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.     

声电效应测井的有限差分模拟

本文研究声电效应测井波场的有限差分模拟算法.忽略井外地层中诱导电磁场对孔隙弹性波的影响,将求解动电耦合波方程组的问题解耦,先计算孔隙弹性波,再计算其诱导电磁场.基于轴对称柱坐标系下的速度-应力交错网格,采用时域有限差分计算井孔流体声波和井外地层孔隙弹性波.将电磁场近似看作似稳场,基于轴对称柱坐标系下的5点式有限差分网格,求解不同时刻的电位Poisson方程,计算诱导电场.结果表明:本文算法可准确模拟频率6.0 kHz的声电效应测井全波;在声波测井频率范围内,电导率、动电耦合系数和动态渗透率的低频近似对伴随电磁场的计算影响不大;地层水平界面导致伴随反射斯通利波的电场和显著的界面电磁波,后者对于探测地层界面具有潜在的应用价值.     

裂缝诱导双相HTI介质地震波场错格伪谱法模拟与波场特征分析

裂缝诱导的双相具有水平对称轴的横向各向同性(HTI)介质模型是由一组平行排列的垂直裂缝嵌入到统计各向同性的流体饱和多孔隙岩石中而组成的,它综合考虑了裂缝型储层岩石的各向异性和孔隙性.高精度的地震波场数值模拟技术是研究该介质中地震波传播规律的主要方法.本文结合错格伪谱法和时间分裂法,求解描述该介质中地震波传播的一阶速度-应力方程.模拟了单层和双层模型中的地震波场,并对其进行了特征分析.研究结果表明:错格伪谱法能有效消除标准网格伪谱法波场模拟结果中出现的数值伪影现象,与时间分裂法结合能够获得稳定的、高精度的模拟结果;裂缝诱导双相HTI介质中的地震波场兼具裂缝各向异性介质和双相介质中传播的地震波的波场特征.     

热弹性介质中波传播特征

深层-超深层油气地震勘探涉及高温介质地震波传播问题,热弹介质参数对地震波传播有重要影响.含弛豫时间修正项的Lord-Shulman双曲型耦合热弹波动方程从理论上预测了热弹性介质中存在快纵波、慢纵波(一种准静态慢纵波,简称热波)和横波的传播,两个纵波为热耗散衰减波而横波不受介质热特性的影响.本文结合平面波频散分析和格林函数法数值模拟,详细研究两个热耗散衰减波的频散和衰减特征,着重分析热导率、热膨胀系数及比热的变化对波速和衰减的影响.研究表明热导率作为主要参数决定了波速与衰减的临界变化,热膨胀系数对波速和衰减的幅度有明显影响,比热则兼顾了前两个热弹系数的影响特征.最后,利用热弹性动力学频率域的二阶格林函数进行波场快照数值模拟,展示热弹性介质中纵波、横波和热波的传播行为.     

二维TI介质非结构网格弹性波矢量逆时偏移

波场延拓得到的多分量波场中既包含纵波信息也包含横波信息,能否在全波场中实现纵横波的分离对各向同性和各向异性逆时偏移都有非常重要的意义.传统的散度旋度分离只适应于各向同性介质而对各向异性介质却无效.在非规则、非结构网格的弹性波数值模拟方法的基础上,发展了一种适应于各向异性介质的波场分离方法.该方法通过求解Christoffel方程,得到相角和极化角的关系,再利用群角和相角的关系,直接得到群角和极化角的关系.该方法与现存的各向异性波场分离相比,获得的计算效率改进更显著,而且存储量小.用简单各向异性模型和SEG各向异性Hess模型进行测试,都得到了较好的效果,证明了本文方法的有效性.     

各向异性衰减薄层地震响应特征研究

薄储层的叠前地震响应特征研究,特别是针对具有速度各向异性的含流体薄层,对储层描述具有十分重要的意义.文中基于波动方程数值模拟方法,正演得到各向同性弹性、各向同性衰减、速度各向异性、各向异性衰减模型的地震波场,并对比分析了四种模型的纵波(PP)和转换横波(PS)地震反射特征.研究结果表明:在衰减介质背景下,引入各向异性,PP和PS波的反射波振幅较弹性介质均减弱,且衰减因素对薄层振幅的影响强于各向异性.同时,VTI各向异性衰减在单频PS振幅曲线上表现出强差异性,而HTI各向异性衰减则会影响PP和PS波单频振幅曲线的极值点幅值和位置,通过分析单频振幅曲线的极值点振幅和极值点位置对各向异性衰减薄层预测有指导作用,尤其对平时较难分辨的VTI各向异性衰减薄层,单频分析方法的优势更明显.     

Reference ellipsoids for anisotropic media

Perturbation methods are common tools for describing wave propagation in weakly anisotropic media. The anisotropic medium is replaced by an average isotropic medium where wave propagation can be treated analytically and the correction for the effect of anisotropy is computed by perturbation techniques. This works well for anisotropies of up to 10%. Some materials (e.g. shales), however, can exhibit a much stronger anisotropy. In this case a background is required which still can be treated analytically but is applicable to stronger P-wave anisotropy. We present an averaging technique to compute a best-fitting ellipsoidal medium to an arbitrary anisotropic medium. Ellipsoidal media are sufficiently simple for analytical expressions to be available for many applications and allow consideration of strong P-wave anisotropy. The averaging of the arbitrary anisotropic medium can be carried out globally (i.e. for the whole sphere) or sectorially (e.g. for seismic waves propagating predominantly in the vertical direction). We derive linear relationships for the coefficients of the ellipsoid which depend on the elastic coefficients of the anisotropic medium. We also provide specifications for best-fitting elliptical and best-fitting isotropic media. Numerical examples for different rocks demonstrate the improved approximation of the anisotropic model obtained using the formulae derived, compared with the conventionally used average isotropic medium.     

含裂隙双相各向异性介质中的地震波传播

基于各向异性介质和含裂隙双相介质中的地震波传播理论,导出了具有四阶对称轴的含裂隙双相各向异性介质的本构关系与波传播的运动方程．指出在含裂隙双相各向异性介质中可能传播６种类型的准纵横波,即快纵波ＱＰ１,慢纵波ＱＰ２,两个分裂的快横波ＱＳＶ１,ＱＳＨ１和两个分裂的慢横波ＱＳＶ２,ＱＳＨ２．并以平面波传播为例作了进一步分析     

基于分数阶时间导数的黏弹性衰减VTI介质中平面波传播

目前在地震勘探频带范围内通常假设品质因子Q与频率无关,且呈衰减各向同性.事实上,相比较速度各向异性,介质的衰减各向异性同样不可忽视.本文将衰减各向异性和速度各向异性二者与常Q模型相结合,建立了黏弹性衰减VTI介质模型,并基于分数阶时间导数理论,给出了对应的本构关系和波动方程.利用均匀平面波分析和Poynting定理,推...     

Microseismic Full Waveform Modeling in Anisotropic Media with Moment Tensor Implementation

Seismic anisotropy which is common in shale and fractured rocks will cause travel-time and amplitude discrepancy in different propagation directions. For microseismic monitoring which is often implemented in shale or fractured rocks, seismic anisotropy needs to be carefully accounted for in source location and mechanism determination. We have developed an efficient finite-difference full waveform modeling tool with an arbitrary moment tensor source. The modeling tool is suitable for simulating wave propagation in anisotropic media for microseismic monitoring. As both dislocation and non-double-couple source are often observed in microseismic monitoring, an arbitrary moment tensor source is implemented in our forward modeling tool. The increments of shear stress are equally distributed on the staggered grid to implement an accurate and symmetric moment tensor source. Our modeling tool provides an efficient way to obtain the Green’s function in anisotropic media, which is the key of anisotropic moment tensor inversion and source mechanism characterization in microseismic monitoring. In our research, wavefields in anisotropic media have been carefully simulated and analyzed in both surface array and downhole array. The variation characteristics of travel-time and amplitude of direct P- and S-wave in vertical transverse isotropic media and horizontal transverse isotropic media are distinct, thus providing a feasible way to distinguish and identify the anisotropic type of the subsurface. Analyzing the travel-times and amplitudes of the microseismic data is a feasible way to estimate the orientation and density of the induced cracks in hydraulic fracturing. Our anisotropic modeling tool can be used to generate and analyze microseismic full wavefield with full moment tensor source in anisotropic media, which can help promote the anisotropic interpretation and inversion of field data.     

二维各向异性介质中地震波场的高阶同位网格有限差分模拟

本文将DRP/opt MacCormack有限差分格式用于模拟二维各向异性介质中的地震波传播.DRP/opt MacCormack是一种同位网格下的差分格式,避免了传统的交错网格在计算各向异性问题时由于变量插值而导致的误差.而且相对于低阶同位网格差分格式,它具有低色散、低耗散的优点.此格式将中心差分算子分成前向和后向两个空间单边差分,然后在4-6步Runge-Kutta时间积分中使用单边差分组合.在具有垂直对称轴的横向各向同性（VTI）模型下,通过对比DRP/opt MacCormack有限差分和谱元方法的模拟结果,验证了前者具有很高的精度和稳定性.由于实际地质条件下TI介质的对称轴通常是倾斜的(TTI),本文在二维三分量框架下模拟TTI介质中的地震波场.结果显示横波分裂和切平面/反平面运动耦合的特征.数值实验表明DRP/opt MacCormack是一种有效的研究各向异性介质中地震波传播规律的差分格式.     

Modelling of viscoacoustic wave propagation in transversely isotropic media using decoupled fractional Laplacians

A new wave equation is derived for modelling viscoacoustic wave propagation in transversely isotropic media under acoustic transverse isotropy approximation. The formulas expressed by fractional Laplacian operators can well model the constant-Q (i.e. frequency-independent quality factor) attenuation, anisotropic attenuation, decoupled amplitude loss and velocity dispersion behaviours. The proposed viscoacoustic anisotropic equation can keep consistent velocity and attenuation anisotropy effects with that of qP-wave in the constant-Q viscoelastic anisotropic theory. For numerical simulations, the staggered-grid pseudo-spectral method is implemented to solve the velocity–stress formulation of wave equation in the time domain. The constant fractional-order Laplacian approximation method is used to cope with spatial variable-order fractional Laplacians for efficient modelling in heterogeneous velocity and Q media. Simulation results for a homogeneous model show the decoupling of velocity dispersion and amplitude loss effects of the constant-Q equation, and illustrate the influence of anisotropic attenuation on seismic wavefields. The modelling example of a layered model illustrates the accuracy of the constant fractional-order Laplacian approximation method. Finally, the Hess vertical transversely isotropic model is used to validate the applicability of the formulation and algorithm for heterogeneous media.     

基于GSLS模型TI介质衰减拟声波方程

随着计算机硬件技术的发展以及高分辨率勘探需求的增加,我们希望能够更准确地模拟地下介质,得到更丰富的地层信息.然而,传统的声学假设并不能描述实际地层所存在各向异性和黏滞性,使得成像分辨率较低.为了实现深部储层的高精度成像,本文同时考虑了介质的各向异性和黏滞性,从TI介质弹性波的基本理论出发,结合各向异性GSLS理论,并通过声学近似方法导出基于GSLS模型的各向异性衰减拟声波方程.数值模拟表明该方程既能准确地描述各向异性介质下的准P波运动学规律,又能体现地层的吸收衰减效应;模型逆时偏移结果表明,在实现成像过程中考虑各向异性和黏滞性的影响,能对高陡构造清晰成像,且剖面振幅相对均衡,分辨率较高.     

含起伏地形地层中点源激发的震电响应研究

地震诱导电磁现象是国内外地学领域十分关注的前沿问题,前人对地震波和电磁场耦合波场的认识主要是基于规则模型获得的.为研究含起伏地表和地下界面的地层中震电波场激发、传播特性,本文采用有限元软件COMSOL Multiphysics模拟点震源激发的电磁场.首先给出频率域二维SHTE模式震电耦合方程组,然后利用COMSOL软件建立计算模型,并求解出点力源激发震电波场的频率域响应,最后利用FFT变换得到地震波场和电磁场的时间域波形.模拟结果表明,震电波场中存在三种类型的电磁信号,第一种是震源直接激发的电磁波;第二种是地震波在分界面处激发的电磁波(包括自由表面、地下不同介质分界面);第三种是伴随地震波的同震信号,前两种电磁波比地震波更早到达远处观测台站,对地震预警有重要意义.此外,研究还发现:当地震波传播至地表并沿着地表传播时,在地表附近空气层中同样记录到了伴随地震波传播的电磁扰动信号,该信号与相同水平源距条件下、地下观测点接收到的电磁信号相同,这与前人的一些观测结果相符.本文研究结果为今后地震电磁信号的解释提供了理论证据.     

Research on propagation properties of elastic waves in two-phase anisotropic media

IntroductionItiswellknownthatanisotropylieswidelyintheundergroundmedia.Anisotropicmediawhicharemetintheseismicengineeringandseismicexplorationofenergyaremainlycausedbytheperiodicthinlayers(PTL)andextensivedilatancyanisotropy(EDA).Insuchmedia,anisotropyleadstomorecomplicatepropagationofseismicwave,thesignificantfeatureinanisotropicmediaisvelocityanisotropy.Infact,undergroundstrataareverycomplicated,whichareusuallycomposedofsolidframeandfluid(suchasoil,gasesorwater)inpores.Inordertostudyseism…     

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.     

利用介质的不均匀分布构建各向异性模型

在复杂区域应力场的作用下, 大范围扩容各向异性(extensive-dilatancy anisotropy, EDA)造成的裂隙定向排列形成了地壳内部介质的不均匀性。 因此, 地壳介质各向异性的描述不仅限于横向各向同性(transversely isotropic, TI)的理论。 我们首先利用自相关函数随机扰动得到水平向小尺度速度不均匀, 然后利用这种不均匀性描述地壳介质中EDA裂隙定向排列所造成的介质各向异性, 利用数值模拟弹性波在该介质中的传播过程验证了利用介质的不均匀性构建介质的各向异性是一个有效、 可靠的方法。 可以将此方法应用到复杂地壳介质结构中, 了解地震波在复杂地壳各向异性介质中的传播特征。     

MODELLING CHANNEL WAVES WITH SYNTHETIC SEISMOGRAMS IN AN ANISOTROPIC IN-SEAM SEISMIC SURVEY1

In-seam seismic surveys with channel waves have been widely used in the United Kingdom and elsewhere to map coal-seams and to detect anomalous features such as dirt bands, seam thinning and thickening, and particularly in-seam faulting. Although the presence of cleat-induced anisotropy has been recognized in the past, almost all previous analyses have assumed homogeneous isotropic or transversely isotropic coal-seams. Channel waves, however, exhibit properties which cannot be fully explained without introducing anisotropy into the coal-seam. In particular, Love-type channel waves are observed for recording geometries where, in a homogeneous isotropic or transversely isotropic structure, the source would not be expected to excite transverse motion. Similarly, modes of channel-wave propagation display the coupled three-component motion of generalized modes in anisotropic substrates, which would not be expected for Rayleigh and Love wave motion in isotropy or in transversely isotropic media with azimuthal isotropy. We model the observed in-seam seismic channel waves with synthetic seismograms to gain an understanding of the effects of cleat-induced anisotropy on the behaviour of channel waves. The results show a reasonable good match with the observations in traveltime, relative amplitudes, dispersion characteristics and particle motions. We demonstrate that anisotropy in the surrounding country rocks contributes significantly to the coupling of channel wave particle motion, although its effect is not as strong as the anisotropy in the coal-seam. We conclude that the effects of cleat- and stress-induced anisotropy are observed and can be modelled with synthetic seismograms, and that anisotropy must be taken into account for the detailed interpretation of channel waves.     

A multi‐azimuth seismic refraction study for a horizontal transverse isotropic medium: physical modelling results

To investigate the characteristics of the anisotropic stratum, a multi‐azimuth seismic refraction technique is proposed in this study since the travel time anomaly of the refraction wave induced by this anisotropic stratum will be large for a far offset receiver. To simplify the problem, a two‐layer (isotropy–horizontal transverse isotropy) model is considered. A new travel time equation of the refracted P‐wave propagation in this two‐layer model is derived, which is the function of the phase and group velocities of the horizontal transverse isotropic stratum. In addition, the measured refraction wave velocity in the physical model experiment is the group velocity. The isotropic intercept time equation of a refraction wave can be directly used to estimate the thickness of the top (isotropic) layer of the two‐layer model because the contrast between the phase and group velocities of the horizontal transverse isotropic medium is seldom greater than 10% in the Earth. If the contrast between the phase and group velocities of an anisotropic medium is small, the approximated travel time equation of a refraction wave is obtained. This equation is only dependent on the group velocity of the horizontal transverse isotropic stratum. The elastic constants A₁₁, A₁₃, and A₃₃ and the Thomsen anisotropic parameter ε of the horizontal transverse isotropic stratum can be estimated using this multi‐azimuth seismic refraction technique. Furthermore, under a condition of weak anisotropy, the Thomsen anisotropic parameter δ of the horizontal transverse isotropic stratum can be estimated by this technique as well.     

Study and application of PS-wave pre-stack migration in HTI media and an anisotropic correction method

Anisotropy correction is necessary during the processing of converted PSwave seismic data to achieve accurate structural imaging, reservoir prediction, and fracture detection. To effectively eliminate the adverse effects of S-wave splitting and to improve PSwave imaging quality, we tested methods for pre-stack migration imaging and anisotropic correction of PS-wave data. We based this on the propagation rules of seismic waves in a horizontal transverse isotropy medium, which is a fractured medium model that reflects likely subsurface conditions in the field. We used the radial (R) and transverse (T) components of PS-wave data to separate the fast and slow S-wave components, after which their propagation moveout was effectively extracted. Meanwhile, corrections for the energies and propagation moveouts of the R and T components were implemented using mathematical rotation. The PS-wave imaging quality was distinctly improved, and we demonstrated the reliability of our methods through numerical simulations. Applying our methods to three-dimensional and three-component seismic field data from the Xinchang-Hexingchang region of the Western Sichuan Depression in China, we obtained high-quality seismic imaging with continuous reflection wave groups, distinct structural features, and specific stratigraphic contact relationships. This study provides an effective and reliable approach for data processing that will improve the exploration of complex, hidden lithologic gas reservoirs.