一种处理色散介质问题的通用时域有限差分方法

色散介质的介电系数是频率的函数,使本构关系在时域成为卷积关系.这就给用时域有限差分方法计算色散介质中波的散射和传播带来了困难.现有算法往往要针对不同色散介质模型推导相应的递推公式,算法的通用性较差.本文完善和发展了移位算子-时域有限差分方法,使之成为一种处理色散介质电磁问题的通用方法.首先,证明了常见的三种色散介质模型(德拜模型、洛伦兹模型和德鲁模型)的介电系数均可以写成适于移位算子法计算的有理分式函数形式.然后,用/t代替jω,过渡到时域,再引入时域移位算子z_t代替时间微分算子来处理有理分式函数形式的介电系数,给出离散时域本构关系的表示式,进而导出时域有限差分方法当中电位移矢量和电场强度之间的关系.最后,计算了几种色散介质的电磁散射,数值结果表明了本文方法和程序的通用性和正确有效性. 关键词： 时域有限差分方法 色散介质 移位算子     

Wave dispersion and attenuation in viscoelastic isotropic media containing multiphase flow and its application

In this paper,we introduce the complex modulus to express the viscoelasticity of a medium.According to the correspondence principle,the Biot-Squirt(BISQ)equations in the steady-state case are presented for the space-frequency domain described by solid displacements and fluid pressure in a homogeneous viscoelastic medium.The effective bulk modulus of a multiphase flow is computed by the Voigt formula,and the characteristic squirt-flow length is revised for the gas-included case.We then build a viscoelastic BISQ model containing a multiphase flow.Through using this model,wave dispersion and attenuation are studied in a medium with low porosity and low permeability.Furthermore,this model is applied to observed interwell seismic data.Analysis of these data reveals that the viscoelastic parameter tanδ is not a constant.Thus,we present a linear frequency-dependent function in the interwell seismic frequency range to express tanδ.This improves the fit between the observed data and theoretical results.     

Power propagation in homogeneous isotropic frequency-dispersive left-handed media

We study transmission at a boundary between a right-handed medium (RHM: epsilon>0, mu>0) and a frequency dispersive left-handed medium [LHM: epsilon(omega)<0, mu(omega)<0 for some omega], both homogeneous and isotropic. In order to account for the dispersion, two types of signal spectra are considered. The first consists of two discrete frequencies, while the second is Gaussian. Explicit expressions for the time-domain fields are obtained, from which the time-averaged Poynting vectors and hence power flow vectors are calculated. In both cases, we find that waves refract at negative angles at a RHM-LHM interface.     

Reduction in the dispersion in the magnetoelastic wave propagation time in yttrium-iron and yttrium-iron-gallium garnet single crystals

The distribution of the internal magnetic field corresponding to a fixed frequency-independent delay is computed in the stage theory approximation. Conditions for the realization of an electrically controlled delay time with minimum dispersion in the whole control range are analyzed. Experimental results obtained on yttrium-iron and yttrium-iron-gallium garnets (YIG and YIGG) magnetized by an inhomogeneous external magnetic field are presented. The mean value of the dispersion was 0.5 sec/GHz in the 2–5 GHz range.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp, 107–111, July, 1979.The authors are grateful to L. N. Bezmaternykh for useful discussions of this paper and to G. I. Shvartsman for providing the single crystals.     

线性黏弹性各向异性介质速度频散和衰减特征研究

地层岩石既非各向同性的,也非完全弹性的,正确地描述波在地层中的传播需要搞清楚岩石的各向异性和黏弹性特征.针对裂缝性地层的裂缝发育方位问题,建立具有任意方位角的方位各向异性黏弹性本构关系.使用均匀平面简谐波分析方法研究其频散关系,得到Christoffel方程,进而获得均匀平面波的复速度、相速度、衰减系数和品质因子的表达式.通过黏弹性方位各向异性页岩和砂岩进行模拟,研究了波场在地层中的传播特征,如相速度、衰减系数和品质因子等随频率、方位和入射角的变化关系 关键词： 黏弹性 各向异性 相速度 衰减系数 品质因子     

Time domain numerical modeling of wave propagation in 2D heterogeneous porous media

This paper deals with the numerical modeling of wave propagation in porous media described by Biot’s theory. The viscous efforts between the fluid and the elastic skeleton are assumed to be a linear function of the relative velocity, which is valid in the low-frequency range. The coexistence of propagating fast compressional wave and shear wave, and of a diffusive slow compressional wave, makes numerical modeling tricky. To avoid restrictions on the time step, the Biot’s system is splitted into two parts: the propagative part is discretized by a fourth-order ADER scheme, while the diffusive part is solved analytically. Near the material interfaces, a space–time mesh refinement is implemented to capture the small spatial scales related to the slow compressional wave. The jump conditions along the interfaces are discretized by an immersed interface method. Numerical experiments and comparisons with exact solutions confirm the accuracy of the numerical modeling. The efficiency of the approach is illustrated by simulations of multiple scattering.     

Experimental study of wave dispersion and attenuation in concrete

Results from an experimental study concerning wave propagation in cementitious materials are presented in this paper. Narrow band pulses at several frequencies were introduced into specimens of cement paste, mortar and concrete allowing direct measurement of longitudinal wave velocities and amplitude for each frequency. It is shown that aggregate content play an important role in wave propagation increasing considerably the wave velocity, while the aggregate size seems to control the attenuation observed. Slight velocity variations observed with frequency are discussed in relation to the degree of inhomogeneity of the materials.     

Electromagnetic wave propagation in random media

The propagation of a narrow frequency band beam of electromagnetic waves in a medium with randomly varying index of refraction is considered. A novel formulation of the governing equation is proposed. An equation for the average Green function (or transition probability) can then be derived. A Fokker-Planck type equation is contained as a limiting case. The results are readily generalized to include the features of the random coupling model and it is argued that the present problem is particularly suited for an analysis of this type.     

Anomalous wave propagation in quasiisotropic media

Based on boundary conditions and dispersion relations, the anomalous propagation of waves incident from regular isotropic media into quasiisotropic media is investigated. It is found that the anomalous negative refraction, anomalous total reflection and oblique total transmission can occur in the interface associated with quasiisotropic media. The Brewster angles of E- and H-polarized waves in quasiisotropic media are also discussed. It is shown that the propagation properties of waves in quasiisotropic media are significantly different from those in isotropic and anisotropic media.     

A surface wave dispersion relation for non-local media

Conditions are obtained for the existence of surface waves at the interface of vacuum and a semi-infinite non-local medium whose inverse dielectric function is assumed to be symmetric in spatial coordinate in the direction perpendicular to the interface. It is shown that these conditions reduce to those obtained by Maradudin in the appropriate limits: for the isotropic case; and for no retardation.     

沙尘大气电磁波多重散射及衰减

为了使干旱沙漠地区的电子系统能够全天候的工作, 必须开展沙尘大气的电磁波多重散射及衰减特性研究. 根据Mie理论、沙尘大气粒子尺寸分布和能见度的关系得到了电磁波沙尘大气传播衰减的计算方法, 计算了不同沙尘大气能见度的37 GHz电磁波的衰减, 与其他经验公式及文献中的实验结果进行比较, 文中方法得到的结果更接近于测量结果. 为了研究较低能见度沙尘暴中电磁波的传播特性, 需研究沙尘大气的多重散射效应. 应用Monte Carlo模拟方法, 在沙尘粒子为干燥和5%水含量时, 模拟了37 GHz和93 GHz电磁波在沙尘大气中传播时考虑多重散射效应的衰减, 并与基于Mie理论的计算结果进行比较, 结果显示, 在37 GHz时, 沙尘大气的多重散射对衰减的影响小, 在93 GHz时多重散射显著, 沙尘大气能见度越低, 多重散射的影响越显著. 粒子水含量增加使电磁波的衰减显著增大, 对多重散射的影响不明显. 因此, 在相同大气能见度下, 沙尘天气越干燥, 多重散射影响越大, 电磁波衰减减小越显著.     

Small amplitude wave propagation in stratified media

Four mutually connected first order linear differential equations for a system of two waves — constituting a set of mathematical models are developed. Small amplitude wave propagation through stratified media have been studied using the mathematical models. Limiting wave solutions are identified as WKB solutions.One of the authors (M.Khan) acknowledges the support of the University Grants Commission (India).     

Modeling of wave propagation in inhomogeneous media

We present a methodology providing a new perspective on modeling and inversion of wave propagation satisfying time-reversal invariance and reciprocity in generally inhomogeneous media. The approach relies on a representation theorem of the wave equation to express the Green function between points in the interior as an integral over the response in those points due to sources on a surface surrounding the medium. Following a predictable initial computational effort, Green's functions between arbitrary points in the medium can be computed as needed using a simple cross-correlation algorithm.