ON FREE WAVE PROPAGATION IN ANISOTROPIC LAYERED MEDIA

The method of reverberation-ray matrix （MRRM） is extended and modified for the analysis of free wave propagation in anisotropic layered elastic media. A general, numerically stable formulation is established within the state space framework. The compatibility of physical variables in local dual coordinates gives the phase relation, from which exponentially growing functions are excluded. The interface and boundary conditions lead to the scattering relation, which avoids matrix inversion operation. Numerical examples are given to show the high accuracy of the present MRRM.

Reflection Characteristics of Layered Media in Polar Mesopause Related to Polar Mesosphere Summer Echoes

Polar mesosphere summer echoes （PMSE） are very strong radar echoes from alti- tudes close to the polar summer mesopause. The data from sounding rocket campaigns indicate that the radar signal to noise ratio （SNR）, electron density and dust charge density of polar meso- sphere in summer show obvious layered structure. In this paper the theory of wave propagation in layered media is used to study the reflectance and SNR at each layer in polar mesosphere. The calculated SNR using theory of dusty plasma is found in good agreement with the experimental result, which may imply that the intensity of the radar echoes reflected by the layered structure in polar mesosphere where polar mesosphere summer echoes used to occur can interpret partially the phenomenon of PMSE. In other words, reflection may play an important role in the occurrence of PMSE.

DYNAMIC BEHAVIOR OF PILES EMBEDDED IN TRANSVERSELY ISOTROPIC LAYERED MEDIA

Dynamic behavior of single pile embedded in transversely isotropic layered media is investigated using the finite element method combined with dynamic stiffness matrices of the soil derived from Green's function for ring loads. The influence of soil anisotropy on the dynamic behavior of piles is examined through a series of parametric studies.

Surface-borehole electric potential survey in layered media and its applications

The method in which a source is set on the surface and electric potential is received in the borehole is called surface-borehole electric potential technique. Technique of surface-borehole electric potential was employed to study electric response of layered formation. The electric potential was obtained by solving Poisson equation with finite difference method. In the course of calculation, forward modeling wilth finite difference method was realized by adopting bandwidth non-zero storage technique and the incomplete Cholesky conjugate gradient method. The results show that method of surface-borehole can acquire anomalous electric potential corresponding tc geo-electric layers. In addition, application of appropriate mathematical operator can improve the resolution. Moreover, overburden low resistivity layers have severe influence on measuring results of surface-borehole electric potential. However, bottom low resistivity layers play a positive role in the measurement.

Apparent resistivity of azimuthal anisotropy layered media

The electric field, equations of boundary conditions and calculation formula of apparent resistivity are derived for the azimuthal anisotropy layered media with the DC method based on the anisotropic Ohm's law. Taking the Schlumberger symmetric system as an example and using the recurrence formula of nuclear function, the paper theoretically simulates a model of four layers with the same anisotropy coefficient for each layer. The deep sounding curves of resistivity and the pattern of contours are obtained for the model. The results show that the theoretical formula is correct, and the deep sounding curves not only exhibit the difference of resistivity among layers but also indicate the anisotropy characteristics of layers.

INVESTIGATION ON THE SCATTERINGOF ELASTIC WAVES (P OR SV) BY A PLANEINTERFACE CRACK IN LAYERED MEDIA

In this paper, the scattering of elastic waves by a plane interface crack in Layered media is investigated. By Fourier integral transform, the method of transfer matrix is extended to the scattering of elastic waves by a plane interface crack in layered media, and the problems are reduced to a set of dual integral equations in matrix form. As an example, the far field modes of scattering of elastic waves by a plane interface crack in a layered half space have been presented. Amplitudes in far field modes are plotted versus incident wave frequency for several groups of different material combinations, and the numerical results show that resonance peaks occur at some frequencies. The frequencies at which the resonanse peaks occur for P and SV waves are almost the same.

Exponential Convergence Theory of the Multipole and Local Expansions for the 3-D Laplace Equation in Layered Media

In this paper,we establish the exponential convergence theory for the multipole and local expansions,shifting and translation operators for the Green's function of 3-dimensional Laplace equation in layered media.An immediate application of the theory is to ensure the exponential convergence of the FMM which has been shown by the numerical results reported in[27].As the Green's function in layered media consists of free space and reaction field components and the theory for the free space components is well known,this paper will focus on the analysis for the reaction components.We first prove that the density functions in the integral representations of the reaction components are analytic and bounded in the right half complex wave number plane.Then,by using the Cagniard-de Hoop transform and contour deformations,estimates for the remainder terms of the truncated expansions are given,and,as a result,the exponential convergence for the expansions and translation operators is proven.

Stress dependence of elastic wave dispersion and attenuation in fluid-saturated porous layered media

The fluid-saturated porous layered(FSPL)media widely exist in the Earth's subsurface and their overall mechanical properties,microscopic pore structure and wave propagation characteristics are highly relevant to the in-situ stress.However,the effect of in-situ stress on wave propagation in FSPL media cannot be well explained with the existing theories.To fill this gap,we propose the dynamic equations for FSPL media under the effect of in-situ stress based on the theories of poroacoustoelasticity and anisotropic elasticity.Biot loss mechanism is considered to account for the stress-dependent wave dispersion and attenuation induced by global wave-induced fluid flow.Thomsen's elastic anisotropy parameters are used to represent the anisotropy of the skeleton.A plane-wave analysis is implemented on dynamic equations yields the analytic solutions for fast and slow P waves and two S waves.Modelling results show that the elastic anisotropy parameters significantly determine the stress dependence of wave velocities.Vertical tortuosity and permeability have remarkable effects on fast and slow P-wave velocity curves and the corresponding attenuation peaks but have little effect on S-wave velocity.The difference in velocities of two S waves occurs when the FSPL medium is subjected to horizontal uniaxial stress,and the S wave along the stress direction has a larger velocity,which implies that the additional anisotropy other than that induced by the beddings appears due to horizontal stress.Besides,the predicted velocity results have the reasonable agreement with laboratory measurements.Our equations and results are relevant to a better understanding of wave propagation in deep strata,which provide some new theoretical insights in the rock physics,hydrocarbon exploration and stress detection in deep-strata shale reservoirs.

Fast integral equation solver for Maxwell's equations in layered media with FMM for Bessel functions

The paper presents a new fast integral equation solver for Maxwell＇s equations in 3-D layered media. First, the spectral domain dyadic Green＇s function is derived, and the 0-th and the 1-st order Hankel transforms or Sommerfeld-type integrals are used to recover all components of the dyadic Green＇s function in real space. The Hankel transforms are performed with the adaptive generalized Gaussian quadrature points and window functions to minimize the computational cost. Subsequently, a fast integral equation solver with O（N2zNxNy log（NzNy）） in layered media is developed by rewriting the layered media integral operator in terms of Hankel transforms and using the new fast multipole method for the n-th order Bessel function in 2-D. Computational cost and parallel efficiency of the new algorithm are presented.

An Adaptive Finite Element PML Method for the Acoustic Scattering Problems in Layered Media

The paper concerns the numerical solution for the acoustic scattering problems in a two-layer medium.The perfectly matched layer(PML)technique is adopted to truncate the unbounded physical domain into a bounded computational domain.An a posteriori error estimate based adaptive finite element method is developed to solve the scattering problem.Numerical experiments are included to demonstrate the efficiency of the proposed method.

Reconstruction of cylindrically layered media using an iterative algorithm with a stable solution

Abstract The reconstruction of cylindrically layered media is investigated in this article. The inverse problem is modeled using a source-type integral equation with a series of cylindrical waves as incidences, and a conventional Born iterative procedure is modified for solving the integral equation. In the modified iterative procedure, a conventional single-point approximation for the calculation of the field inside media is replaced by a multi-points approximation to improve the numerical stability of its solution. Numerical simulations for different permittivity distributions are demonstrated in terms of artificial scattering data with the procedure. The result shows that the procedure enjoys both accuracy and stability in the numerical computation.

Domain Decomposition for Quasi-Periodic Scattering by Layered Media via Robust Boundary-Integral Equations at All Frequencies

We develop a non-overlapping domain decomposition method(DDM)for scalar wave scattering by periodic layered media.Our approach relies on robust boun-dary-integral equation formulations of Robin-to-Robin(RtR)maps throughout the frequency spectrum,including cutoff(or Wood)frequencies.We overcome the obsta-cle of non-convergent quasi-periodic Green functions at these frequencies by incor-porating newly introduced shifted Green functions.Using the latter in the defini-tion of quasi-periodic boundary-integral operators leads to rigorously stable computations of RtR operators.We develop Nystr̈om discretizations of the RtR maps that rely on trigonometric interpolation,singularity resolution,and fast convergent windowed quasi-periodic Green functions.We solve the tridiagonal DDM system via recursive Schur complements and establish rigorously that this procedure is always completed successfully.We present a variety of numerical results concerning Wood frequencies in two and three dimensions as well as large numbers of layers.

Non-Darcy flows in layered porous media(LPMs)with contrasting pore space structures

Compared to single layer porous media,fluid flow through layered porous media(LPMs)with contrasting pore space structures is more complex.This study constructed three-dimensional(3-D)pore-scale LPMs with different grain size ratios of 1.20,1.47,and 1.76.The flow behavior in the constructed LPMs and single layer porous media was numerically investigated.A total of 178 numerical experimental data were collected in LPMs and single layer porous media.In all cases,two different flow regimes(i.e.,Darcy and Non-Darcy)were observed.The influence of the interface of layers on Non-Darcy flow behavior in LPMs was analyzed based pore-scale flow data.It was found that the available correlations based on single layer porous media fail to predict the flow behavior in LPMs,especially for LPM with large grain size ratio.The effective permeability,which incorporated the influence of the interface is more accurate than the Kozeny-Carman equation for estimating the Darcy permeability of LPMs.The inertial pressure loss in LPMs,which determines the onset of the Non-Darcy flow,was underestimated when using a power law expression of mean grain size.The constant B,an empirical value in the classical Ergun equation,typically equals 1.75.The inertial pressure loss in LPMs can be significantly different from it in single lager porous media.For Non-Darcy flow in LPMs,it is necessary to consider a modified larger constant B to improve the accuracy of the Ergun empirical equation.

Experimental investigation on rainfall infiltration and solute transport in layered porous and fractured media

Layered structures with upper porous and lower fractured media are widely distributed in the world. An experimen- tal investigation on rainfall infiltration and solute transport in such layered structures can provide the necessary foundation for effectively preventing and forecasting water bursting in mines, controlling contamination of mine water, and accomplishing ecological restoration of mining areas. A typical physical model of the layered structures with porous and fractured media was created in this study. Then rainfall infiltration experiments were conducted after salt solution was sprayed on the surface of the layered structure. The volumetric water content and concentration of chlorine ions at different specified positions along the profile of the experiment system were measured in real-time. The experimental results showed that the lower fractured media, with a considerably higher permeability than that of the upper porous media, had significant effects on preventing water infil- tration. Moreover, although the porous media were homogeneous statistically in the whole domain, spatial variations in the features of effluent concentrations with regards to time, or so called breakthrough curves, at various sampling points located at the horizontal plane in the porous media near the porous-fractured interface were observed, indicating the diversity of solute transport at small scales. Furthermore, the breakthrough curves of the outflow at the bottom, located beneath the underlying fractured rock, were able to capture and integrate features of the breakthrough curves of both the upper porous and fractured media, which exhibited multiple peaks, while the peak values were reduced one by one with time.

Dispersion function of Rayleigh waves in porous layered half-space system

Rayleigh wave exploration is based on an elastic layered half-space model. If practical formations contain porous layers, these layers need to be simplified as an elastic medium. We studied the effects of this simplification on the results of Rayleigh wave exploration. Using a half-space model with coexisting porous and elastic layers, we derived the dispersion functions of Rayleigh waves in a porous layered half-space system with porous layers at different depths, and the problem of transferring variables to matrices of different orders is solved. To solve the significant digit overflow in the multiplication of transfer matrices, we propose a simple, effective method. Results suggest that dispersion curves differ in a low- frequency region when a porous layer is at the surface; otherwise, the difference is small.

Seismic Waves in a Layered Half-Space from an Arbitrary Buried Source

In this paper, a transfer matrix and a three-dimensional dynamic response of a layered half-space to an arbitrary buried source are derived with the aid of a technique which combines the Laplace and two-dimensional Fourier transforms in a rectangular coordinate system. This method is clear in concept, and the corresponding formulas given in the paper are simple and convenient for marine seismic prospecting and other fields' applications. An example is presented and the calculated results are in good agreement with those of the finite element method (FEM).

Measurement of Attenuation of Ultrasonic Propagating through the Thin Layer Media with Time Delay Spectrum

The ultrasonic attenuation coefficient is one of the most important acoustic parameters to character the performance of a thin layer media, but it can not be measured due to mutual superposition of multiple reflected waves at the same interface in ultrasonic testing. Ultrasonic pulse echo and lamb wave to evaluate the thin layer media can not obtain attenuation coefficient at present. In this paper, analytical method was used to study the acoustics characteristic of thin layer media with the ultrasonic echo testing. Meanwhile, the process of ultrasonic attenuation measurement was presented. Simulation and experimental investigation is focused on a thin layer of rubber. Attenuation coefficient was introduced and evaluation mathematics model was established by the two echoes cross-correlation with and without the thin layer media based on the time delay spectrum. It involved the parameters related to the acoustic properties of the thin layer media. Through calculating the sound velocity and acoustic impedance with the evaluation model, it can deduce the relation between the attenuation coefficient and the frequency. Through analyzing the simulation results, it indicated that the attenuation coefficients were invariable with the varying of the frequency. However, the attenuation coefficients increased with the frequency increasing by ultrasonic testing the thin layer of rubber. The reason was that the attenuation factor was not taken into account during the simulation. This method overcomes shortcomings that the traditional ultrasonic testing can not evaluate the thin layer media whose thickness is less than motivation wavelength. It is a new solution to study the attenuation characteristic and on-line nondestructive evaluation in the thin layer media.

Study on electric variations of media in epicentral area by geomagnetic transfer functions

Taking the graph of the apparent resistivity Pyx in Lanzhou area, its geomagnetic transfer function variations andthe investigation of moderate-strong local earthquakes as example and from.the viewpoint of seismomagnetic effect,the authors found that subterranean conductivity values might be applied to the division of Lanzhou areafrom the surface downward into four layers, i. e., the anomalous, the transitional,the non-anomalous and theanomalous layer. Only the transfer function modular |A| and |B|,magnetic azimuth ap with its variance ap,and the total variance yi in the anomalous layers showed obvious anomalies with time changes. Thus, it could beconjectured that the anomalous layer was closely associated with the anisotropic variations of conductivity of thesubterranean media in the seismicity area.This phenomenon might provide a way to the further study of itsmechanism. It is needed to study the inherent connotation deeply.

Analytical solutions for dynamic pressures of coupling fluid-solid-porous medium due to P wave incidence

Wave reflection and refraction in layered media is a topic closely related to seismology,acoustics,geophysics and earthquake engineering.Analytical solutions for wave reflection and refraction coefficients in multi-layered media subjected to P wave incidence from the elastic half-space are derived in terms of displacement potentials.The system is composed of ideal fluid,porous medium,and underlying elastic solid.By numerical examples,the effects of porous medium and the incident wave angle on the dynamic pressures of ideal fluid are analyzed.The results show that the existence of the porous medium,especially in the partially saturated case,may significantly affect the dynamic pressures of the overlying fluid.

A note on the equivalence of three major propagator algorithms for computational stability and efficiency

It is shown in this note that the three methods, the orthonormalization method, the minor matrix method and the recursive reflection-transmission matrix method are closely related and solve the numerical instability in the original Thomson-Haskell propagator matrix method equally well. Another stable and efficient method based on the orthonormalization and the Langer block-diagonal decomposition is presented to calculate the response of a horizotttal stratified model to a plane, spectral wave. It is a numerically robust Thomson-Haskell matrix method for high frequencies, large layer thicknesses and horizontal slownesses. The technique is applied to calculate reflection-transmission coefficients, body wave receiver functions and Rayleigh wave dispersion.