Notice that this vector also starts at the origin, and can point in any direction as long as it remains perpendicular to the first component. Semiautomated fault interpretation based on seismic. Cu u, where is the symmetric covariance matrix, is an eigenvector and. In the first installment, we indicated that the primary reason to do a principal component analysis pca in excel was to increase our own understanding. Learn more about the basics and the interpretation of principal component. Dec 25, 2014 ever wonder whats the mathematics behind face recognition on most gadgets like digital camera and smartphones. We will start by looking at the geometric interpretation of pca when \\mathbfx\ has 3 columns, in other words a 3dimensional space, using measurements. Reservoir characterization is an important component of oil and gas. Principal component analysis pca and selforganizing maps som are components of unsupervised machine learning methods that have. A genealogical interpretation of principal components analysis. The art and science of seismic interpretation christopher liner.
Principal component analysis pca is routinely employed on a wide range of problems. Tabachnick and fidell 2001, page 588 cite comrey and lees 1992 advise regarding sample size. This continues until a total of p principal components have been calculated, equal to the original number of variables. You will learn how to predict new individuals and variables coordinates using pca. In addition to the developments in all aspects of conventional processing, this twovolume set represents a comprehensive and complete coverage of the modern trends in the seismic industryfrom time to depth, from 3d to 4d, from 4d to 4c, and from isotropy to anisotropy. The algorithm helped obtain the optimal enhanced seismic volume that is preferable for the structural interpretation of seismic.
Principal component analysis ricardo wendell aug 20 2. Fundamentally, the interpretation of waveletdependent attributes is an inverse. The application of principal components analysis to seismic. Methodological issues in determining the dimensionality of composite health measures using principal component analysis. The first edition of this book was the first comprehensive text. Seismic data interpretation using the hough transform and principal component analysis this article has been downloaded from iopscience. Lower triassic jialingjiang formation, sichuan basin, china. Principal components analysis pca using the gha network enables the extraction of information regarding seismic reflections and uniform neighboring traces. In addition, the students will acquire basic knowledge about seismic amplitude reflections from lithological boundaries within the subsurface. May 29, 2009 by combining the variability of multiple components, principal component spectra highlight stratigraphic features that can be interpreted using a seismic geomorphology workflow. Bringing the ie up to date has added more than 200 pages of additional text. A simple principal component analysis example brian russell, august, 2011. Principal component analysis pca is a canonical and widely used method for dimensionality reduction of multivariate data. Complete the following steps to interpret a principal components analysis.
You can use the size of the eigenvalue to determine the number of principal components. The variance for each principal component can be read off the diagonal of the covariance matrix. To meet the needs of traditional seismic data interpretation. Interpreting the principal components analysis pca. If there are only a few missing values for a single variable, it often makes sense to delete an entire row of data. Principal component analysis report sheet descriptive statistics. Pca is a useful statistical method that has found application in a variety of elds and is a common technique for nding patterns in data of high dimension. Eigen values and vectors of matrices for a theoretical development of the principal component analysis and its interpretation it is necessary to use some results on the canonical reduction of.
Principal component spectral analysis geoscienceworld. One technique commonly used to uncover such structure is principal components analysis, which identifies the primary axes of variation in data and projects the samples onto these axes in a graphically. Most textbooks teach us to perform matrix multiplication by. Geologic pattern recognition from seismic attributes. The use and interpretation of principal component analysis. One statistical tool that is capable of doing such feature is the principal component analysis pca. Interpret the key results for principal components analysis. The matrix x has the following singular value decomposition svd, see refs 11 and appendix b. In the second section, we will look at eigenvalues and. Principal component analysis is equivalent to major axis regression. Discover the best principal component analysis books and audiobooks.
Costa1 1sao carlos institute of physics, university of sao paulo, sao carlos, sp, brazil. F or example, we might ha ve as our data set both the height of all the students in a class, and the mark the y recei ved for that paper. The theoreticians and practitioners can also benefit from a detailed description of the pca applying on a certain set of data. The object of seismic interpretation is to extract all the geologic information possible from the data as it relates to structure, stratigraphy, rock properties, and perhaps reservoir fluid changes in space and time liner, 1999. The r syntax for all data, graphs, and analysis is provided either in shaded boxes in the text or in the caption of a figure, so that the reader may follow along. This book on principal component analysis pca is a significant contribution to the field of data analysis. Jan 23, 2017 principal component analysis pca is routinely employed on a wide range of problems. Eigenvalues also called characteristic values or latent roots are the variances of the principal components. By combining the variability of multiple components, principal component spectra highlight stratigraphic features that can be interpreted using a seismic geomorphology workflow.
In this tutorial, we will look at the basics of principal component analysis using a simple numerical example. Issues related to the underlying data will affect pca and this should be considered when generating and interpreting results. This tutorial focuses on building a solid intuition for how and why principal component analysis. Whatever method of factor extraction is used it is recommended to analyse the. Multiattribute analyses employing principal component analysis pca and selforganizing maps are components of a machinelearning interpretation workflow. Any feelings that principal component analysis is a narrow subject should soon be dispelled by the present book. Principal component analysis using r november 25, 2009 this tutorial is designed to give the reader a short overview of principal component analysis pca using r. Jan 23, 2014 this modern introduction to seismic data processing in both exploration and global geophysics demonstrates practical applications through real data and tutorial examples. This book begins with an introduction that is more philosophical than. The book ends with an overview of how seismic attributes aid data interpretation. The second principal component is calculated in the same way, with the condition that it is uncorrelated with i. Determine the minimum number of principal components that account for most of the variation in your data, by using the following methods. Suyun hu, wenzhi zhao, zhaohui xu, hongliu zeng, qilong fu, lei jiang, shuyuan shi, zecheng wang, wei liu.
Factor analysis and principal component analysis pca. These data values define pndimensional vectors x 1,x p or, equivalently, an n. Well also provide the theory behind pca results learn more about the basics and the interpretation of principal component analysis in our previous article. Elastic properties and their spatial arrangement geometric distribution must be considered. Seismic acquisition and processing principles, seismic well tie, basic seismic interpretation techniques, structural and stratigraphic interpretation using seismic data, map generation, velocities and depth conversion, seismic amplitude and attribute analysis, play and prospect evaluation. Statistical classification techniques, which work on seismic attributes such as amplitude, have found increasing use within traditional interpretation workflows johann. Principal component analysis is central to the study of multivariate data.
The first step in pca is to move the data to the center of the. Well for most part it has something to do with statistics. Semiautomated fault interpretation based on seismic attributes bo zhang, the university of oklahoma, yuancheng liu, dgb earth sciences, michael pelissier, formerly at marathon oil corporation, currently with roc oilbohai company, and nanne hemstra, dgb earth sciences summary 3d fault interpretation is a time consuming and tedious task. Discover principal component analysis books free 30day. The major goal of principal components analysis is to reveal hidden structure in a data set. The seismic data analyzed are seismic traces with 20, 25, and 30 hz ricker wavelets. Pca has been validated as a method to describe ses differentiation within a population. His research interests are broad, but aspects of principal component analysis have fascinated him and kept him busy for over 30 years. In such scenarios, fitting a model to the dataset, results in. The descriptive statistics table can indicate whether variables have missing values, and reveals how many cases are actually used in the principal components. A simple principal component analysis example brian. The application of principal components analysis takes advantage of the high degree of redundancy in the seismic data set to determine its statistical behavior and reduce it to its essential features. The introduction of principal component analysis principal component analysis method is a kind of multiple analysis method to search comprehensive index in several indexes, a kind of effective way to solve the problem of multitarget integrated evaluation, a statistical analysis method by dimension reduction techniques to multiple variables. This r tutorial describes how to perform a principal component analysis pca using the builtin r functions prcomp and princomp.
Pca is particularly powerful in dealing with multicollinearity and. Seismic attributes for prospect identification and reservoir. It also includes the core concepts and the stateoftheart methods in data analysis and feature. Seismic facies identification and classification using. If your goal is the pca itself, a better choice of tool might be r, matlab, or similar tool. From the detection of outliers to predictive modeling, pca has the ability of projecting the observations described by variables into few orthogonal components defined at where the data stretch the most, rendering a simplified overview. In this post, however, we will not do sorry to disappoint you face recognition as we reserve this for future post while i. This book introduces readers to the field of seismic data interpretation and evaluation, covering themes such as petroleum exploration and high resolution. It is extremely versatile with applications in many disciplines. In this book, the reader will find the applications of pca in fields such as image processing, biometric, face recognition and speech processing. Although the term principal component analysis is in common usage. Find definitions and interpretation guidance for every statistic and graph that is provided with the principal components analysis. By mapping the three largest principal components using the three primary colors of red, green, and blue, we could represent more than 80% of the spectral variance with.
Independent component analysis for reservoir geomorphology and unsupervised seismic facies classification in the taranaki basin, new zealand david luborobles. Seismic attribute analysis deep learning with neural networks h1 h2 h3. In particular, principal component analysis pca is a multivariate statistical. The area of ssa has been developing fast and several monographs have appeared already, e. Churning seismic attributes with principal component analysis. Problems or pitfalls in seismic analysis may arise from glitches during acquisition, processing and interpretation. Seismic interpretation in the age of big data seg technical. The present investigation involved the interpretation of old secondary seismic sections in order to come up with a subsurface structure with an aim of identifying and delineating possible hydrocarbon traps and prospective areas.
Pca involves a statistical procedure which orthogonally transforms a set of possibly correlated observations into set of values of linearly uncorrelated variables called principal components. Seismic interpretation with machine learning geo expro. Seismic graph analysis to aid seismic interpretation interpretation. Key output includes the eigenvalues, the proportion of variance that the component explains, the coefficients, and several graphs. References to eigenvector analysis or latent vector analysis may also camou. Read principal component analysis books like apollo experience report guidance and control systems lunar module mission programer and an introduction to mathematical taxonomy for free with a free 30day trial. A simple principal component analysis example brian russell. A generalized linear model for principal component. Principal components analysis spss annotated output. One of the most commonly faced problems while dealing with data analytics problem such as recommendation engines, text analytics is highdimensional and sparse data. Performing pca in r the do it yourself method its not difficult to perform. Recall that the loadings plot is a plot of the direction vectors that define the model.
The original version of this chapter was written several years ago by chris dracup. The use and interpretation of principal component analysis in. Simply defined, seismic interpretation is the science and art of inferring the. Principal component analysis and selforganizing maps. These could be based on analysis of either the seismic waveforms or the seismic attributes. The raw data in the cloud swarm show how the 3 variables move together. The application of principal components analysis to. Seismic principal components analysis using neural networks. This book demystifies the art and science of seismic interpretation, serving as a guide as to what seismic data is, how it is interpreted, and how it can be used for.
Here are some of the questions we aim to answer by way of this technique. The area of indpedent component analysis is another one that. Is there a simpler way of visualizing the data which a priori is a collection of points in rm, where mmight be large. Otherwise, faults must be jumped using reflection character, sequence analysis. Original content in datapages find the book in the aapg store. The students should know stateoftheart interpretation techniques for 2d and 3d seismic data.
Abstractduring the seismic interpretation process, geoscientists rely on their experience and visual analysis to assess the similarity between. We find the second component so that it is perpendicular to the first components direction. Pitfalls in interpretation misra 2018 wiley online books wiley. In the first section, we will first discuss eigenvalues and eigenvectors using linear algebra. This book is aimed at raising awareness of researchers, scientists and engineers on the benefits of principal component analysis pca in data analysis. Oz yilmaz has expanded his original volume on processing to include inversion and interpretation of seismic data. Interpretation of results and methods of classifying households into ses groups are also discussed. The first edition of this book ie, published in 1986, was the first book devoted entirely to principal component analysis pca.
They should know structural analysis and seismic stratigraphy as methods for interpretation. To this end, the process of extracting information from sampled conformations over a trajectory, and checking whether the sampling is a robust representation of an ensemble of conformations accessible to the protein, are tasks well suited for statistical analysis. The standard context for pca as an exploratory data analysis tool involves a dataset with observations on pnumerical variables, for each of n entities or individuals. Principal component analysis, or pca, is a powerful statistical tool for analyzing data sets and is formulated in the language of linear algebra. This book catalogues the majority of specialized tools necessary to work. Principal component analysis pca as one of the most popular multivariate data analysis methods. W e could then perform statistical analysis to see if the height of a student has an y effect on their mark.
Advanced seismic interpretation is a course designed for graduate students. Applications include the exploratory analysis 9 and visualization of large data sets, as well as the denoising and decorrelation of inputs for algorithms in statistical learning2, 6. The vertical seismic profile, acquired with an array of 3c receivers and either a single source or several arranged in a multi component configuration, provides an ideal high fidelity calibration tool for seismic projects involved in the application of seismic anisotropy. The book requires some knowledge of matrix algebra. Principal components analysis is a technique that requires a large sample size. Pdf seismic data interpretation using the hough transform. This first principal component is fixed and we now add a second component to the system. Learn from principal component analysis experts like bob andrepont and g. Finally, some authors refer to principal components analysis rather than principal component analysis. Applying principal component analysis to seismic attributes for interpretation of evaporite facies.
Multiattribute analyses employing principal component analysis pca and self organizing maps are components of a machinelearning interpretation workflow. The underlying physics and mathematics of the various seismic analysis methods are presented, giving students an appreciation of their limitations and potential for creating. Ian jolliffe is professor of statistics at the university of aberdeen. To acquire skills in interpretation of 3d seismic data to enhance theoretical knowledge of seismic structural interpretation, stratigraphic interpretation, reservoir identification and evaluation, and horizon and formation attributes. A loadings plot would show a large coefficient negative or positive for the. At many times, we face a situation where we have a large set of features and fewer data points, or we have data with very high feature vectors. Principal components analysis is based on the correlation matrix of the variables involved, and correlations usually need a large sample size before they stabilize. Data analysis and interpretation was done using smt. He is author or coauthor of over 60 research papers and three other books. Seismic attributes are an invaluable aid in the interpretation of seismic data. Principal component analysisa powerful tool in 29 curve is quite small and these factors could be excluded from the model. Principal component analysis most common form of dimensionality reduction the new variablesdimensions are linear combinations of the original ones are uncorrelated with one another orthogonal in original dimension space capture as much of the original variance in the data as possible are called principal components. Nevertheless the method is very subjective because the cutoff point of the curve is not very clear in the above chart.
Principal component analysis pca is a mainstay of modern data analysis a black box that is widely used but poorly understood. As such, principal components analysis is subject to the same restrictions as regression, in particular multivariate normality, which can be evaluated with the mvn package. Seismic data interpretation and evaluation for hydrocarbon. Investigations thus far indicate the information can be reduced to 10% of the original data base size.
Although one of the earliest multivariate techniques it continues to be the subject of much research, ranging from new model based approaches to algorithmic ideas from neural networks. To understand the distinction between impedance and reflectiv. The goal of this paper is to dispel the magic behind this black box. Interpret all statistics and graphs for principal components. Let us now go back and fine a visual interpretation of equation 1, which you recall was written. Over the past two decades, the industry has seen significant advancements in interpretation capabilities, strongly driven by increased computer power and associated. The application of principal component analysis on. Lower triassic jialingjiang formation, sichuan basin, china suyun hu, wenzhi zhao, zhaohui xu, hongliu zeng, qilong fu, lei jiang, shuyuan shi, zecheng wang, and wei liu.
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