Characterization of dipping fractures in a transverselyisotropic background

Although it is believed that natural fracture sets predominantly have near‐vertical orientation, oblique stresses and some other mechanisms may tilt fractures away from the vertical. Here, we examine an effective medium produced by a single system of obliquely dipping rotationally invariant fractures embedded in a transversely isotropic with a vertical symmetry axis (VTI) background rock. This model is monoclinic with a vertical symmetry plane that coincides with the dip plane of the fractures. Multicomponent seismic data acquired over such a medium possess several distinct features that make it possible to estimate the fracture orientation. For example, the vertically propagating fast shear wave (and the fast converted PS‐wave) is typically polarized in the direction of the fracture strike. The normal‐moveout (NMO) ellipses of horizontal reflection events are co‐orientated with the dip and strike directions of the fractures, which provides an independent estimate of the fracture azimuth. However, the polarization vector of the slow shear wave at vertical incidence does not lie in the horizontal plane – an unusual phenomenon that can be used to evaluate fracture dip. Also, for oblique fractures the shear‐wave splitting coefficient at vertical incidence becomes dependent on fracture infill (saturation). A complete medium‐characterization procedure includes estimating the fracture compliances and orientation (dip and azimuth), as well as the Thomsen parameters of the VTI background. We demonstrate that both the fracture and background parameters can be obtained from multicomponent wide‐azimuth data using the vertical velocities and NMO ellipses of PP‐waves and two split SS‐waves (or the traveltimes of PS‐waves) reflected from horizontal interfaces. Numerical tests corroborate the accuracy and stability of the inversion algorithm based on the exact expressions for the vertical and NMO velocities.     

Correction factors for SSI effects predicted by simplified models: 2D versus 3D rectangular embedded foundations

The effects of soil‐structure interaction (SSI) are often studied using two‐dimensional (2D) or axisymmetric three‐dimensional (3D) models to avoid the high cost of the more realistic, fully 3D models, which require 2 to 3 orders of magnitude more computer time and storage. This paper analyzes the error and presents correction factors for system frequency, system damping, and peak amplitude of structural response computed using impedances for linear in‐plane 2D models with rectangular foundations, embedded in uniform or layered half‐space. They are computed by comparison with results for 3D rectangular foundations with the same vertical cross‐section and different aspect ratios. The structure is represented by a single degree‐of‐freedom oscillator. Correction factors are presented for a range of the model parameters. The results show that in‐plane 2D approximations overestimate the SSI effects, exaggerating the frequency shift, the radiation damping, and the reduction of the peak amplitude. The errors are larger for stiffer, taller, and heavier structures, deeper foundations, and deeper soil layer. For example, for a stiff structure like Millikan library (NS response; length‐to‐width ratio ≈ 1), the error is 6.5% in system frequency, 44% in system damping, and 140% in peak amplitude. The antiplane 2D approximation has an opposite effect on system frequency and the same effect on system damping and peak relative response. Linear response analysis of a case study shows that the NEHRP‐2015 provisions for reduction of base shear force due to SSI may be unsafe for some structures. The presented correction factor diagrams can be used in practical design and other applications.     

北京平原区断裂构造重力异常识别研究

区域重力异常蕴含丰富的断裂构造特征信息.采用小波多尺度分解、归一化总水平导数垂向导数(NVDR THDR)和剖面2.5D重力异常反演方法对北京平原区高精度区域重力资料进行了处理,获得了主要断裂构造平面位置、长度、规模、汇交关系及深浅延伸特征,分析了利用重力异常识别断裂的效果.结果表明:(1 )北京平原区NE向断裂平面延...     

Three-dimensional domino model in geodynamo

The Lagrangian formalism is applied to consider temporal evolution of the ensemble of interacting magnetohydrodynamical cyclones governed by Langevin-type equations in a rotating medium. This problem is relevant for fast-rotating convective objects such as the cores of planets and a number of stars, where the Rossby numbers are far below unity and the geostrophic balance of the forces takes place. The paper presents the results of modeling for both the two-dimensional (2D) case when the cyclones can rotate relative to the rotation axis of the whole system in the vertical plane, and for the case of spatial rotation by two angles. It is shown that variations in the heat flux on the outer boundary of the spherical shell modulate the frequency of the reversals of the mean dipole magnetic field, which agrees with the three-dimensional (3D) modeling of the planetary dynamo. Applications of the model for giant planets are discussed, and an explanation for some episodes in the history of the geomagnetic field in the past is suggested.     

二维地质体的瞬变电磁场响应特征

直接从时间域出发 ,应用时域有限差分方法 (FDTD)分析地下和地面的瞬变响应。由于二维情况便于图形表示 ,采取了线源二维地电模型。通过对二层均匀地电结构和含二维低阻体时地面垂直感生电动势曲线的计算 ,说明瞬变场响应有滞后现象 ,即异常地质体一旦引起瞬变响应 ,就会往后延时 ,并使响应延续较长时间。在实际的工程勘察中 ,曾用 3～ 5ms以后的延迟时间探测过较浅的异常体 ,如 2 0m至 150m深度范围内的地下老窑采空区 ,并取得了较好的探测效果 ,上述数字模拟结果为以往的实践提供了理论依据     

Quasi-static deformation of a viscoelastic half-space by a displacement dislocation

The correspondence principle is used to get the Laplace transformed solution of the problem of the quasi-static deformation of a viscoelastic half-space by a shear displacement dislocation from the corresponding static elastic results. The transformed solution is inverted for the Voigt and the Maxwell viscoelastic models. It is shown that, for a vertical dip-slip fault, the surface displacements for the viscoelastic case are identical with the elastic displacements. In the case of a vertical strike-slip fault, detailed numerical results are obtained for both a point source and a finite rectangular source. It is found that the results for the viscoelastic models differ significantly from the corresponding elastic results.     

A STUDY OF MAGNETOTELLURIC STATIC DISTORTION IN THE CONTEXT OF INTRUSIVE VOLCANISM1

MT data from a detailed 84-site grid array (28 × 12 km) in the Paraná Basin (Brazil) reveal a high degree of frequency-independent and parallel amplitude distortion. The Palaeozoic sediments across the survey area are covered by 1.2 km of flood basalts. A deep well-log provides some control regarding the emplacement of thin diabase sills but information regarding vertical feeder dikes is non-existent. The degree of parallel behaviour is identified using anisotropy ratios which quantify the extent and bandwidth of the distortion characteristics. A 2D modelling study is carried out using the concept of a horizontally layered (1D) basin with superimposed, small-scale inhomogeneities. Two likely geological distortion structures are considered. The first represents at- or near-surface (0 to 100 m) inhomogeneities. The second represents thin but vertically elongate dikes. The two distortion effects are found to produce different and characteristic behaviour in the H-polarization (TM) mode model data. The modelled E-polarization (TE) mode data are undistorted and provide control. The model developed to represent vertical dikes gives rise to a characteristic frequency dependence which is distinct from that of the undistorted response. This model also generates subparallel distortion effects which give rise to a form of variance in the response estimates as a function of location. The behaviour occurs, importantly, in both the amplitude and phase of the distorted data. A comparison of the normalized amplitude data, observed and modelled, indicates a high degree of correspondence down to a low frequency limit (< 0.1 Hz) where additional and deep contributions to the observed response become apparent. The modelling results and data characteristics indicate that the survey area is underlain by a series of closely parallel, thin intrusive dikes (a dike swarm).     

非轴对称条件下用三维模式匹配法计算电阻率测井响应

采用模式匹配法研究了非轴对称条件下普通电阻率测井响应.根据非轴对称的地层模型,建立了新型的坐标系,确定在井轴与地层法线所形成的XOY平面上用数值方法,与此面垂直的方向上用解析方法.在XOY平面上的数值分析中,构建了广义特征值问题;在Z轴方向的解析部分中,人为地划分了一些介质层,并根据电磁场在层界面的连续性条件,推导出了各层之间场量的传递关系,从而摒弃了传统上二维模式匹配法中的复杂的反射阵和透射阵理论,完成了三维模式匹配理论.多种地层模型的数值结果对比表明,该方法在轴对称条件下的计算结果和二维模式匹配法的计算结果具有很好的一致性.此外,应用此算法还研究了倾斜地层等各种非轴对称的地层模型电阻率测井响应,系统地考察了井斜角对普通电阻率测井响应的影响.     

Kinematic parameters of pure‐ and converted‐mode waves in elastic orthorhombic media

I derive the kinematic properties of single‐mode P, S1, and S2 waves as well as converted PS1, PS2, and S1S2 waves in elastic orthorhombic media including vertical velocity, two normal moveout velocities defined in vertical symmetry planes, and three anelliptic parameters (two of them are defined in vertical symmetry plane and one parameter is the cross‐term one). I show that the azimuthal dependence of normal moveout velocity and anellipticity is different in phase and group domains. The effects on‐vertical‐axis singularity and on‐vertical‐axis triplication are considered for pure‐mode S1 and S2 waves and converted‐mode S1S2 waves. The conditions and properties of on‐vertical‐axis triplication are defined in terms of kinematic parameters. The results are illustrated in four homogeneous orthorhombic models and one multilayered orthorhombic model with no variation in azimuthal orientation for all the layers.     

PARAXIAL RAY TRACING IN 3D INHOMOGENEOUS,ANISOTROPIC MEDIA1

Many investigations of the propagation elastic waves within the earth require a technique for producing synthetic seismograms which is capable of modelling 3D propagation effects. Ray methods are an excellent option for these problems, because they can be made fully 3D and allow a relatively quick and flexible computation of synthetic seismograms. However, the two point problem of finding the ray which connects exactly a specific source and receiver, may still be difficult and time consuming. Therefore, application of the paraxial method, which allows extrapolation of the information on a given ray to nearby receiver locations, is very valuable. With this approach, great savings in computation time and significant simplification of computer codes are possible. We investigate the application of the paraxial ray method to two problems in which the effects of 3D seismic wave propagation are important. The first is a model of a reef structure. In this case, we consider synthetic seismograms for a VSP experimental configuration. When the SV source and well are located along the axis of the reef, only 2D propagation effects are observed. If the source-receiver plane is located to the side of the reef, however, the 3D shape of the reef causes significant amplitudes to be predicted for shear-wave arrivals on the transverse component of the synthetic seismograms. The second example is a ID, layered earth model, but it includes two layers which are azimuthally anisotropic due to the presence of aligned, vertical fractures. This anisotropy leads to 3D raypaths. Synthetic seismographs are presented for a cross-hole geometry both for an equivalent isotropic model and for the direction parallel to the fractures and at an angle of 45° to the fractures in the anisotropic case. These synthetics show that the differences between the isotropic case and the case for source and receivers aligned with the plane of the fractures are small and subtle. On the other hand, the predictions for the direction at 45° to the cracks show shear-wave splitting and significant transverse component signal. These results have important implications for both modelling and for applications such as tomography. It is clear that for some of the cases considered, a 2D algorithm will lead to errors in interpretation of data. In addition, ray-based tomographic techniques will have great difficulty in obtaining a well-defined 2D planar image when the signals are propagating in regions outside the image plane.     

2.5D modelling, inversion and angle migration in anisotropic elastic media

2.5D modelling approximates 3D wave propagation in the dip‐direction of a 2D geological model. Attention is restricted to raypaths for waves propagating in a plane. In this way, fast inversion or migration can be performed. For velocity analysis, this reduction of the problem is particularly useful. We review 2.5D modelling for Born volume scattering and Born–Helmholtz surface scattering. The amplitudes are corrected for 3D wave propagation, taking into account both in‐plane and out‐of‐plane geometrical spreading. We also derive some new inversion/migration results. An AVA‐compensated migration routine is presented that is simplified compared with earlier results. This formula can be used to create common‐image gathers for use in velocity analysis by studying the residual moveout. We also give a migration formula for the energy‐flux‐normalized plane‐wave reflection coefficient that models large contrast in the medium parameters not treated by the Born and the Born–Helmholtz equation results. All results are derived using the generalized Radon transform (GRT) directly in the natural coordinate system characterized by scattering angle and migration dip. Consequently, no Jacobians are needed in their calculation. Inversion and migration in an orthorhombic medium or a transversely isotropic (TI) medium with tilted symmetry axis are the lowest symmetries for practical purposes (symmetry axis is in the plane). We give an analysis, using derived methods, of the parameters for these two types of media used in velocity analysis, inversion and migration. The kinematics of the two media involve the same parameters, hence there is no distinction when carrying out velocity analysis. The in‐plane scattering coefficient, used in the inversion and migration, also depends on the same parameters for both media. The out‐of‐plane geometrical spreading, necessary for amplitude‐preserving computations, for the TI medium is dependent on the same parameters that govern in‐plane kinematics. For orthorhombic media, information on additional parameters is required that is not needed for in‐plane kinematics and the scattering coefficients. Resolution analysis of the scattering coefficient suggests that direct inversion by GRT yields unreliable parameter estimates. A more practical approach to inversion is amplitude‐preserving migration followed by AVA analysis. SYMBOLS AND NOTATION A list of symbols and notation is given in Appendix D .     

Aquifer Vulnerability Assessment Based on Sequence Stratigraphic and 39Ar Transport Modeling

A large‐scale groundwater flow and transport model is developed for a deep‐seated (100 to 300 m below ground surface) sedimentary aquifer system. The model is based on a three‐dimensional (3D) hydrostratigraphic model, building on a sequence stratigraphic approach. The flow model is calibrated against observations of hydraulic head and stream discharge while the credibility of the transport model is evaluated against measurements of ³⁹Ar from deep wells using alternative parameterizations of dispersivity and effective porosity. The directly simulated 3D mean age distributions and vertical fluxes are used to visualize the two‐dimensional (2D)/3D age and flux distribution along transects and at the top plane of individual aquifers. The simulation results are used to assess the vulnerability of the aquifer system that generally has been assumed to be protected by thick overlaying clayey units and therefore proposed as future reservoirs for drinking water supply. The results indicate that on a regional scale these deep‐seated aquifers are not as protected from modern surface water contamination as expected because significant leakage to the deeper aquifers occurs. The complex distribution of local and intermediate groundwater flow systems controlled by the distribution of the river network as well as the topographical variation (Tóth 1963) provides the possibility for modern water to be found in even the deepest aquifers.     

DEPTH IMAGING OF OFFSET VERTICAL SEISMIC PROFILE DATA1

Depth migration consists of two different steps: wavefield extrapolation and imaging. The wave propagation is firmly founded on a mathematical frame-work, and is simulated by solving different types of wave equations, dependent on the physical model under investigation. In contrast, the imaging part of migration is usually based on ad hoc‘principles’, rather than on a physical model with an associated mathematical expression. The imaging is usually performed using the U/D concept of Claerbout (1971), which states that reflectors exist at points in the subsurface where the first arrival of the downgoing wave is time-coincident with the upgoing wave. Inversion can, as with migration, be divided into the two steps of wavefield extrapolation and imaging. In contrast to the imaging principle in migration, imaging in inversion follows from the mathematical formulation of the problem. The image with respect to the bulk modulus (or velocity) perturbations is proportional to the correlation between the time derivatives of a forward-propagated field and a backward-propagated residual field (Lailly 1984; Tarantola 1984). We assume a physical model in which the wave propagation is governed by the 2D acoustic wave equation. The wave equation is solved numerically using an efficient finite-difference scheme, making simulations in realistically sized models feasible. The two imaging concepts of migration and inversion are tested and compared in depth imaging from a synthetic offset vertical seismic profile section. In order to test the velocity sensitivity of the algorithms, two erroneous input velocity models are tested. We find that the algorithm founded on inverse theory is less sensitive to velocity errors than depth migration using the more ad hoc U/D imaging principle.     

Precast industrial buildings in Southern Europe: loss of support at frictional beam-to-column connections under seismic actions

This paper presents the evaluation of the loss-of-support conditions in frictional beam-to-column connections of industrial precast concrete buildings under seismic actions. This type of connection is widespread throughout Southern Europe in non-seismically designed industrial precast buildings. First, geometric properties of industrial precast buildings and of the frictional beam-to-column connections, together with reference values for the friction coefficient, are reviewed. Then, earthquake time histories taken from the European Strong-Motion sets and recordings of the two major shocks of the 2012 Emilia-Romagna events are presented and discussed showing the importance of the vertical component. Two dynamic models of increasing complexity are used to ascertain loss-of-support conditions under seismic action. The first model is an elastic one, representing a single frame of the industrial buildings. Results are obtained according to: (1) 2D analyses, disregarding the time correlation between the response peaks along the horizontal and vertical directions, (2) 2D analyses taking into account time correlation, and (3) 3D analyses to evaluate also directionality effects. The second model is a 2D non-linear planar frame developed within the OpenSees framework. Results show that simplified (linear) models are a good proxy to more refined (non-linear) ones. However, one must resort to non-linear models if differential displacements between beam and column are of interest. The non-linear numerical investigations show that friction coefficient, horizontal and vertical periods and damping, and column reinforcement ratio are the key variables in estimating the loss-of-support conditions.     

Comparison of 3D, 2D and 1D numerical approaches to predict long period earthquake ground motion in the Gubbio plain, Central Italy

In this work we studied the performance of different numerical approaches to simulate the large amplifications of long period earthquake ground motion within the Gubbio plain, a closed-shape intra-mountain alluvial basin of extensional tectonic origin in Central Italy, observed during the Umbria-Marche 1997 seismic sequence. Particularly, referring to the Sep 26 1997 M_w6.0 mainshock, we considered the following numerical approximations: (a) 3D model, including a kinematic model of the extended seismic source, a layered crustal structure, and the basin itself with a simplified homogeneous velocity profile; (b) 2D model of a longitudinal and transversal cross-section of the basin, subject to vertical and oblique incidence of plane waves with time dependence at bedrock obtained by the 3D simulations; (c) 1D model. 3D and 2D numerical simulations were carried out using the spectral element code GeoELSE, exploiting in 3D its implementation in parallel computer architectures. 3D numerical simulations were successful to predict the observed large amplification of ground motion at periods beyond about 1 s, due to the prominent onset of surface waves originated at the southern edge of the basin and propagating northwards. More specifically, the difference of 3D vs 2D results is remarkable, since the latter ones fail to approach such large amplification levels, even when an oblique incidence of plane waves is considered.     

基于BTTB矩阵的快速高精度三维磁场正演

本文改进了一种快速、高精度空间域三维正演算法,用来计算地下场源在水平观测面产生的磁异常ΔT场及其梯度场,以解决传统空间域正演计算效率低的问题.算法采用长方体对场源区域进行剖分,观测点与场源剖分单元体中心点在水平面上的投影重合.改进的算法具有以下三个特点:(1)采用无解析奇点的解析解公式计算磁异常,保证计算精度.(2)通...     

Effect of grain scale alignment on seismic anisotropy and reflectivity of shales

The elastic properties and anisotropy of shales are strongly influenced by the degree of alignment of the grain scale texture. In general, an orientation distribution function (ODF) can be used to describe this alignment, which, in practice, can be characterized by two Legendre coefficients. We discuss various statistical ODFs that define the alignment by spreading from a mean value; in particular, the Gaussian, Fisher and Bingham distributions. We compare the statistical models with an ODF resulting from pure vertical compaction (no shear strain) of a sediment. The compaction ODF may be used to estimate how the elastic properties and anisotropy evolve due to burial of clayey sediments. Our study shows that the three statistical ODFs produce almost identical correspondence between the two Legendre coefficients as a function of the spreading parameter, so that the spreading parameter of one ODF can be converted to the spreading parameter of another ODF. In most cases it is then sufficient to apply the spreading parameter for the ODF instead of the two Legendre coefficients. The effect of compaction on the ODF gives a slightly different correspondence between the two Legendre coefficients from that for the other models. In principle, this opens up the possibility of distinguishing anisotropy effects due to compaction from those due to other processes. We also study reflection amplitudes versus angle of incidence (AVA) for all wave modes, where shales having various ODFs overlie an isotropic medium. The AVA responses are modelled using both exact and approximation formulae, and their intercepts and gradients are compared. The modelling shows that the S‐wave velocity is sensitive to any perturbation in the spreading parameter, while the P‐wave velocity becomes increasingly sensitive to a perturbation of a less ordered system. Similar observations are found for the AVA of the P‐P and P‐SV waves. Modelling indicates that a combined use of the amplitude versus offset of P‐P and P‐SV reflected waves may reveal certain grain scale alignment properties of shale‐like rocks.     

Modeling vertical stratification of CO2 injected into a deep layered aquifer

The vertical stratification of carbon dioxide (CO₂) injected into a deep layered aquifer made up of high-permeability and low-permeability layers, such as Utsira aquifer at Sleipner site in Norway, is investigated with a Buckley–Leverett equation including gravity effects. In a first step, we study both by theory and simulation the application of this equation to the vertical migration of a light phase (CO₂), in a denser phase (water), in 1D vertical columns filled with different types of porous media: homogeneous, piecewise homogeneous, layered periodic and finally heterogeneous. For each case, we solve the associated Riemann problems and propose semi-analytical solutions describing the spatial and temporal evolution of the light phase saturation. These solutions agree well with simulation results. We show that the flux continuity condition at interfaces between high-permeability and low-permeability layers leads to CO₂ saturation discontinuities at these interfaces and, in particular, to a saturation increase beneath low-permeability layers. In a second step, we analyze the vertical migration of a CO₂ plume injected into a 2D layered aquifer. We show that the CO₂ vertical stratification under each low-permeability layer is induced, as in 1D columns, by the flux continuity condition at interfaces. As the injection takes place at the bottom of the aquifer the velocity and the flux function decrease with elevation and this phenomenon is proposed to explain the stratification under each mudstone layer as observed at Sleipner site.     

龙门山高倾角逆断层结构与孕震机制

针对汶川8.0级地震的主破裂面是否以陡立倾角延伸至地壳深部的争议,我们的研究旨在明确发震断层形态随深度分布的二维结构特征, 即断层的倾角及相应段落的深度, 并在此基础上分析发震断层的孕震和发震机理. 利用子空间置信域非线性反演方法, 通过拟合近场的同震水准变形, 获得了分别对应于清平-北川和南坝-青川发震断层的二维弹性位错模型. 结果显示, 此次龙门山中央断裂带的发震断层系统存在明显的南北分区特征. 以北川-南坝为过渡带, 北川以南至清平的发震构造为二元结构, 包括两部分:一是浅部高倾角的逆断层, 倾角在70°~80°以上, 底部深度可达10~15 km, 同震位错主要发生在10 km以上深度, 平均位错超过6 m;二是深部缓倾角的逆断层, 反演得其倾角约25°, 底部可达30 km深度, 位错主要分布于断层的顶部和底部, 平均位错约4 m. 南坝以北的发震断层为单一结构的逆断层, 倾角约60°~70°, 逆断层位错分布于10 km深度以上, 平均位错小于2 m.余震分布和主震震源机制也支持清平以南发震断层为二元结构的推论. 有限元模拟显示,在二元结构的逆断层系统中, 通过提高断层面上正的库仑应力, 深部缓倾角的逆断层活动对浅部高倾角逆断层有明显的促震作用. 模拟还显示地壳缩短不是现今松潘地块地表垂直变形的主要原因, 垂直变形更可能反映了青藏高原东缘相对四川盆地的差异抬升. 对高倾角逆断层的库仑应力作用显示, 差异抬升对龙门山逆断层活动有重要的促进作用.