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.

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.

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.

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.

Three-Dimensional Convection in an Inclined Porous Layer Subjected to a Vertical Temperature Gradient

In this paper,we study the onset and development of three-dimensional convection in a tilted porous layer saturated with a liquid.The layer is subjected to a gravitational field and a strictly vertical temperature gradient.Typically,problems of thermal convection in tilted porous media saturated with a liquid are studied by assuming constant different temperatures at the boundaries of the layer,which prevent these systems from supporting conductive(non-convective)states.The boundary conditions considered in the present work allow a conductive state and are representative of typical geological applications.In an earlier work,we carried out a linear stability analysis of the conductive state.It was shown that at any layer tilt angles,the most dangerous type of disturbances are longitudinal rolls.Moreover,a non-zero velocity component exists in z-direction.In the present work,threedimensional non-linear convection regimes are studied.The original three-dimensional problem is reduced to two-dimensional one with an analytical expression for the velocity z-component v_(z)=v_(z)(x,y).It is shown that the critical Rayleigh number values obtained through numerical solutions of the obtained 2D problem by a finite difference method for different layer inclination angles,are in a good agreement with those predicted by the linear theory.The number of convective rolls realized in nonlinear calculations also fits the linear theory predictions for a given cavity geometry.Calculations carried out at low supercriticalities show that a direct bifurcation takes place.With increasing supercriticality,no transitions to other convective regimes are detected.The situation studied in this problem can be observed in oil-bearing rock formations under the influence of a geothermal temperature gradient,where the ensuing fluid convection can affect the distribution of oil throughout the layer.

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.

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.

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.

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.

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.

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.

Perfectly matched layer implementation for ADI-FDTD in dispersive media

Alternating direction implicit finite difference time domain （ADI-FDTD） method is unconditionally stable and the maximum time step is not limited by the Courant stability condition, but rather by numerical error. Compared with the conventional FDTD method, the time step of ADI-FDTD can be enlarged arbitrarily and the CPU cost can be reduced. 2D perfectly matched layer （PML） absorbing boundary condition is proposed to truncate computation space for ADI-FDTD in dispersive media using recursive convolution（RC） method and the 2D PML formulations for dispersive media are derived. ADI-FDTD formulations for dispersive media can be obtained from the simplified PML formulations. The scattering of target in dispersive soil is simulated under sine wave and Gaussian pulse excitations and numerical results of ADI-FDTD with PML are compared with FDTD. Good agreement is observed. At the same time the CPU cost for ADI-FDTD is obviously reduced.

Degradation of AZ31 and AZ91 magnesium alloys in different physiological media:Effect of surface layer stability on electrochemical behaviour

This work deals with the degradation of AZ31 and AZ91 magnesium alloys when they are exposed to three types of physiological media for seven days at 37°C:Ringer's,Hanks\and simulated body fluid(SBF)solutions.A combination of immersions tests and surface characterisation methods were employed to evaluate the attack on the surface,and the stability of the formed corrosion product layers for each alloy/electrolyte system.Measurements of the Mg-ion released into the electrolytes were also carried out in order to be correlated with the degradation of the alloys.Electrochemical impedance spectroscopy(EIS)and potentiodynamic polarisation(PDP)techniques were employed to compare the performance of the alloys in these different aggressive electrolytes.According to the obtained results,the Mg-alloys exposed to Hanks'media were the less affected,which fact was attributed to a higher stability of the corrosion products layer formed in this medium,in comparison of those formed in Ringer's and SBF solutions.In add让ion,the corrosion damage was lower for AZ91 than for AZ31 alloy in all environments due to its higher Al content.The mass loss rates calculated from both immersion tests and electrochemical methods followed the same trend for comparative purposes between alloys.

Numerical modeling of solute transport in deformable unsaturated layered soil

The effect of soil stratification was studied through numerical investigation based on the coupled model of solute transport in deformable unsaturated soil. The theoretical model implied two-way coupled excess pore pressure and soil deformation based on Biot's consolidation theory as well as a one-way coupled volatile pollutant concentration field developed from the advection-diffusion theory. Embedded in the model, the degree of saturation, fluid compressibility, self-weight of the soil matrix, porosity variance, longitudinal dispersion, and linear sorption were computed. Based on simulation results of a proposed three-layer landfill model using the finite element method, the multi-layer effects are discussed with regard to the hydraulic conductivity, shear modulus, degree of saturation, molecular diffusion coefficient, and thickness of each layer. Generally speaking, contaminants spread faster in a stratified field with a soft and highly permeable top layer; soil parameters of the top layer are more critical than the lower layers but controlling soil thicknesses will alter the results. This numerical investigation showed noticeable impacts of stratified soil properties on solute migration results, demonstrating the importance of correctly modeling layered soil instead of simply assuming the averaged properties across the soil profile.

Dynamical System of Three Magnetic Layers in the Presence of Porous Media

This paper concerns the linear stability of three viscous fluid layers in porous media. The system is composed of a middle fluid embedded between two semi-infinite fluids, in which the effect of the normal magnetic field is to introduce. The principle aim of this work is to investigate the influence of fluid viscosity and the porosity effect on the growth rate in the presence of normal magnetic field. The parameters governing the layers flow system, the magnetic properties and porosity effects strongly influence the wave forms and their amplitudes and hence the stability of the fluid. The stability criteria are discussed theoretically and numerically and stability diagrams are obtained, where regions of stability and instability are identified. It is found that the stabilizing role for the magnetic field is retarded when the flow is in porous media. Moreover, the increase in the values of permeability parameters plays a dual role, in stability behavior. It has been found that the phenomenon of the dual (to be either stabilizing or destabilizing) role is found for increasing the permeability parameter. It is established that both the viscosity coefficient and the magnetic permeability damps the growth rate, introducing stabilizing influence. The role of the magnetic field and Reynolds number is to increase the amplitude of the disturbance leading to the destabilization state of the flow system, promote the oscillatory behavior. Influence of the various parameters of the problem on the interface stability is thoroughly discussed.

Shear-horizontal transverse-electric seismoelectric waves in cylindrical double layer porous media

The shear-horizontal(SH) waves excited by the shear source in a borehole are easy to analyze due to the simple waveform. The borehole-side structures make the formation properties discontinuous. We consider a cylindrical double layer structure and study the borehole shear-horizontal and transverse-electric(SH-TE) seismoelectric waves. We first derive the expressions of the basic field quantities, and simulate the acoustic field and electric field using the real axis integral method. Compared with the wave fields of an infinitely homogeneous porous medium outside the borehole, the cylindrical layered structure makes the multi-mode cylindrical Love waves and their accompanying electric fields excited.Next, in order to study the interface response law of the inducing electric fields, we use the secant integral method to calculate the interface converted electromagnetic waves and analyze the causes of each component. It is found that an interface response occurs each time the SH wave impinges the interface in the layered porous medium. The results show that the SH-TE mode has a potential application for borehole-side interface detection in geophysical logs.

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).

Study on Folds of Equal Thickness Multi-layerSandwiched in Different Thickness Media

The theoretical model and non-homogeneous differential equation of equal thickness multi-layer folds sandwiched in different thickness and same character media are established by elastic and plastic mechanics. The special answer of the non-homogeneous differential equation and the common answer of the homogeneous differential equation are deduced by applying logistic equation and special function, and the dominant wavelength theory of equal thickness multi-layer folds sandwiched in different thickness and same character media. In addition, the experimental folding in both elastic and sticky materials proves the dominant wavelength theory.

Parameter Inversions of Multi-Layer Media of Mars Polar Region with Validation of SHARAD Data

HF (high frequency) radar sounder technology has been developed for several missions of Mars surface/subsurface exploration. This paper presents a model of rough surface and stratified sub-surfaces to describe the multi-layer structure of Mars polar deposits. Based on numerical simulation of radar echoes from rough surface/stratified interfaces, an inversion approach is developed to obtain the parameters of Polar Layered Deposits, i.e. layers thickness and dielectric constants. As a validation example, the SHARAD radar sounder data of the Promethei Lingula of Mars South Polar region is adopted for parameters inversion. The result of stratification is also analyzed and compared with the optical photo of the deep cliff of Chasma Australe canyon. Dielectric inversions show that the deposit media are not uniform, and the dielectric constants of the Promethei Lingula surfaces are large, and become reduced around the depth of 20 m - 30 m, below where most of the deposits are nearly pure ice, except a few thin layers with a lot of dust.

多孔介质壁面湍流边界层的研究进展

多孔介质壁面的可渗透性加强了界面附近的动量和能量输运,增加了多孔介质壁面湍流边界层中流动的复杂性.多孔介质壁面直接影响着湍流边界层中的湍流结构时空演化及各种物理量的生成机制和输运特性.本工作总结了多孔介质壁面湍流边界层统计特性和湍流结构特性的最新研究进展.首先,概述了多孔介质基底特性对边界层湍流特性的影响,包括对平均统计量、壁面摩擦因数和湍流结构的研究,指出多孔壁面湍流边界层的结构特性与开尔文-亥姆霍兹(Kelvin-Helmholtz,KH)不稳定性密切相关;其次,总结了多孔介质边界层中大尺度湍流结构对近壁区小尺度湍流结构的调制作用;最后,给出了该领域的未来研究方向.