TR method (TRM): A separation and stress inversion method for heterogeneous fault-slip data driven by Andersonian extensional and compressional stress regimes

The recently proposed TR method (TRM) which uses the slip preference of the faults to separate heterogeneous fault-slip data in extensional and compressional Andersonian stress regimes, is enhanced so as to determine stress tensors with the use of the Wallace–Bott slip criterion. Published natural fault-slip data from the extensional region of Tympaki, Crete, Greece and artificial fault-slip data modeled from the Chelungpu thrust, activated during the 1999 Chi–Chi earthquake in Taiwan, have been used as case studies. In the first case, the fault-slip data previously considered as homogeneous might actually be of heterogeneous origin as they determine two distinct stress tensors that both fit well with the neotectonic faulting deformation of the region. In the second case, where the fault-slip data belonging to three different subsets are of low diversity, the TRM succeeds in defining the driving stress tensors. The Misfit Angle minimization criterion can adequately separate the fault-slip data between two subsets when the percentage of the “Stress Tensor Discriminator Faults” is higher than approximately 70%.     

基于矩张量反演的传感器校准方法应用和对比

矩张量反演理论是研究深部岩体破裂机制的有效手段,而监测台站/传感器校准对获取准确的矩张量结果十分重要。为求得更加准确的校准系数和矩张量结果,提出一种新的传感器校准方法——搜索校准法。将该方法和监测网校准法分别应用于加利福尼亚州北部的Geysers地热田微震监测数据中,并综合考虑不同震源机制参数、预设校准系数、噪声添加方式及噪声水平等因素的影响,进行两种校准方法有效性对比的理论计算和模拟分析。结果表明：两种校准方法均可通过微震监测数据获得稳定的校准系数,且校准后的震源成分及应力状态分布均更加集中;所有模拟工况下,两种校准方法均可有效降低矩张量反演误差;低噪声条件下,两种方法对应的矩张量反演误差较小且十分接近;混合噪声和高噪声条件下,搜索校准法的准确性和稳定性多优于监测网校准法;进而优选出Geysers地热田微震监测数据更加可靠的矩张量结果。研究思路和结论为微地震矩张量研究提供了进一步指导。     

阻抗张量分解进行大地电磁静校正的研究

地表电性不均匀体对大地电磁测深的静态影响,会使大地电磁测深曲线产生十分严重的畸变,如何进行静校正以获得合理的区域构造响应,引起了国内外大地电磁专家的广泛关注。阻抗张量分解就是近几年发展起来的一种有效的方法。在全面论述阻抗张量分解进行大地电磁静校正原理的基础上,通过模型试算证明了该方法的有效性。     

Present-day stress tensors along the southern Caribbean plate boundary zone from inversion of focal mechanism solutions: A successful trial

This paper presents a compilation of 16 present-day stress tensors along the southern Caribbean plate boundary zone (PBZ), and particularly in western and along northern Venezuela. As a trial, these new stress tensors along PBZ have been calculated from inversion of 125 focal mechanism solutions (FMS) by applying the Angelier & Mechler's dihedral method, which were originally gathered by the first author and published in 2005. These new tensors are compared to those 59 tensors inverted from fault-slip data measured only in Plio-Quaternary sedimentary rocks, compiled in Audemard et al. (2005), which were originally calculated by several researchers through the inversion methods developed by Angelier and Mechler or Etchecopar et al.The two sets of stress tensors, one derived from geological data and the other one from seismological data, compare very well throughout the PBZ in terms of both stress orientation and shape of the stress tensor. This region is characterized by a compressive strike-slip (transpressional senso lato), occasionally compressional, regime from the southern Mérida Andes on the southwest to the gulf of Paria in the east. Significant changes in direction of the maximum horizontal stress (σ_H = σ₁) can be established along it though. The σ₁ direction varies progressively from nearly east-west in the southern Andes (SW Venezuela) to between NW-SE and NNW-SSE in northwestern Venezuela; this direction remaining constant across northern Venezuela, from Colombia to Trinidad. In addition, the σ_V defined by inversion of focal mechanisms or by the shape of the stress ellipsoid derived from the Etchecopar et al.'s method better characterize whether the stress regime is transpressional or compressional, or even very rarely trantensional at local scale.The orientation and space variation of this regional stress field in western Venezuela results from the addition of the two major neighbouring interplate maximum horizontal stress orientations (σ_H): roughly east-west trending stress across the Nazca-South America type-B subduction along the pacific coast of Colombia and NNW-SSE oriented one across the southern Caribbean PBZ. Meanwhile, northern Venezuela, although dextral strike-slip (SS) is the dominant process, NW-SE to NNW-SSE compression is also taking place, which are both also supported by recent GPS results.     

Equivalent Permeability and Simulation of Two-Phase Flow in Heterogeneous Porous Media

The problem of calculating equivalent grid block permeability tensors for heterogeneous porous media is addressed. The homogenization method used involves solving Darcy's equation subject to linear boundary conditions with flux conservation in subregions of the reservoir and can be readily applied to unstructured grids. The resulting equivalent permeability tensor is stable as defined relative to G-convergence. It is proposed to use both conforming and mixed finite elements to solve the local problems and compute approximations from above and below of the equivalent permeability, respectively. Comparisons with results obtained using periodic, pressure and no-flux boundary conditions and the renormalization method are presented. A series of numerical examples demonstrates the effectiveness of the methodology for two-phase flow in heterogeneous reservoirs.     

Analytical expressions to determine the isothermal compressibility tensor and the isobaric thermal expansion tensor for monoclinic crystals: application to determine the direction of maximum compressibility in jadeite

Expressions are presented to allow the simple determination of the magnitudes and directions of the principal axes for the isothermal compressibility tensor and the isobaric thermal expansion tensor for monoclinic crystals. The method is applied to re-evaluate the apparently contradictory results that have recently been obtained for the direction of maximum compressibility in jadeite. The term ‘unit strain’ to describe these second rank tensors is discouraged and the use of the representation quadric for visualisation of second rank tensors is recommended.     

Determination of the orientation of 29Si chemical shift tensors using rotorsynchronized MAS NMR of single crystals: forsterite (Mg2SiO4)

A novel approach is presented to determine both the main axis values and the orientation of ²⁹Si chemical shift tensors using slow rotation of single crystals at the magic angle (MAS). Provided that the MAS frequency is less than the chemical shift anisotropy and that the radiofrequency (r.f.) pulse excitation is rotorsynchronized the single crystal MAS spectra consist of a mixture of absorptive and dispersive line shape contributions to each MAS sideband. Changing systematically the timing of the r.f. excitation with respect to the rotor position a set of spectra is obtained which allows a precise determination of the chemical shift tensors and their orientations with respect to the crystal axis system despite MAS. This method offers both large resolution enhancement and a considerable time saving, in comparison to the traditional determination of chemical shift tensors, where the angular dependence of the resonance frequency at three orthogonal crystal orientations is measured. Both methods are compared using forsterite as test sample.     

Anisotropic Variation Law of Rock Permeability with the Burial Depth of Limestone

Permeability tensors of both macrofracture and microfracture systems were measured progressively along the depth of limestone formations at severed sites. It was found that the principal permeability values KX, Ky and Kz in these permeability tensors all decrease simultaneously and logarithmically with depth. However, the limestone aquifers are composed of an upper region where the larger permeability ellipsoid is upright or prolate and characterized by Kz>Kx and Kz>Ky, a transitional zone, and a lower zone whose smaller permeability ellipsoid is horizontal or oblate and characterized by KZ相似文献   

Equivalent Permeability and Simulation of Two-Phase Flow in Heterogeneous Porous Media

The problem of calculating equivalent grid block permeability tensors for heterogeneous porous media is addressed. The homogenization method used involves solving Darcy's equation subject to linear boundary conditions with flux conservation in subregions of the reservoir and can be readily applied to unstructured grids. The resulting equivalent permeability tensor is stable as defined relative to G-convergence. It is proposed to use both conforming and mixed finite elements to solve the local problems and compute approximations from above and below of the equivalent permeability, respectively. Comparisons with results obtained using periodic, pressure and no-flux boundary conditions and the renormalization method are presented. A series of numerical examples demonstrates the effectiveness of the methodology for two-phase flow in heterogeneous reservoirs.     

Induced anisotropy during plastic straining

The restrictions imposed by the form-invariance principle on the structure of the elasto-plastic constitutive law for small strains are examined. It is shown that the yield and plastic potential functions may depend on the joint invariants of the stress and plastic strain tensors in addition to their dependence on the direct invariants of these tensors and additional scalar hardening parameters such as the plastic work; inclusion of the joint invariants as parameters in the constitutive functions allows for induced anisotropy during plastic deformation. It is demonstrated that the physical meaning of the joint invariants is related to the deviation of the principal directions of the stress tensor from those of the plastic strain tensor. It is also shown that only three cases of anisotropy (orthorhombic, transverse and isotropy) are possible in the types of material models discussed herein. The model proposed in this paper does not imply coaxiality between the principal directions of the stress and, plastic strain increment tensors; however, implications of the assumption of coaxiality on the structure of the constitutive equations is investigated. It is shown that coaxiality does not necessarily imply isotropy, but no deviations from coaxiality can be expected in isotropic materials.     

裂隙岩体三维柔度张量的数值试验方法

在裂隙岩体二维柔度张量数值试验的基础上,建立了裂隙岩体三维柔度张量及其表征单元体积（REV）尺度研究的简化数值试验方法。首先根据岩体裂隙的统计参数及分布规律,运用蒙特卡罗方法在研究域内获得与实际岩体裂隙同分布的三维随机裂隙网络,提取位于不同方位的岩体试件,运用二维柔度张量的数值试验方法求出各个平面方向上的二维柔度张量,然后根据二维与三维柔度张量的拓扑关系,用数学方法求解裂隙岩体的三维柔度张量。对于含3组正交全贯通裂隙的岩体,通过数值试验获得的柔度张量与理论解相比,其主对角线上各参数的误差在5%以内,表明该数值试验方法较为可靠。最后将此方法运用到小湾水电站工程中,确定左岸坝区裂隙岩体的应力REV为11 m×11 m×11 m,并获得该区域裂隙岩体的三维柔度张量。     

Finite element evaluation of diffusion and dispersion tensors in periodic porous media with advection

This paper presents three-dimensional finite element simulations to evaluate diffusion and dispersion tensors in periodic porous media in the presence of an advective velocity field. These tensors are evaluated in the framework of the double-scale expansion technique. Two problems, a Newtonian flow and a vector-valued advection–diffusion equation, have to be sequentially solved at the pore scale. Finite element techniques to approximate these problems are proposed and analyzed. Numerical results in three-dimensional networks of spheres are presented to quantitatively assess the impact of the pore morphology and of the advection velocity on the diffusion and dispersion tensors.     

Characterization of various types of deformation and their corresponding deviatoric stress tensors using microfault analysis

Considering an ideally prefractured material, based on Mohr's representation and Bott's model, we define the geometry and the peculiarities of the different theoretical fault domains which are likely to be reactivated under different tectonic regimes. The theoretical striations associated with the different types of deformation are also calculated. The compressive strike-slip, extensive strike-slip, radial extensive and constrictive types of deformation are specified. In the second part of this paper, using Etchecopar's computer-aided method, a quantitative structural analysis of various types of superficial deformation has been carried out in different study areas (southern France, Greece, Spain, Tunisia and Nigeria). The geometry of the microfault domains, as well as the nature of the associated tensors are determined for each type of regional deformation. The problem of the spatial homogeneity of the tensors deduced by the microtectonic analysis within the framework of a particular tectonic phase is also discussed.     

Tensor visualizations in computational geomechanics

We present a novel technique for visualizing tensors in three dimensional (3D) space. Of particular interest is the visualization of stress tensors resulting from 3D numerical simulations in computational geomechanics. To this end we present three different approaches to visualizing tensors in 3D space, namely hedgehogs, hyperstreamlines and hyperstreamsurfaces. We also present a number of examples related to stress distributions in 3D solids subjected to single and load couples. In addition, we present stress visualizations resulting from single‐pile and pile‐group computations. The main objective of this work is to investigate various techniques for visualizing general Cartesian tensors of rank 2 and it's application to geomechanics problems. Copyright © 2002 John Wiley & Sons, Ltd.     

Correlation of fabric tensors for granular materials using 2D DEM

Acta Geotechnica - Soil fabric anisotropy can be quantitatively assessed by means of fabric tensors introduced as internal variables in constitutive models and defined by unit vectors along the...     

Some applications of the Mohr diagram for three-dimensional strain

The Mohr diagram for strain is rarely used in its full form, as a representation of three-dimensional strain. Recent attention has focused on various uses of the Mohr circle to express two-dimensional strain tensors. This contribution redescribes the Mohr diagram for three-dimensional strain and illustrates some new applications. The Mohr diagram for any strain ellipsoid provides an immediate method for ellipsoid shape classification. However, its greatest new potential is considered to be in the representation of strain ellipses as sections of ellipsoids.Any plane section of a strain ellipsoid can be plotted on the ellipsoid's Mohr diagram: it is here called a ‘Mohr locus’ because it is constructed as a locus of points representing the sheaf of lines which can be considered to define the plane. Mohr loci for sectional ellipses have a variety of forms, according to their orientation in the strain ellipsoid. Generally oblique sections are represented by loops bounded by the three principal circles. Their most leftward and rightward points are the plane's principal axes. Any Mohr locus can be transformed into a Mohr circle for the sectional ellipse.Mohr diagrams with Mohr loci have considerable potential as a graphical method of deriving best-fit strain ellipsoids from natural strain data. This is illustrated in three examples.     

Fault analysis and paleostress evolution in large strain regions: methodological and geological discussion of the southeastern Himalayan fold-and-thrust belt in Pakistan

We document the structure and kinematics of the southeastern part of the fold-and-thrust belt of the Pakistani Himalaya. Field analysis documents the importance of strike–slip faulting associated with folding. Accordingly, a transpression regime is inferred to be responsible for variable amounts of shortening, from fault block to fault block. The analysis of fault populations that affect the Mesozoic to early Miocene sediments allows distinguishing two paleostress tensor directions: a dominant NW–SE compression and a minor E–W compression are compatible with buckling around the N–S axis of the near-by Hazara-Kashmir syntaxis. From the lack of both systematic overprinting-relationships and spatial trend (the two tensors were obtained at different locations) we conclude that in each location any of these two shortening directions can dominate. The distribution of the paleostress tensors substantiates a transpressional regime due to far-field Himalayan compression and a lateral escape component of the allochthonous fold-and-thrust belt away from the growing Hazara-Kashmir anticline.     

Glyph and hyperstreamline representation of stress and strain tensors and material constitutive response

Results of numerical analyses of boundary value problems in geomechanics include output of three‐dimensional stress and strain states. Two‐dimensional plots of stress–stress or stress–strain quantities, often used to represent such output, do not fully communicate the evolution of stress and strain states. This paper describes the use of glyphs and hyperstreamlines for the visual representation of three dimensional stress and strain tensors in geomechanics applications. Glyphs can be used to represent principal stress states as well as normal stresses at a point. The application of these glyphs is extended in this paper to represent strain states. The paper introduces a new glyph, called HWY glyph for the representation of shear tensor components. A load step‐based hyperstreamline is developed to show the evolution of a stress or strain tensor under a general state of loading. The evolution of stress–strain states from simulated laboratory tests and a general boundary value problem of a deep braced excavation are represented using these advanced visual techniques. These visual representations facilitate the understanding of complex multidimensional stress–strain soil constitutive relationships. The visual objects introduced in this paper can be applied to stress and strain tensors from general boundary value problems. Copyright © 2003 John Wiley & Sons, Ltd.     

Brittle tectonic structures and palaeostress analysis in the Isle of Wight,Wessex basin,southern U.K.

Brittle tectonic analysis of Cretaceous–Paleogene sediments at a total of 17 sites located in the Isle of Wight (U.K.) enables four main tectonic events that occurred prior to and after the folding to be identified and successive palaeostress tensors to be determined using the inversion method. Three of the events can be shown to have occurred prior to the folding: (1) a syn-sedimentary extension of Upper Cretaceous age; (2) a strike-slip faulting regime with an ESE–WNW direction of compression; (3) a compressional regime, marked by strike-slip faulting, with an NNE–SSW to N–S direction of compression. The fourth and last compressional event took place after the folding and is characterised both by reverse and strike-slip faulting, with a dominant N–S direction of compression. Syn-folding faults also developed between the third and fourth events. All four events can be connected to the extensional tectonics and different steps of structural inversion, both of which were integral to the development and evolution of the Wessex basin.     

An inverse problem in microtectonics for the determination of stress tensors from fault striation analysis

A method is proposed to compute some characteristics of a possible stress tensor related to striations measured in a given faulted area. If several tectonic phases are responsible for the striations the method separates and determines the successive stress tensors. The iterative algorithm consists of alternatively: (a) sorting the data attributed to a tectonic phase; and (b) computing the characteristics of the stress tensor of this phase. The method is tested using an application to synthetic and actual data.