Anisotropic effective conductivity in fractured rocks by explicit effective medium methods

In this work, we assess the use of explicit methods for estimating the effective conductivity of anisotropic fractured media. Explicit methods are faster and simpler to use than implicit methods but may have a more limited range of validity. Five explicit methods are considered: the Maxwell approximation, the T‐matrix method, the symmetric and asymmetric weakly self‐consistent methods, and the weakly differential method, where the two latter methods are novelly constructed in this paper. For each method, we develop simplified expressions applicable to flat spheroidal “penny‐shaped” inclusions. The simplified expressions are accurate to the first order in the ratio of fracture thickness to fracture diameter. Our analysis shows that the conductivity predictions of the methods fall within known upper and lower bounds, except for the T‐matrix method at high fracture densities and the symmetric weakly self‐consistent method when applied to very thin fractures. Comparisons with numerical results show that all the methods give reliable estimates for small fracture densities. For high fracture densities, the weakly differential method is the most accurate if the fracture geometry is non‐percolating or the fracture/matrix conductivity contrast is small. For percolating conductive fracture networks, we have developed a scaling relation that can be applied to the weakly self‐consistent methods to give conductivity estimates that are close to the results from numerical simulations.     

电磁勘探中各向异性研究现状和展望

电各向异性广泛存在于自然界中,已成为电磁勘探资料解释中不可忽视的因素.特别是在一些沉积岩地区,由于层理发育导致地下介质电阻率随电流方向发生变化,表现出很强的各向异性导电性.此时,利用各向同性模型进行电磁数据解释将引起很大的误差.本文回顾了电磁勘探中电各向异性研究的历史,简要介绍电各向异性成因、数值模拟中的数学描述及电各向异性介质中电磁场正反演模拟方法等研究现状,总结电各向异性在大地电磁、可控源电磁、航空电磁和感应测井等方面的最新研究进展及未来的挑战.随着多维电磁数据采集及正反演模拟技术的进步和计算能力的提高,给电各向异性信息提取和应用带来了新的契机.电各向异性研究将在矿产资源勘查、油气存储与运移特征分析、地下水和地热、环境工程地质调查、大地构造及地质灾害预测等方面发挥积极作用.

     

Sensitivity and inversion of marine electromagnetic data in a vertically anisotropic stratified earth

The controlled‐source electromagnetic (CSEM) and magnetotelluric method (MT) are two techniques that can be jointly used to explore the resistivity structure of the earth. Such methods have, in recent years, been applied in marine environments to the exploration and appraisal of hydrocarbons. In many situations the electric properties of the earth are anisotropic, with differences between resistivity in the vertical direction typically much higher than those in the horizontal direction. In cases such as this, the two modes of the time‐harmonic electromagnetic field are altered in different ways, implying that the sensitivity to the earth resistivity may vary significantly from one particular resistivity component (scalar, horizontal or vertical) to another, depending on the measurement configuration (range, azimuth, frequency or water depth). In this paper, we examine the sensitivity of the electromagnetic field to a vertically anisotropic earth for a typical set of configurations, compare inversion results of synthetic data characterizing a vertically anisotropic earth obtained using the isotropic and anisotropic assumptions and show that correctly accounting for anisotropy can prevent artefacts in inversion results.     

地震勘探中小尺度非均匀性的描述及长波长理论

地球物理成像解释的一个重要问题是,地震波传播时其本身受到地质体中小尺度非均匀性的影响,对该问题的研究具有重要的意义且备受关注.据此,本文首先从统计意义上的表示形式来描述小尺度非均匀性,给出一种拓展了小尺度非均匀性择优取向的随机介质建模新方法,重点阐述了建模过程中对误差处理的重要性.其次讨论了地震波在水平层状介质中传播时的长波长理论,并指出对该理论的适用条件进行研究的重要意义.且还基于ID随机层状介质,从局部各向异性因子曲线的角度对长波长理论进行了研究,并讨论了密度及泊松比扰动对曲线形态的影响.最后,从对ID和2D随机介质进行数值模拟的角度重点研究长波长理论不能满足的情况下地震记录的特点,为了便于对比分析,文中也计算了ID随机介质在不同平均化长度下,通过长波长理论得到的等效介质的理论走时(走时的计算是在弱各向异性假设条件下完成的),并给出有指导意义的结论.     

地震勘探中小尺度非均匀性的描述及长波长理论

地球物理成像解释的一个重要问题是,地震波传播时其本身受到地质体中小尺度非均匀性的影响,对该问题的研究具有重要的意义且备受关注. 据此,本文首先从统计意义上的表示形式来描述小尺度非均匀性,给出一种拓展了小尺度非均匀性择优取向的随机介质建模新方法,重点阐述了建模过程中对误差处理的重要性. 其次讨论了地震波在水平层状介质中传播时的长波长理论,并指出对该理论的适用条件进行研究的重要意义.且还基于1D随机层状介质,从局部各向异性因子曲线的角度对长波长理论进行了研究,并讨论了密度及泊松比扰动对曲线形态的影响. 最后,从对1D和2D随机介质进行数值模拟的角度重点研究长波长理论不能满足的情况下地震记录的特点,为了便于对比分析,文中也计算了1D随机介质在不同平均化长度下,通过长波长理论得到的等效介质的理论走时(走时的计算是在弱各向异性假设条件下完成的),并给出有指导意义的结论.     

Analytical approximations of bulk and shear moduli for dry rock based on the differential effective medium theory

Differential effective medium theory has been applied to determine the elastic properties of porous media. The ordinary differential equations for bulk and shear moduli are coupled and it is more difficult to obtain accurate analytical formulae about the moduli of dry porous rock. In this paper, in order to decouple these equations we first substitute an analytical approximation for the dry‐rock modulus ratio into the differential equation and derive analytical solutions of the bulk and shear moduli for dry rock with three specific pore shapes: spherical pores, needle‐shaped pores and penny‐shaped cracks. Then, the validity of the analytical approximations is tested by integrating the full differential effective medium equation numerically. The analytical formulae give good estimates of the numerical results over the whole porosity range for the cases of the three given pore shapes. These analytical formulae can be further simplified under the assumption of small porosity. The simplified formulae for spherical pores are the same as Mackenzie's equations. The analytical formulae are relatively easy to analyse the relationship between the elastic moduli and porosity or pore shapes and can be used to invert some rock parameters such as porosity or pore aspect ratio. The predictions of the analytical formulae for experimental data show that the formulae for penny‐shaped cracks are suitable to estimate the elastic properties of micro‐crack rock such as granite, they can be used to estimate the crack aspect ratio while the crack porosity is known and also to estimate the crack porosity evolution with pressure if the crack aspect ratio is given.     

Contact line friction and surface tension effects on seismic attenuation and effective bulk moduli in rock with a partially saturated crack

The effect of surface phenomena occurring at the interfaces between immiscible fluids and a solid on the seismic attributes of partially saturated rocks has not yet been fully studied. Meanwhile, over the past two decades considerable progress has been made in the physics of wetting to understand effects such as contact line friction, contact line pinning, contact angle hysteresis, and equilibrium contact angle. In this paper, we developed a new rock physics model considering the aforementioned effects on seismic properties of the rock with a partially saturated plane-strain crack. We demonstrated that for small wave-induced stress perturbations, the contact line of the interface meniscus will remain pinned, while the meniscus will bulge and change its shape through the change of the contact angles. When the stress perturbation is larger than a critical value, the contact line will move with advancing or receding contact angle depending on the direction of contact line motion. A critical stress perturbation predicted by our model can be in the range of ∼10²−10⁴ Pa, that is typical for linear seismic waves. Our model predicts strong seismic attenuation in the case when the contact line is moving. When the contact line is pinned, the attenuation is negligibly small. Seismic attenuation is associated with the hysteresis of loading and unloading bulk moduli, predicted by our model. The hysteresis is large when the contact line is moving and negligibly small when the contact line is pinned. Furthermore, we demonstrate that the bulk modulus of the rock with a partially saturated crack depends also on the surface tension and on the contact angle hysteresis. These parameters are typically neglected during calculation of the effecting fluid moduli by applying different averaging techniques. We demonstrate that contact line friction may be a dominant seismic attenuation mechanism in the low frequency limit (<∼10 Hz) when capillary forces dominate over viscous forces during wave-induced two-phase fluid flow.     

西吉县西南山区典型黄土地震滑坡高密度电法物探解译分析

本文运用高密度电法对宁夏西吉县西南山区典型的黄土地震滑坡进行了探测,并结合钻探资料进行验证分析,目的是查明滑坡区域的地层结构、黄土厚度、基岩埋深、富水地段以及空间展布等特征.结果表明:电阻率参数能够很好的反应研究区的地层分布特征,表层疏松干燥的黄土为高阻反映,随着埋深增加,含水量较大的黄土呈现出低阻反映,在黄土与泥岩接触带饱水区呈现低阻反映;滥泥河流域典型的黄土梁斜坡具有阳坡黄土沉积薄、富水层薄、基岩埋深浅的特征,而在阴坡则表现出黄土沉积厚、富水层厚、基岩埋深大的特征.探测结果可有效的应用于黄土地震滑坡的勘察,为进一步开展黄土地震滑坡的成因机理和防治研究提供参考数据.     

Full waveform inversion of SH‐ and Love‐wave data in near‐surface prospecting

We develop a two‐dimensional full waveform inversion approach for the simultaneous determination of S‐wave velocity and density models from SH ‐ and Love‐wave data. We illustrate the advantages of the SH/Love full waveform inversion with a simple synthetic example and demonstrate the method's applicability to a near‐surface dataset, recorded in the village ?achtice in Northwestern Slovakia. Goal of the survey was to map remains of historical building foundations in a highly heterogeneous subsurface. The seismic survey comprises two parallel SH‐profiles with maximum offsets of 24 m and covers a frequency range from 5 Hz to 80 Hz with high signal‐to‐noise ratio well suited for full waveform inversion. Using the Wiechert–Herglotz method, we determined a one‐dimensional gradient velocity model as a starting model for full waveform inversion. The two‐dimensional waveform inversion approach uses the global correlation norm as objective function in combination with a sequential inversion of low‐pass filtered field data. This mitigates the non‐linearity of the multi‐parameter inverse problem. Test computations show that the influence of visco‐elastic effects on the waveform inversion result is rather small. Further tests using a mono‐parameter shear modulus inversion reveal that the inversion of the density model has no significant impact on the final data fit. The final full waveform inversion S‐wave velocity and density models show a prominent low‐velocity weathering layer. Below this layer, the subsurface is highly heterogeneous. Minimum anomaly sizes correspond to approximately half of the dominant Love‐wavelength. The results demonstrate the ability of two‐dimensional SH waveform inversion to image shallow small‐scale soil structure. However, they do not show any evidence of foundation walls.     

二连盆地“三明治”电性结构特征及其对古生界的研究意义

由于长期以来东北地区晚古生代的构造属性一直被认为是海西期褶皱带或碰撞造山带,而一直被作为中、新生代盆地的变质结晶基底成为油气勘查的禁区,限制了古生界的油气勘探和开发."佳木斯—兴蒙地块"新认识及二连盆地赛51井取得的石炭纪碳酸盐岩油藏的发现,开辟了二连盆地古生界油气勘探的新领域.本文对二连盆地3条典型的CEMP电测量资料进行了二维电阻率反演,结合研究区地震反射资料、钻孔电测井资料、钻井岩芯资料、岩石露头资料,揭示了二连盆地具有"三明治"的电性结构特征,同时指出二连盆地古生界广泛分布,在古生界与中生界之间广泛分布一套以玄武岩、安山岩、凝灰岩等为主的火山岩.这种"三明治"电性结构特征不但给古生界的研究提供了线索和依据,而且火山岩(高阻层)与其下伏古生界地层(低阻层)之间可形成良好的储盖组合(或生储盖组合),其对于古生界油气勘探的研究具有重要的意义.同时,认为二连盆地中、新生界和古生界的构造沉积演化主要经历了4个重要阶段,即:泥盆纪的南北差异性升降阶段、石炭-二叠纪的地层稳定沉积阶段、三叠纪-晚侏罗世的古生代盆地被改造和中新生代盆地构造格架形成的重要演化阶段以及中新生代的地层沉积阶段.     

二连盆地“三明治”电性结构特征及其对古生界的研究意义

由于长期以来东北地区晚古生代的构造属性一直被认为是海西期褶皱带或碰撞造山带,而一直被作为中、新生代盆地的变质结晶基底成为油气勘查的禁区,限制了古生界的油气勘探和开发."佳木斯—兴蒙地块"新认识及二连盆地赛51井取得的石炭纪碳酸盐岩油藏的发现,开辟了二连盆地古生界油气勘探的新领域.本文对二连盆地3条典型的CEMP电测量资料进行了二维电阻率反演,结合研究区地震反射资料、钻孔电测井资料、钻井岩芯资料、岩石露头资料,揭示了二连盆地具有"三明治"的电性结构特征,同时指出二连盆地古生界广泛分布,在古生界与中生界之间广泛分布一套以玄武岩、安山岩、凝灰岩等为主的火山岩.这种"三明治"电性结构特征不但给古生界的研究提供了线索和依据,而且火山岩(高阻层)与其下伏古生界地层(低阻层)之间可形成良好的储盖组合(或生储盖组合),其对于古生界油气勘探的研究具有重要的意义.同时,认为二连盆地中、新生界和古生界的构造沉积演化主要经历了4个重要阶段,即:泥盆纪的南北差异性升降阶段、石炭-二叠纪的地层稳定沉积阶段、三叠纪-晚侏罗世的古生代盆地被改造和中新生代盆地构造格架形成的重要演化阶段以及中新生代的地层沉积阶段.     

电法勘探中并行数据采集与传统数据采集效率的比较研究

在电法数据的采集方面:传统的电法勘探数据采集量少、时间长,从而效率较低,通过研究地震勘探中并行数据采集的优点,使电法勘探数据采集模拟地震勘探的数据采集方式.并行电法数据采集采用两种主要的采集方法：一种是单极供电（称为AM法）、另一种是双极供电（称为ABM法）.本文主要通过对数据量的分析比较得出: 在同样电极组合条件下,并行采集物理点的数据是随着电极数量的增加而成二次抛物线增长,从而使电法勘探数据采集效率得到空前提高.     

Geometrical characteristics of phase and group velocity surfaces in anisotropic media

The phase and group velocity surfaces are essential for wave propagation in anisotropic media. These surfaces have certain features that, especially, for shear waves result in complications for modelling and inversion of recorded wavefields. To analyse wave propagation in an anisotropic model, it is important to identify these features in both the phase and group domains. We propose few characteristics for this analysis: the energy flux angle, decomposed in the polar and azimuth angle correction angles and enhancement factor, which is able to characterize both singularity points and triplication zones. The very simple equation that controls the triplications is derived in the phase domain. The proposed characteristics are illustrated for elastic and acoustic anisotropic models of different symmetry classes.     

An Analytical Study for the Dispersion of Pollutants in a Finite Layer under Low Wind Conditions

A steady-state three-dimensional analytical model for the dispersion of a pollutant from a continuously emitting point source in a finite inversion layer has been proposed. The advection along the mean wind and the diffusion in all three directions have been accounted. A closed-form analytical solution of the proposed problem has been obtained using the method of integral transform and the same happens out to be non-Gaussian. Various limiting cases including the crosswind integrated concentration and the standard Gaussian-plume formula have been deduced from the solution obtained.The present model has been evaluated using Hanford diffusion experiment (DORAN et al., 1984) in stable conditions and IIT diffusion experiment (SINGH et al., 1991) in unstable conditions. The dispersion parameters have been computed using the various sigma schemes in accordance with the available observations. The proposed model has performed reasonably well with the data from both the diffusion experiments considered here.     

Analysis of attenuation and dispersion of propagating wave due to the coexistence of three fluid phases in the pore volume

In exploration geophysics, the efforts to extract subsurface information from wave characteristics exceedingly depend on the construction of suitable rock physics model. Analysis of different rock physics models reveals that the strength and magnitude of attenuation and dispersion of propagating wave exceedingly depend on wave-induced fluid flow at multiple scales. In current work, a comprehensive analysis of wave attenuation and velocity dispersion is carried out at broad frequency range. Our methodology is based on Biot's poroelastic relations, by which variations in wave characteristics associated with wave-induced fluid flow due to the coexistence of three fluid phases in the pore volume is estimated. In contrast to the results of previous research, our results indicate the occurrence of two-time pore pressure relaxation phenomenon at the interface between fluids of disparate nature, that is, different bulk modulus, viscosity and density. Also, the obtained results are compatible with numerical results for the same 1D model which are accounted using Biot's poroelastic and quasi-static equation in frequency domain. Moreover, the effects of change in saturation of three-phase fluids were also computed which is the key task for geophysicist. The outcomes of our research reveal that pore pressure relaxation phenomenon significantly depends on the saturation of distinct fluids and the order of saturating fluids. It is also concluded that the change in the saturation of three-phase fluid significantly influences the characteristics of the seismic wave. The analysis of obtained results indicates that our proposed approach is a useful tool for quantification, identification and discrimination of different fluid phases. Moreover, our proposed approach improves the accuracy to predict dispersive behaviour of propagating wave at sub-seismic and seismic frequencies.     

Research Note: On the error behaviour of force and moment sources in simplicial spectral finite elements

The representation of a force or moment point source in a spectral finite-element code for modelling elastic wave propagation becomes fundamentally different in degenerate cases where the source is located on the boundary of an element. This difference is related to the fact that the finite-element basis functions are continuous across element boundaries, but their derivatives are not. A method is presented that effectively deals with this problem. Tests on one-dimensional elements show that the numerical errors for a force source follow the expected convergence rate in terms of the element size, apart from isolated cases where superconvergence occurs. For a moment source, the method also converges but one order of accuracy is lost, probably because of the reduced regularity of the problem. Numerical tests in three dimensions on continuous mass-lumped tetrahedral elements show a similar error behaviour as in the one-dimensional case, although in three dimensions the loss of accuracy for the moment source is not a severe as a full order.     

Fair function minimization for interpretation of magnetic anomalies due to thin dikes, spheres and faults

A new method is proposed to interpret magnetic anomalies due to a thin dike, a sphere, and a fault like structure, where depth, horizontal location, effective magnetization intensity and effective magnetization inclination of a buried structure are simultaneously obtained. The proposed method is based on Fair function minimization and also on stochastic optimization modeling. This new technique was firstly tested on a theoretical synthetic data randomly generated by a chosen statistical distribution from a known model with different random noises components. This mathematical simulation shows a very close agreement between the assumed and the estimated parameters. The applicability and validity of this method are thereafter applied to magnetic anomaly data taken from United States, Australia, India, and Brazil. The agreement between the results obtained by the new method and those obtained by other interpretative methods is good and comparable. Moreover, the depth obtained by such a method is found to be in high accordance with that obtained from drilling information.     

储层双相介质地震波传播理论及流体预测方法

双相介质波传播理论作为油气勘探开发领域的前沿课题,可建立地下储层性质与地面观测数据之间的定量关系,同时可为储层的流体预测提供理论支撑.在阐述储层基本特征的基础上,本文回顾了单一孔隙、含复杂孔隙结构、部分饱和多相流体、各向异性(裂缝系统)双相介质理论的研究进程.同时系统地回顾了基于双相介质理论的波场响应模拟和流体预测方法的发展进程和应用现状,并在前人研究的基础上给出了对地震波场正演和流体预测方法相关研究未来发展趋势的思考和认识,对双相介质理论的应用前景进行了展望.     

Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 7. Single-phase megascale flow models

This work is the seventh in a series that introduces and employs the thermodynamically constrained averaging theory (TCAT) for modeling flow and transport in multiscale porous medium systems. This paper expands the previous analyses in the series by developing models at a scale where spatial variations within the system are not considered. Thus the time variation of variables averaged over the entire system is modeled in relation to fluxes at the boundary of the system. This implementation of TCAT makes use of conservation equations for mass, momentum, and energy as well as an entropy balance. Additionally, classical irreversible thermodynamics is assumed to hold at the microscale and is averaged to the megascale, or system scale. The fact that the local equilibrium assumption does not apply at the megascale points to the importance of obtaining closure relations that account for the large-scale manifestation of small-scale variations. Example applications built on this foundation are suggested to stimulate future work.