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.

Crustal wide-angle reflection imaging along Lianxian-Gangkou profile in Guangdong province,China

A 400 km-long wide-angle seismic experiment along Lianxian-Gangkou profile in South China was carried out to study contact relationship between southeast continental margin of Yangtze block and northwest continental margin of Cathaysia block. We reconstructed crustal wide-angle reflection structure by the depth-domain pre-stack migration and the crustal velocity model constructed from the traveltime fitting. The wide-angle reflection section shows different reflection （from crystalline basement and Moho） pattern beneath the Yangtze and Cathaysia blocks, and suggests the Wuchuan-Sihui fault is the boundary between them. A cluster of well-developed reflections on Moho and in its underlying topmost mantle probably comes from alternative thin layers, which may be seismic signature of strong interaction between crust and mantle in the tectonic environment of lithosphere extension.

Crustal structure of the eastern Dabie orogenic belt from the seismic tomography and wide-angle reflection studies

The studies of seismic tomography and wide-angle reflection have been carried out to reveal the velocity structUrebeneath the eastern Dabie orogenic belt. The result from the seismic tomography shows the high velocity bodiesmight be positioned to a depth of only about 1 .5 km below sea level within the Dabie ultra-high pressure metamorphic (UHPM) belt; the fan-profile shows the Shuihou-Wuhe fault, the demarcation between the South Dabieand the North Dabie, slopes to the south-west at a dip angle of about 45° in the bottom of upper crust. The wideangle reflection shows the middle crustal boundaries and the complex features from the lower crust.

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.

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.

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.

Joint exploration of crustal structure in Fuzhou basin and its vicinities by deep seismic reflection and high-resolution refraction as well as wide-angle reflection/refraction

The Fuzhou basin and its vicinities are located at the northern end of the southeastern coastal seismic zone of the mainland of China. By the joint explorations of high-resolution seismic refraction and wide-angle reflection/refraction as well as deep seismic reflection in the region, which is the first synthetic profile in China, its fine velocity structure and geometric structure from the ground to Moho discontinuity is obtained. The result shows that the crust is obviously layered with a thickness of about 32 km. Basically, it consists of two parts: upper crust and lower crust. The velocity of the upper crust is 5.9-6.2 km/s in which there is a 3-4-km-thick weak low-velocity layer between the depths of 10-15 km, while the velocity of the lower crust in the range of 6.3-7.2 km/s. There exists a strong velocity gradient layer about 3 km thick above the Moho discontinuity whose velocity increases from 6.5 to 7.27 km/s. There exist high-angle normal faults that are small in size and extend only in the shallow crust. These faults are the secondary developed on the hanging wall of westward dipping low-angle normal faults. Thus, their seismogenic ability is limited, however, there exists a high-angle deep fault in the crust from Changle-Zaoan fault zone to seashore fault zone. This deep fault has cut the interface between the upper and lower crusts and Moho discontinuity, and may be the deep structure to trigger destructive earthquake source in future to affect Fuzhou City. These results have advanced the detecting precision of the deep structure in the southeastern coastal seismic zone of the mainland of China. In the aspect of the combined feature of the deep and shallow extensional structures that consist of the westward dipping low-angle normal faults and secondary normal faults on their hanging walls in the upper crust, it is firstly obtained that a united structural interpretation has deepened the knowledge about the deep dynamic process in the southeastern coastal seismic zone. At the same time, in synthetic application of deep seismic detecting methods for deep tectonic background, it possesses a wide referenced meaning to the other regions.

The deep background of large-scale,Mesozoic Cu-Au-W metallogenesis in northeastern South China:Constraints from Yingshan-Changshan wide-angle seismic reflection/refraction data

To investigate the geodynamic processes of Mesozoic large-scale mineralization in South China,we deployed a 350-km-long,wide-angle seismic reflection/refraction sounding profile between Yingshan in Hubei and Changshan in Zhejiang.This profile traverses the Cu-Au metallogenic belt in the middle and lower reaches of the Yangtze River(YMB),the Jiangnan W-polymetal metallogenic belt(JNMB),and the Qinhang Cu-polymetal metallogenic belt(QHMB).Our imaging results reveal various interesting velocity features along the profile.(1)The velocity structure is characterized by vertical layering and horizontal blocking;(2)the YMB is marked by high velocity and high V_(p)/V_(s) ratios in general with a significantly uplifted Moho interface and a thin crust of~31 km,and the lower crust contains high-velocity anomalies and has the characteristics of a crustmantle transition zone;(3)the JNMB is bounded by the Jiangnan fault and Jingdezhen-Huangshan fault and has low-velocity anomalies and low V_(p)/V_(s) ratios;and(4)the QHMB is characterized by high-velocity anomalies and high V_(p)/V_(s) ratios.The highvelocity anomalies in the YMB and QHMB represent relatively Cu-Au-rich mafic juvenile lower crust.The formation of this kind of crust is considered to be related to mantle-derived magma underplating or residues of Neoproterozoic oceanic crustal materials,and it also provided sources for large-scale Cu-Au mineralization in the Mesozoic.The JNMB has features similar to those of ancient crusts enriched in W-Sn,the partial melting of which played a leading role in the formation of the superlarge W deposits in this belt.Considering these results and other regional geological data,we propose that a large-scale oblique upwelling of the asthenosphere along the collisional belt of the Yangtze and Cathaysia blocks during the Mesozoic was the deep driving mechanism for the explosive mineralization of Cu,Au,and W in northeastern South China.The boundaries of the blocks or terrains and discontinuities of the lithosphere were the main channels for deep heat and magmas and therefore controlled the spatial distribution of the metallogenic belt.

Characteristics of crustal variation and extensional break-up in the Western Pacific back-arc region based on a wide-angle seismic profile

The marginal sea and back-arc basins in the Western Pacific Ocean have become the focus of tectonics due to their unique tectonic location.To understand the deep crustal structure in the back-arc region,we present a 545-kmlong active-source ocean bottom seismometer(OBS)wide-angle reflection/refraction profile in the East China Sea.The P wave velocity model shows that the Moho depth rises significantly,from approximately 30 km in the East China Sea shelf to approximately 16 km in the axis of the Okinawa Trough.The lower crustal high-velocity zone(HVZ)in the southern Okinawa Trough,with V_(p) of 6.8-7.3 km/s,is a remarkable manifestation of the mantle material upwelling and accretion to the lower crust.This confirms that the lower crustal high-velocity mantle accretion is developed in the southern Okinawa Trough.During the process of back-arc extension,the crustal structure of the southern Okinawa Trough is completely invaded and penetrated by the upper mantle material in the axis region.In some areas of the southern central graben,the crust may has broken up and entered the initial stage of seafloor spreading.The discontinuous HVZs in the lower crust in the back-arc region also indicate the migration of spreading centers in the back-arc region since the Cenozoic.The asthenosphere material upwelling in the continent-ocean transition zone is constantly driving the lithosphere eastward for episodic extension,and is causing evident tectonic migration in the Western Pacific back-arc region.

Wide-angle incidence and P-wave transmission

Polarity reversals may occur to transmitted P waves if the incidence angle is greater than the critical incidence angle. We analyze the characteristics of reflection and transmission coefficients under the condition of wide incidence angle based on Zoeppritz equations. We find that for specific conditions, as the incidence angle increases, the characteristic curve of the transmitted P-wave coefficient enters the third quadrant from the first quadrant through the origin, which produces a transition in the transmitted P wave and the corresponding coefficient experiences polarity reversal. We derive the incidence angle when the transmitted P-wave coefficient is zero and verify that it equals zero by using finite-difference forward modeling for a single-interface model. We replace the water in the model reservoir by gas and see that the reservoir P-wave velocity and density decrease dramatically. By analyzing the synthetic seismogram of the transmitted P wave in the single-interface model, we show that the gas-saturated reservoir is responsible for polarity reversal.

Three-dimensional crustal velocity structure of P-wave in East China from wide-angle reflection and refraction surveys

The 3-D crustal structure of P-wave velocity in East China is studied based on the data obtained by wide-angle seismic reflection and refraction surveys.The results suggest that a deep Moho disconti-nuity exists in the western zone of the study region,being 35―48 thick.High-velocity structure zones exist in the upper crust shallower than 20 km beneath the Sulu and Dabie regions.The cause of high-velocity zones is attributable to high-pressure metamorphic(HPM) and ultra-high-pressure metamorphic(UHPM) terranes with high velocity and density exhuming up to the upper crust in the Sulu and Dabie orogenies.Anomalous zones of low velocity are in the lower crust,about 30 km beneath the Sulu and Dabie regions.The Moho discontinuity is as deep as 38 km beneath the Dabie region,deeper than those in the surrounding areas.The Moho discontinuity beneath the Sulu orogenic region is also a little deeper than those in its vicinity,being about 32 km.The deep Moho discontinuity zone implies that the low crustal velocity structure zone is in that region.The low-velocity characteristics in the lower crust are probably related to the remnant crustal root of the old mountains due to the orogeny in the Sulu and Dabie regions.The high-velocity anomalous zones in the upper crust and low-velocity anomalous zones in the lower crust beneath the Sulu region are all located northeast of the northern segment of the Tan-Lu fault.However,the high-and low-velocity anomalous zones beneath the Dabie region are located southwest of the southern segment of the Tan-Lu fault.Such a distribution of the velocity-anomalous zones looks to be attributable a left lateral slip motion along the Tan-Lu fault.The distribution pattern of the velocity-anomalous zones may show some evidence for the left strike-slip motion regime of the Tan-Lu fault.

Accuracy design of ultra-low residual reflection coatings for laser optics

Refractive index inhomogeneity is one of the important characteristics of optical coating material, which is one of the key factors to produce loss to the ultra-low residual reflection coatings except using the refractive index inhomogeneity to obtain gradient-index coating. In the normal structure of antireflection coatings for center wavelength at 532 nm, the physical thicknesses of layer H and layer L are 22.18 nm and 118.86 nm, respectively. The residual reflectance caused by refractive index inhomogeneity（the degree of inhomogeneous is between -0.2 and 0.2） is about 200 ppm, and the minimum reflectivity wavelength is between 528.2 nm and 535.2 nm. A new numerical method adding the refractive index inhomogeneity to the spectra calculation was proposed to design the laser antireflection coatings, which can achieve the design of antireflection coatings with ppm residual reflection by adjusting physical thickness of the couple layers. When the degree of refractive index inhomogeneity of the layer H and layer L is-0.08 and 0.05 respectively, the residual reflectance increase from zero to 0.0769% at 532 nm. According to the above accuracy numerical method, if layer H physical thickness increases by 1.30 nm and layer L decrease by 4.50 nm, residual reflectance of thin film will achieve to 2.06 ppm. When the degree of refractive index inhomogeneity of the layer H and layer L is 0.08 and -0.05 respectively, the residual reflectance increase from zero to 0.0784% at 532 nm. The residual reflectance of designed thin film can be reduced to 0.8 ppm by decreasing the layer H of 1.55 nm while increasing the layer L of 4.94 nm.

A review of anomalous refractive and reflective metasurfaces

Abnormal refraction and reflection refers to the phenomenon in which light does not follow its traditional laws of propagation and instead is subject to refraction and reflection at abnormal angles that satisfy a generalization of Snell’s law.Metasurfaces can realize this phenomenon through appropriate selection of materials and structural design,and they have a wide range of potential applications in the military,communications,scientific,and biomedical fields.This paper summarizes the current state of research on abnormal refractive and reflective metasurfaces and their application scenarios.It discusses types of abnormal refractive and reflective metasurfaces based on their tuning modes(active and passive),their applications in different wavelength bands,and their future development.The technical obstacles that arise with existing metasurface technology are summarized,and prospects for future development and applications of abnormal refractive and reflective metasurfaces are discussed.

基于反射光谱的薄膜光学常数和厚度测试

薄膜的光学常数(折射率、消光系数)和厚度决定了镀膜零件的光学性能,因此根据实际条件掌握薄膜的光学常数和厚度是膜系结构设计和性能优化的重要环节。本文采用傅里叶红外光谱仪测试薄膜样品的反射光谱曲线,通过单纯形优化算法拟合反射光谱曲线,借助不同色散模型,构建目标优化函数,获得薄膜光学常数和厚度,拟合结果与采用椭偏仪测试的结果具有较好的一致性。将拟合得到的薄膜光学参数及厚度代入反射率理论计算模型,通过理论计算模型得到的反射率曲线和实验测试曲线吻合良好,折射率测试结果与计算结果的最大相对误差小于1.8%,厚度测试结果的相对误差不大于0.4%,考虑消光系数的反射光谱拟合曲线与测试曲线相对误差的最大值小于2%。该方法只需测量薄膜的反射光谱曲线,通过计算就能得到薄膜的光学常数及厚度。该方法测试计算简单、精度高、适用范围广,对光学薄膜结构设计、优化和加工具有一定的实际应用价值。

草状氧化铝微结构渐变折射率的计算及实验研究

针对草状氧化铝的微纳结构对折射率的影响,采用台体计算法与柱体计算法计算氧化铝的体积,使用Clausius-Mossotti方程式与MATLAB软件拟合计算微纳结构的折射率变化,使用TFC软件进行拟合,最终计算出草状氧化铝的渐变折射率,研究其微结构的形貌特征及渐变折射率的分布,计算其可见光减反射性能。采用电子束沉积氧化铝薄膜,通过对沉积温度、水煮工艺等参数的优化,获得了不同结构的草状氧化铝纳米薄膜,制备了可见光波段420~680 nm的减反射薄膜。

直角三棱镜补充视角的密封圈缺陷检测研究

为解决三维激光检测中被测物体底面点云无法被高效获取的问题,本文提出了基于直角三棱镜折射原理的补充视角三维点云扫描获取方法。该方法使用直角三棱镜将底面图像折射到侧面,弥补了三维检测的底面检测视角缺失的问题,补充了底面检测视角。本文以密封圈作为缺陷检测对象,采用结构光三维相机采集三维点云。与直接扫描法相比,本方法可以一次性实时、快速地寻找出密封圈完整的表面缺陷,尤其使底面缺陷检测变得更容易,且无需设置特殊的夹取装置或复杂的机械臂等机械结构,仅需增加一块直角三棱镜。实验证实,直角三棱镜补充视角的点云扫描方法能够达到成像要求,对常见的密封圈断裂缺陷与塌陷缺陷均可很好的检出,检测准确率可达到100,满足密封密封圈缺陷检测的需求。

地震宽角反射/折射方法发展述评

本文从地震宽角反射/折射方法的仪器装备、观测系统、观测实验、震相识别、数据分析等主要技术环节的出现、改进、发展、完善,回顾了该方法的百年发展历史.按照我们的见解,将其发展过程分为萌芽期、诞生期、成长期和发展期.对于早期的追溯,重点放在方法的孕育和诞生起到关键作用的人物和事件上,并且尽可能详细;对后期的回顾,聚焦在方法的技术内容的萌发、出现、改进、应用和重点文献等方面,如,何时出现了剖面方法、相遇和追逐观测、地震宽角反射/折射剖面数据的完备性等,成果表述不作为重点,而且叙述简略.述及了天然地震学、地震折射勘探、地震反射勘探、电子技术、通讯技术、测量技术、计算机技术、计算数学等相关学科的进步,对地震宽角反射/折射方法发展的促进作用.展望未来,宽角反射/折射方法在我国深部探测与矿产资源勘查领域大有可为.以此文致敬追寻科学真理的地学前辈.