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.

Frequency-Dependent FDTD Method Using DSP for Arbitrary Dispersive Media

A new frequency dependent finite difference time domain (FD FDTD) method using digital signal processing (DSP) is proposed. The dispersive media is characterized as an infinite impulse response (IIR) filter, directly leading to FDTD equations. The representation of a dispersive medium is therefore converted to a problem of digital IIR design. It is shown that the numerical results are consistent with analytic solution.

SPACE-TIME DISCONTINUOUS GALERKIN METHOD FOR MAXWELL EQUATIONS IN DISPERSIVE MEDIA

In this paper, a unified model for time-dependent Maxwell equations in dispersive media is considered. The space-time DG method developed in [29] is applied to solve the un-derlying problem. Unconditional L2-stability and error estimate of order O？τr＋1＋hk＋1/2？ are obtained when polynomials of degree at most r and k are used for the temporal dis-cretization and spatial discretization respectively. 2-D and 3-D numerical examples are given to validate the theoretical results. Moreover, numerical results show an ultra-convergence of order 2r＋1 in temporal variable t.

Time-domain Wave Propagation in Dispersive Media

The equation of time-domain wave propagation in dispersive media and the explicit beam propagation method are presented in this paper.This method is demonstrated by the short optical pulses in a directional coupler with second order dispersive effect and shows to be in full agreement with former references.This method is simple,easy and practical.

Two Concepts in Optics of Anisotropic Dispersive Media and Polariton Case in Coordinate-Invariant Way

Two concepts of phenomenological optics of homogeneous, anisotropic and dispersive media are compared, the younger and more general concept of media with spatial dispersion and the older concept of (bi)-anisotropic media with material tensors for electric and magnetic induction which only depend on the frequency. The general algebraic form of the polarization vectors for the electric field and their one-dimensional projection operators is discussed without the degenerate cases of optic axis for which they become two-dimensional projection operators. Group velocity and diffraction coefficients in an approximate equation for the slowly varying amplitudes of beam solutions are calculated. As special case a polariton permittivity for isotropic media with frequency dispersion but without losses is discussed for the usual passive case and for the active case (occupation inversion of two energy levels that goes in direction of laser theory) and the group velocity is calculated. For this active case, regions of frequency and wave vector with group velocities greater than that of light in vacuum were found. This is not fully understood and due to large diffraction is likely only to realize in guided resonator form. The notion of “negative refraction” is shortly discussed but we did not find agreement with its assessment in the original paper.

Prediction on dispersion in elastoplastic unsaturated granular media

This study focuses on the propagation of the plane wave in the elastoplastic unsaturated granular media,and the wave equations and dispersion equations are derived for the media under the framework of Cosserat theory.Due to symmetry,five different wave modes are considered and predicted for the elastoplastic unsaturated granular media based on the Cosserat theory,including two longitudinal waves,one rotational longitudinal wave and two coupled transverse–rotational transverse waves.The correspondence is discussed between these Cosserat wave modes and the classical wave modes.Based on the dispersion equations,the dispersion behaviors are obtained for the five Cosserat wave modes.The results indicated that the different stress-strain stages,including the elastic,hardening and softening stages,have obvious effect on the dispersion behaviors of the Cosserat wave modes.

Predicting suitability of different scale-dependent dispersivities for reactive solute transport through stratified porous media

In this paper,the behavior of breakthrough curves(BTCs) for reactive solute transport through stratified porous media is investigated.A physical laboratory model for layered porous media was constructed,in which thin layer of gravel was sandwiched in between two thick layers of natural soil.Gravel layer and natural soil layers were hydraulically connected as single porous continuum.A constant source of tracer was connected through gravel layer and elucidated at different sampling points in the direction of flow.Flexible multiprocess non-equilibrium(MPNE) transport equation with scale-dependent dispersivity function was used to simulate experimental BTCs of reactive solute transport through layered porous media.The values of equilibrium sorption coefficient and other input parameters were obtained experimentally.The simulation of BTC was performed using MPNE model with scale-dependent dispersivity.The simulation of different scale-dependent dispersivities was then compared and it was found that for field scale of estimation of dispersivity,asymptotic and exponential dispersivity functions performed better.In continuation to the comparison of simulated BTCs obtained using different models,spatial moment analysis of each aforesaid scale-dependent dispersivity model was also done.Spatial moment analysis provides the information related to mean solute mass,rate of mass travel,and mean plume dispersion.Linear and constant dispersivities showed higher variance as compared to asymptotic and exponential dispersion functions.This supports the field applicability of asymptotic and exponential dispersivity functions.The BTCs were also found to elucidate a nonzero concentration with time,which was clearly affected by physical non-equilibrium.In natural condition,such information is required in effective aquifer remediation process.

Experimental study on the velocity-dependent dispersion of the solute transport in different porous media

The hydrodynamic dispersion is an important factor influencing the reactive solute transport in the porous media, and many previous studies assumed that it linearly varied with the average velocity of the groundwater flow. Actually, such linear relationship has been challenged by more and more experimental observations, even in homogeneous media. In this study, we aim to investigate the relationship between hydrodynamics dispersion and the flow velocity in different types of porous media through a laboratory-controlled experiment. The results indicate that (1) the dispersion coefficient should not be a linear function of the flow velocity when the relationship between the flow velocity and the hydraulic gradient can be described by Darcy's law satisfactorily;(2) Power function works well in describing the dispersion coefficient changing with the flow velocity for different types of porous media, and the power value is between 1.0-2.0 for different particle sizes.

A Solution of the Burger’s Equation Arising in the Longitudinal Dispersion Phenomenon in Fluid Flow through Porous Media by Mixture of New Integral Transform and Homotopy Perturbation Method

The main aim of the paper is to examine the concentration of the longitudinal dispersion phenomenon arising in fluid flow through porous media. These phenomenon yields a partial differential equation namely Burger’s equation, which is solved by mixture of the new integral transform and the homotopy perturbation method under suitable conditions and the standard assumption. This method provides an analytical approximation in a rapidly convergent sequence with in exclusive manner computed terms. Its rapid convergence shows that the method is trustworthy and introduces a significant improvement in solving nonlinear partial differential equations over existing methods. It is concluded that the behaviour of concentration in longitudinal dispersion phenomenon is decreases as distance x is increasing with fixed time t > 0 and slightly increases with time t.

INSTABILITY AND DISPERSIVITY OF WAVE PROPAGATION ININELASTIC SATURATED/UNSATURATED POROUS MEDIA

A model based on the Biot theory for simulating coupled hydro-dynamic behavior in saturated-unsaturated porous media was utilized with integration of the inertial coupling effect between the solid-fluid phases of the media into the model. Stationary instability and dispersivity of wave propagation in the media in one-dimensional problem were analyzed. The effects of the following factors on stationary, instability and dispersivity were discussed. They are the viscous and inertial couplings between the solid and the fluid phases, compressibility of the mixture composed of solid grains and pore fluid, the degree of saturation, visco-plastic (rate dependent inelastic) constitutive behavior of the solid skeleton under high strain rate. results and conclusion obtained by the present work will provide some bases or clues for overcoming the difficulties in numerical modelling of wave propagation in the media subjected to strong and shock loading.

Pattern Structure of Deterministic Displacement in Random Porous Media with Dispersion Effect

A new model — model of random porous media degradation via several fluid displacing, freezing, and thawing cycles is introduced and investigated in this paper. The fluid transport is based on the deterministic method with dispersion effect. The result shows that the topology and the geometry of the porous media have a strong effect on displacement processes. The cluster size of viscous fingering (VF) pattern in percolation cluster increases with the increase of iteration parameter n. When iteration parameter , VF pattern does not change with n. We find that the displacement fluid forms trapping regions in random porous media with dispersion effect. And the trapping regions will expand with the increasing of the iteration parameter n. When r (throat size) and , the peak value of the distribution increases as n increases, where is the normalized distribution of throat sizes after different displacement-damages but before freezing. The peak value of the distribution reaches a maximum when and , where is the normalized distribution of the size of invaded throat. This result is different from invasion percolation. It is found that the sweep efficiency E increases along with the increasing of iteration parameter n and decreases with the network size L, and E has a minimum as L increases to the maximum size of lattice. The VF pattern in percolation cluster has one frozen zone and one active zone.

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.

Wave field forward modeling and theoretical analysis of weakness in discrete media

The elasticity, viscosity, and the relationships derived from rheology weakness properties are taken into account in mechanics. Comparing with the corresponding relationships derived from damage mechanics, we find the weakness factor has the same significance as the damage factor. We simulate the wave field using a staggered-grid pseudospectral method to show the influence of the weakness factor qualitatively. Applying the analytical solution of plane waves, we give the velocity and attenuation coefficient of three body waves, which are affected by the wave frequency and the weakness factor of saturated discrete media. Our results show that velocity decreases with increasing weakness factor, the attenuation coefficient increases with an increase in the weakness factor, and that the influence of weakness depends on the mode of the body waves.

Sensitivity of seismic attenuation and dispersion to dynamic elastic interactions of connected fractures: Quasi-static finite element modeling study

Prediction of seismic attenuation and dispersion that are inherently sensitive to hydraulic and elastic properties of the medium of interest in the presence of mesoscopic fractures and pores,is of great interest in the characterization of fractured formations.This has been very difficult,however,considering that stress interactions between fractures and pores,related to their spatial distributions,tend to play a crucial role on affecting overall dynamic elastic properties that are largely unexplored.We thus choose to quantitatively investigate frequency-dependent P-wave characteristics in fractured porous rocks at the scale of a representative sample using a numerical scale-up procedure via performing finite element modelling.Based on 2-D numerical quasi-static experiments,effects of fracture and fluid properties on energy dissipation in response to wave-induced fluid flow at the mesoscopic scale are quantified via solving Biot's equations of consolidation.We show that numerical results are sensitive to some key characteristics of probed synthetic rocks containing unconnected and connected fractures,demonstrating that connectivity,aperture and inclination of fractures as well as fracture infills exhibit strong impacts on the two manifestations of WIFF mechanisms in the connected scenario,and on resulting total wave attenuation and phase velocity.This,in turn,illustrates the importance of these two WIFF mechanisms in fractured rocks and thus,a deeper understanding of them may eventually allow for a better characterization of fracture systems using seismic methods.Moreover,this presented work combines rock physics predictions with seismic numerical simulations in frequency domain to illustrate the sensitivity of seismic signatures on the monitoring of an idealized geologic CO_(2) sequestration in fractured reservoirs.The simulation demonstrates that these two WIFF mechanisms can strongly modify seismic records and hence,indicating that incorporating the two energy dissipation mechanisms in the geophysical interpretation can potentially improving the monitoring and surveying of fluid variations in fractured formations.

Propagation of Iamb waves in adhesively bonded multilayered media

The effect of introducing attenuation on Lamb wave dispersion curves is studied in this paper. Attenuation is introduced to a three-layered composite plate by an adhesive bond layer with viscous behavior. No changes are required to the transfer matrix formulation for the propagation of elastic waves. By introduction of a complex wavenumber, the model can be used to the propagation of attenuative Lamb waves. Numerical examples for a three-layered aluminium-epoxy-aluminium plate show that attenuation values of each mode in plates are related not only to attenuation, but also to the thickness of the bonded layer, which is in agreement with practical situations.

AN ANALYTICAL SOLUTION FOR AN EXPONENTIAL- TYPE DISPERSION PROCESS

The dispersion process in heterogeneous porous media is distance-dependent, which results from multi-scaling property of heterogeneous structure. An analytical model describing the dispersion with an exponential dispersion function is built, which is transformed into ODE problem with variable coefficients, and obtained analytical solution for two type boundary conditions using hypergeometric function and inversion technique. According to the analytical solution and computing results the difference between the exponential dispersion and constant dispersion process is analyzed

Azimuthal moveout response of seismic waves in two-phase anisotropic media

Dispersion and attenuation occur while seismic wave travels through cracks filled with fluids,which lead to the anisotropism of seismic azimuthal travel time.Based on latest rock physics models,this study aims to simulate seismic azimuthal moveout responses(AMR) and analyze the factors affecting this attribute.By numerical modeling,it is found that the AMR is very sensitive to the parameters of the cracks,especially these related to fluid;therefore AMR has the potential to qualitatively or even quantitatively identify cracks.

WELL-DISPERSED NANODIAMOND AQUEOUS SUSPENSIONS——PREPARATION,PROPERTIES AND APPLICATIONS

Well-dispersed nanodiamond(ND) aqueous suspensions in both acidic and alkaline environments is prepared by mechanochemical treatment. All the ND particles in the suspensions are smaller than 100nm in dimension with a narrow size distribution, and no destabilization phenomena were detected in a duration of more than one year. Stable dispersion of ND in the media may attributed to the strong electrostatic repulsion between particles because of the adsorption of dispersants, while mechanical forces may strengthen this adsorption reaction. Good adaptability and applicability of the suspensions to the change of ND concentration and surrounding temperature are observed, and improved performances of ND diamonds are obtained when used in ultrafine polishing and composite plating.

VTI介质改进声学近似qP波交错网格正演模拟

Alkhalifah提出的声学假设近似令沿TI介质对称轴的qSV波速度近似为0,建立了相应的qP波波动方程并进行了数值模拟,但存在两个不足:一是方程中存在退化的qSV波解,不是纯qP波波动方程;二是方程不适用于ε<δ(ε和δ为Thomsen参数)的介质。为此,在Liang等的工作基础上,将改进声学近似方法的思想引入qP波频散关系和一阶波动方程推导。令qSV波的精确频散关系中的圆频率为0,同时结合椭圆分解,推导了VTI介质纯qP波解耦频散关系,利用改进标量算子的空间域渐近近似建立了VTI介质改进声学近似qP波一阶速度—应力波动方程,采用交错网格有限差分算法实现了基于改进声学近似的VTI介质纯qP波正演模拟。频散关系分析和数值示例表明,基于改进声学近似的qP波一阶波动方程不包含退化qSV波,是纯qP波方程,与弹性波波动方程模拟结果吻合较好,具有较高精度,并且该方程在ε≥δ和ε<δ的VTI介质中均是稳定的,同时也适用于复杂VTI介质。

粘弹频变固液解耦流体因子地震反演方法研究及应用

地震波在含油气储层中传播时,因为波致流的影响,会发生振幅衰减与弹性参数频散现象,使得地震流体预测描述成为可能。但是,这些现象产生理论不明确和数学表达精度不高,使得含油气识别困难。为此,本研究首先根据地震振幅衰减与弹性参数频散现象,利用Chapman孔裂隙衰减理论考虑波致流影响,引入挤喷流效应,构建粘弹介质固液解耦流体因子。然后,推导构建关于流体因子的反射系数特征方程,并与Zoeppritz方程和Aki近似方程对比分析,验证新方程的精度。最后,基于叠前地震数据的分角度、分频带变化信息,提出粘弹频变固液解耦流体因子反演方法,并利用该流体因子在胜利油田胜北地区进行储层含油气性预测。研究结果表明,新构建的粘弹频变固液解耦流体因子对储层油气具有较强的敏感性,提出的地震反射特征方程和反演方法准确可靠,实际储层流体预测结果与测井解释结果吻合度较高,为复杂储层流体识别提供新的思路和方法。