Parallel Cross Sections Research Articles

An automated method for topology consistent processing of parallel geological cross-sections based on topology reasoning

The 3D modeling method based on parallel geological cross-sections is suitable for modeling large-scale bedrock geological bodies. However, there are usually more branching, pinch-out strata, deformation structures (such as faults and folds), and the correspondence problem of geological boundaries between adjacent cross-sections. These problems have become the most crucial obstacle in the current application of 3D geological modeling based on parallel geological cross-sections. To this end, this paper proposes a topological reasoning automatic processing method for the consistency of parallel geological cross-sections to obtain topologically consistent adjacent cross-sections efficiently. The method involves (1) Stratigraphic inference based on the distance and topological relationships, transforming strata with m:n relationships into three relatively simple cases of 1:1, 1:n, and 1:0; (2) Splitting branching strata based on the Voronoi diagram, transforming strata with 1:n relationships into 1:1 relationships; (3) Dealing pinch-out strata based on the method of filling virtual strata, transforming strata with 1:0 relationships into 1:1 relationships (4) Topologically consistent processing of stratigraphic boundaries based on automatic recognition of no-corresponding arcs and addition of virtual stratum. Based on experiments in the Longtoushan Hill area in Jiangsu Province, China, and the southeast side of Chandler Mountain, Alabama, USA, this method can effectively replace the many manual processes such as determining the location of pinch-out adding auxiliary cross-sections and performing branching strata correspondence in the current application of 3D geological modeling based on arc segments. The geological cross-sections processed based on this method have an exemplary data structure and consistent topological relationships. The 3D geological modeling algorithm based on parallel cross-sections has the advantages of low algorithm complexity, high automation, and stable modeling quality.

A Middle Devonian vernal pool ecosystem provides a snapshot of the earliest forests.

The dichotomy of the earliest ecosystems into deltaic and floodplain forests was a long-standing view in paleobotany. The morphological traits such as nonbranching rootlets, bifurcating rhizomes, and bulbous bases of the primitive trees such as Eospermatopteris and lycopsids were considered adaptations to the lowland deltaic environments. In contrast, the traits of Archaeopteris trees such as wood, hierarchical branching networks of roots, and true leaves are an adaptation to the upland floodplain environments. The discovery of the Town of Cairo Highway Department (TCHD) fossil site in Upstate New York, where all major clades occupied a floodplain environment casts doubt on the validity of the environmental partition by the earliest trees at the higher taxonomic levels. This study aims to test the hypothesis of the environmental partition at the local scale by reconstructing the fossilized forest-floor landscape, the changes in the landscape over time, and the distribution patterns of the trees along the local environmental gradient at the TCHD site. To reconstruct the fossilized forest floor and to determine the environmental variations at the local scale, seven parallel cross-sections were drawn from south to north at THCH. The outcrop at the quarry floor measured 300 m in the north-south, and varied around 100–150 m in east-west direction. Primary sedimentary structures, the thickness of the sedimentary deposits that formed the forest floor and the surrounding quarry walls, paleosol features, and mega-fossils were measured, recorded, described, and mapped. Up to 3 meters deep drill-cores were extracted from the forest floor. The data was used to correlate the sedimentary deposits, and reconstruct the preserved landscape. Three dominant landscape features including an abandoned channel, an old-grown forest, and a local depression were recognized. These landscape features influenced greatly the pattern of local drainage, slope-gradients, patterns and durations of seasonal water pooling, paleosol developments, fossil distribution, and depositional environments. There is no evidence of environmental partitioning by trees at higher taxonomic levels at the local scale. The size and morphology of the root systems didn’t determine the distribution of the trees along the local environmental gradient such as drainage patterns but played important roles in tree stabilization. Forests would go through self-thinning as they matured. Upon comparison, it was found that the forests in unstable environments showed greater resiliency compared to forests established in the stable environments.

Along-strike structural variation in a salt-influenced fold and thrust belt: Analysis of the Kuqa depression

The Kuqa depression is associated with complex salt structures. Variation in fold geometries and subsalt fault activities were investigated using parallel cross-sections to reveal detailed along-strike variations within the Keshen 5 segment and their controlling factors. Along-strike variations were identified in both suprasalt and subsalt units. Linkages, such as the location of a transfer zone, were apparent, while the distribution of variations above and below the salt layer were decoupled. The results indicate that the pre-existing salt wall is the key factor driving along-strike variations because it acts as a weak zone that influences deformation propagation. Suprasalt structural variation results in different sediment depths, which have a significant impact on subsalt fault activity. In the eastern segment, fault activity decreases from the hinterland to the basin. In contrast, owing to the pre-existing salt wall and deep sedimentation near the hinterland in the western segment, the fault beneath the salt wall is characterized by maximum displacement. This study reveals the connection between suprasalt and subsalt deformation and the role of that a salt diapir plays in along-strike structural evolution variations for the Keshen 5 segment of the Kuqa depression. These findings are relevant for understanding along-strike deformation propagation and structural variation in other fold and thrust systems.

Approximation of 3D objects by piecewise linear geometric interpolants of their 1D cross-sections

In this paper we introduce a method for reconstruction of 3D objects from their 1D parallel cross-sections by set-valued interpolation. We regard a 3D object as the graph of a set-valued function defined on a planar domain, with the given 1D cross-sections as its samples. The method is based on a triangulation T of the sampling points in the planar domain and it is modular: for each triangle in T the corresponding 1D cross-sections are geometrically interpolated by a union of polyhedrons. The union of these interpolants over all triangles of T constitutes the approximating 3D object. Properties of this approximation are studied, in particular we derive the approximation order of the error, measured by the symmetric difference metric.

Specificity of the 137Cs distribution in arable elementary landscape-geochemical system contaminated during the accident at the Chernobyl NPP

The main goal of the work was to check whether the regularity in the 137Cs distribution, established in the undisturbed forest elementary landscape-geochemical system (ELGS: i.e., the upper - slope - closing depression), is the same in the meadow system. Cs-137 activity was measured with a step of 1 m by field gamma-spectrometer along three parallel cross-sections, the two of them 185 m long and 15 m away from each other, the third one in between (at the selected measurement points). Obtained results confirmed that despite plowing after the accident 137Cs variation in the arable ELGS demonstrate a pronounced and stable cyclic regularity close to synchronic (r = 0.744, n = 155). 137Cs vertical distribution studied in 44 soil cores down to the depth of 40 cm in 2–5 cm increments (541 specimen in total) confirmed the field plowing after the accident. The radionuclide inventory in the top 10–20 cm layer correlated with the field gamma-spectrometry measurement at the corresponding sampling point. The revealed regular variability of 137Cs distribution in arable conditions allowed us to suggest existence of the universal mechanism responsible for the secondary distribution of elements in ELGS. In our opinion water is the only factor and working body which can produce such an effect. If our hypothesis is correct the obtained results provide valuable information for improving spatial schemes of pollution monitoring and fertilizer application.

S‐Wave Receiver Function Analysis of the Pampean Flat‐Slab Region: Evidence for a Torn Slab

AbstractFlat‐slab subduction is an atypical form of subduction where the downgoing plate assumes a low‐angle or subhorizontal geometry as it descends beneath the overriding plate. These systems have profound impacts on upper‐plate deformation and volcanism, yet there are outstanding questions regarding the causes, initiation, and termination of flat‐slab subduction. The Pampean flat‐slab region, located in the South American Cordillera, is an ideal locale to study the evolution of these systems due to its well‐constrained geologic history and the continuity of subduction along the western margin of the continent. In this work, we utilize S wave receiver functions (SRFs) to measure the thicknesses and geometry of the subducting Nazca plate lithosphere and the overriding South American plate within the region. Results from this study show overthickened Nazca Plate crust (~15–20 km thick) in the flat‐slab region. Prior to the slab steepening, SRFs indicate a velocity increase rather than a decrease at the top of slab crust, which is consistent with a transition from basalt to eclogite within the crust as it dehydrates. Margin parallel cross sections are consistent with differing transitions between flat‐subduction and more‐typical subduction occurring to the north and south. In the north, the transition appears to be gradual, consistent with slab bending. To the south, SRFs indicate an abrupt change, consistent with slab tearing. These differences are consistent with significant variations in slab rheology along the margin, which may reflect differing thermal regimes. This work has global implications for the three‐dimensional effects of flat‐slab subduction.

Support-free hollowing for 3D printing via Voronoi diagram of ellipses

3D printing, also called additive manufacturing, has been increasingly popular and printing efficiency has become more critical. To print artifacts faster with less material, thus leading to lighter and cheaper printed products, various types of void structureshave been designed and engineered inside of shape models. In this paper, we present a novel method for generating support-free elliptic hollowing for 3D shapes which can entirely avoid additional supporting structures. To achieve this, we perform the ellipse hollowing in one of the cross sectional polygons and then extrude the hollowed ellipses to the other parallel cross sections. To efficiently pack the ellipses in the polygon, we construct the Voronoi diagram of ellipses to reason the free-space around the ellipses and other geometric features by taking advantage of the available algorithm for the efficient and robust construction of the Voronoi diagram of circles. We demonstrate the effectiveness and feasibility of our proposed method by designing and printing support-free hollow for various 3D shapes using Poretron, the program which computes the hollow by embedding appropriate APIs of the Voronoi Diagram Machine library that is freely available from Voronoi Diagram Research Center. It takes a 3D mesh model and produces an STL file which can be either fed into a 3D printer or postprocessed.

CT Attenuation of Pericoronary Adipose Tissue in Normal Versus Atherosclerotic Coronary Segments as Defined by Intravascular Ultrasound.

The factors influencing genesis of atherosclerosis at specific regions within the coronary arterial system are currently uncertain. Local mechanical factors such as shear stress as well as metabolic factors, including inflammatory mediators released from epicardial fat, have been proposed. We analyzed computed tomographic (CT) attenuation of pericoronary adipose tissue in normal versus atherosclerotic coronary segments as defined by intravascular ultrasound (IVUS). We evaluated the data sets of 29 patients who were referred for invasive coronary angiography and in whom IVUS of 1 coronary vessel was performed for clinical reasons. Coronary CT angiography was performed within 24 hours from invasive coronary angiography. Computed tomographic angiography was performed using dual-source CT (Siemens Healthcare; Forchheim, Germany). A contrast-enhanced volume data set was acquired (120 kV, 400 mA/rot, collimation 2 × 64 × 0.6 mm, 60-80 mL intravenous contrast agent). Intravascular ultrasound was performed using a 40-MHz IVUS catheter (Atlantis; Boston Scientific Corporation, Natick, Mass) and motorized pullback at 0.5 mm/s. Sixty corresponding coronary artery segments within the coronary artery system were identified in both dual source computed tomography and IVUS using bifurcation points as fiducial markers. In dual source computed tomography data sets, 8 serial parallel cross sections (2-mm slice thickness) were rendered orthogonal to the center line of the coronary artery for each segment. For each cross section, pericoronary adipose tissue within a radius of 3 mm from the coronary artery and enclosed within the epicardium (excluding coronary veins and myocardium) was manually traced and mean CT attenuation values were obtained. Intravascular ultrasound was used to define coronary segments as follows: presence of predominantly fibrous atherosclerotic plaque (hyperechoic), presence of predominantly lipid-rich atherosclerotic plaque (hypoechoic), and absence of atherosclerotic plaque. In IVUS, 20 coronary segments with fibrous plaque, 20 segments with lipid-rich plaque, and 20 coronary segments without plaque were identified. The mean CT attenuation of pericoronary adipose tissue for segments with any coronary atherosclerotic plaque was -34 ± 14 Hounsfield units (HU), as compared with -56 ± 16 HU for segments without plaque (P = 0.005). The density of pericoronary fat in segments with fibrous versus lipid-rich plaque as defined by IVUS was not significantly different (-35 ± 19 HU vs -36 ± 16 HU, P = 0.8). Mean CT attenuation of pericoronary adipose tissue is significantly lower for normal versus atherosclerotic coronary segments. This supports a hypothesis of different types of pericoronary adipose tissue, the more metabolically active of which might exert local effects on the coronary vessels, thus contributing to atherogenesis.

Small devices for longitudinal compensation in overhead power lines

Distributed-series impedance (DSI) technology for overhead power lines is under active development in the United States and Russia. DSI can be used for a wide range of application, for example, for redistribution of power flows in parallel lines and cross sections; phase balancing; increasing the power-transfer capability, stability, and reliability of the functioning of an electric-power network; and reducing power losses. This article describes the principles of operation of the DSI and proposes a generalized analytical model, which illustrates the concept of controlling the reactance introduced by means of a device in a power line. The structure of an inductive-capacitive DSI with two capacitors made by OAO G.M. Krizhizhanovskii Energetics Institute in cooperation with AO NTTs FSK EES is described in detail. This work discusses general characteristics and parameters of the device. The main modes of operation of the developed DSI prototypes are presented. The feasibility of the devices has been confirmed during trial operation.

Comparison of Residual Stress Measured by Diffraction Method and Matrix Etching Method in SiC Fiber Reinforced Titanium Matrix Composites

Measurement and modeling of residual stresses in SiC fiber reinforced titanium matrix composites (SiCf/Ti) are still a challenge. Diffraction method and matrix etching method can characterize the strains of matrix and fiber, respectively. A In this work, SiCf/Ti samples with perpendicular and parallel cross-sections to the fibers have been fabricated, and the residual stresses were measured by X-ray diffraction and matrix etching. The results showed that the axial matrix stress in sample with perpendicular cross-sections to the fibers was larger than that in sample with parallel cross-sections to the fibers, while the axial matrix stress calculated from etching was consistent with that from X-ray diffractions based on triaxle stress model, confirming the reliability of triaxle stress model.

3D geological modelling based on 2D geological map

ABSTRACTCurrent methods for constructing a 3D geological model of an area require field drilling or measured section data which are often not available over large areas. 2D geological maps not only contain information on the distribution of geological strata but also provide sufficient geometric, topological and semantic information for 3D geological modelling. This paper presents a method for constructing a detail 3D model from 2D geological maps. First, a series of parallel cross sections is automatically created from the 2D geological map and the corresponding relationships of the geological objects in the cross sections are recorded. Second, a contour algorithm is used to connect these cross sections to establish a 3D geological model of the study area. The spacing of cross sections has strong impact on the result, we proposed a rule to determine the spacing of cross sections adaptively. As a case study, the method was applied to construct a 3D geological model for Xing-gang area in Chongqing city. The results of this case study suggest that the method is effective to construct a quality 3D geological model solely based on the information from a 2D geological map of the area.​​​​​

Using laterally compatible cross sections to infer fault growth and linkage models in foreland thrust belts

We investigate changes in shortening, displacement and fold geometry to understand the detailed along-strike structural variation within fold-thrust belts, and infer thrust growth and linkage mechanisms. Field observations from the Vercors in SE France are used to characterise deformation style in the region. Parallel cross sections are constructed, analysed and used to create shortening and thrust displacement profiles from the northern to southern Vercors. Sections show changes in structural style and shortening accommodation from thrust-dominated in the north to fold-dominated in the south. The total shortening distance in the Vercors does not change significantly along strike (3400–4650 m), however displacements along individual thrust zones do vary significantly and displacement profiles show a range in displacement gradients (16–107 m/km). Despite relatively simple shortening patterns in the Vercors, sections show a more complex 3D internal structure of the fold-thrust belt. Thrust displacements and geometries suggest both large-scale thrust zones and small-scale thrusts are soft linked, transferring displacement along strike through transfer zones. Short, soft-linked thrust segments indicate an intermediate stage of thrust growth and linkage, well documented for normal fault systems, which form prior to the formation of thrust branches and hard-linked displacement transfer.

Estimation and simulation for geospatial porosity and permeability data

Reservoir simulation of \(\hbox {CO}_2\) sequestration, energy recovery, and environmental contamination scenarios must be accompanied by uncertainty quantification. Typically this is done by stochastically modeling porosity and permeability fields, simulating realizations based on the model, and then numerically simulating flow and transport. The challenge is to generate simulated porosity and permeability fields with characteristics as similar as possible to those known of the reservoir under study. In this paper we focus on the first two steps above in analyzing a large 3-dimensional array of geospatial porosity data and using the results to produce simulated data with characteristics mimicking those of the original porosity observations. The spatial covariance is empirically approximated from horizontal cross sections of the data via a kernel principle component analysis yielding dimension reduction. Simulations in three dimensions are produced by linking consecutive parallel cross sections via conditioning on a small subarray of the data. The conditional simulations effectively reproduce observed channeling, an important large scale feature of interest in the sub-surface relevant to transport of contaminates. The original porosity data is non-Gaussian and requires additional analysis and transformation to generate both porosity and permeability fields.

Geometry characterization and depth determination of deep water reservoirs: the case of the Jebel Sidi Abd Er Rahmane region (Cap Bon, northeastern Tunisia)

This paper shows a new method that allows determining the accurate depths of the top and the bottom of the water reservoirs at every point in the field. We have applied this method on the Jebel Sidi Abd Er Rahmane region in the northeast of Tunisia. This region shows the outcrop of the most old sedimentary series in the Cap Bon peninsula which spread from the Middle Eocene to Quaternary. The construction of real parallel structural cross sections covering the study region has allowed the depth and the continuation of the water reservoirs by establishing isobaths maps with a 25-m contour interval to be followed. These maps reveal that the maximum depth of the base of the water reservoirs is between 850 and 2900 m below sea level which explain the presence of thermal springs in this region. Folding that affect sedimentary series in the Jebel Sidi Abd Er Rahmane region has led these reservoirs to crop out in the surface with important width and length and strata dip between 20° and 35° which provided a continuous recharge to these reservoirs.

Accurate Surface Reconstruction in 3D Using Two-dimensional Parallel Cross Sections

In medical imaging or computational biology, it is required to reconstruct a surface from contours in cross sections for visualization and further processing. We propose a method to generate a surf...

Hyperplane sections, Gröbner bases, and Hough transforms

The purpose of this paper is twofold. In the first part we concentrate on hyperplane sections of algebraic schemes, and present results for determining when Gröbner bases pass to the quotient and when they can be lifted. The main difficulty to overcome is the fact that we deal with non-homogeneous ideals. As a by-product we hint at a promising technique for computing implicitization efficiently.In the second part of the paper we deal with families of algebraic schemes and the Hough transforms. We compute the dimension of the Hough transforms, and show that in some interesting cases it is zero. Then we concentrate on their hyperplane sections; some results and examples hint at the possibility of reconstructing external and internal surfaces of human organs from the parallel cross-sections obtained by tomography.

Parametric 3D reconstruction of the distribution density of point objects

The parametric reconstruction method has been developed for solving the problems concerning computer simulation of the 3D distributions of discrete objects, which are commonly specified by the parallel cross sections in the initial point cloud. The role of simulation and the model itself is examined as applied to the visualization of 3D distributions of objects and the analysis of microscopy data. The conceptual prerequisites and particularities of the technical implementation of the proposed method are compared with the lofting technique, which is widespread in modern 3D simulation systems. The peculiarities of method application are demonstrated by the example of reconstruction based on a series of model data.

Differential axial contrast of optical sections: laser microtomography and quantitative 3D reconstruction

Specific features of the quantitative laser microtomography of biological samples are discussed. The method exhibits the main advantages of a confocal microscope (rapid measurement of a stack of parallel optical cross sections and accurate displacement of an object along the optical axis). A relatively high contrast is reached owing to the superposition of pairwise complementary images on neighboring cross sections. A simple and convenient algorithm for image processing does not require additional software and can be computerized using a conventional graphic editor. The applicability of the method is illustrated using volume measurements of a single cell of an early mouse embryo.

Extracting topographic swath profiles across curved geomorphic features

Abstract. We present a new method to extend the widely used geomorphic technique of swath profiles towards curved geomorphic structures such as river valleys. In contrast to the established method that hinges on stacking parallel cross sections, our approach does not refer to any individual profile lines, but uses the signed distance from a given baseline (for example, a valley floor) as the profile coordinate. The method can be implemented easily for arbitrary polygonal baselines and for rastered digital elevation models as well as for irregular point clouds such as laser scanner data. Furthermore it does not require any smoothness of the baseline and avoids over- and undersampling due to the curvature of the baseline. The versatility of the new method is illustrated by its application to topographic profiles across valleys, a large subduction zone, and the rim of an impact crater. Similarly to the ordinary swath profile method, the new method is not restricted to analyzing surface elevations themselves, but can aid the quantitative description of topography by analyzing other geomorphic features such as slope or local relief. It is even not constrained to geomorphic data, but can be applied to any two-dimensional data set such as temperature, precipitation or ages of rocks.

Stability and vibration analysis of axially-loaded shear beam-columns carrying elastically restrained mass

Classical shear beams only consider the deflection resulting from sliding of parallel cross-sections, and do not consider the effect of rotation of cross-sections. Adopting the Kausel beam theory where cross-sectional rotation is considered, this article studies stability and free vibration of axially-loaded shear beams using Engesser’s and Haringx’s approaches. For attached mass at elastically supported ends, we present a unified analytical approach for obtaining a characteristic equation. By setting natural frequencies to be zero in this equation, critical buckling load can be determined. The resulting frequency equation reduces to the classical one when cross-sections do not rotate. The mode shapes at free vibration and buckling are given. The frequency equations for shear beam-columns with special free/pinned/clamped ends and carrying concentrated mass at the end can be obtained from the present. The influences of elastic restraint coefficients, axial loads and moment of inertia on the natural frequencies and buckling loads are expounded. It is found that the Engesser theory is superior to the Haringx theory.