一种特殊二维各向异性介质中的准瑞利面波的传播

针对弹性参数满足一种特殊形式的二维各向异性介质，结合边界条件，求解波动方程组，得到了该种介质中传播的准瑞利波的波速度满足的方程，进而探讨了该种介质中传播的准瑞利面波的传播规律。

Reflection coefficients of P-SV waves in weak anisotropic media

We introduce the Thomsen anisotropic parameters into the approximate linear reflection coefficient equation for P-SV wave in weakly anisotropic HTI media. From this we get a new, more effective, and practical reflection coefficient equation. We performed forward modeling to AVO attributes, obtaining excellent results. The combined AVO attribute analysis of PP and PS reflection data can greatly reduce ambiguity, obtain better petrophysical parameters, and improve parameter accuracy.

The analysis and application of simplified two-parameter moveout equation for C-waves in VTI anisotropy media

Several parameters are needed to describe the converted-wave （C-wave） moveout in processing multi-component seismic data, because of asymmetric raypaths and anisotropy. As the number of parameters increases, the converted wave data processing and analysis becomes more complex. This paper develops a new moveout equation with two parameters for C-waves in vertical transverse isotropy （VTI） media. The two parameters are the C-wave stacking velocity （Vc2） and the squared velocity ratio （7v,i） between the horizontal P-wave velocity and C-wave stacking velocity. The new equation has fewer parameters, but retains the same applicability as previous ones. The applicability of the new equation and the accuracy of the parameter estimation are checked using model and real data. The form of the new equation is the same as that for layered isotropic media. The new equation can simplify the procedure for C-wave processing and parameter estimation in VTI media, and can be applied to real C-wave processing and interpretation. Accurate Vc2 and Yvti can be deduced from C-wave data alone using the double-scanning method, and the velocity ratio model is suitable for event matching between P- and C-wave data.

Adaptive Finite Element Modeling of Marine Controlled-Source Electromagnetic Fields in Two-Dimensional General Anisotropic Media

In this paper, we extend the scope of numerical simulations of marine controlled-source electromagnetic (CSEM) fields in a particular case of anisotropy (dipping anisotropy) to the general case of anisotropy by using an adaptive finite element approach. In comparison to a dipping anisotropy case, the first order spatial derivatives of the strike-parallel components arise in the partial differential equations for generally anisotropic media, which cause a non-symmetric linear system of equations for finite element modeling. The adaptive finite element method is employed to obtain numerical solutions on a sequence of refined unstructured triangular meshes, which allows for arbitrary model geometries including bathymetry and dipping layers. Numerical results of a 2D anisotropic model show both anisotropy strike and dipping angles have great influence on the marine CSEM responses.

Integral Equation Method for Electromagnetic Wave Propagation in Stratified Anisotropic Dielectric-Magnetic Materials

We investigate the propagation of electromagnetic waves in stratified anisotropic dielectric-magnetic materialsusing the integral equation method (IEM).Based on the superposition principle, we use Hertz vector formulations ofradiated fields to study the interaction of wave with matter.We derive in a new way the dispersion relation, Snell's lawand reflection/transmission coefficients by self-consistent analyses.Moreover, we find two new forms of the generalizedextinction theorem.Applying the IEM, we investigate the wave propagation through a slab and disclose the underlyingphysics, which are further verified by numerical simulations.The results lead to a unified framework of the IEM for thepropagation of wave incident either from a medium or vacuum in stratified dielectric-magnetic materials.

Fracture property identification method based on shrinkage factor particle swarm optimization

In the multi-wave and multi-component seismic exploration,shear-wave will be split into fast wave and slow wave,when it propagates in anisotropic media. Then the authors can predict polarization direction and density of crack and detect the development status of cracks underground according to shear-wave splitting phenomenon. The technology plays an important role and shows great potential in crack reservoir detection. In this study,the improved particle swarm optimization algorithm based on shrinkage factor is combined with the Pearson correlation coefficient method to obtain the fracture azimuth angle and density. The experimental results show that the modified method can improve the convergence rate,accuracy,anti-noise performance and computational efficiency.

P-wave attenuation anisotropy in TI media and its application in fracture parameters inversion

The existence of aligned fractures in fluid-saturated rocks leads to obvious attenuation anisotropy and velocity anisotropy. Attenuation anisotropy analysis can be applied to estimate fracture density and scale, which provide important information for reservoir identification. This paper derives P-wave attenuation anisotropy in the ATI media where the symmetry axis is in the arbitrary direction theoretically and modifies the spectral ratio method to measure attenuation anisotropy in the ATI media, thus avoiding a large measurement error when applied to wide azimuth or full azimuth data. Fracture dip and azimuth can be estimated through attenuation anisotropy analysis. For small-scale fractures, fracture scale and fracture density can be determined with enhanced convergence if velocity and attenuation information are both used. We also apply the modified spectralratio method to microseismic field data from an oilfield in East China and extract the fracture dip through attenuation anisotropy analysis. The result agrees with the microseismie monitoring.

General solutions for special orthotropic piezoelectric media

This paper presents the forms of the general solution for general anisotropic piezoelectric media starting from the basic equations of piezoelasticity by using the operator method introduced by Lur’e (1964), and gives the analytical form of the general solution for special orthotropic piezoelectric media. This paper uses the non-uniqueness of the general solution to obtain the generalized LHN solution and the generalized E-L solution for special orthotropic piezoelectric media. When the special orthotropic piezoelectric media degenerate to transversely piezoelectric media, the solution given by this paper degenerates to the solution for transversely isotropic piezoelectric media accordingly, so that this paper generalized the results in transversely isotropic piezoelectric media.

Effects of axial cyclic loading at constant confining pressures on deformational characteristics of anisotropic argillite

Triaxial cyclic loading tests have been performed to assess the influence of plastic deformation on inelastic deformational properties of anisotropic argillite with bedding planes which is regarded as a kind of transversely isotropic media.Considering argillite's anisotropy and inelastic deformational properties,theoretical formulae for calculating oriented elastic parameters were deduced by the unloading curves,which can be better fitted for the description of its elasticity than loading curves.Test results indicate that with the growth of accumulated plastic,strain,the apparent elastic modulus of argillite decreases in a form of exponential decay function,whereas the apparent Poisson ratio increase in a form of power equation.A ratio of unloading recoverable strain to the total strain increment occurred during a loading cycle is defined to illustrate the characteristic relations between anisotropic coupled elasto-plastic deformation and plastic strain.It is significant to observe that high stress level and plastic history have an inhibiting effect on argillite anisotropy.

Effective Anisotropic Dielectric Properties of Crystal Composites

Transformation fieM method （TFM） is developed to estimate the anisotropic dielectric properties of crystal composites having arbitrary shapes and dielectric properties of crystal inclusions, whose principal dielectric axis are different from those of anisotropic crystal matrix. The complicated boundary-value problem caused by inclusion shapes is circumvented by introducing a transformation electric field into the crystal composites regions, and the effective anisotropic dielectric responses are formulated in terms of the transformation field. Furthermore, the numerical results show that the effective anisotropie dielectric responses of crystal composites periodically vary as a function of the rotating angle between the principal dielectric axes of inclusion and matrix crystal materials. It is found that at larger inclusion volume fraction the inclusion shapes induce profound effect on the effective anisotropic dielectric responses.

Electron-Irradiation Induced Nanocrystallization of Pb（ll） in Silica Gels Prepared in High Magnetic Field

In a previous study, structure of silica gels prepared in a high magnetic field was investigated. While a direct application of such anisotropic silica gels is for an optical anisotropic medium possessing chemical resistance, we show here their possibility of medium in materials processing. In this direction, for example, silica hydrogels have so far been used as media of crystal growth. In this paper, as opposed to the soft-wet state, dried silica gels have been investigated. We have found that lead （II） nanocrystallites were formed induced by electron irradiation to lead （ll）-doped dried Hydrogels made from a sodium metasilicate solution doped with silica gels prepared in a high magnetic field such as B = 10 T. lead （II） acetate were prepared. The dried specimens were irradiated by electrons in a transmission electron microscope environment. Electron diffraction patterns indicated the crystallinity of lead （II） nanocrystallites depending on B. An advantage of this processing technique is that the crystallinity can be controlled through the strength of magnetic field B applied during gel preparation. Specific skills are not required to control the strength of magnetic field.

Acoustic numerical simulation for VTI media

The generality to anisotropy of the earth media can be proved by a lot of research and observation, which is shown by the elastic parameters of the seismic wave changes with the direction of propagation. Actually, computational efficiency is very low, when simulating on the elastic anisotropie media, for the complicated and multi-parameters computation, which becomes a disadvantage to the succeeding migration and imaging pro-cedure. Using acoustic approximation in the VT[ media is an advisable simplification for the elastic wave simu-lation in that setting S-velocity into zero can greatly reduce the computational amount as well as get the same simulation effect. The authors get an acoustic approximation formula, then gain an anisotropic wave equation with 2-order in time and 4-order in space by inverse Fourier transformation, and dispel with the dispersion by adopting the high order finite difference operator in space and remove the edge reflection using the absorption attenuation boundary. Finally, the feasibility and effectiveness of this algorithm can be proved by the snaps and synthetic records.

Research on ray tracing in VTI medium based on different models

The study on seismic anisotropy is one of the difficult problems in the field of geophysics nowadays.As a method of ray theory,the seismic anisotropy ray tracing is an important means to study the anisotropic seismic wave propagation. The traditional ray tracing system formulated in terms of elastic parameters in the anisotropy is more complicated than that in the isotropic case. Considering the difficulty,a kind of ray tracing system formulated in terms of phase velocity and group velocity is introduced. The new method is similar to the expressions for isotropic media,and avoids the trouble of determining the eigenvalue vector at each time. Besides the ray tracing numerical simulation of different models of vertical transversely isotropic( VTI) medium is carried out,in order to verify the accuracy and applicability of the method and further study the characteristics of wave field propagation in different VTI mediums. The study is certainly valuable in reference for later processing of the anisotropic seismic data.

Finite element simulation on percolation of low permeability reservoir with permeability anisotropy

In low permeability porous media which permeability anisotropy is ubiquitous,the percolation of fluid no longer follows linear Darcy’s Law.Oil-water two phase flow equation of low permeability reservoir with permeability anisotropy is established based on generalized Darcy’s law and starting pressure gradient,corresponding finite element program is developed and simulated based on the Finite Element Program Generator system (FEPG).The results show that energy-gathering exists in the flow event of flowing area front in low permeability reservoir.In the process of energy-gathering,the flow velocity changed little but increased rapidly as soon as the pressure gradient exceeded the starting pressure gradient of the reservoir,then gradually stabilized.The greater the starting pressure gradient is,the greater the near wellbore pressure drop is,the smaller the area influenced by the reservoir pressure changes caused by water injection and oil recovery.The greater the starting pressure gradient is,the lower the water saturation in same point of the reservoir is,the smaller the water flood swept area is.There will be more difficulties in water injection to the same extent.

Method of Earthquake Prediction Based on the Soliton Mechanisms of Some Shocks

In this paper, a new method of earthquakes prediction taking into account the influence of strain solitary waves as a ＂trigger＂ of some shocks is presented. Methods of forecasting are based on evaluating trajectories of individual solitons and clarification of shocks probability. Solitary waves are considered in solid anisotropic elastic medium and proved that there exist the motion equations solutions in the form of solitary waves. Predicting the trajectories of solitary waves related to the moment problem for the special case of Chebyshev system of functions or exponential problem. This problem is solved using special bijective mapping. Seismic process in the region of Japanese Islands, March 11,2011 is analyzed as an example.

Exact elastic impedance tensor for isotropic media

The existing expressions of elastic impedance,as the generalized form of acoustic impedance,represent the resistance of subsurface media to seismic waves of non-normal incidence,and thus include information on the shear-wave velocity.In this sense,conventional elastic impedance is an attribute of the seismic reflection and not an intrinsic physical property of the subsurface media.The derivation of these expressions shares the approximations made for reflectivity,such as weak impedance contrast andisotropic or weakly anisotropic media,which limits the accuracy of reflectivity reconstruction and seismic inversion.In this paper,we derive exact elastic impedance tensors of seismic P-and S-waves for isotropic media based on the stress-velocity law.Each componentof the impedance tensor represents a unique mechanical property of the medium.Approximations of P-wave elastic impedance tensor components are discussed for seismic inversion and interpretation.Application to synthetic data and real data shows the accuracy and robust interpretation capability of the derived elastic impedance in lithology characterizations.

An Inverse Problem for Maxwell's Equations in Anisotropic Media

The authors consider Maxwell＇s equations for an isomagnetic anisotropic and inhomogeneous medium in two dimensions, and discuss an inverse problem of determining the permittivity tensor （ε1,ε2,ε2,ε3 ） and the permeability μ in the constitutive relations from a finite number of lateral boundary measurements. Applying a Carleman estimate, the authors prove an estimate of the Lipschitz type for stability, provided that ε1,ε2,ε3,μ satisfy some a priori conditions.

Analytic solution to the magnetotelluric response over anisotropic medium and its discussion

In the present paper,from the second order partial differential equations for solving the magnetotelluric(MT) fields of general anisotropic medium,we first obtained the second order partial differential equations for some anisotropic media with special conductivity(e.g.diagonal anisotropy,transverse anisotropy,azimuthal anisotropy,etc.) by simplifying the electrical conductivity tensor of anisotropic medium.And then we obtained the analytic solutions to MT fields for the case of transverse and azimuthal anisotropy through converting the conductivity parameter based on that of diagonal anisotropy.We further discussed the influence of the selection of integral limit and step length on precision in solving the analytic solutions for MT fields of isotropic medium.Finally,we presented the MT responses of two transverse and azimuthal anisotropic media as well as some applications of the analytic solutions to MT fields of anisotropic medium.

The influence of rock anisotropy on elliptical-polarization state of inhomogenously refracted P-wave

This paper discusses the influence of the anisotropy parameters on elliptical-polarization of the inhomogenously refracted P-wave induced at VTI-media interface.For this refracted P-wave,we have derived,the equations of the elliptical-polarization trajectory.Following the elliptical-polarization trajectory,we calculated the effects of the rock anisotropic-parameters on the polarization state,with a Poincare-sphere-like representation,for several varying media parameters.It is noted that the size,shape and initial phase angle of the elliptical-polarization trajectory are all depending the anisotropy media,as well as on the incident-angle.We expect that the findings from this paper would be applied to practical applications of seismic exploration.

Comment on “A numerical investigation of the acoustic mode waves in a deviated borehole penetrating a transversely isotropic formation”

In the paper"A numerical investigation of the acoustic mode waves in a deviated borehole penetrating a transversely isotropic formation"by Liu et al.[1]numerical experiments are reported for a dipole sonic logging scenario with a deviated borehole penetrating a VTI anisotropic medium.In such a situation it is important to clearly define the meaning of group and phase velocities as this has led to much confusion in the literature as discussed by Miller,Horne and Walsh[2].