, the TECs of aluminum samples are determined in the temperature range of 29-748K, confirming not only the precision within 5 × 10-7 K-1 and the accuracy within 0.4% from 298K to 448K but also the high sensitivity non-contact measurement of the lower reflectivity surface induced by the sample oxidization from 448 K to 748 K.