A scattering model for perfectly conducting random surfaces I. Model development

Abstract

The standard integral equation for the surface current is solved iterativcly to obtain an estimate of the surface current on a perfectly conducting randomly rough surface. The far-zone scattered fields and the backscattering coefficients for vertical, horizontal and cross-polarizations are then computed using this current estimate. The polarized backscattering coefficients are explicit functions of the surface parameters and reduce to the Kirchhoff solution in the high-frequency region and to the first-order perturbation solution in the low-frequency region. The cross-polarized scattering coefficient reduces to the second-order perturbation result in the low-frequency region and to zero in the high-frequency limit. A comparison is made with scattering measurements taken under laboratory conditions on a random surface with ka equal to 0-44 and kl equal to 3-25 ( l is the correlation length) It is found that better agreement is obtained with the current model than with the first-order perturbation model in predicting polarized scattering. It is also shown that the separation between VV and HH polarizations decreases gradually with frequency and approaches zero in the high-frequency limit     

A scattering model for perfectly conducting random surfaces II. Range of validity

Abstract

A recent st udy of the range of validity of the surface scattering model by Eftimiu using a two-dimensional surface is re-examined with a more realistic surface correlation function that is everywhere-differentiable and vanishes gradually at infinity. Ii is shown that a sufficient condition on the range of validity is that cos² θ [(kσ)²/(kc)^1/2]exp{?[2kc(1?sinθ)]^1/2} ? 1 where k is the electrical wave-number, 0 is the angle of incidence and a and c are the surface standard deviation and the surface correlation parameter respectively.     

Light scattering from anisotropic, randomly rough, perfectly conducting surfaces

An approach is introduced for performing rigorous numerical simulations of electromagnetic wave scattering from randomly rough, perfectly conducting surfaces. It is based on a surface integral technique, and consists of determining the unknown electric surface current densities from which the electromagnetic field everywhere can be determined. The method is used to study the scattering of a p-polarized beam from an anisotropic Gaussian, randomly rough, perfectly conducting surface. It is demonstrated that the surface anisotropy gives rise to interesting and pronounced signatures in the angular intensity distribution of the scattered light. The origins of these features are discussed.     

Computer programs for application of equations describing elastic and electromagnetic wave scattering from planar interfaces

MATLAB programs are presented which solve equations describing the scattering of plane elastic and electromagnetic waves from a planar interface separating homogenous, isotropic, and semi-infinite geologic media. The PSHSV program calculates and plots amplitude (reflection and refraction/transmission) coefficients, square root energy ratios, energy coefficients, and phase changes for elastic waves of P-, SH- or SV-type incident on an interface between elastic media. The EHEV program calculates and plots amplitude coefficients, square root energy ratios, energy coefficients, and phase changes for electromagnetic waves of EH- or EV-type incident on an interface between dielectric media. The applicability of the programs is demonstrated through the presentation of solutions (plotted as a function of incidence angle) obtained for geologic environments commonly encountered in seismic and ground penetrating radar applications.     

A program to compute EM scattering of plane wave by a perfectly conducting half-plane in a finitely conducting layered half-space

A FORTRAN program utilizing an integral equation calculates 10 field quantities relating to the electromagnetic (EM) scattering of plane wave by a perfectly conducting half-plane buried in a finitely conducting layered half-space. The computing algorithm is executable on a computer of small storage capacity such as PDP 11/40 and as such is useful to many exploration scientists without the facility of a mainframe computer, for computing model curves to interpret field data.     

Electromagnetic scattering from finite conductivity wind-roughened water surfaces

Numerical moment-method calculations of the electromagnetic backscattering from experimentally measured wind-roughened water surfaces that were previously made assuming perfectly conducting surfaces have been repeated taking into account the finite conductivity of sea water. The finite conductivity of the scattering medium was treated using impedance boundary conditions. Comparison with the earlier calculations shows that the backscattering drops slightly at horizontal polarization and much more dramatically at vertical polarization when the finite conductivity is considered. At small and moderate incidence angles, the magnitudes of the scattering drops are consistent with that predicted by the two-scale scattering model. The asymmetry in the upwind and downwind looking scattering that results from the non-uniform distribution of the Braggresonant electromagnetically small-scale waves across the larger scale waves is unaffected by the reduced conductivity at horizontal polarization and reduced very slightly at vertical polarization. The limitations of the two-scale model are essentially the same whether the surface is treatedwith perfect or sea-water conductivity.     

Adaptive contouring of three-dimensional surfaces

An adaptive method of contouring a bivariate surface defined over arbitrarily spaced data in two dimensions is introduced. The method has two stages: 1. Produce a Bézier polynomial surface defined over a union of triangles. 2. Use this surface to compute the required contour levels. Using positional data only, this method produces a C¹-continuous surface and contours which can be made arbitrarily close to being C¹-continuous. The contour is represented as a piecewise linear approximation to the C¹-continuous contour.The method computes a linear representation of the surface in the neighborhood of the contour using an adaptive degree reduction algorithm. This algorithm is used to minimize the number of subdivisions necessary to obtain the desired smoothness of the contour. As a result of this adaptive subdivision, no contours are missed due to the coarseness of the original data points.     

应用ACA算法快速分析导体目标电磁散射特性

提出了一种分析导体目标电磁散射特性的有效数值方法,该方法以矩量法为基础,将自适应交叉近似算法应用于远场组阻抗矩阵的低秩压缩计算,并且结合等效偶极子法加速抽取阻抗矩阵元素的填充。与传统矩量法相比,计算时间和内存消耗都得到了有效缩减,数值结果证明了该方法的精确性和有效性。     

A mesh reconfiguration scheme for speeding up Monte Carlo simulations of electromagnetic scattering by random rough surfaces

Traditional methods of Monte Carlo simulations of random rough surface scattering that use the finite element method involve the generation of multiple meshes for the purpose of taking ensemble averages. We propose a mesh reconfiguration scheme that instead uses a single master mesh. The main idea is to locally modify only the air–surface interface region in the mesh for each instance of a random rough surface. This method achieves a four fold improvement in computation time without any loss of accuracy.     

Electromagnetic wave scattering from the sea surface in the presence of wind wave patterns

The study is concerned with electromagnetic wave (EM) scattering by a random sea surface in the presence of coherent wave patterns. The coherent patterns are understood in a broad sense as the existence of certain dynamical coupling between linear Fourier components of the water wave field. We show that the presence of weakly nonlinear wave patterns can significantly change the EM scattering compared to the case of a completely random wave field. Generalizing the Random Phase Approximation (RPA) we suggest a new paradigm for EM scattering by a random sea surface.

The specific analysis carried out in the paper synthesizes the small perturbation method for EM scattering and a weakly nonlinear approach for wind wave dynamics. By investigating, in detail, two examples of a random sea surface composed of either Stokes waves or horse-shoe (‘crescent-shaped’) patterns the mechanism of the pattern effect on scattering is revealed. Each Fourier harmonic of the scattered EM field is found to be a sum of contributions due to different combinations of wave field harmonics. Among these ‘partial scatterings’ there are phase-dependent ones and, therefore, the intensity of the resulting EM harmonic is sensitive to the phase relations between the wind wave harmonics. The effect can be interpreted as interference of partial scatterings due to the co-existence of several phase-related periodic scattering grids. A straightforward generalization of these results enables us to obtain, for a given wind wave field and an incident EM field, an a priori estimate of whether the effects due to the patterns are significant and the commonly used RPA is inapplicable. When the RPA is inapplicable, we suggest its natural generalization by re-defining the statistical ensemble for water surface. First, EM scattering by an ‘elementary’ constituent pattern should be considered. Each such scattering is affected by the interference because the harmonics comprising the pattern are dynamically linked. Then, ensemble averaging, which takes into account the distribution of the pattern parameters (based on the assumption that the phases between the patterns are random), should be carried out. It is shown that, generally, this interference does not vanish for any statistical ensemble due to dynamical coupling between water wave harmonics. The suggested RPA generalization takes into account weak non-Gaussianity of water wave field m contrast to the traditional RPA which ignores it.     

Wetting of rough three-dimensional superhydrophobic surfaces

Wetting of rough three-dimensional periodic surfaces is studied. The contact angle of liquid with a rough surface (θ) is different from that with a smooth surface (θ₀) due to the difference in the contact area and effect of the air pockets. For non-wetting liquids (θ₀>π/2), the contact angle increases with roughness and may approach the value of π (superhydrophobic surface). For high θ₀, a homogeneous solid-liquid interface, as well as a composite solid-liquid-air interface with air pockets at the valleys of rough surface are possible. These two interfaces correspond to different states of equilibrium and result in different θ. A probability-based approach is introduced to handle the multiple states of equilibrium and to calculate θ. It is found also that increasing droplet size has the same effect as increasing period of roughness (size of asperities). For larger droplets and for larger asperities, the composite interface is less likely. For applications involving liquid’s transport near rough walls of a channel, an analogy between a droplet of non-wetting liquid and a gas bubble in wetting liquid is proposed. In order to increase bubbles mobility, the contact angle and the contact angle hysteresis should be minimized. Practical recommendations for design of superhydrophobic surfaces are formulated.     

三维树木的真实感模拟

为了降低虚拟场景中树木等非规则景物的模拟难度,提出了一种基于L系统的树木模拟方法.针对树木真实感不足的问题,提出了4种改进方法.在阐述了L系统的基本思想的基础上,构造了三维树木模型,引入随机性使树木生成各种形态,模拟了风力影响下的树木形态,通过LOD技术和阴影效果提高了树木绘制的真实感.实验结果表明,该方法可以有效地模拟具有多种形态的树木,同时使树木的真实感更强.     

TBSIM: A computer program for conditional simulation of three-dimensional Gaussian random fields via the turning bands method

The simulation of spatially correlated Gaussian random fields is widespread in geologic, hydrologic and environmental applications for characterizing the uncertainty about the unsampled values of regionalized attributes. In this respect, the turning bands method has received attention among practitioners, for it allows multidimensional simulations to be generated at the CPU cost of one-dimensional simulations.This work provides and documents a set of computer programs for (i) constructing three-dimensional realizations of stationary and intrinsic Gaussian random fields, (ii) conditioning these realizations to a set of data and (iii) back-transforming the Gaussian values to the original attribute units. Such programs can deal with simulations over large domains and handle anisotropic and nested covariance models.The quality of the proposed programs is examined through an example consisting of a non-conditional simulation of a spherical covariance model. The artifact banding in the simulated maps is shown to be negligible when thousands of lines are used. The main parameters of the univariate and bivariate distributions, as well as their expected ergodic fluctuations, also prove to be accurately reproduced.     

A program for perspective views of three-dimensional surfaces

A numerical method is proposed for solving linear differential equations of second order without first derivatives. The new method is superior to de Vogelaere's for this class of equations, and for non-linear equations it becomes an implicit extension of de Vogelaere's method. The global truncation error at a fixed steplength h is bounded by a term of order h⁴, and the interval of absolute stability is [?2.4, 0]. The work of Coleman and Mohamed (1978) is readily adapted to provide truncation error estimates which can be used for automatic error control. It is suggested that the new method should be used in preference to de Vogelaere's for linear equations, and in particular to solve the radial Schrödinger equation. the radial Schrödinger equation.     

调频连续波高度表的计算机仿真

介绍了使用SPW软件对调频连续波高度表进行计算机仿真的情况,包括高度表的工作原理、数学模型的建立和和性能仿真等内容,并给出了定性和定量的仿真结果.仿真主要针对噪声信道和理想信道,在VHF/UHF波段及S波段进行了模拟测高,结果表明工作频率对高度表的测高精度影响不大,但宽带调频高度衷具有更好的测高精度和更强的抗干扰能力.     

Computer simulation of barrier-island migration

Five depositional subenvironments are commonly recognized in barrier island complexes: lower shoreface, middle shoreface, beach-upper shoreface, eolian, and lagoon. Facies belonging to these subenvironments can be characterized in terms of primary structures and sediment attributes. The facies assemblages which occur in the geologic record differ according to strandline still-stand, transgression, or regression and rates of basin subsidence. A FORTRAN program was developed to produce graphic output to aid in understanding facies relationships produced by these controlling parameters.