A mathematical model for orientation data from macroscopic elliptical conical folds

An iterative least-squares technique to fit circular and elliptical conical surfaces to orientation data from folds is presented. A statistical model is used which assumes that each data point is an observation from a Fisher distribution. The mean of this distribution is assumed to lie on the curve to be fitted. Estimates of variances and covariances for the fitting parameters are calculated, and confidence intervals for the cone axis and half apical angle are estimated from variances and covariances. A normal test with null hypothesis that the cone angle is 90° determines if a conical model fits the data better than a cylindrical model. AnF test is used to determine whether an elliptical cone is a better model than a circular cone. In this fashion, macroscopic folds are classified into cylindrical, circular conical, or elliptical conical folds. Examples of these three types of fold are given. The Wynd Syncline near Jasper, Alberta is the first natural elliptical conical fold described as such.     

A mathematical model for orientation data from macroscopic conical folds

Statistical techniques are developed to classify folds into one of three classes: cylindrical, conical, or neither. A translated version of Bingham's distribution on the sphere is applied to orientation data fron conical folds. Iterative least-squares techniques are used to determine the best-fitting small circle (or cone), and confidence intervals for the cone axis and half apical angle are developed. Examples of a cylindrical and a conical fold are given. Another fold is neither cylindrical nor conical and is classified as pseudoconical. Relationships between the Bingham and Fisher distributions are presented.     

A mathematical model for orientation data from macroscopic cylindrical folds

An asymptotic form of Bingham's distribution on the sphere is applied to orientation data from cylindrical folds. Data from cylindrical folds typically form two clusters, one cluster for each fold limb. A bimodal distribution is obtained by fitting a unimodal distribution to each cluster. One parameter of the distribution gives the fold axis, another parameter is directly related to the curvature of the fold limb. Certain tests of hypotheses based on this distribution are the same as tests based on the Dimroth—Watson (symmetric girdle)distribution. One such is the test of whether two folds have the same fold axis.     

褶皱构造的曲率分析及其裂缝估算--以江汉盆地王场褶皱为例

曲面曲率的几何意义可以反映曲面一点邻近区域的具体形态和变形特征,因而可以用来研究褶皱层面的变形特征、构造样式及其可展性.褶皱面裂缝发育主要为一组张裂系,张裂隙走向与最大主曲率的方向垂直.褶皱构造的主曲率在一定程度上可以反映与褶皱有关的张裂隙的发育情况.对于圆柱状褶皱可以估算与褶皱有关的裂缝孔隙度和渗透率.以王场褶皱构造面为例,通过计算二次趋势面的特征值和特征向量得到褶皱构造面主曲率的大小和方向,确定该褶皱为圆柱状褶皱,并对与之相关的裂缝孔隙度和渗透率进行了估算.     

Striated conical structures and related fractures in bituminous coal of the southern Canadian Rocky Mountains

Striated structures, many of which are conical in form, are common mesoscopic features in bituminous and semi-anthracite coals of the southern Canadian Rocky Mountains. The structures are planar, conical to pyramidal in outline and are characterized by striae which radiate from a common apex and bifurcate or “horsetail” to form secondary structures on the master surface. They are up to 20 cm in length, 4 cm in width and have apical angles varying from 10° to 50°. The striated structures occur at numerous localities in both highly sheared and relatively unsheared coal seams.The conical striated structures closely resemble some shatter cones developed in fine-grained rocks, whereas the planar striated structures are somewhat similar to chevron-structured, hackle-marked joints. The pyramidal structures are apparently unique to coal. All three types of structures are considered to be the result of brittle shear fracture based on their occurrence, orientation, and morphology. The apparently restricted occurrence of the structures to coal is likely a function of the homogeneity, and low tensile and compressive strength of bituminous and semi-anthracite coals, possibly augmented by high inter- and/or intra-particle gas pressure resulting from devolatization of the coal during progressive coalification.     

Conical folds and apparent rotations in paleomagnetism (a case study in the Southern Pyrenees)

The so-called apparent rotation was defined as the angular deviation between a local paleomagnetic direction (after the standard bedding correction) and their corresponding paleomagnetic reference [J. Geophys. Res. 85 (1980) 3659]. In this paper, we make a theoretical exploration on this concept and we conclude that (depending on the number, sequence, orientation and magnitude of the deformation axes that have affected to the rock volume) the apparent rotation may be the addition of a vertical-axis rotation plus a spurious rotation. The later is an error whose origin is the inappropriate application of the bedding correction during the restoration (which does not fit the reverse sequence of deformations). Then, Apparent rot. (s.l.) (δ)=Spurious rot. (θ)+Vertical-axis rot. (β).Conical folds are complex geometries that cannot be restored by using the bedding correction. However, appearance of apparent and spurious rotations has not been studied even though the presence of this kind of folds is very common in fold and thrust belts. In this paper, we show a way to restore these structures and its associated paleomagnetic data by means of forward modelling on a stereographic projection. The modelling has to be based on a good characterization of the geometry (fold axis orientation) and understanding of the kinematics of the fold. General modelling has also allowed us to predict the apparent rotation in conical synclines. Its magnitude depends on the semiapical angle and on the degree of development of the fold; the sense of the rotation (clockwise or counter-clockwise) will depend on the sense of rotation the fold axis.The western External Sierras provide an excellent case study of apparent rotations due to the presence of a conical fold in the footwall (Ebro foreland basin) of the South Pyrenean sole thrust. In addition, a vertical-axis clockwise rotation up to 47° (32° in average) has been detected in the hagingwall. An apparent rotation up to 28° (20° in average) is observed in the footwall of the structure when a simple bedding correction is used. This deviation does not fit with the expected Ebro basin direction (reference) and is caused by the effect of the Riglos conical syncline, developed by the flexure of the foot wall ramp of the South Pyrenean sole thrust. The forward modelling carried out considering the geometry and kinematics (non significant rotations in the autochthonous foot wall) of this structure predicts very well the paleomagnetic observations in the field (geographic coordinates) with angular departures of only 5° (in average). The only application of the bedding correction would introduce errors (spurious rotations up to 21°, 12 in average) related to the conical geometry that would not allow the differentiation of these distinct structural units.     

The properties of anisotropic conical failure surfaces in relation to the Mohr–Coulomb criterion

An earlier publication¹ considered the properties of circular conical failure surfaces whose axes coincide with the space diagonal in principal stress space. The present work uses a similar approach to analyse conical surfaces that are offset from the space diagonal. It is shown that cones fitted to the Mohr–Coulomb surface in triaxial compression contain a potential singularity. The occurrence and location of the singularity depends on the Mohr–Coulomb friction angle to which the surface is fitted in triaxial extension. It is shown that for a cone fitted to the same friction angle in both triaxial extension and compression, singular conditions occur when that angle reaches \documentclass{article}\pagestyle{empty}\begin{document}$ \sin ^{ - 1} \left({\sqrt 7 - 2} \right)\left({ = 40.22^\circ } \right) $\end{document}. Even cones fitted to smaller friction angles give significant overestimations of material strength for certain stress paths.     

Modified perspective cylindrical map projection

Some of the famous cylindrical projections are defined by a geometric process that is based on the perspective. This process can be imagined as a semitransparent sphere wrapped by a tube, secant, or tangent, with the same center; then all features of the sphere surface are projected onto the tube surface by light rays from a source in the equatorial plane. Just by changing the light source’s position and tube’s diameter, different maps can result. In every cylindrical perspective projections, distortions are functions of latitude only, thus, the value of distortion is fixed along a parallel (or a small circle). Therefore, distortion isograms are parallels (or small circles), symmetrical in relation of the equator. Consequently, it is suitable for territories having narrow band shape, extended by the equator (or an oblique equator). The proposed projection in this paper introduces another possible adjustment in cylindrical projections, in which axis of cylinder does not pass through the center of the sphere. This may satisfy case, where territories have a closed curve shape. By comparing the distribution of distortions in other famous perspective cylindrical projections (Lambert, stereographic, and central), with that in the proposed modified perspective cylindrical projection, it was found that distribution of area distortion in the proposed projection can be considered better than others. Therefore, in relation to area representation, the modified perspective cylindrical projection can be considered suitable for mapping regions, having shape close to an ellipse.     

一种解析正圆锥状褶皱和复杂环带的方法——三点法

圆锥状褶皱是与圆柱状褶皱几何特征不同但又有一定联系的构造,在自然界并不少见,不仅可以出现于圆柱状褶皱的尾端,而且常见于多期构造变形迭加的地区。作者在辽宁省鞍本地区进行变质岩构造解析时,也遇到了多个不同尺度的圆锥状褶皱。     

圆锥状褶皱的几何分析

长期以来,地质学家习惯于把不同类型和不同成因的褶皱的基本形态当作圆柱状几何性状处理,建立了褶曲构造的基本几何要素,并且以此作为划分构造均匀区段的几何准则。从最近十余年来关于区域变质造山带的大量观测研究证明,还有另一种褶皱,即圆锥状褶皱,广泛发育于褶皱复杂的变质岩系之中,在不同尺度上显示其控制作用和对区域构造格架的影响。     

An alternative interpretation for the formation of doubly plunging folds in sandstone terrains

Folds are marvellous features of mountain terrains, but despite extensive research, many fundamental problems have still not been solved. In terrains of sandstone, fold hinges are rarely straight lines but curved, forming a pattern characterized by doubly plunging, elliptical dome‐and‐basin structures. Such structures are an obvious manifestation of coeval or successive shortening deformation in two orthogonal principal directions in the horizontal plane. Based on an anatomic investigation of the fold pattern of sandstone beds at the rocky beaches of Saint‐Jean‐Port‐Joli (Quebec, Canada), we propose that the doubly plunging folds may result from a transition from a plane deformation to a constrictional deformation due to auxetic effects of quartz‐rich rocks. The sandstone beds possessed potentially such negative values of Poisson's ratio that, when placed under compression in one direction, they become contracted in the transverse direction, producing a series of doubly plunging folds. Further work is needed to approve or disapprove the interpretation.     

朝鲜平南盆地叠加褶皱构造特征

对于朝鲜平南盆地沉积盖层内发育的倒转褶皱,过去一般认为是直立褶皱的次级从属褶皱。通过对平南盆地内倒转褶皱发育区详细的地质调查,结合煤炭开发过程中获得的地质及钻探资料,提出平南盆地内叠加褶皱的主要识别标志为：地质平面图上呈现不同类型的两组褶皱脊线的交叉;倒转褶皱的轴面被直立褶皱改造弯曲;直立褶皱的两翼发育的倒转褶皱表现为两组牵引褶皱。查明了平南盆地存在3个阶段的褶皱构造：第一阶段为东西向的倒转褶皱,形成于印支期;第二阶段褶皱为东西向的直立褶皱,形成于早燕山期;第三阶段褶皱为北北东向的直立褶皱,形成于晚燕山期。     

Stability charts for wet conical deposits

conclusion Presented are results of a 3-D limit-equilibrium stability analysis of wet conical deposits. A simplified methodology to include the effect of increased pore pressures, resulting from a brief and heavy rainfall, is suggested. The results, condensed into charts, enable one to estimate the factor of safety of a conical heap. Furthermore, one can predict also the volume of potential failure and thus assess its cost. knowledge of both factor of safety and cost of potential failure may lead towards a more rational design as compared to knowledge of the safety factor alone.The outlined 3-D procedure can be extended to deal with earthquake stability via the conventional pseudo-static approach and the proper modification of the moment equilibrium equation. Moreover, if the pore-pressure distriution in a specific case is known, one can use the dimensional algorithm (i.e., Equation 4) together with a general numerical procedure to assess the safety of that problem.     

Flow pattern within a Permian submarine slump recorded by oblique folds and deformed fossils, Ulladulla, south-eastern Australia

The flow pattern within a slump in Permian marine rocks of the southern Sydney Basin, Australia, is recorded by folds and deformed fossils. Abundant brachiopod and bryzoan fossils in the slumped rocks are relatively undeformed, but fossil crinoid stems have been deformed by relative rotation of individual ossicles. Measurement of the strain indicates that the deformation of the crinoids is consistent with flexural flow folding within the slump. Previous models assume that curved slump fold axes remain parallel to the enveloping bedding surface of a slump sheet. Detailed measurements of the orientation of slump folds in this study found fold axes to be oblique to bedding, which is interpreted as a result of folds plunging downward towards the flanks of the slump or slump lobes. In the present model, fold axes are not generally parallel to the strike of the fold axial surface, and this can explain differences between the orientations of slump fold axes and axial surfaces when these are used as directional indicators of slump movement.     

Laboratory experiments on three-dimensional deformable granular landslides on planar and conical slopes

Landslides of subaerial and submarine origin may generate tsunamis with locally extreme amplitudes and runup. While the landslides themselves are dangerous, the hazards are compounded by the generation of tsunamis along coastlines, in enclosed water bodies, and off continental shelves and islands. Tsunamis generated by three-dimensional deformable granular landslides were studied on planar and conical hill slopes in the three-dimensional NEES tsunami wave basin at Oregon State University based on the generalized Froude similarity. A unique pneumatic landslide tsunami generator (LTG) was deployed to control the kinematics and acceleration of the naturally rounded river gravel and cobble landslides to simulate broad ranges of landslide shapes and velocities along the slope. Lateral and overhead cameras are used to measure the landslide shapes and kinematics, while acoustic transducers provide the shape of the subaqueous deposits. The subaerial landslide shape is extracted from the camera images as the landslide propagates under gravity down the hill slope, and surface reconstruction of the landslide is conducted using the stereo particle image velocimetry (PIV) system on the conical hill slope. Subaerial landslide surface velocities are measured with a planar PIV system on the planar hill slope and stereo PIV system on the conical hill slope. The submarine deposits are characterized by the runout distances and the deposit thickness distributions. Larger cobbles are observed producing hummock type features near the maximum runout length. These unique laboratory landslide experiments serve to validate deformable landslide models as well as provide the source characteristics for tsunami generation.     

湘中盆地龙山穹窿构造样式及其成因机制

本文选取湘中盆地龙山穹窿体为研究对象,主要沿二条近正交剖面开展了详细的野外地质调查、构造解析工作。系统地对龙山穹窿体进行了地层产状、轴面劈理产状、逆冲断层及其擦痕线理进行了测量和统计。根据褶皱样式与轴面劈理的配套关系,并结合卷入叠加变形的地层,以及轴面劈理的错切关系综合分析,确定NE-SW向褶皱叠加在近WNW-ESE向(近EW向)褶皱之上,确定叠加干涉样式属于Ramsay分类中典型的穹盆叠加样式。在区域地质关系与演化对比基础上,确定龙山穹窿是加里东期和燕山期褶皱复合叠加变形的结果;依据剖面构造分析及前人研究成果,确定泥盆系与前泥盆系间的区域性角度不整合和南华系与基底间拆离断层为两套区域性潜在滑脱层,并认为滑脱层在龙山穹隆体形成和发育过程中具有控制作用。通过对二期古构造应力场的恢复,重建了区域构造演化,建立了龙山穹窿体由拆离断层及软弱层控制的褶皱叠加构造模型。龙山穹窿体的褶皱叠加过程在华南大陆,特别是雪峰山造山带构造演化中具有代表性,表明加里东运动和燕山运动的叠加和复合是雪峰山造山带的重要构造表现形式,这为深入研究雪峰山造山带结构与演化提供了依据。     

Regional flow perturbation folding within an exhumation channel: A case study from the Cycladic Blueschists

Kilometre-scale cylindrical folds and associated parasitic folds that trend at small angles to the transport lineation are analysed along a 100-km-long transport-normal segment of the Cycladic Blueschists in an attempt to reconstruct the 3D structural architecture within an exhumation channel. Reversals in the polarity of both fold vergence and the hinge/lineation obliquity occur in a flow-normal direction, defining transport-parallel culmination and depression surfaces that root downwards onto an underlying detachment. Fold patterns generated around culmination and depression surfaces support models of flow-perturbation folding where folds initiate at small angles or sub-parallel to transport in response to wrench-dominated differential shearing. Successive culmination and depression surfaces are separated from one another by along strike distances of ∼20 km, although atypical fold geometries developed in the flanks of major culmination and depressions follow their own patterns, revealing that smaller perturbations occur within the larger scheme. Major culminations are interpreted to reflect regions of surging flow marked by increased velocity during exhumation, whilst the opposite is true for depressions. This behaviour implies that on a regional scale, differential shear varies laterally in an irregular-sinusoidal manner defining areas of relative high and relative low displacement within the exhumation channel.     

Elastostatic deformation of a half-space under conical loading

In the idealised modelling of ground distortion induced by a freely deposited heap of granular material, consideration is given to a fundamental problem in classical elasticity whereby an axisymmetric distribution of vertical conical loading is applied to the surface of a half-space. Closed-form expressions are derived for the deformed shape of the surface, and three variations of the integral transform method are described for determining stresses and displacements within the half-space. Extensive numerical results are presented in graphical form.     

Movement of water through the thick unsaturated zone underlying Oro Grande and Sheep Creek Washes in the western Mojave Desert,USA

Previous studies indicate that a small quantity of recharge occurs from infiltration of streamflow in intermittent streams in the upper Mojave River basin, in the western Mojave Desert, near Victorville, California. Chloride, tritium, and stable isotope data collected in the unsaturated zone between 1994 and 1998 from boreholes drilled in Oro Grande and Sheep Creek Washes indicate that infiltration of streamflow occurs to depths below the root zone, and presumably to the water table, along much of Oro Grande Wash and near the mountain front along Sheep Creek Wash. Differences in infiltration at sites along each wash are the result of hydrologic variables such as proximity to the mountain front, quantity of streamflow, and texture of the subsurface deposits. Differences in infiltration between the washes are the result of large-scale geomorphic processes. For example, Oro Grande wash is incised into the Victorville fan and infiltration has occurred at approximately the same location over recent geologic time. In contrast, Sheep Creek Wash overlies an active alluvial fan and the stream channel can move across the fan surface through time. Infiltration does not occur to depths below the root zone at control sites outside of the washes. Electronic Publication     

贵州省织纳煤田煤炭资源潜力评价

织纳煤田含煤地层上二叠统为海陆交互相沉积,含煤层数多,厚度大,煤质较好。通过区内含煤性、煤层煤质及聚煤规律研究,对煤炭资源潜力及勘查开发前景做出综合评价。以向斜构造为基本单元划分了15个赋煤单元和2个赋煤小区,共圈定了81个预测区,预测2000m以浅潜在资源量334.325 6亿t,探获资源储量191.646 0亿t,总资源量525.971 6亿t,并提出煤炭资源勘查开发利用建议:6个近期部署区优先安排普查,10个中期部署区考虑安排预查,9个远期部署区目前暂不宜开展勘查工作。