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.     

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.     

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.     

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.     

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.     

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.     

Fast compressional wave attenuation and dispersion due to conversion scattering into slow shear waves in randomly heterogeneous porous media

Within the viscosity-extended Biot framework of wave propagation in porous media, the existence of a slow shear wave mode with non-vanishing velocity is predicted. It is a highly diffusive shear mode wherein the two constituent phases essentially undergo out-of-phase shear motions (slow shear wave). In order to elucidate the interaction of this wave mode with propagating wave fields in an inhomogeneous medium the process of conversion scattering from fast compressional waves into slow shear waves is analyzed using the method of statistical smoothing in randomly heterogeneous poroelastic media. The result is a complex wave number of a coherent plane compressional wave propagating in a dynamic-equivalent homogeneous medium. Analysis of the results shows that the conversion scattering process draws energy from the propagating wave and therefore leads to attenuation and phase velocity dispersion. Attenuation and dispersion characteristics are typical for a relaxation process, in this case shear stress relaxation. The mechanism of conversion scattering into the slow shear wave is associated with the development of viscous boundary layers in the transition from the viscosity-dominated to inertial regime in a macroscopically homogeneous poroelastic solid.     

Dynamic correlation in wave propagation in random media

Field spectra are analyzed to yield the time-resolved statistics of pulsed transmission through quasi-one-dimensional dielectric media with static disorder. The normalized intensity correlation function with displacement and polarization rotation for an incident pulse of linewidth sigma at delay time t is a function only of the field correlation function, which is identical to that found for steady-state excitation, and of kappa(sigma)(t), the residual degree of intensity correlation at points at which the field correlation function vanishes. The dynamic probability distribution of normalized intensity depends only upon kappa(sigma)(t). Steady-state statistics are recovered in the limit sigma-->0, in which kappa(sigma=0) is the steady-state degree of correlation.