基于Origin的概率累积曲线的计算与绘制
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摘要
图解法计算沉积物粒度参数在沉积学研究中被广泛应用,但需要通过手工作图求累积曲线,是一项相当繁杂的劳动。通用计算软件Origin拥有很强的函数计算和绘图功能,不仅可以批量计算图解粒度参数,同时还可以直接绘制(分段)概率累积曲线图;其实施过程操作简单,仅需点击菜单命令,无需编写任何语句,有利于不懂编程的沉积分析人员进行数据分析,有很大的应用价值。文章随机选取10个不同沉积环境下形成的松散沉积物样本,利用Origin求解各样本粒度累积曲线的百分位数,在其内嵌的Excel表格中计算粒度参数,并用Origin的制图功能绘制粒度概率累积曲线与沉积组分分段直线图。Origin与手工作图计算的结果之间的差值(绝对值平均)及方差都很小(0.004 2~0.018 6)。计算结果表明Origin在粒度参数计算方面完全可以代替手工作图,不仅操作简单,而且精度非常高。
The dynamical conditions of transport and deposition of sedimentary materials are usually inferred from their grain size, which is a fundamental property of the materials and may tell us much about the origins and history of the materials. Moment technique and graphical technique are the two principal methods to calculate grain size parameters for sedimentary analysis. In using the moment technique, calculation of the grain size parameters can be handled automatically with the help of computers, while in using the graphical technique the probabilistic cumulative frequency curve of a sedimentary sample has to be artificially drawn in advance to obtain percentiles of the sample's grain size distribution that are used to calculate the grain size parameters. Thus artificial drawing is a hard and time consuming work and is not beneficial to data in large batch processing. However, the difference in the grain size characteristics of the sediment samples from different sedimentary environments could be clearly shown in the probabilistic cumulative frequency curves with sub-population linear segments and the curves are widely used in sedimentary analysis. Therefore, drawing of the probabilistic cumulative frequency curves is an essential technique in sedimentary analysis even it is a troublesome job. The general calculating software, Origin, has very powerful functions for calculation and graphic drawing. It not only can calculate the particle size parameters by opening the embedded Excel Data Sheets that contain the grain size data and operate the data in batches, but also can directly draw grain size frequency distribution curves and probabilistic cumulative grain size curves with the linear sub-population segments simultaneously. The operation process for calculating the grain size parameters and drawing the cumulative curves in Origin is very easy and the whole process is simply to execute the menu command by mouse clicks without any programming. It is very suitable for analyzers, especially for those who have no coding skills, to analyze the data of particle size in sedimentary studies and thus has great application value. In this paper, we present an example in which a step by step guide to calculating the grain size parameters and drawing probabilistic cumulative grain size curves with the linear sub-population segments using Origin was carried out. Ten loose sediment samples, which were taken from different depositional environments in China, were selected for the calculation and drawing. The samples included beach sand, coastal wind sand, inland wind sand, river sand, lagoon sediment, old red sand and loess. The values of the percentiles and the grain size parameters obtained by this way were compared with the values that were calculated by artificial drawing. The comparison showed that the results calculated using Origin were very close to those calculated by the artificial method. The difference in values(absolute value average) between the two methods calculated from a single sample or all of the samples ranged from 0.003 7 to 0.013 3 with variances from 0.004 2 to 0.018 6. The comparison indicates that we can completely replace the artificial graphic technique with the calculation using Origin in grain size analysis.
The dynamical conditions of transport and deposition of sedimentary materials are usually inferred from their grain size, which is a fundamental property of the materials and may tell us much about the origins and history of the materials. Moment technique and graphical technique are the two principal methods to calculate grain size parameters for sedimentary analysis. In using the moment technique, calculation of the grain size parameters can be handled automatically with the help of computers, while in using the graphical technique the probabilistic cumulative frequency curve of a sedimentary sample has to be artificially drawn in advance to obtain percentiles of the sample's grain size distribution that are used to calculate the grain size parameters. Thus artificial drawing is a hard and time consuming work and is not beneficial to data in large batch processing. However, the difference in the grain size characteristics of the sediment samples from different sedimentary environments could be clearly shown in the probabilistic cumulative frequency curves with sub-population linear segments and the curves are widely used in sedimentary analysis. Therefore, drawing of the probabilistic cumulative frequency curves is an essential technique in sedimentary analysis even it is a troublesome job. The general calculating software, Origin, has very powerful functions for calculation and graphic drawing. It not only can calculate the particle size parameters by opening the embedded Excel Data Sheets that contain the grain size data and operate the data in batches, but also can directly draw grain size frequency distribution curves and probabilistic cumulative grain size curves with the linear sub-population segments simultaneously. The operation process for calculating the grain size parameters and drawing the cumulative curves in Origin is very easy and the whole process is simply to execute the menu command by mouse clicks without any programming. It is very suitable for analyzers, especially for those who have no coding skills, to analyze the data of particle size in sedimentary studies and thus has great application value. In this paper, we present an example in which a step by step guide to calculating the grain size parameters and drawing probabilistic cumulative grain size curves with the linear sub-population segments using Origin was carried out. Ten loose sediment samples, which were taken from different depositional environments in China, were selected for the calculation and drawing. The samples included beach sand, coastal wind sand, inland wind sand, river sand, lagoon sediment, old red sand and loess. The values of the percentiles and the grain size parameters obtained by this way were compared with the values that were calculated by artificial drawing. The comparison showed that the results calculated using Origin were very close to those calculated by the artificial method. The difference in values(absolute value average) between the two methods calculated from a single sample or all of the samples ranged from 0.003 7 to 0.013 3 with variances from 0.004 2 to 0.018 6. The comparison indicates that we can completely replace the artificial graphic technique with the calculation using Origin in grain size analysis.
引文
BLOTT S J and PYE K.2001.Gradistat:A grain size distribution and statistics package for the analysis of unconsolidated sediments.Earth Surface Processes and Landforms,26:1237-1248.
蔡国富,范代读,尚帅,吴伊婧,邵磊.2014.图解法与矩值法计算的潮汐沉积粒度参数之差异及其原因解析.海洋地质与第四纪地质,34(1):195-204.[CAI Guofu,FAN Daijiu,SHANG Shuai,WUYijing and SHAO Lei.2014.There are differences in the tidal sedimentary grain size parameters calculated by the graphic method and the moment method.Marine Geology and Quaternary Geology,34(1):195-204.]
FOLK P L and WARD W D.1957.Brazos Reviver bar:A study in the significance of grain size parameters.Journal of Sedimentary Petrology,27:3-26.
FRIEDMEN G M and SANDERS J E.1982.Principles of sedimentology.New York:Whiley,78-80.
范家爵.1989.绘制粒度概率累积频率曲线图的PC-1500计算方法.勘察科学技术,(1):12-17.[FAN J.1989.PC-1500 Calculation Method for Drawing Probability Cumulative Frequency Graph of Grain Size.Investigation of Science and Technology,(1):12-17.]
GALE S J and HOAREP G.1991.Quaternary Sediments Petrographic methods for the study of unlithified Rocks.New York:Halsted Press,1-323.
LIRO Maciej.2015.Differences in the reconstructions of the depositional environment of overbank sediments performed using the C/M diagram and cumulative curve analyses.Landform,29:35-40.
刘岫峰.1991.沉积岩实验室研究方法.北京:地质出版社,1-299.[LIUXiufeng.1991.Research Methods of Sedimentary Rock Laboratory.Beijing:Geological Publishing House,1-299.]
刘子玉,李勇.2007.GRAPHER在粒度分析中的应用.江汉石油科技,(2):9-10.[LIU Ziyu and LI Yong.2007.Application of GRAPHERin Particle Size Analysis.Jianghan Petroleum Science and Technology,(2):9-10.]
MCCAVE I N and SYVITSKI J P M.1991.Principle and methods of geological particle size analysis.In:SYVITSKI J P M.Principle methods,and application of particle size analysis.New York:Cambridge University Press,3-21.
MCMANUS J.1988.Grain size determination and interpretation.In:TUCKER M.Techniques in Sedimentology.London:Blackwell Scientific Publication,63-85.
MYCIELSKADOWGIALLO E,LUDWIKOWSKAKEDZIA M.2011.Alternative interpretations of grain-size data from Quaternary deposits.Geologos,17(4):189-203.
孟洁,温小浩,李保生,牛东风,赵占仑,孙业凤,杨庆江.2016.腾格里沙漠南缘土门剖面末次冰消期层段粒度特征及其反映的古气候.海洋地质与第四纪地质,36(1):165-176.[MENG Jie,WENXiaohao,LI Baosheng,NIU Dongfeng,ZHAO Zhanlun,SUN Yefeng and YANG Qingjiang.2016.Grain-Size Distribution Along Thetumen Section of Southern Tengger Desert,Northwestern China and Its Paleoclimatic Implications During the Last Deglacial.Marine Geology&Quaternary Geology,36(1):165-176.]
N’GUESSAN YA,WOGNIN V,COULIBALY A,MONDE S,WANGOT E and AKA K.2011.Granulometric analysis and environment of deposits of superficial sands of the Adjin lagoon(C?te d’Ivoire).Revue Paralia,4:6.15-6.28.
OMOTOYE S J,FADIYA S L and ADESIYAN T A.2016.Sedimentological Study and Heavy Mineral Analysis of Sediment Samples from Well-S,Niger Delta,Nigeria.Universal Journal of Geoscience,4(3):51-61.
RASHI M.2011.Tsunami-sediment signatures in the Manakudy estuary along the west coast of India.Journal of Tsunami Society International,30(2):94.
SWAN D,CLAYNE J J and LUTERNAUER J L.1978.Grain-size statistics I:Evaluation of Folk and Ward graphic measures.Journal of Sedimentary Petrology,47:863-878.
SWAN D,CLAYNE J J and LUTERNAUER J L.1979.Grain-size statistics II:Evaluation of grouped moment measures.Journal of Sedimentary Petrology,48:487-500.
孙东怀,鹿化煜,David Rea,孙有斌,吴胜光.2000.中国黄土粒度的双峰分布及其古气候意义.沉积学报,18(3):327-335.[SUNDonghuai,LU Huayu,David Rea,SUN Youbin and WUShengguang.2000.Bimode Grain-size Distribution of Chinese Loess and Its Paleoclimate Implication.Acta Sedimentologica Sinica,18(3):327-335.]
VISHER G S.1969.Grain size distributions and depositional processes.Journal of Sedimentary Research,39(3):1074-1106.
WALPOLE R E,MYERS S L and YE K.2004.Probability&Statistics for Engineers&Scientists.Beijing:Tsinghua University Press,201-203.
万一兴,郑卓,萧一亭,汤永杰,陈聪.2016.珠江口岛屿全新世沙堤的年代与沉积环境.热带地理,36(3):388-398.[WAN Yixing,ZHENG Zhuo,XIAO Yiting,TANG Yongjie and CHENCong.2016.The age and sedimentary environment of the Holocene sand dunes in the Pearl River estuary.Tropical Geography,36(3):388-398.]
王为,吴正.2006.基于MATLAB的图解粒度参数计算.热带地理,26(3):239-242.[WANG Wei and WU Zheng.2006.Fuzzy Particle Size Calculation Based on MATLAB.Tropical Geography,26(3):239-242.]
王为.1999.计算机绘制粒度分布曲线的插值方法.中国沙漠,19(1):12-16.[WANG Wei.1999.Interpreting method of particle size distribution curve by computer.China Desert,19(1):12-16.]
吴晓涛.1994.沉积物粒度参数图解法的电算程序.海洋科学,(5):13-14.[Wu X.1994.Computer program method of sediment Graphic grain size parameter.Marine Science,(5):13-14.]
徐开志,忠实.1983.粒度分析的电算处理及其应用.长春地质学院学报,(2):101-108.[XU Kaizhi and ZHONG Shi.1983.Computing and application of grain size analysis.Changchun Institute of Geology,(2):101-108.]
徐士良.1989.计算机常用算法.北京:清华大学出版社,1-290.[XUShiliang.1989.Computer commonly used algorithm.Beijing:Tsinghua University Press,1-290.]
徐树建,潘保田,张慧,李琼.2005.末次冰期旋回风成沉积物图解法与矩值法粒度参数的对比.干旱区地理,28(2):194-198.[XUShujian,PAN Baotian,ZHANG Hui and LI Qiong.2005.Comparison of Particle Size Parameters of Cyclone Sediment in the Last Glacial Period.Arid Land Geography,28(2):194-198.]
张建伟.2014.Origin 9.0科技绘图与数据分析超级学习手册.北京:人民邮电出版社,1-429.[ZHANG Jianwei.2014.Origin 9.0 Handbook of Technical Drawing and Data Analysis Super Learning.Beijing:People's Posts and Telecommunications Press,1-429.]
张永成,王洪辉,谭桂花.2010.基于Excel VBA的图解粒度参数计算.成都理工大学学报(自然科学版),37(6):650-653.[ZHANGYongcheng,WANG Honghui and TAN Guihua.2010.Design of graph granularity parameters based on Excel VBA.Journal of Chengdu University of Technology(Natural Science Edition),37(6):650-653.]
蔡国富,范代读,尚帅,吴伊婧,邵磊.2014.图解法与矩值法计算的潮汐沉积粒度参数之差异及其原因解析.海洋地质与第四纪地质,34(1):195-204.[CAI Guofu,FAN Daijiu,SHANG Shuai,WUYijing and SHAO Lei.2014.There are differences in the tidal sedimentary grain size parameters calculated by the graphic method and the moment method.Marine Geology and Quaternary Geology,34(1):195-204.]
FOLK P L and WARD W D.1957.Brazos Reviver bar:A study in the significance of grain size parameters.Journal of Sedimentary Petrology,27:3-26.
FRIEDMEN G M and SANDERS J E.1982.Principles of sedimentology.New York:Whiley,78-80.
范家爵.1989.绘制粒度概率累积频率曲线图的PC-1500计算方法.勘察科学技术,(1):12-17.[FAN J.1989.PC-1500 Calculation Method for Drawing Probability Cumulative Frequency Graph of Grain Size.Investigation of Science and Technology,(1):12-17.]
GALE S J and HOAREP G.1991.Quaternary Sediments Petrographic methods for the study of unlithified Rocks.New York:Halsted Press,1-323.
LIRO Maciej.2015.Differences in the reconstructions of the depositional environment of overbank sediments performed using the C/M diagram and cumulative curve analyses.Landform,29:35-40.
刘岫峰.1991.沉积岩实验室研究方法.北京:地质出版社,1-299.[LIUXiufeng.1991.Research Methods of Sedimentary Rock Laboratory.Beijing:Geological Publishing House,1-299.]
刘子玉,李勇.2007.GRAPHER在粒度分析中的应用.江汉石油科技,(2):9-10.[LIU Ziyu and LI Yong.2007.Application of GRAPHERin Particle Size Analysis.Jianghan Petroleum Science and Technology,(2):9-10.]
MCCAVE I N and SYVITSKI J P M.1991.Principle and methods of geological particle size analysis.In:SYVITSKI J P M.Principle methods,and application of particle size analysis.New York:Cambridge University Press,3-21.
MCMANUS J.1988.Grain size determination and interpretation.In:TUCKER M.Techniques in Sedimentology.London:Blackwell Scientific Publication,63-85.
MYCIELSKADOWGIALLO E,LUDWIKOWSKAKEDZIA M.2011.Alternative interpretations of grain-size data from Quaternary deposits.Geologos,17(4):189-203.
孟洁,温小浩,李保生,牛东风,赵占仑,孙业凤,杨庆江.2016.腾格里沙漠南缘土门剖面末次冰消期层段粒度特征及其反映的古气候.海洋地质与第四纪地质,36(1):165-176.[MENG Jie,WENXiaohao,LI Baosheng,NIU Dongfeng,ZHAO Zhanlun,SUN Yefeng and YANG Qingjiang.2016.Grain-Size Distribution Along Thetumen Section of Southern Tengger Desert,Northwestern China and Its Paleoclimatic Implications During the Last Deglacial.Marine Geology&Quaternary Geology,36(1):165-176.]
N’GUESSAN YA,WOGNIN V,COULIBALY A,MONDE S,WANGOT E and AKA K.2011.Granulometric analysis and environment of deposits of superficial sands of the Adjin lagoon(C?te d’Ivoire).Revue Paralia,4:6.15-6.28.
OMOTOYE S J,FADIYA S L and ADESIYAN T A.2016.Sedimentological Study and Heavy Mineral Analysis of Sediment Samples from Well-S,Niger Delta,Nigeria.Universal Journal of Geoscience,4(3):51-61.
RASHI M.2011.Tsunami-sediment signatures in the Manakudy estuary along the west coast of India.Journal of Tsunami Society International,30(2):94.
SWAN D,CLAYNE J J and LUTERNAUER J L.1978.Grain-size statistics I:Evaluation of Folk and Ward graphic measures.Journal of Sedimentary Petrology,47:863-878.
SWAN D,CLAYNE J J and LUTERNAUER J L.1979.Grain-size statistics II:Evaluation of grouped moment measures.Journal of Sedimentary Petrology,48:487-500.
孙东怀,鹿化煜,David Rea,孙有斌,吴胜光.2000.中国黄土粒度的双峰分布及其古气候意义.沉积学报,18(3):327-335.[SUNDonghuai,LU Huayu,David Rea,SUN Youbin and WUShengguang.2000.Bimode Grain-size Distribution of Chinese Loess and Its Paleoclimate Implication.Acta Sedimentologica Sinica,18(3):327-335.]
VISHER G S.1969.Grain size distributions and depositional processes.Journal of Sedimentary Research,39(3):1074-1106.
WALPOLE R E,MYERS S L and YE K.2004.Probability&Statistics for Engineers&Scientists.Beijing:Tsinghua University Press,201-203.
万一兴,郑卓,萧一亭,汤永杰,陈聪.2016.珠江口岛屿全新世沙堤的年代与沉积环境.热带地理,36(3):388-398.[WAN Yixing,ZHENG Zhuo,XIAO Yiting,TANG Yongjie and CHENCong.2016.The age and sedimentary environment of the Holocene sand dunes in the Pearl River estuary.Tropical Geography,36(3):388-398.]
王为,吴正.2006.基于MATLAB的图解粒度参数计算.热带地理,26(3):239-242.[WANG Wei and WU Zheng.2006.Fuzzy Particle Size Calculation Based on MATLAB.Tropical Geography,26(3):239-242.]
王为.1999.计算机绘制粒度分布曲线的插值方法.中国沙漠,19(1):12-16.[WANG Wei.1999.Interpreting method of particle size distribution curve by computer.China Desert,19(1):12-16.]
吴晓涛.1994.沉积物粒度参数图解法的电算程序.海洋科学,(5):13-14.[Wu X.1994.Computer program method of sediment Graphic grain size parameter.Marine Science,(5):13-14.]
徐开志,忠实.1983.粒度分析的电算处理及其应用.长春地质学院学报,(2):101-108.[XU Kaizhi and ZHONG Shi.1983.Computing and application of grain size analysis.Changchun Institute of Geology,(2):101-108.]
徐士良.1989.计算机常用算法.北京:清华大学出版社,1-290.[XUShiliang.1989.Computer commonly used algorithm.Beijing:Tsinghua University Press,1-290.]
徐树建,潘保田,张慧,李琼.2005.末次冰期旋回风成沉积物图解法与矩值法粒度参数的对比.干旱区地理,28(2):194-198.[XUShujian,PAN Baotian,ZHANG Hui and LI Qiong.2005.Comparison of Particle Size Parameters of Cyclone Sediment in the Last Glacial Period.Arid Land Geography,28(2):194-198.]
张建伟.2014.Origin 9.0科技绘图与数据分析超级学习手册.北京:人民邮电出版社,1-429.[ZHANG Jianwei.2014.Origin 9.0 Handbook of Technical Drawing and Data Analysis Super Learning.Beijing:People's Posts and Telecommunications Press,1-429.]
张永成,王洪辉,谭桂花.2010.基于Excel VBA的图解粒度参数计算.成都理工大学学报(自然科学版),37(6):650-653.[ZHANGYongcheng,WANG Honghui and TAN Guihua.2010.Design of graph granularity parameters based on Excel VBA.Journal of Chengdu University of Technology(Natural Science Edition),37(6):650-653.]
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