TRILINEAR DIAGRAM REVISITED: APPLICATION, LIMITATION, AND AN ELECTRONIC SPREADSHEET PROGRAM

Abstract. The trilinear diagram has been used extensively in hydrochemical studies. The concept of hydrochemical facies based on the trilinear diagram can effectively characterize the chemical composition of water in a qualitative manner. However, its application is rather limited for quantitative and precise study, because it is difficult, if not impossible, to distinguish various mechanisms that may cause similar change in water chemistry by this diagram alone. This limitation is illustrated with various hypothetical water-rock interactions and mixing trends plotted on the trilinear diagram.     

Ground water quality assessment using multi-rectangular diagrams

A new graphical technique is proposed here for classifying chemical analyses of ground water. In this technique, a diagram is constructed using rectangular coordinates. The new diagram, called a multi-rectangular diagram (MRD), uses adjacent multi-rectangles in which each rectangle represents a specific ground water type. This new diagram has the capability to accommodate a large number of data sets. MRDs have been used to classify chemical analyses of ground water in the Chaj Doab area of Pakistan to illustrate this new approach. Using this graphical method, the differentiated ground water types are calcium bicarbonate, magnesium bicarbonate, sodium bicarbonate, and sodium sulfate. Sodium bicarbonate emerges as the most abundant ground water type. MRDs also offer a visual display of the Chebotarev sequence of ground water quality evolution.     

Visualization of Aqueous Geochemical Data Using Python and WQChartPy

Graphical methods have been widely used for visualization, classification, and interpretation of aqueous geochemical data to obtain a better understanding of surface and subsurface hydrologic systems. This method note presents WQChartPy, an open-source Python package developed to plot a total of 12 diagrams for analysis of aqueous geochemical data. WQChartPy can handle various data formats including Microsoft Excel, comma-separated values (CSV), and general delimited text. The 12 diagrams include eight traditional diagrams (trilinear Piper, Durov, Stiff, Chernoff face, Schoeller, Gibbs, Chadha, and Gaillardet) and four recently proposed diagrams (rectangle Piper, color-coded Piper, contour-filled Piper, and HFE-D) that have not been implemented in existing graphing software. The diagrams generated by WQChartPy can be saved as portable network graphics (PNG), scalable vector graphics (SVG), or portable document format (PDF) files for scientific publications. Jupyter and Google Colab notebooks are available online to illustrate how to use WQChartPy with example datasets. The geochemical diagrams can be generated with several lines of Python codes. Source codes of WQChartPy are publicly available at GitHub ( https://github.com/jyangfsu/WQChartPy ) and PyPI ( https://pypi.org/project/wqchartpy/ ).     

Pay the PIED Piper: Guidelines to Visualize Large Geochemical Datasets on Piper Diagrams

The Piper diagram has increased in popularity since its 1944 introduction and is now one of the most familiar and effective tools in the hydrogeologist's toolbox. Within the Piper diagram, three points on three related plots fully display the major ionic species of a water sample. Recently the size and availability of datasets have increased as additional field measurements and modeling results are shared more effectively in online databases. This growth presents opportunities and challenges for data analysis and conveyance—larger and longer datasets increase the potential to identify trends and patterns, but traditional Piper diagrams are quickly overwhelmed by large datasets as dense points overlap and become obscured. We present guidelines for effectively displaying large geochemical datasets on traditional Piper diagrams and new code that adds novel functionality for following these generic guidelines. This code, plotting interesting environmental data with Piper diagrams (PIED Piper), can be run within the Matlab environment or through a stand-alone graphical user interface, and is the first Matlab code to generate Piper diagrams. The illustrative examples herein demonstrate (1) how limitations in displays of large datasets may be overcome with translucent symbology, contours, and heatmaps to identify trends and patterns, (2) how clusters of similar points can be identified and differentiated with convex hulls, and (3) how temporal-and-spatial patterns may be visually diagnosed with image groups and movies. The guidelines discussed in these examples will aid PIED Piper users to achieve the two goals of effective big data visualization: analysis and communication.     

水化学分析方法在地下水异常核实中的应用

地震前兆识别中的异常核实工作是提高地震分析预报能力的重要环节。"四图一法"是地下水异常核实中有效的水化学分析方法,其中Piper图和Schoeller图用于判定地下水化学类型和补给关系,Gibbs图用于判定地下水化学成分来源,Giggenbach三角图用于判定地下水的水岩平衡状态和是否有深部活动信息,以及混合比例法用于计算地下水的混合程度。同时,介绍了水化学分析方法在异常核实应用中的水样采集、测试方法和基本原理。使用水化学分析方法,有助于判定异常的构造或非构造活动影响因素,提高异常判定的科学水平。     

Vibration of surface foundations of arbitrary shapes

Presented is a systematic procedure for generating impedance (or compliance) matrices for foundations with arbitrary shapes, resting on an elastic half-space medium. A technique to decompose prescribed harmonic tractions on the half-space medium is employed to solve analytically the differential wave equations in cylindrical coordinates. However, the interaction stresses due to the vibration of a foundation with arbitrary shape are described in rectangular coordinates, and assumed to be piecewise constant in the region of the arbitrary shape. A coordinate transformation matrix is introduced for the piecewise constant tractions in order to use the solution of the differential wave equations in cylindrical coordinates. Finite element modelling is assumed in rectangular coordinates for the foundation itself. The impedance matrix is then obtained for the finite element model, using a variational principle and the reciprocal theorem. A simple example of a rigid square plate resting on a half-space medium and subjected to vertical excitation is used to demonstrate the efficiency and effectiveness of the procedure. Some numerical aspects are investigated and some possible extensions of the procedure are also discussed.     

山西省4口井(泉)水化学特征与水氡映震效能研究

对山西4口水化学观测井（泉）及周边地表水进行水化学和氢氧同位素分析,利用Piper图、durov图、Na-K-Mg三角图等方法研究其水化学特征及成因,得出井（泉）水岩平衡程度、热储温度、地下水循环深度及地下水补给来源详情;分析了井（泉）水氡测项映震特征,应用水氡映震效果与水岩平衡程度、地下水循环深度表现出的特征,评价了地震监测效能。评价结果显示夏县井、奇村井优于临猗井,适于开展地震水化学观测;定襄泉应用该水化学方法评价尚存不足之处,需要探索适用于该类观测泉点的物理与化学相结合的评价方法。     

Assessment of seasonal groundwater quality and potential saltwater intrusion: a study case in Urmia coastal aquifer (NW Iran) using the groundwater quality index (GQI) and hydrochemical facies evolution diagram (HFE-D)

Coastal aquifers are at threat of salinization in most parts of the world. This work investigated the seasonal hydrochemical evolution of coastal groundwater resources in Urmia plain, NW Iran. Two recently proposed methods have been used to comparison, recognize and understand the temporal and spatial evolution of saltwater intrusion in a coastal alluvial aquifer. The study takes into account that saltwater intrusion is a dynamic process, and that seasonal variations in the balance of the aquifer cause changes in groundwater chemistry. Pattern diagrams, which constitute the outcome of several hydrochemical processes, have traditionally been used to characterize vulnerability to sea/saltwater intrusion. However, the formats of such diagrams do not facilitate the geospatial analysis of groundwater quality, thus limiting the ability of spatio-temporal mapping and monitoring. This deficiency calls for methodologies which can translate information from some diagrams such Piper diagram into a format that can be mapped spatially. Distribution of groundwater chemistry types in Urmia plain based on modified Piper diagram using GQI_Piper(mix) and GQI_Piper(dom) indices that Mixed Ca–Mg–Cl and Ca-HCO₃ are the dominant water types in the wet and dry seasons, respectively. In this study, a groundwater quality index specific to seawater intrusion (GQI_SWI) was used to check its efficiency for the groundwater samples affected by Urmia hypersaline Lake, Iran. Analysis of the main processes, by means of the Hydrochemical Facies Evolution Diagram (HFE-Diagram), provides essential knowledge about the main hydrochemical processes. Subsequently, analysis of the spatial distribution of hydrochemical facies using heatmaps helps to identify the general state of the aquifer with respect to saltwater intrusion during different sampling periods. The HFE-D results appear to be very successful for differentiating variations through time in the salinization processes caused by saltwater intrusion into the aquifer, distinguishing the phase of saltwater intrusion from the phase of recovery, and their respective evolutions. Both GQI and HFE-D methods show that hydrochemical variations can be read in terms of the pattern of saltwater intrusion and groundwater quality status. But generally, in this case (i.e. saltwater and not seawater intrusion) the HFE-D method was presented better efficiency than GQI method (including GQI_Piper and GQI_SWI).     

Mechanical formulations for bilinear and trilinear hysteretic models used in base isolators

The best known model for numerically simulating the hysteretic behavior of various structural components is the bilinear hysteretic system. There are two possible mechanical formulations that correspond to the same bilinear model from a mathematical viewpoint. The first one consists of a linear elastic spring connected in series with a parallel system comprising a plastic slider and a linear elastic spring, while the second one comprises a linear elastic spring connected in parallel with an elastic-perfectly plastic system. However, the bilinear hysteretic model is unable to describe either softening or hardening effects in these components. In order to account for this, the bilinear model is extended to a trilinear one. Thus, two trilinear hysteretic models are developed and numerically tested, and the analysis shows that both exhibit three plastic phases. More specifically, the first system exhibits one elastic phase, while the second one exhibits two elastic phases according to the level of strain amplitude. Next, the change of slope between the plastic phases in unloading does not occur at the same displacement level in the two models. Furthermore, the dissipated energy per cycle in the first trilinear model, as proven mathematically and explained physically, decreases in the case of hardening and increases in the case of softening, while in the second trilinear model the dissipated energy per cycle remains unchanged, as is the case with the bilinear model. Numerical examples are presented to quantify the aforementioned observations made in reference to the mechanical behavior of the two trilinear hysteretic models. Finally, a set of cyclic shear tests over a wide range of strain amplitudes on a high damping rubber bearing is used in the parameter identification of the two different systems, namely (a) trilinear hysteretic models of the first type connected in parallel, and (b) trilinear hysteretic models of the second type also connected in parallel. The results show that the complex nonlinear shear behavior of high damping rubber bearings can be correctly simulated by a parallel system which consists of only one component, namely the trilinear hysteretic system of the first type. The second parallel system was not able to describe the enlargement of the dissipated hysteresis area for large strain amplitudes.     

地球化学数据库管理平台的建设与思考

为更好地发挥地球化学数据及方法在异常分析及震情跟踪研判中的作用,提高地球化学数据获取的便利性及数据存储的可靠性,规范异常核实及流动观测等地球化学样品的采集及检测流程,实现地球化学数据的自动分析及相关图件的自动绘制,中国地震台网中心建立了基于Linux系统的地球化学数据库管理平台,该平台应用数据库、地理信息系统(GIS)、WebGIS等技术,集成了样品送检、实验室检测、报告产出、数据存储筛选下载分析、图件绘制等功能,利用Piper图、Na-K-Mg三角图、同位素分析等方法,分析不同样品的地球化学特征,并给出相关图件。平台自推广以来,收集了大量的地球化学数据,提升了数据的可利用性,降低了地球化学数据分析的技术门槛,在异常性质分析及震情跟踪研判中发挥了作用。     

An Excel macro for generating trilinear plots

This computer note describes a method for creating trilinear plots in Microsoft Excel. Macros have been created in MS Excel's internal language: Visual Basic for Applications (VBA). A simple form has been set up to allow the user to input data from an Excel worksheet. The VBA macro is used to convert the triangular data (which consist of three columns of percentage data) into X-Y data. The macro then generates the axes, labels, and grid for the trilinear plot. The X-Y data are plotted as scatter data in Excel. By providing this macro in Excel, users can create trilinear plots in a quick, inexpensive manner.     

Hydrochemical facies of groundwater in the Gaza Strip,Palestine / Faciès hydrochimiques de l’eau souterraine dans la Bande de Gaza,Palestine

Abstract

Abstract Groundwater in the Gaza Strip is the only source of water for domestic, agricultural and industrial uses. Extensive pumping has caused serious quantitative and qualitative problems in the aquifer. The hydrochemical facies are evaluated using the trilinear diagram for 200 water samples. Groundwater in the north and west is mostly characterized by Ca-Mg-HCO₃ facies (alkaline water), and in the south and east by Na-Cl-SO₄ facies (saline water). Sand dunes and rainfall are the major factors controlling the distribution of hydrochemical facies. The eastern edge of the sand dune belt is considered the barrier that separates the two major facies. Brackish water flowing from the east is mixed with rainwater which infiltrates through the sand dunes to the aquifer. Other factors, e.g. seawater intrusion and extensive pumping, play a minor role in the distribution of the hydrochemical facies.     

A simultaneous interpretation,by wind speed and direction,of ambient air negative ion density in Athens,Greece

A recently developed data presentation technique, the rectangular wind frequency isopleth diagram, has been applied to examine the effect of wind speed and direction, acting simultaneously, on ambient air negative ion densities. The large negative ion concentration decreases in the majority of directions and wind speed intervals, while that of the small ions increases, as the wind speed increases. The local maxima and minima, occurring in some sectors, are properly discussed.     

A Background Color Scheme for Piper Plots to Spatially Visualize Hydrochemical Patterns

The combination of ternary diagrams of cations and anions with a central diamond graph make the Piper plot very useful in visualizing groundwater chemistry datasets. One of the major drawbacks is that it is hard to link spatial attributes of the dataset to the plot. In this study, we propose a background color scheme of the Piper plot so that spatial representations of these data can be colored according to their location in the Piper plot. The color scheme is chosen to have maximum resolution while still being perceptually uniform. The linking between Piper plot and maps through this color scheme allows the interpretation of the trends and processes deduced from the Piper plot in terms of the location in the aquifer, the geology, and the groundwater flow dynamics. The colored Piper plot is applied to a groundwater quality dataset of the Condamine Alluvium in Queensland, Australia.     

NOMOGRAMS TO INTERPRET CRONE PEM DATA USING A DIPPING SHEET MODEL*

The response of a rectangular plate to the Crone PEM system has been investigated for different values of depth, dip and conductance parameters. The conductance aperture diagram is presented to estimate the conductance and depth to the top of a vertical sheet. Information regarding dip and depth may be obtained using the appropriate nomogram.     

Incipient motion of gravel in a bottomless arch culvert

Incipient motion was investigated for four gravel substrate materials in a bottomless arch culvert and a rectangular flume.Different methods for calculating Shields parameter at incipient motion(θ_c) based upon local flow parameters were explored.An incipient motion region for bottomless arch culverts in fully turbulent flow was defined with two bounding curves on Shields diagram.The variation ofθ_c as a function of relative roughness was examined.Also,a method that utilizes measured flow velocities to determine stable substrate particle diameters for bottomless arched culverts is presented as an alternative to the Shields diagram.     

Improved streamlines and time-of-flight for streamline simulation on irregular grids

Streamline methods have shown to be effective for reservoir simulation. For a regular grid, it is common to use the semi-analytical Pollock’s method to obtain streamlines and time-of-flight coordinates (TOF). The usual way of handling irregular grids is by trilinear transformation of each grid cell to a unit cube together with a linear flux interpolation scaled by the Jacobian. The flux interpolation allows for fast integration of streamlines, but is inaccurate even for uniform flow. To improve the tracing accuracy, we introduce a new interpolation method, which we call corner-velocity interpolation. Instead of interpolating the velocity field based on discrete fluxes at cell edges, the new method interpolates directly from reconstructed point velocities given at the corner points in the grid. This allows for reproduction of uniform flow, and eliminates the influence of cell geometries on the velocity field. Using several numerical examples, we demonstrate that the new method is more accurate than the standard tracing methods.     

均匀介质中MRS方法三维模型的核磁共振响应

MRS方法三维含水体的核磁共振正演计算涉及两个难点：①激发场表达式的快速计算,该表达式为包含双重Bessel函数乘积的积分式,将该表达式分为两个积分区间,第一积分区间应用贝塞尔函数的汉克尔函数表述式及其大宗量渐近特性,将其转化为Fourier正（余）弦变换,采用快速计算方法实现数值计算;另一积分区间的计算直接应用一般的数值积分算法即能获得较高的计算精度。②三维含水体的空间离散化,提供柱坐标和直角坐标中的两种离散方法,可对任意形状的三维含水体进行构建。在此基础上,开发出相应的正演程序,并进行几种常见的三维含水体的MRS正演,对其初始振幅曲线进行规律总结。结果表明,三维含水体的MRS振幅响应与层状含水层振幅响应类似,使用收发共圈的工作模式将难以辨别地下含水体的空间形态。     

广东地区地震动衰减和场地响应的研究

根据广东数字地震台网14个地震台的249条波形资料，研究了广东地区的衰减模型和各台站的场地响应. 采用三段几何衰减模型拟合，得到了广东地区的几何衰减函数. 同时也采用线性几何衰减模型和两段几何衰减模型对观测数据进行了拟合. 残差比较表明，线性几何衰减模型的残差最大，两段几何衰减模型的残差其次，而三段几何衰减模型的残差最小. 由此可以推论广东地区采用三段几何衰减模型具合理性和适用性. 得到广东地区非弹性衰减Q值随频率f的关系为Q(f)=481.5·f0.31；14个台站的场地响应均没有显示出明显的放大效应，这与它们均处于岩石地基相符.     

用椭圆衰减关系模型计算任意场点烈度及地震动参数的数值方法

用椭圆衰减关系计算地震动或地震烈度,比较经典的做法是建立极坐标系,采用极坐标方程的方法.给出了一种在直角坐标系中即可求解的用椭圆衰减关系计算地震动或地震烈度的数值计算方法.另外,地震动椭圆衰减关系,应满足一定的模型要求,才能更客观地反映实际的地震动衰减物理过程.本算法的附加功能能够鉴别非标准的椭圆衰减关系.