Dependence of borehole shear‐horizontal‐wave seismoelectric response on soil textures

The phenomenon of acoustic waves inducing electric fields in porous media is called the seismoelectric effect. Earlier investigators proposed the usage of seismoelectric effect for well logging. Soil texture has a strong influence on the coupled wave fields during shallow surface explorations. In this article, we study the borehole pure shear‐horizontal wave and the coupling transverse‐electric field (acoustic–electrical coupling wave fields) in the partially saturated soil. Combined with related theories, we expand the formation parameters to partially saturated forms and discuss the influence of soil texture conditions on the seismoelectric wave fields. The results show that the elastic and electrical properties of porous media are sensitive to water saturation. The compositions of the acoustic and electric fields for different soil textures do not change, but the waveforms differ. We also use the secant integral method to simulate the interface‐converted electromagnetic waves. The results show that interface response strength is greatly influenced by soil texture. In addition, considering the sensitivity of the inducing electric field to fluid salinity, we also simulate the time‐domain waveforms of electric field for different pore fluid salinity levels. The results show that as the salinity increases, the electric field amplitude decreases monotonically. The above conclusions have certain significance for the application of borehole shear wave and its coupled electric fields for resource exploration, saturation assessment and groundwater pollution monitoring.     

Numerical Simulation of the Effect of a DC Electric Field on Seismic Wave Propagation with the Pseudospectral Time Domain Method

We have modeled the effect of a direct current (DC) electric field on the propagation of seismic waves by the pseudospectral time domain (PSTD) method, based on a set of governing equations for the poroelastic media. This study belongs to the more general term of the seismoelectric coupling effect. The set of physical equations consists of the poroelastodynamic equations for the seismic waves and the Maxwell's equations for the electromagnetic waves; the magnitude of the seismoelectric coupling effect is characterized by the charge density, the electric conductivity, the Onsager coefficient, a function of the dielectric permittivity, the fluid viscosity, and the zeta potential. The poroelastodynamic vibration of a solid matrix generates an electric oscillation with the form of streaming current via the fluctuation of pore pressure. Meanwhile, fluctuating pore pressure also causes oscillatory variation of the electric resistivity of the solid matrix. The simulated poroelastic wave propagation and electric field variation with an existing background DC electric field are compared with the results of a physical experiment carried out in an oilfield. The results show that the DC electric field can significantly affect the propagating elastic energy through the seismoelectric coupling in a wide range of the seismic frequency band.     

平面S波在饱和多孔热弹性介质边界的反射问题研究

针对饱和多孔介质中热弹性波的传播特性问题,基于多孔介质理论和广义的热弹性模型,研究平面S波在饱和多孔热弹性介质边界上的反射问题.以考虑流-固耦合的饱和多孔介质波动方程和热-弹耦合的广义热弹性基本方程出发,建立饱和多孔介质的热-流-固耦合弹性波动模型.通过引入势函数并考虑自由透水和绝热的边界条件,经过理论推导最终给出在饱...     

Isolation of plane shear wave using water saturated trench barrier

The article presents a theoretical investigation of the propagation of normally and obliquely incident plane shear waves past a rectangular trench filled up with water saturated soil sandwiched between anisotropic elastic media. The motivation for this work is due to the effectiveness of the isolation of waves by the in-filled rectangular trench. Unlike the most of the previous researchers, this model considers the soil–structure interaction effects and directly determines the influence of barrier in the form of in-filled trench on the mode of wave propagation. It is of interest to determine the reflection and transmission coefficients, and the energy partition distribution of shear waves in the in-filled rectangular trench showing the influence of barrier on the propagation of waves. An extensive parametric study through numerical computation is carried out to investigate the influence of the material properties of the in-filled trench and the amplitude ratios on shear waves. The in-filled trench barrier directly declines the intensity of waves significantly in such a way that the waves do not create any hazards to the nearby structures, if exists at all.     

基于临界孔隙度模型的地震波传播

基于岩石物里学中临界孔隙度模型,建立一种简洁的均匀弹性流体饱和孔隙介质模型,进行地震波传播研究.首先定义了构建目标模型的基本力学模型:介绍了全孔隙度区间内基本力学模型和目标孔隙介质的含义,其中基本力学模型除了完全弹性固体模型S和完全弹性流体模型F还包括临界孔隙模型C.然后通过等效力学模型推出了目标力学模型介质本构关系的组分表达形式.文中分别通过直接求取弹性参数的表达形式和运用应力应变关系两种方法得到介质模型的本构关系,进而得到该模型波动方程的组分表达形式.最后对这种介质模型进行了地震波传播的数值模拟,结合模拟结果分析孔隙对地震波传播的影响.     

THE APPLICATION OF PML BOUNDARY CODITIONS IN THE SIMULATION OF SEISMIC WAVE BY THE HIGH-ORDER STAGGERED-GRID FINITE DIFFERENCES AT THE TRANSVERSELY ISOTROPIC MEDIA

In the realm of the numerical simulation, finite difference method and finite element method are more intuitive and effective than other simulation methods. In the process of simulating seismic wave propagation, the finite differences method is widely used because of its high computational efficiency and the advantage of the algorithm is more efficient. With the demand of precision, more and more researchers have proposed more effective methods of finite differences, such as the high-order staggered-grid finite differences method, which can restore the actual process of wave propagation on the premise of ensuring accuracy and improving the efficiency of operation. In the past numerical simulation of seismic wave field, different models of isotropic medium are mostly used, but it is difficult to reflect the true layer situation. With the research demand of natural seismology and seismic exploration, the research on anisotropic media is more and more extensive. Transversely isotropic(TI)media can well simulate the seismic wave propagation in the formation medium, such as gas-bearing sandstone, mudstone, shale et al., the character of TI media is reflected by introducing the Thomsen parameters to reflect its weak anisotropy of vertical direction by using Thomson parameter. Therefore, studying the process of seismic wave propagation in TI media can restore the true information of the formation to the greatest extent, and provide a more reliable simulation basis for the numerical simulation of seismic wave propagation. In the geodynamic simulation and the numerical simulation of the seismic wave field, under the limited influence of the calculation area, if no boundary conditions are added, a strong artificial boundary reflection will be generated, which greatly reduces the validity of the simulation. In order to minimize the influence of model boundaries on the reflection of seismic waves, it is often necessary to introduce absorbing boundary conditions. At present, there are three types of absorption boundary conditions: one-way wave absorption boundary, attenuation absorption boundary, and perfectly matched layer(PML)absorption boundary. In terms of numerical simulation of seismic waves, the boundary absorption effect of PML is stronger than the first two, which is currently the most commonly used method, and it also represents the cutting-edge development direction of absorption boundary technology. The perfectly matched layer absorbing boundary is effectively applied to eliminating the reflective waves from model boundaries, but for transversely isotropic medium, the effect of the absorbing is not very well. For this reason, the elastic dynamic wave equations in transversely isotropic media are derived, and we describe a second-order accurate time, tenth-order accurate space, formulation of the Madariaga-Virieux staggered-grid finite difference methods with the perfectly matched layer(PML)are given. In addition, we have established vertical transversely isotropic(VTI)media and arbitrary inclined tilted transversely isotropic(TTI)media models, using a uniform half-space velocity model and a two-layer velocity model, respectively. By combining the actual geoscience background, we set the corresponding parameters and simulation conditions in order to make our model more research-oriented. When setting model parameters, different PML thickness, incident angle, source frequency and velocity layer models were transformed to verify the inhibition of boundary reflection effect by PML absorption boundary layer. The implementations of this simulation show that the formula is correct and for the transversely isotropic(TI)media of any angular symmetry axis, when the thickness of the PML layer reaches a certain value, the seismic wave reflection effect generated by the artificial boundary can be well suppressed, and the absorption effect of PML is not subject to changes in incident angle and wave frequency. Therefore, the results of our study indicate that our research method can be used to simulate the propagation process of seismic waves in the transversely isotropic(TI)media without being affected by the reflected waves at the model boundary to restore the actual formation information and more valuable geological research.     

双变参数标量纵波方程正演模拟方法

常见弹性波动理论的建立是基于介质均匀这一基本假设,实际介质的非均匀性非常普遍.为研究连续介质中波的传播特征,本文从弹性力学中建立弹性波动方程的三个基本方程出发,考虑连续介质弹性参数的空变特征,建立非均匀介质的弹性波动方程,利用Alkhalifah声学近似思想建立位移表征的纵波波动方程,利用本征值问题求解方法建立标量波频率-波数域传播算子,从而建立描述纵波传播的标量波方程,其中波函数为纵波位移的散度,不同于均匀介质标量波方程的波函数为位移势.随后推导含PML边界波动方程差分格式并建立不同模型数值模拟进行数值试算,与均匀假设标量波方程和变密度方程对比证明本方法的准确性和稳定性.     

Seismoelectric numerical simulation in 2D vertical transverse isotropic poroelastic medium

Seismoelectric coupling in an electric isotropic and elastic anisotropic medium is developed using a primary–secondary formulation. The anisotropy is of vertical transverse isotropic type and concerns only the poroelastic parameters. Based on our finite difference time domain algorithm, we solve the seismoelectric response to an explosive source. The seismic wavefields are computed as the primary field. The electric field is then obtained as a secondary field by solving the Poisson equation for the electric potential. To test our numerical algorithm, we compared our seismoelectric numerical results with analytical results obtained from Pride's equation. The comparison shows that the numerical solution gives a good approximation to the analytical solution. We then simulate the seismoelectric wavefields in different models. Simulated results show that four types of seismic waves are generated in anisotropic poroelastic medium. These are the fast and slow longitudinal waves and two separable transverse waves. All of these seismic waves generate coseismic electric fields in a homogenous anisotropic poroelastic medium. The tortuosity has an effect on the propagation of the slow longitudinal wave. The snapshot of the slow longitudinal wave has an oval shape when the tortuosity is anisotropic, whereas it has a circular shape when the tortuosity is isotropic. In terms of the Thomsen parameters, the radiation anisotropy of the fast longitudinal wave is more sensitive to the value of ε, while the radiation anisotropy of the transverse wave is more sensitive to the value of δ.     

油水两相渗流多孔介质弹性波传播动力学模型研究

弹性波在储层渗流场中的传播与衰减规律是研究波场强化采油动力学机理的重要基础.基于等效流体理论和饱和静态流体弹性波传播Biot理论,建立油水两非混相流体渗流条件下储层多孔介质中弹性波传播的动力学模型,通过算例求解与分析,发现含油水两相渗流储层多孔介质中同时存在着3种纵波P1、P2、P3和1种横波S;受频率和含水饱和度的影响,各波波速和品质因子呈现出不同变化规律,4种体波波速与频率、饱和度正相关,P1、P2波品质因子与饱和度正相关,P3和S波品质因子与饱和度负相关;最后,通过与传统静态弹性波模型结果对比,进一步分析了宏观渗流场对弹性波传播特征的影响规律,为揭示低频人工地震波辅助强化采油技术的动力学机理和工艺参数优化提供了重要理论依据.     

Poynting and polarization vectors based wavefield decomposition and their application on elastic reverse time migration in 2D transversely isotropic media

With the progress in computational power and seismic acquisition, elastic reverse time migration is becoming increasingly feasible and helpful in characterizing the physical properties of subsurface structures. To achieve high-resolution seismic imaging using elastic reverse time migration, it is necessary to separate the compressional (P-wave) and shear (S-wave) waves for both isotropic and anisotropic media. In elastic isotropic media, the conventional method for wave-mode separation is to use the divergence and curl operators. However, in anisotropic media, the polarization direction of P waves is not exactly parallel to the direction of wave propagation. Also, the polarization direction of S-waves is not totally perpendicular to the direction of wave propagation. For this reason, the conventional divergence and curl operators show poor performance in anisotropic media. Moreover, conventional methods only perform well in the space domain of regular grids, and they are not suitable for elastic numerical simulation algorithms based on non-regular grids. Besides, these methods distort the original wavefield by taking spatial derivatives. In this case, a new anisotropic wave-mode separation scheme is developed using Poynting vectors. This scheme can be performed in the angle domain by constructing the relationship between group and polarization angles of different wave modes. Also, it is performed pointwise, independent of adjacent space points, suitable for parallel computing. Moreover, there is no need to correct the changes in phase and amplitude caused by the derivative operators. By using this scheme, the anisotropic elastic reverse time migration is more efficiently performed on the unstructured mesh. The effectiveness of our scheme is verified by several numerical examples.     

地壳介质弹性和电性各向异性研究的新进展

分析了地壳介质各向异性研究的现状，指出了弹性和电性各向异性研究中存在的问题，提出了联合利用弹性和电性各向异性研究地球介质特征及提取物性参数的正反演方法．理论研究和地震过程的实际资料表明，将弹性和电性结合起来研究地壳介质各向异性具有清晰明确的物理意义，是各向异性研究的一个非常有发展前景的新领域。     

横向非均匀介质中弹性地震波传播的数值模拟

应用混合变量弹性动力学方程和线性常微分方程组的矩阵指数解法，将层状介质中广泛应用的弹性波传播矩阵解法推广至横向非均匀介质，给出了一种可计算复杂地质体中弹性波传播的广义传播矩阵数值解法。该方法可模拟任意震源及所产生的各种体波、面波，数值结果表明具有很高的计算精度。     

Surface waves in a micropolar elastic solid containing voids

The present paper investigates the effect of voids on the propagation of surface waves in a homogeneous micropolar elastic solid medium which contains a distribution of vacuous pores (voids). The general theory for surface wave propagation in micropolar elastic media containing voids has been presented. Particular cases of surface waves (Rayleigh’s, Love’s and Stoneley’s) in micropolar media which contain vacuous pores have been deduced from the above general theory. Discussions have been made in each case to highlight the effect of voids and micropolar character of the material medium separately. Their joint effect has also been studied in details. Modulation of Rayleigh wave velocity has been studied numerically. It is observed that Love waves are not affected by the presence of voids.     

饱水介质波动分析的谐波输入初始间断的处理方法

本文以饱水两相介质的土力学模型为研究对象,在假定两相介质为弹性介质条件下,采用了显式有限元法和透射边界进行了饱和弹性半空间动力响应问题的研究。为避免谐波输入初始间断的影响,文中提出了一个处理函数,并以弹性半空间为算例,对饱水介质和单相介质分别进行了在底边界P波垂直入射时的动力响应分析,验证了该处理函数的有效性和实用性。     

饱和土沉积谷场地对平面SV波的散射问题的解析解

把波函数展开方法用于饱和多孔介质中波的传播的研究中,给出了不同土层界面条件（透水条件和不透水条件）下具有饱和土沉积层的圆弧形沉积河谷场地对平面SV波散射问题的解析解. 其中沉积谷软土场地用饱和多孔介质的Biot动力学理论模拟,半空间场地用单相介质弹性动力理论模拟. 对于入射角大于临界入射角时,产生的面波的波函数用有限Fourier级数展开,这种方法适用于较大的入射波频率范围,这是现存的数值方法所不能比拟的一大优点. 文中算例分析了入射波频率和入射角对地震地面运动的影响.     

COMPUTATION OF ZERO-OFFSET VERTICAL SEISMIC PROFILES INCLUDING GEOMETRICAL SPREADING AND ABSORPTION*

Synthetic vertical seismic profiles (VSP) provide a useful tool in the interpretation of VSP data, allowing the interpreter to analyze the propagation of seismic waves in the different layers. A zero-offset VSP modeling program can also be used as part of an inversion program for estimating the parameters in a layered model of the subsurface. Proposed methods for computing synthetic VSP are mostly based on plane waves in a horizontally layered elastic or anelastic medium. In order to compare these synthetic VSP with real data a common method is to scale the data with the spherical spreading factor of the primary reflections. This will in most cases lead to artificial enhancement of multiple reflections. We apply the ray series method to the equations of motion for a linear viscoelastic medium after having done a Fourier transformation with respect to the time variable. This results in a complex eikonal equation which, in general, appears to be difficult to solve. For vertically traveling waves in a horizontally layered viscoelastic medium the solution is easily found to be the integral along the ray of the inverse of the complex propagation velocity. The spherical spreading due to a point source is also complex, and it is equal to the integral along the ray of the complex propagation velocity. Synthetic data examples illustrate the differences between spherical, cylindrical, and plane waves in elastic and viscoelastic layered media.     

三维层状孔隙介质中弹性波的一种积分表达式I：理论

孔隙介质弹性波传播理论在地球物理勘探、地震工程和岩土动力学等领域有着广泛的应用.而孔隙介质中的弹性波受孔隙度、渗透率、流体黏滞系数等参数的影响,因此研究波场的传播特征将有助于分析和提取这些信息.本文在Biot理论的基础上,针对三维层状孔隙介质模型,利用在合成理论地震图的研究中已经被证实具有稳定、高效且适用范围较广的Luco-Apsel-Chen（LAC）广义反透射方法,给出了弹性波场的一种积分形式的半解析解,可通过数值方法高效、准确地计算层状孔隙介质中的理论波场,所以该积分形式的半解析解可为三维层状孔隙介质波场传播特征的理论数值模拟研究提供一种新的途径和手段.     

Modelling the wave phenomena in acoustic and elastic media with sharp variations of physical properties using the grid‐characteristic method

This paper introduces a novel method of modelling acoustic and elastic wave propagation in inhomogeneous media with sharp variations of physical properties based on the recently developed grid‐characteristic method which considers different types of waves generated in inhomogeneous linear‐elastic media (e.g., longitudinal, transverse, Stoneley, Rayleigh, scattered PP‐, SS‐waves, and converted PS‐ and SP‐waves). In the framework of this method, the problem of solving acoustic or elastic wave equations is reduced to the interpolation of the solutions, determined at earlier time, thus avoiding a direct solution of the large systems of linear equations required by the FD or FE methods. We apply the grid‐characteristic method to compare wave phenomena computed using the acoustic and elastic wave equations in geological medium containing a hydrocarbon reservoir or a fracture zone. The results of this study demonstrate that the developed algorithm can be used as an effective technique for modelling wave phenomena in the models containing hydrocarbon reservoir and/or the fracture zones, which are important targets of seismic exploration.     

对波达波夫和Pride震电波方程组的对比分析

用Biot介质参数说明了波达波夫震电波方程组中弹性动力学 参数的含义，解释了第一类和第二类震电效应的意义，在忽略第一类震电效应条件下将该方 程组与Pride方程组进行比较，说明了二者在描述第二类震电效应方面的异同点. 同时指出 ：波达波夫方程组忽略了流体与固体的耦合质量；方程中的黏性耗散项丢掉了一个孔隙度因 子，依据该方程组计算出的弹性波和转换电场的幅度将偏大；边界条件之一存在错误，会影 响对波在界面上的反射透射规律的描述.