The computations of reflection coefficients of multilayer structure based on the reformulation of Thomson-Haskell method

A reformulation of the Thomson-Haskell method is presented for calculating the reflection coefficients of multilayer structure immersing in the coupling fluid. Instead of directly multiplying the layer propagator matrix, the new method splits the layer propagator matrix and excursively determines the interface stiffness matrix starting from the bottom half-space with known stiffness. A formulation for the reflection coefficients is derived based on the obtained interface stiffness matrix of the top layer. This scheme can be applied to a single solid layers or layered structures containing both fluid and solid layers. It keeps the simplicity but naturally excludes the exponential growth term and thus can be applied at any frequency range. Its validity and feasibility were experimentally proved by the measurement of the reflection coefficients of a three layered structure of aluminum–glass–aluminum and a sandwiched layer structure of two 250 μm stainless plates filled with 100 μm deionized water based on the inversion of V(z, t) technique. The result of experiments is consistent with the theoretical calculation. The reformulation of the Thomson-Haskell method offers an efficient and effective solution for calculating the acoustic reflection coefficients of multilayer structures of any configurations.     

Full wave-field reflection coefficient inversion

This paper develops a Bayesian inversion for recovering multilayer geoacoustic (velocity, density, attenuation) profiles from a full wave-field (spherical-wave) seabed reflection response. The reflection data originate from acoustic time series windowed for a single bottom interaction, which are processed to yield reflection coefficient data as a function of frequency and angle. Replica data for inversion are computed using a wave number-integration model to calculate the full complex acoustic pressure field, which is processed to produce a commensurate seabed response function. To address the high computational cost of calculating short range acoustic fields, the inversion algorithms are parallelized and frequency averaging is replaced by range averaging in the forward model. The posterior probability density is interpreted in terms of optimal parameter estimates, marginal distributions, and credibility intervals. Inversion results for the full wave-field seabed response are compared to those obtained using plane-wave reflection coefficients. A realistic synthetic study indicates that the plane-wave assumption can fail, producing erroneous results with misleading uncertainty bounds, whereas excellent results are obtained with the full-wave reflection inversion.     

广义反透射系数的物理意义

一种体系化的高效率的算法被广泛应用于分层均匀介质中有源波动方程的数值计算,它能够计算出所考察时间窗内的全波震相;该算法的关键之处,便是应用了广义反透射系数方法,广义反透射系数包含所有层间分界面反透射波及转换波的影响.本文利用图示及级数展开方法,对其物理含义进行了较为深入的分析,这对于更好地理解理论波场的合成,有较好的参考意义.     

Geoacoustic inversion based on reflection model of effective density fluid approximation

In order to obtain the physical and geoacoustic properties of marine sediments,an inverse method using reflection loss of different grazing angles is presented.The reflection loss is calculated according to the reflection model of effective density fluid approximation.A two-step hybrid optimization algorithm combining differential evolution and particle swarm optimization along with Bayesian inversion is employed in estimation of porosity,mean grain size,mass density and bulk modulus of grains.Based on the above physical parameters,geoacoustic parameters,including sound speed and attenuation,are further calculated.According to the numerical simulations,we can draw a conclusion that all the parameters can be well estimated with the exception of bulk modulus of grains.In particular,this indirect inverse method for bottom geoacoustic parameters performs high accuracy and strong robustness.The relative errors are 0.092%and 17%,respectively.Finally,measured reflection loss data of sandy sediments at the bottom of a water tank is analyzed,and the estimation value,uncertainty and correlation of each parameter are presented.The availability of this inverse method is verified through comparison between inverse results and part of measured parameters.     

Reconstruction of the Sea Bottom Parameters for Coherent Seismoacoustic Sounding: I. Decision Rules

We have developed an algorithm for reconstructing the geoacoustic parameters of bottom layers using parametric models of the formation of signals reflected from a layered halfspace during coherent sounding of the bottom of a sea shelf. We propose a method for layer-by-layer reconstruction that makes it possible to efficiently search for a solution in the multiparameter space with limited a priori data.     

基于等效密度流体近似反射模型反演海底参数

为了获取海底沉积物的物理和地声特性,根据等效密度流体近似反射模型得到的不同掠射角下的海底反射损失,利用差分进化算法和粒子群算法相结合的两级混合优化算法以及Bayesian反演方法对海底沉积物的孔隙度、平均颗粒粒度、颗粒质量密度以及颗粒体积弹性模量进行反演,再根据这4个物理参数的估计值进一步计算出海底地声参数,包括声速和衰减。通过反演结果与仿真真值的比较可以看出,除颗粒体积弹性模量外,得到的估计结果是令人满意的,特别是这种间接反演海底地声参数的方法对地声参数的估计具有较高的精确性和较强的稳健性,相对误差分别为0.092%和17%。最后,对实验室水池池底沙质沉积物的反射损失数据进行处理,给出了沙质沉积物各参数的估计值、不确定性和相关性,并通过反演结果与部分实测参数值的比较验证了反演方法的可行性。      

Subbottom profiling using a ship towed line array and geoacoustic inversion

Bottom profiling traditionally uses broadband signals received on a line array at long ranges to estimate the bottom layer structure and thickness. In this paper, a subbottom profiling method is developed and applied to a ship-towed line array using the same ship towed source to estimate the subbottom layer structure and thickness. A ship towed line-array system can be used to estimate bottom properties using geoacoustic inversion and can cover a wide area in a short time. It needs some prior information about the subbottom structure and layer thickness, without which the solution can be ambiguous and even erratic when resolving parameters over a wide area. It is shown that the required subbottom information can be obtained from the time-angle relation by beamforming the same acoustic signal data used for geoacoustic inversion. The time-angle analysis is used to expose the prevalent physics intrinsic to geoacoustic inversion. One finds that the tau-p relation of the bottom and the bottom reflection coefficients, sampled at discrete angles associated with bottom and multiple surface-bottom returns, are often adequate, for many practical applications, to uniquely determine the geoacoustic bottom at low (< or =1 kHz) frequencies.     

An accurately fast algorithm of calculating reflection/transmission coefficients

For the boundary between transversely isotropic media with a vertical axis of symmetry (VTI media), the interface between a liquid and a VTI medium, and the free-surface of an elastic half-space of a VTI medium, an accurately fast algorithm was presented for calculating reflection/transmission (R/T) coefficients. Specially, the case of post-critical angle incidence was considered. Although we only performed the numerical calculation for the models of the VTI media, the calculated results can be extended to the models of transversely isotropic media with a horizontal axis of rotation symmetry (HTI media). Compared to previous work, this algorithm can be used not only for the calculation of R/T coefficients of the boundary between ellipsoidally anisotropic media, but also for that between generally anisotropic media, and the speed and accuracy of this algorithm are faster and higher. According to the anisotropic parameters of some rocks given by the published literature, we performed the calculation of R/T coefficients by using this algorithm and analyzed the effect of the rock anisotropy on R/T coefficients. We used Snell’s law and the energy balance principle to perform verification for the calculated results. Supported by the Natural Science Foundation of Shaanxi Province, China (Grant No. 2007D15)     

Reflection characterization of multilayer surface films

The reflection of linearly polarized light from a multilayer system of ultrathin dielectric surface films is investigated both analytically in the long-wavelength limit and numerically by the standard way of calculating the reflection characteristics for the layered medium. The second-order approximate formulas for reflection coefficients and characteristic reflection angles are derived and their accuracy is estimated. It is shown that approximate expressions obtained for reflection parameters of multilayer system in the long-wavelength limit are of immediate interest to the solution of the inverse problem for ultrathin layered surface structures. Innovative possibilities for optical diagnostics are generated by means of polarizing and principal angles. For determining the parameters of multiple surface layers an appropriate method is found by combining differential reflectance with ellipsometry.     

基于等效密度流体模型的地声参数分析

目前的地声参数反演多采用液态海底模型,但是实际海底为多孔弹性海底。该文在等效密度流体模型基础上,通过计算液态海底和多孔弹性海底的反射系数及传播损失,给出了等效密度流体模型和液态海底模型的等效性分析。数值仿真结果表明在低频情况下,多孔弹性海底给出的快纵波声速与等效密度流体模型给出的声速以及等效密度流体的实部与真实的海底密度基本一致。将等效密度流体模型近似看作液态海底模型进行反射系数和传播损失计算,在小掠射角和远距离时,计算结果表明与多孔弹性海底计算结果具有较好一致性,从而以此为依据确定海底为液态,进行地声参数反演。     

Coherent transmission and reflection of a two-dimensional planar photonic crystal

A method for modeling the radial distribution function for particles of a two-dimensional planar photonic crystal in the form of a monolayer of spatially ordered monodisperse spherical particles is proposed. The coherent transmission and reflection coefficients for layers under normal illumination are calculated in the quasi-crystalline approximation of the multiple wave scattering theory. The dependence of the coherent transmission and reflection of the layer on the degree of ordering of the spherical particles is investigated. The influence of the long-range order on the coherent transmission and reflection coefficients for layers with triangular, square, and hexagonal lattices is estimated. Monolayers of weakly absorbing dielectric and strongly absorbing metallic particles are considered.     

双相多孔锂离子电池液/固界面的声反射与声透射

采用传递矩阵法,同步联立改进的Biot理论,对含液固界面的双相多孔锂离子电池的超声反射与透射系数进行理论求解。考虑锂离子的摇摆特性对电极力学性能的影响,计算了对应状态下液/固界面的双相多孔锂离子电池声反射及透射系数的角度谱与频率谱。同时,构建了不同荷电状态时含单元锂离子电池的频域仿真模型,以萃取对应的超声反射及透射角度谱及频率谱,并与理论计算结果对比吻合良好。随后,以多单元锂离子电池为例,在不同的荷电状态下,分析了反射与透射系数随斜入射角度、入射波频率的变化关系,并分别指出了其角度谱及频率谱特征点随荷电状态的变化特征,为锂离子电池运行状态的超声无损测量提供了理论基础。     

利用海底反射信号进行地声参数反演的方法

针对现有反演方法的缺点,提出了一种基于海底反射信号的地声参数高分辨反演方法.它利用短距离声源在不同深度上发射宽带线性调频信号,采用垂直阵进行接收,首先通过匹配滤波方法提取多径到达信息,然后利用海底反射损失曲线,反演海底表层的声速和密度,最后利用浅底层反射信号估计沉积层参数.由于海水中直达波受到内波的强烈影响,选择海底表面反射作为参考,用以可靠地计算浅底层反射的相对到达时间和幅度,从而估计出沉积层的厚度、速度和衰减系数.通过海上实验,验证了利用浅底层反射信号反演参数的有效性. 关键词： 海底参数 反演 浅底层反射信号     

Studies of the ocean-bottom reflection coefficient at angles of total internal reflection

For practical-purpose studies in underwater acoustics, a new method is proposed to determine the bottom reflection coefficient on the basis of multiple bottom-surface reflections. The method allows one to obtain the angular dependence of the bottom reflection coefficient at grazing angles from several degrees to several tens of degrees in the audio and infrasonic frequency bands. The sound field structure is studied in deep-water regions of the Black (2000 m) and Arabian (4000 m) seas at frequencies within 10–400 Hz. For the regions under investigation, the frequency-angular dependence of the reflection coefficient is obtained with the use of the proposed method. The data for the Black Sea are compared with those provided by the conventional method based on the use of single and double bottom and bottom-surface reflections. Experimental data on the values and variations of the bottom reflection coefficient are presented for different deepwater and shallow-water regions of the World Ocean. The presence of shear waves in the bottom sediments is revealed, and the effect of these waves on the frequency-angular dependence of the reflection coefficient is demonstrated.     

Optical reflection from dielectric layers containing metal particles formed by ion implantation

Dielectric layers with silver nanoparticles, which are synthesized in a soda-silicate glass by implantation of 60-keV ions with a dose of 7.0×10¹⁶ Ag⁺/cm² at an ion current density of 10 μmA/cm², are analyzed. The depth of silver distribution was measured by Rutherford backscattering. Data on optical characteristics of composite layers were obtained from the transmission spectra and from the reflection, which were measured both from the side of an implanted glass surface and from the unimplanted side. To calculate reflection spectra, a multilayer plane-parallel film structure was considered, which was modeled on the basis of the matrix method using complex Fresnel coefficients. Dielectric functions of separate layers were determined using the Maxwell-Garnet theory of an effective medium. A qualitative agreement between the experimental and the model optical spectra was obtained taking into account a nonuniform depth distribution of metal nanoparticles in a composite material.     

Elastic resonances of a periodic array of fluid-filled cylindrical cavities embedded in an elastic matrix

The resonant scattering by a periodic infinite array of fluid-filled cylindrical cavities in an elastic matrix is studied. The exact reflection and transmission coefficients of the array are calculated by means of a multiple scattering formalism taking into account all the interactions between the cavities. Numerical results are next given for low frequencies for which only the longitudinal and transverse zero modes propagate. A first study based on the analysis of the transmission coefficients clearly shows that the resonances of the array can be classified into two sets: those close to the resonances of a single cavity and those due to a resonant coupling between a cavity and its nearer neighbors. The resonant coupling is due to the interaction between the whispering-gallery surface waves propagating around each cavity. In the case of cavities with very close spacing, it is observed that the dispersion curves of the waves propagating along the array can also be classified into two sets: those with a positive group velocity have cut-off frequencies that correspond to the resonances of a single cavity, those with a negative group velocity have cut-off frequencies that correspond to the resonances resulting from the strong coupling. A new method for the analysis of the resonances is presented. It is based on the properties of the scattering matrix and consists in studying the resonant eigenvalues of the scattering matrix of the array once the background is removed. For the detection of very fine resonances, as well as in the separation of several resonances very close to each other, this method proves to be more efficient than one based on the analysis of the reflection and transmission coefficients.     

Total reflection X-ray fluorescence spectrometry for quantitative surface and layer analysis

Measurements of X-ray fluorescence spectra versus grazing incident angles provide information on elemental composition as well as density and thickness of near surface layers. Calculations of fluorescence intensities are presented, which are used for the evaluation of data obtained by total reflection X-ray fluorescence (TXRF) spectrometry. The calculation is based on a matrix formalism to account for standing wave phenomena due to transmission and reflection in layered material. For the determination of concentrations the model makes additional use of the fundamental parameter technique in order to include absorption and enhancement effects of the fluorescence radiation. On the basis of experimental data some capabilities of this nondestructive and contactless probing technique are presented.     

Electromagnetic wave transmission and reflection by a quasi-periodic layered semiconductor structure

The specific features of electromagnetic wave reflection and transmission through the periodic and quasi-periodic layered semiconductor structures placed into a parallel plate waveguide are studied. The effect of the structure parameters and dissipation in semiconductor layers on the reflectance (transmittance) of electromagnetic wave is examined. The comparative analysis of the electromagnetic wave reflectance characteristics in the structures with different types of symmetry is carried out.     

Resolving meso-scale seabed variability using reflection measurements from an autonomous underwater vehicle

Seabed geoacoustic variability is driven by geological processes that occur over a wide spectrum of space-time scales. While the acoustics community has some understanding of horizontal fine-scale geoacoustic variability, less than O(10(0)) m, and large-scale variability, greater than O(10(3)) m, there is a paucity of data resolving the geoacoustic meso-scale O(10(0)-10(3)) m. Measurements of the meso-scale along an ostensibly "benign" portion of the outer shelf reveal three classes of variability. The first class was expected and is due to horizontal variability of layer thicknesses: this was the only class that could be directly tied to seismic reflection data. The second class is due to rapid changes in layer properties and/or boundaries, occurring over scales of meters to hundreds of meters. The third class was observed as rapid variations of the angle/frequency dependent reflection coefficient within a single observation and is suggestive of variability at scales of meter or less. Though generally assumed to be negligible in acoustic modeling, the second and third classes are indicative of strong horizontal geoacoustic variability within a given layer. The observations give early insight into possible effects of horizontal geoacoustic variability on long-range acoustic propagation and reverberation.     

Modeling elastic wave forward propagation and reflection using the complex screen method.

Formulation for calculating forward propagation and reflection in a 3D elastic structure based on the complex-screen method is given in this paper. The calculation of reflections is formulated based on the local Born approximation. When using a small angle approximation, the backscattering operator reduces to a screen operator which is similar to the forward screen propagator. Combining the forward propagator and backscattering operator together, the new method can properly handle the multiple forward scattering and single backscattering in a 3D heterogeneous model. Using a dual-domain technique, the new method is highly efficient in CPU time and memory savings. For models where reverberation and resonance scattering can be neglected, this method provides a fast and accurate algorithm. Synthetic seismograms for two-dimensional elastic models are calculated with this method and compared with those generated by the finite-difference method. The results show that the method works well for small to medium scattering angles and medium velocity contrasts.