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1. Several generic methods are defined the same method name can be used for other objects belonging to other packages These generic functions use their first argument as a signature in order to decide upon the exact function that will be triggered this signature consists of an object of a given RGeostats class show display the contents of an object belonging to a class print display the contents of an object belonging to a class It may give similar results as the show generic function but is used sometimes differently for specific printouts plot displays the contents of an object belonging to a class Some generic methods have been added although they are specific to RGeostats objects only ascii write dumps the contents of an object belonging to a class in an ASCII file according to a specific format The format is explained separately together with the class description In the following example where dbobj stands for an object of the class db the following command plot dbobj automatically launches the plot command for the db class command db plot Therefore the previous command is exactly similar to db plot dbobj This mechanism is essential in order to understand that the same generic func tion can have different arguments according to the object to which it is applied Finally some additional functions have been added that can be considered as pseudo generic the first argument cannot be an RG
2. 0 Anisotropy Rotation Flag 0 Drift characteristics 1 000000 Matrix of sills 14 4 Model demonstration A special demonstration script is provided in the standard demo command which enables the user to visualize the aspect of the different basic structures The procedure generates graphic windows where all the basic structures which correspond to covariances or variograms are displayed 4 by page It suffices to launch the demonstration script by typing demo RGeostats model The script generates the following pages if variogram models ol Figure 1 Model demonstration Page 1 Nugget Effect Exponential 3 3 x a o o o o T T T T T o T T T T T 0 0 02 04 06 08 1 0 0 0 02 04 06 08 1 0 Spherical Gaussian 2 o lt o o o T T T T T 0 0 02 04 06 08 1 0 0 0 02 04 06 08 1 0 52 0 4 0 8 0 0 0 04 0 08 0 12 0 00 Figure 2 Model demonstration Page 2 Cubic J T l T T 0 0 02 04 06 08 1 0 J Bessel T T T T T 0 0 02 04 06 08 1 0 53 0 8 1 2 0 4 0 0 0 8 0 4 0 0 Cardinal Sine 0 0 0 2 04 06 08 1 0 K Bessel 0 0 0 2 04 06 0 8 1 0 Figure 3 Model demonstration Page 3 Gamma Cauchy o _ o o o S o o o o o T T T T T se T T T T T 0 0 02 04 06 08 1 0 0 0 02 04 06 08 1 0 Stable Linear 54 Figure 4 Mode
3. 33 4 II 2 h lt 1 C h 0 where e C is the sill e a is the range e h refers to the isotropic distance 47 14 1 25 Spline 2 This is a generalized covariance defined for a first order random function it needs a second order polynomial drift defined for any space dimension K h Cx 2 2 h lt a where e C is the multiplicative coefficient also called sill in the interface e ais the scale factor also called range in the interface 14 2 Anisotropy This paragraph describes the way RGeostats handles the anisotropy We first recall that a model is a combinaison of several basic structures Each basic structure corresponds to one of the structures listed and illustrated in the previous paragraph Each basic structure at least the ones which require a range definition can be anisotropic Traditionally two sorts of anisotropies can be distinguished e the geometric anisotropy the ranges are different in different directions so that a simple stretch of the space in the relevant direction would bring the structure back to isotropy e the zonal anisotropy in one given direction of the space the variability corresponding to the sill is smaller than in any other direction of the space First let us note that both anisotropies require the definition of the rotation system in which the anisotropy will be expressed we will then speak of the main anisotropy orthogonal directions 14 2 1 Geometric
4. 5 Installing the RGeostats package Dil Installing Rina e DE ES pe ne e 5 2 Required package LL 5 3 Additional contributions 5 4 Installing an additional contribution 6 Getting started with RGeostats 6 1 Loading the package LL 6 2 Additional information on RGeostats LL Il Description of the Package RGeostats 7 Organization 8 Classes 9 Accessors 10 Generic methods 11 ASCII format 59 11 12 Classes 12 3 1 12 3 2 12 3 3 12 3 4 12 3 5 12 4 Neigh 12 4 1 12 4 2 12 4 3 12 4 4 12 4 5 12 5 Anam 12 5 1 12 5 2 12 5 3 12 5 4 12 5 5 11 SN ah Weak aaa Se Se eee hak A AAA pe IR 12 E 12 ACCRSSOLS sali ome E AAA 13 Generic functions o 14 Utilities e a tada 14 ASCII formati amp vont yo E A ee 16 Nato e A e dai 17 Pel si a di A a a en 17 AGCEssors uil Di a Be hed log a e 19 Generic functions o 20 Utilities e dd tad 20 ASCII Tornatore LEE tt A 21 a DADAS Li e oe al E e AAA AA es 22 Field ita ibi y ed A a AAA gr gy aes 22 Accesso Al ala la Da A 24 Generic functions s o 24 Utiliti S 2 i taa ie E a e ada 25 ASCII formatie heck a cage A att REE A 25 DOVE aa Reese all LR Si ee ee ee re 26 Fields ii pe ie eee Pe ae ee e os 26 ACCESS e eni dala tee he fe e tka a 28 Generic functions 5 0 50004 28 Utilities earn ELIA e eten 29 AS CHMform at ie doce gu a a 29 UNO WIRE nai ee BAB Bee r
5. RGeostats 7 Organization The RGeostats package offers a set of objects They belong to classes according to the S4 mechanism defined in the methods package Each geostatistical procedure in RGeostats uses these objects as input arguments together with some additional parameters some procedures produce one object as output Each class has some generic methods some accessors and some specific utilities attached A generic method is a function which has an implementation for an object of any class An accessor is a specific function which gives access read or write to the different items of the object of any class A utility is a function designed specifically to address an object of a given class 8 Classes The different classes of RGeostats are characterized by their names To get more information on objects of one class the user can type the command class class_ name where class_name is the name of one of the previous classes for example class db The list of classes follows db data base containing the input data or the output results vario experimental spatial characteristics calculated from data such as exper imental variograms covariances generalized variograms model model describing the spatial characteristics such as the variogram the covariance or the generalized covariance model neigh set of parameters describing the selection of samples used for processing a target point called neighborhood anam
6. mension is equal to the space dimension If the experimental variograms the following information is dumped out for each lag the weight attached to the lag usually the number of pairs the average distance the variogram value 21 12 3 Model The Model class contains the information of the structural model composed of one or several basic structures Note that the drift information which is usually attached to the Model definition is not stored within an object of the class Model The model is the necessary ingredient for geostatistical procedures such as krig ing or simulations as it describes the structural characteristics for any distance and any direction in the space 12 3 1 Field An object of the class Model contains the following fields ndim Space dimension nvar Number of variables basics An array of objects belonging to the class melem used to describe the basic structures and described below An object of the class Melem contains the following fields vartype Type of basic structure In RGeostats their is a large number of basic structures available however not that all basic structures are not available in any case in particular some of them are limited to certain range of space dimension others are not available depending on the degree of intrinsicity of the model The following list shows the available basic structures together with their corresponding names Nugget Effect nugget effect compone
7. set of parameters used to transform a sampled variable from its initial distribution to a gaussian standardized law and vice versa rule the lithotype rule used to convert one or two gaussian random functions into a categorical variable facies through thresholds thresh a set of intervals used to convert a variable into a categorical variable or a set of indicators polygon a set of one or several polysets Each polyset is a closed broken line defined in 2 D tokens a set of object definitions used for object base simulations These major classes also use the following auxiliary sub classes that the user should ignore vardir a directional experimental variogram Any object of the vario class is a set of one or several objects of the vardir class melem a basic covariance structure Any object of the model class is a set of one or several objects of the melem class polyset a 2 D broken line Any object of the polygon class is a set of one or several objects of the polyset class 9 Accessors An accessor is an operator which enables the user to read or write one field of an object belonging to a given class using a simple syntax without having to know anything concerning the internal structure of the class There are four generic accessors characterized by their symbol to read the value of a slot of an object value read accessor lt to assign a value to a slot of an object value write accessor to re
8. anisotropy When the main anisotropy directions have been defined the geometric anaisotropy consists in defining the ranges along these different directions For the covariance evaluation the generic formula defined in the previous para graph is used For example the isotropic spherical covariance is defined in the 2 D space as 48 where e C is the sill e a is the isotropic range We now consider the anisotropic spherical covariance considering that the main anisotropy directions coincide with the main axes of the system otherwise we must simply perform the rotation beforehand The ranges are defined in the two main anisotropy directions therefore along X and Y denoted as a and ay The value A of the general formula must be replaced by the weighted distance 2 2 C Ax Ay 14 3 Zonal anisotropy When the main anisotropy directions have been defined we must defined the direction in which the variable shows no variability say the Y direction for example Then it can almost be considered as a geometric anisotropy where the range along the Y direction is set to a large arbitrary distance However it is not trivial to enter such as a large distance For that reason in the interactive way to input a model function model input it suffices to set con ventionally the anisotropy range in the Y direction to NA The range printed as N A in the anisotropy direction confirms that this direction corresponds to the
9. different specific functions used to fit the model will not be described in this paragraph model eval Evaluate the Model for a given set of variables a given direction and a given set of distances model extend Convert a monovariate model into a multivariate one model grid Create a new grid with a variable containing the value of the model evaluated at each grid node model input Define the model interactively model pgs Given the model of the underlying Random Gaussian variable and an experimental variogram of indicators evaluate the theoretical vari ogram according to the PGS method model sample Sample a model along the lags of an experimental variogram specified in an object of the Vario class model window Return information on the graphic window containing the graphic representation of a model This information essentially concerns the extension of the window and its possible dilation 12 3 5 ASCII format Format of the ASCII file for an object of the model class e Dimension of the space e Number of variables e Dimension of the field used to build the stationary equivalent covariance of generalized covariance e Radius of the convolution ball only used for gradient calculation e Number of basic structures covariance variogram or generalized covari ance e Number of basic drift functions For each basic structure e the type see the appendix for the list of basic structures 25 e the range In
10. genuine sill in particular this parameter contributes to the slope value in the case of linear variogram range Range of the structure The term range is generic as it corresponds to a scaling factor for the distances regardless of the fact that the co variance actually presents a genuine range in particular this parameter contributes to the slope value in the case of linear variogram Note that the range actually corresponds to the practical range rather than the theoretical one param Third parameter necessary for some special basic structures such as power model for example flag aniso Flag which tells if some anisotropy must be considered or not This flag when FALSE shortens the calculations and gains computing time aniso rotmat Array which gives the rotation matrix used in an anisotropic case flag aniso TRUE Its dimension is equal to the space dimension aniso coeffs Array which gives the anisotropy coefficients that divides the isotropic range in order to obtain the anisotropic range along each di rection after rotation For more information on the models please refer to the Model Appendix 23 12 3 2 Accessors These are the different read write accessors of some variables in the model class model ndim Space dimension model nvar Number of variables model ncova Number of basic structures not available for writing model basics Array of objects of class Melem containing the characteristics
11. of a basic structure These are the different read write accessors of some variables in the melem class melem vartype Type of the basic structure melem sill Array of sills or slopes melem range Range or scale factor melem param Third parameter melem flag aniso Flag telling if the anisotropy is required melem aniso rotmat Anisotropy rotation matrix melem aniso coeffs Array of anisotropy coefficients This is the read write accessor of an array in the class modell i The object of the melem class containing the basic structure i 12 3 3 Generic functions model plot Represent the contents of a model graphically This function cor responds to the generic command plot model print Print the contents of an object belonging to the Model class This function corresponds to the generic command print model read Create a new object belonging to the Model class by reading the contents of an ASCII file according to a format specific to the RGeostats package This function corresponds to the generic command ascii read model write Write the contents of an object of the Model class into an ASCII file according to a format specific to the RGeostats package This function corresponds to the generic command ascii write 24 12 3 4 Utilities These utilities are specific to the Model class They will be merely described in this manual The interested user will use the on line help for more informa tion Note that the
12. the lags The output is a structure of class vardir vario i The experimental structural tool in the direction for all pairs of variables and for lags The output is a structure of class vardir These are the different read write accessors of some arrays in the class vardir vardir i j k The experimental structural tool for the pair of variables and j and for the lag k The output is a list composed of three element sw weight hh distance and gg structural tool vardirli j The experimental structural tool for the pair of variables and j for all the lags The output is a structure of class vardir 12 2 3 Generic functions vario plot Represent the contents of a experimental structural tool graphi cally This function corresponds to the generic command plot vario print Print the contents of an object belonging to the Vario class This function corresponds to the generic command print vario read Create a new Vario object by reading the contents of an ASCII file according to a format specific to the RGeostats package This function corresponds to the generic command ascii read vario write Write the contents of a Vario object into an ASCII file according to a format specific to the RGeostats package This function corresponds to the generic command ascii write 12 2 4 Utilities These utilities are specific to the Vario class They will be merely described in this manual The interested user will use the
13. to one of the following formats CSV IRAP or ZYCOR the two last format are limited to Regular Grid data bases 12 1 5 ASCII format Format of the ASCII file for an object of the db class e A header line containing the list of locators see the corresponding defini tion in the Fields paragraph If the object is a grid file the header contains e the number of grid meshes in each direction e the coordinate of the grid origin lower left corner in each direction e the value of the grid mesh in each direction The set of values e the set of real values corresponding to the different variables measured at the samples We usually consider one sample per line The set of real values is optional in the case of Grid Db 16 12 2 Vario The Vario class contains the information of the experimental variogram calcu lated from one or several variables contained in a data base The term variogram is generic as it covers the following structural tools Variogram e Covariance Centered Transitive Covariogram Madogram Variogram of order 1 e Rodogram Variogram of order 1 2 e Variogram of a Poisson weighted variable If the data base contains several variables with locator z the corresponding experimental structural tools are then multivariate we obtain several cross variograms instead of a variogram for example Finally the experimental structural tools can be calculated in several directions samples are compared a
14. Image Neighborhood in 2 D with a radius of 5 the number of grid nodes contained in a Neighborhood is equal to 121 For a skipping ratio of 1 all 121 samples are used for a skipping ratio of 2 only 61 samples are selected 27 12 4 2 Accessors These are the different read write accessors of some variables in the neigh class neigh ndim Space dimension neigh type Type of the Neighborhood 0 Unique Neighborhood 1 Bench Neighborhood 2 Moving Neighborhood neigh flag sector Tells if the Moving Neighborhood search uses sectors neigh flag aniso Tells if the Moving Neighborhood uses anisotropic distance neigh flag rotation Tells if the anisotropy of the Moving Neighborhood is defined in a rotated system neigh nmini Minimum number of samples in the Moving Neighborhood neigh nmaxi Maximum number of samples in the Moving Neighborhood neigh nsect Number of angular sectors neigh nsmax Maximum number of selected samples per angular sector neigh width Width of the bench for Bench Neighborhood neigh dmax Maximum isotropic distance neigh coeffs Array of anisotropic coefficients neigh rotmat Rotation matrix for the anisotropy neigh radius Radius for the Image Neighborhood neigh skip Skipping ratio for the Image Neighborhood 12 4 3 Generic functions neigh print Print the contents of an object belonging to the Neigh class This function corresponds to the generic command print neigh plot Represent the contents of an obj
15. Polysets from a plot in order to produce a new Polygon polygon inside Checks if a set of points characterized by the vectors of first two coordinates belong to a Polygon or not polygon projec Apply the current projection to the vertices of a Polygon polygon start Attach a Polygon to be used by a C code This function should only be used prior to a call to C code which expects a Polygon the Polygon will be connected using the slot number returned by the function polygon start 12 6 5 ASCII format Format of the ASCII file for an object of the polygon class e Number of Polysets in the Polygon For each Polyset e Number of vertices e 2 D Coordinates of the polyset vertices 33 12 7 Thresh An object of the Thresh class contains a set of threshold intervals Each interval is constituted by its two bounds defined or not 12 7 1 Fields An object of the Thresh class presents the following fields nclass Number of intervals bounds Matrix defining the lower and upper bounds of the intervals 12 7 2 Accessors These are the different read write accessors of some variables in the Thresh class thresh nclass Number of intervals thresh bounds Matrix of bounds This is the read write accessor of an array in the Thresh class threshl i j The j bound of the i interval The argument i is limited to the number of intervals nclass and the argument j is limited to 2 thresh j The vector of the j bound for a
16. RGeostats Manual D Renard F Ors June 20 2014 Abstract This document constitutes the users manual for the package RGeostats It gives an overall presentation of the package developed using R lan guage For a more detailed description of each function the reader will refer to its on line documentation Finally some tutorials are also avail able in the standard RGeostats distribution which enable the interested user to run some examples on provided data sets You should refer to the Getting Started manual for installation of RGeostats package Part I History of the RGeostats package The Centre de G ostatistique of the Ecole des Mines de Paris spent several years developing different commercial libraries or softwares in the past Let us mention e GEOSLIB the first geostatistical library in FORTRAN e BLUEPACK a geostatistical package that lasted over 10 years and was famous in most mining and oil companies over the world e SIMPACK a package dedicated to geostatistical stochastic simulations e HERESIM a package developed jointly with Institut Frangais du P trole based on the Plurigaussian simulation technique e ISATIS the geostatistical toolbox developed jointly and commercialized by G ovariances It is therefore a tradition for the Centre de G ostatistique to imagine produce and commercialize the algorithms developed by scientists so that practitioner can apply these fancy techniques to the different field
17. ad the value of a slot of an object which is considered as an array array read accessor lt to assign a value to a slot of an object which is considered as an array array write accessor The accessors will be illustrated here using the example of the db class which will be described more exhaustively in subsequent paragraph An accessor is designed in order to question the dimension of the space in which the db is established db ndim Another accessor gives access to the coordinates of the grid origin db x0 Note that as such an accessor is only valid in the case of a grid it will return an error is used for a db not organized as a grid An object of the db class stores the data values within the field items which consists in a data frame the columns corresponds to the fields and the rows to the samples Therefore if we want to access to the value of the third variable for the second sample we should use the syntax db items 2 3 Instead using the read accessor we will use the equivalent accessor db 2 3 10 Generic methods Any object belonging to a class has a set of generic methods attached according to the S4 mechanism To get more information on these generic methods use the command methods method_ name where method_ name corresponds to the name of the generic function For example methods plot Some new generic functions and pseudo generic functions have been added in the RGeostats package
18. ard where you can Download RGeostats package according to the Operating System where you want to use the package this operation requires that you register to the Board first Ask any question about any issue you may encounter Learn on how to use specific parts of the package by reviewing the corresponding Tutorial e the Documentation directory where you can find several case studies each case study contains a PDF file where the case study is fully described the ASCII file s that are used in the case study however these data sets are already contained in the distribution and can be loaded using the data procedure e the Demo directory where you can find several demonstration scripts e the Function directory where you can find the on line help for all functions The package is provided for few platforms For each platform RGeostats is provided as a single file in an archive format The extension of the archive file depends upon the platform e Windows 32 or 64 bits file with extension zip e LINUX 32 bits file with extension linux32 tar gz e LINUX 64 bits file with extension linux64 tar gz e Mac file with extension tgz 5 Installing the RGeostats package 5 1 InstallingR The package R must be installed first R is a free software environment for statistical computing and graphics It compiles and runs on a wide variety of UNIX platforms Windows and MacOS This package can be downloaded from
19. ax Practical bounds in the Gaussian scale anam pzmin anam pzmax Practical bounds in the Raw scale anam aymin anam aymax Absolute bounds in the Gaussian scale anam azmin anam azmax Absolute bounds in the Raw scale anamf variance Variance of the data anam psi Array of coefficients of the Hermite polynomials This is the read write accessor of an array in the Anam class anam i The coefficient of the i Hermite polynomial 30 12 5 3 Generic functions anam print Print the contents of an object belonging to the Anam class This function corresponds to the generic command print anam read Create a new object of the Anam class by reading the contents of an ASCII file according to a format specific to the RGeostats package This function corresponds to the generic command ascii read anam write Write the contents of an object of the Anam class into an ASCII file according to a format specific to the RGeostats package This function corresponds to the generic command ascii write 12 5 4 Utilities These utilities are specific to the Anam class They will be merely described in this manual The interested user will use the on line help for more information anam fit Fit the Gaussian Anamorphosis starting from a Raw variable anam y2z Transform a Gaussian variable into a Raw variable using the Anamor phosis Transform function stored in an object of the Anam class anam z2y Transform a Raw variable into a Gaussian var
20. class polygon npol Number Polysets contained in the Polygon polygon surface Surface of the Polygon polygon xlim Minimum and maximum coordinates of the polygon along X polygon ylim Minimum and maximum coordinates of the polygon along Y This is the read write accessor of an array in the Polygon class polygonli The i Polyset polygonl i j the 2 D coordinates of the jt vertex of the il Polyset 32 12 6 3 Generic functions polygon plot Represent the contents of an object of the Polygon class graph ically This function corresponds to the generic command plot polygon print Print the contents of an object belonging to the Polygon class This function corresponds to the generic command print polygon read Create a new object of the Polygon class by reading the con tents of an ASCII file according to a format specific to the RGeostats package This function corresponds to the generic command ascii read polygon write Write the contents of an object of the Polygon class into an ASCII file according to a format specific to the RGeostats package This function corresponds to the generic command ascii write 12 6 4 Utilities These utilities are specific to the Polygon class They will be merely described in this manual The interested user will use the on line help for more information polygon create Create a new Polygon or add a new Polyset to an already existing Polygon polygon digit Digitize one or several new
21. dard case The next parameters are only used for the Shadow option although they must be defined anyway e The slope of the shadow e The lower truncation value e The upper truncation value The next parameters are only used for the Shift and the Shadow options although they must be defined anyway e The shift value along X e The shift value along Y e The shift value along Z 37 The rest of this file contains the definition of the different nodes used to define the Lithotype Rule We must first define e The number of subsequent nodes Per node we must define e The type of the parent node e The rank of the parent node e The orientation of the parent node The type of the node 0 Facies 1 Threshold along Y1 2 Threshold along Y2 e The rank of the new node starting from 1 The rank of the facies 12 9 Tokens An object of the Tokens class contains the characteristics of the families of tokens used when performing an Object Based Simulation Each family of tokens contain a variable number of parameters depending on its type as well as its proportion 12 9 1 Fields An object of the Tokens class presents the following fields nbtokens Number of token families nbparams Total number of parameters describing the geometry of the tokens types List of the token types props Array giving the proportion for each token family These proportions should add up to 1 mean Array of centers for the param
22. e a 42 LASS JeBessels n h h ulia ao PE ee 42 14 1 8 K Bessel i i iii e a a a a a a 42 1A E an a O 42 TAN VO Cauchy apua five Torna RRR pe T 43 TA Dl Stable xc ale e a 43 TACISIO Linear ii dee e E E da 43 1AL LIS Ponet 2424 chs le tee Dee Pr AE ee 44 14 1 140Order 1 GO i a e aea e h ee es 44 14 1 15 Order 3 GG curan ee T es 44 141 16 Splin GO e ir RE A Ae ae ow od oP Te aT 45 14 0 1 7 Order 5 GC i a i ee a a a S a i a a i a 45 TAVIS COSMOS supu e ea a e Ae o a 45 14 119 Triangle i i te AA de id SE A la eagle et 46 14 1 20 Cosexp 2 di 2 ee e ee ee a 46 TALE2LExp2dfactizzo ie th AE e e 46 La ADO Expract da dt eli e ea 47 141623 REID ii ai ale done LI Sn 47 14 1 24Pentamodel LL 47 14 De 25S PH tot dae ee de ALA At AAA 48 14 2 Amisottopy Sio tt dine La Ae ee ee Ee eee G 48 14 2 1 Geometric anisotropy LL 48 14 3 Zonal anisotropy sreca aeh aa 49 14 4 Model demonstration 2 0 2 002 0000 0 000 51 15 Projections 58 62 List of Figures Model demonstration Model demonstration Model demonstration Model demonstration Model demonstration Model demonstration NO lo A W N Model demonstration Page leek pol a Rte He ei a 52 Page EZ e ilo le ila Rh eB i d 53 Paesi bea ob EN eet BS 54 Page aie ick oral TE aa 55 Pages dic alal a 56 Page i des LL a aa BA 57 Page ET ii CORRE ae ap Ga 58 63
23. e attached to grid nodes in the case of the estimation of the average target variable over blocks for example each cell is conventionally centered on the grid node The array of locators dimension number of fields A locator is a specific identifier followed by its rank starting from 1 A locator indicates the role that a given field for the data base plays The list of identifiers follows e x coordinate e z data variable on which the actual calculations are processed e v measurement error variance e f auxiliary variable used as external drift e g gradient components e 1 lower bounds for intervals e u upper bounds for intervals 12 e p proportion for categorical variables facies For example the field attached to the locator x1 gives the first coordinates of the samples contained in the data base locator f2 gives the second external drift There is no limitation for the rank as RGeostats is designed for any number of variables and any space dimension There are some other locators which can only be either present or absent there is no rank e w weighting variable e code code variable e sel the selection 12 1 2 Accessors These are the different read write accessors of some attributes in the class db flag grid the grid status db ndim the space dimension db x0 the coordinates of the grid origin If the data base is not organized as a grid NA is returned when reading an error is
24. e end of the line e a missing numeric value is replaced by the string 999 Note that the exact spelling must be used including the final decimal point 12 Classes This paragraph gives more information for each class of the RGeostats package It describes systematically e the different fields contained in an object of the class e the syntax of the different accessors e the generic functions e the utilities e the other functions specific to each class are merely described in this manual The user should refer to their on line manual for more informa tion 11 12 1 Db This class is used to store input data set or output results It corresponds to a set of columns also called fields defined on a set of samples The variables are numeric only and stored as real values even if they can be printed in integer format The samples can be either organized as a regular grid or non organized set of isolated points 12 1 1 Fields The Db class contains the following slots flag grid tells if the data base is organized as a grid or not ndim Dimension of the space If the data base is organized as a regular grid x0 array dimension ndim which gives the coordinates of the grid origin lowest values for each coordinate dx array dimension ndim which gives the extension of the grid mesh in all space direction nx array dimension ndim which gives the number of grid nodes along each axis Note that if cells ar
25. ect of the Neigh class graphically This function corresponds to the generic command plot neigh read Create a new object of the Neigh class by reading the contents of an ASCII file according to a format specific to the RGeostats package This function corresponds to the generic command ascit read neigh write Write the contents of an object of the Neigh class into an ASCII file according to a format specific to the RGeostats package This function corresponds to the generic command ascii write 28 12 4 4 Utilities These utilities are specific to the Neigh class They will be merely described in this manual The interested user will use the on line help for more information neigh init Create an object of the class Neigh according to one of the possible types neigh input Create an object of the Neigh class interactively 12 4 5 ASCII format Format of the ASCII file for an object of the neigh class e Type of Neighborhood 0 Unique neighborhood 1 Bench neighborhood 2 Moving neighborhood 3 Image neighborhood For the Unique Neighborhood no other parameter is required For the Bench Neighborhood e Cross validation flag 1 to switch this option ON 0 otherwise e Width of the bench along the last space dimension for example along the third coordinate in the 3 D case For the Moving Neighborhood e Cross validation flag 1 to switch this option ON 0 otherwise e Flag for a search using angular sectors e Min
26. endices 14 Model definition The package RGeostats offers a list of basic structures that can be used in order to construct a Model Each basic structure is now described with its exact formula We recall that e the basic structure includes covariances variograms or generalized covari ances e a covariance is a particular variogram bounded a variogram and there fore a covariance0 is a particular generalized covariance e a basic structure is valid for certain space dimensions e in all subsequent formulae the value h defines the modulus of the isotropic distance therefore this distance is always positive e some covariance use a practical range which corresponds to the distance beyond which the covariance reaches 95 of the sill value 14 1 List of the Basic structures 14 1 1 Nugget Effect This is a covariance defined for any space dimension C h Cod h where e Co is the sill e 6 h is a function which returns 1 if h 0 and 0 for strictly positive distance 40 14 1 2 Exponential This is a covariance defined for any space dimension Ci U cea 3 where e C is the sill e ais the practical range e s 2 995732 14 1 3 Spherical This is a covariance defined up to the third space dimension where e C is the sill e ais the range 14 1 4 Gaussian This is a covariance defined for any space dimension C O x ep 4 where e C is the sill e a is the practical ra
27. eostats already existing object as we are precisely creating it Instead the user must provide the name of the class as a signature Otherwise the signature is asked interactively The following command gives an example of a pseudo generic function used to read an object of the class db from the ASCII file called myfile The resulting object will be stored in the RGeostats object called mydb mydb lt ascii read signature db filename myfile Note that the command methods method_name is not valid for the pseudo generic commands In the following we will make no difference between generic and pseudo generic methods The following pseudo generic methods have been added 10 ascii read read the contents of an object belonging to a class from an ASCII file according to a specific format digitize digitize an object from a graphic plot 11 ASCII format Each class has a method for reading or writing the contents of an object which belongs to this class in an ASCII file The format is obviously specific to each class Several features are common to these methods whatever the class e the values numeric or alphanumeric are separated by blank spaces They may be coded on any number of lines the line change is not significant e an alphanumeric variable may not contain any blank unless the variable is enclosed within quotes e comments can be inserted anywhere a comment starts with the char acter and extends until th
28. eters defining the geometry of the tokens stdev Array of radii for the parameters defining the geometry of the tokens 38 12 9 2 Generic functions token print Print the contents of an object belonging to the Token class This function corresponds to the generic command print 12 9 3 Utilities These utilities are specific to the Tokens class They will be merely described in this manual The interested user will use the on line help for more information token input Define a new object of the Token class interactively 13 The graphics This paragraph gives the general information on the graphics used in RGeostats A first remarks is that each graphic page contains several scenes by default some applications may only use one figure plot of a db but other applications benefit from this multiple scenes behavior plot a multivariate variogram or model The technique used for this multiple scenes i e split screen is incompatible with the other multi screen procedure such as mfrow The multiple scene organization is compatible with another split of the screen al ready defined by the user For this sake all the graphic procedures of RGeostats provide the reset parameter e if reset TRUE default value any graphic will first erase any already existing page subdivision e if reset FALSE the current page subdivision is kept and the current graphic which may itself be subdivided is produced in the current scene 39 App
29. ew variable you should use the command db add beforehand db extract Retrieve one or several variables from a data base into a separate data frame structure db getcol Return the rank a variable within the data base from its locator type and rank db getname Return the name of a variable within the data base from its locator type and rank db grid init Create a new data base organized as a Regular Grid tailored from an already existing input data base The new Grid covers the initial data base in all the directions of the space db grid locate Return the absolute grid node located close to a point whose coordinates are given as input arguments db indicator Create new variables in the data base corresponding to the indicators of the variable corresponding to a z locator given the set of threshold passed as argument as an object belonging to the thresh class db info Return a list of data base characteristics db locate Set the locator for one or several variables within a data base db normalize Normalize a set of variables defined by their field numbers within the data base db polygon Use an input polygon to select the samples of the data base Reg ular Grid or Set of Points which are included within at least one of the polysets constituting the Polygon passed as argument as an object of the polygon class db projec Apply the projection of a data base The characteristics of the projection must be defined be
30. for the Shadow Lithotype Rule rule dsup Relief truncation for the Shadow Lithotype Rule rule shift Shift for the Shifted Lithotype Rule rule nodes Array defining the node characteristics 12 8 3 Generic functions rule print Print the contents of an object belonging to the Rule class This function corresponds to the generic command print rule plot Represent the contents of an object of the Rule class graphically This function corresponds to the generic command plot 36 rule read Create a new object of the Rule class by reading the contents of an ASCII file according to a format specific to the RGeostats package This function corresponds to the generic command ascii read rule write Write the contents of an object of the Rule class into an ASCII file according to a format specific to the RGeostats package This function corresponds to the generic command ascii write 12 8 4 Utilities These utilities are specific to the Rule class They will be merely described in this manual The interested user will use the on line help for more information rule input Define a new object of the Rule class interactively 12 8 5 ASCII format Format of the ASCII file for an object of the rule class e Mode used for the definition of the Lithotype Rule 0 Standard option 1 Shift Rule definition 2 Shadow Rule definition e The correlation coefficient between the two underlying gaussian random functions only used in the stan
31. forehand using the command projec define db read format Create a data base organized as a Regular Grid by reading the contents of an ASCII file according to the format BMP or ZYCOR db rename Change the name of a variable within a data base db rule Convert a numerical variable into a new categorical variable according to a Lithotype Rule passed as argument as an object of the rule class and a set of proportions either passed as an argument if stationary or contained in proportion variables of the data base otherwise 15 db selcombine Combine the currently created selection to a selection already existing within the data base using a logical operation or and not xand xor db sel Create a selection variable This command also allows the creation of a new selection as the on the fly transformation of already existing variables db start Attach a data base to be used by a C code This function should only be used prior to a call to C code which expects a data base the data base will be connected using the slot number returned by the function db start db stat Calculate the statistics count mean variance correlation minimum maximum or one or several fields of the data base db thresh Convert a numerical variable into a categorical variable using the thresholding information passed as argument as an object of the thresh class db write format Write the contents of a data base in an ASCII file according
32. here e C is the sill e ais the period 45 14 1 19 Triangle This is a covariance defined for a one dimension space h C h Cx 1 x09 h lt a a where e C is the sill e a is the range e f is a function which returns 1 if f is true and 0 otherwise 14 1 20 Cosexp This is a covariance defined for a one dimension space C h C x cos x exp 5 where e C is the sill e ais the pratical range e s 2 995732 e a is the period 14 1 21 Exp2dfact This is a covariance defined for any space dimension Ct C x exp hap Too hi azp s a s where e C is the sill e ais the practical range e s 2 995732 e h p refers to the distance in the 2 D plane e h refers to the distance in any subsequent space dimension 46 14 1 22 Expfact This is a covariance defined for any space dimension C h C x exp hi aifs where e C is the sill e ais the practical range e s 2 995732 e h refers to the distance in any space dimension 14 1 23 Reg1D This is a covariance defined for 1 dimension only C h Cx 1 34 1 1 2 h lt 0 5 O h C x 2 32 1 1 g4 05 lt h lt 1 C h 0 h gt 1 where e C is the sill e ais the range e h refers to the distance in 1 dimension 14 1 24 Pentamodel This is a covariance which corresponds to the spherical model calculated in R after fourth order mont e upscaling C h C x 1 2 4
33. iable using the Anamor phosis Transform function stored in an object of the Anam class 12 5 5 ASCII format Format of the ASCII file for an object of the anam class e Number of Hermite polynomials e Minimum absolute value for Z e Maximum absolute value for Z e Minimum absolute value for Y e Maximum absolute value for Y e Minimum practical value for Z e Maximum practical value for Z e Minimum practical value for Y e Maximum practical value for Y 31 e Flag for Storage of Calculation Results if 1 the coefficients of the Hermite polynomials are printed next If calculations are dumped out e Calculated variance e Coefficients of the Hermite polynomials vector of dimension equal to the number of Hermite polynomials 12 6 Polygon An object of the Polygon class contains one or several Polysets A Polyset if a 2 D closed polyline which is used to e select samples lying within the Polyset e delineate a domain where the average of the variable must be estimated 12 6 1 Fields An object of the Polygon class presents the following fields sets An array of objects belonging to the class Polyset used to describe the basic closed polyline An object of the class Polyset contains the following fields x Array of coordinates along X of the polyline vertices y Array of coordinates along Y of the polyline vertices 12 6 2 Accessors These are the different read write accessors of some variables in the Polygon
34. imum number of samples below which the treatment is not performed e Maximum number of samples in the neighborhood e Number of angular sectors e Maximum number of samples per angular sector e Maximum isotropic radius of the neighborhood For the Image Neighborhood e Cross validation flag 1 to switch this option ON 0 otherwise e Skipping ratio e Radius of the Image Neighborhood 0 central node 29 12 5 Anam The Anam class describes the Gaussian Anamorphosis Transform which enables the transformation of a variable from a raw variable denoted Z to a normal ized gaussian scale variable denoted Y and vice versa This transform is captured as a polynomial expansion using a limited set of Hermite polynomi als For the back transform from gaussian to raw scale the raw variable is assumed to be bounded 12 5 1 Fields An object of the class Anam contains the following fields nh Number of Hermite polynomials in the expansion pymin pymax Practical bounds in the Gaussian scale pzmin pzmax Practical bounds in the Raw scale aymin aymax Absolute bounds in the Gaussian scale azmin azmax Absolute bounds in the Raw scale variance Variance of the data used to scale the Gaussian Anamorphosis Transform psi Array of coefficients of the Hermite polynomials 12 5 2 Accessors These are the different read write accessors of some variables in the anam class anam nh Number of Hermite polynomials anam pymin anam pym
35. is the exponent defined as the third argument which must lie within 0 2 14 1 14 Order 1 GC This is a generalized covariance defined for an intrinsic random function defined for any space dimension where e C is the multiplicative coefficient also called sill in the interface e ais the scale factor also called range in the interface 14 1 15 Order 3 GC This is a generalized covariance defined for a first order random function it needs a first order polynomial drift defined for any space dimension K h C x y a where e C is the multiplicative coefficient also called sill in the interface e ais the scale factor also called range in the interface 44 14 1 16 Spline GC This is a generalized covariance defined for a first order random function it needs a first order polynomial drift defined for any space dimension xy cx 8 8 where e C is the multiplicative coefficient also called sill in the interface e ais the scale factor also called range in the interface 14 1 17 Order 5 GC This is a generalized covariance defined for a second order random function it needs a second order polynomial drift defined for any space dimension K h C x ol a where e C is the multiplicative coefficient also called sill in the interface e ais the scale factor also called range in the interface 14 1 18 Cosinus This is a covariance defined for a one dimension space C h C x cos 2 w
36. issued when writing db dx the meshes of the grid If the data base is not organized as a grid NA is returned when reading an error is issued when writing db nx the number of grid meshes If the data base is not organized as a grid NA is returned when reading an error is issued when writing db locators the list of locators for the different fields of the data base db names the list of names for the different fields of the data base db items the set of values for the different fields of the data base produced as a data frame db nech number of samples It is not defined when writing db natt number of variables It is not defined when writing These are the different read write accessors of some arrays in the class dbli j the value for the field j for the sample i dbji the values for all fields for the sample i 13 dbJ j the values of field j for all samples db all the values of the data base gives the same result as the command db or dbSitems Errors are issued if the rank of the field or the rank of the sample is erroneous 12 1 3 Generic functions db digit Digitize a point location from a graphic screen If a data base is passed as argument return the characteristics of the sample from a Reg ular Grid or the Set of Points closest to the digitized point This function corresponds to the generic command digitize db plot Represent the contents of a data base graphically This function co
37. istech fr Nicolas BEZ nicolas bez ird fr Nicolas DESASSIS nicolas desassis mines paristech fr Helene BEUCHER helene beucher mines paristech fr Fabien ORS fabien ors mines paristech fr Florence LAPORTE Another interesting function R standard gives the position where the package has been loaded by typing search The following information is obtained in the R session the contents depends upon the R version the user s environment and the list of packages already loaded 1 GlobalEnv package RGeostats package Repp 4 package stats package graphics package grDevices 7 package utils package datasets package methods 10 Autoloads package base The order of the loaded packages may vary depending on the user s preferences It is easy to see that here RGeostats is loaded in position 2 The user can then type the following command in order to get the list of all the procedures included in RGeostats ls pos 2 Another way to learn about each command say my_command is to ask for its calling arguments by typing args my command But obviously the best solution is to get the information on the command by typing my_ command The information can even be displayed in a more sophisticated manner is the user has launched a HTML browser beforehand by typing the following com mand at least once in the R session help start Part II Description of the Package
38. l demonstration Page 4 Power Order 1 GC 0 4 0 0 0 0 0 2 04 06 08 1 0 Cosinus Triangle 15 20 1 0 0 0 0 5 0 0 02 04 06 08 1 0 Figure 5 Model demonstration Page 5 Cosexp Exp2dfact a 4 2 o 2 o 4 eS o o o o o T T T T T So T T T T T 0 0 02 04 06 08 1 0 0 0 02 04 06 08 1 0 Expfact Reg1D x 2 _ o wa o o sl T T T T T 0 0 02 04 06 08 1 0 0 0 02 04 06 08 1 0 56 0 8 0 4 0 0 0 8 0 4 0 0 Figure 6 Model demonstration Page 6 Pentamodel q T T T T T 0 0 02 04 06 08 1 0 Storkey T T T T T 0 0 02 04 06 08 1 0 57 0 15 0 05 0 25 0 8 0 4 0 0 Spline 2 0 0 0 2 04 06 0 8 1 0 Wendland1 0 0 0 2 04 06 08 1 0 Figure 7 Model demonstration Page 7 Wendland2 0 8 0 4 i 0 0 15 Projections The package RGeostats handles the projections In fact the different classes and methods of this package are connected with a projection system which itself is based on the mapproj and mapproject packages The projection parameters are saved in the RGeostats Environment File until they are either cancelled or modified 58 Contents I History of the RGeostats package 1 What is RGeostats 2 Who can use RGeostats 3 The reference to RGeostats 4 Where can I find RGeostats
39. les in a space of any dimension n we will designate this package as Rn R package However some techniques are not defined for any space dimension nor any number of variables treated simultaneously a special test restricts their usage 1 What is RGeostats RGeostats is provided as a binary R package for Windows Linux and Mac platform It provides e all the R procedures with the corresponding on line help use the command func_ name to access the on line help of the function func_ name e the object library of the geostatistical code Geoslib e some demonstration case studies the user can run them using the com mand demo with the available data sets Note that the source code corresponding to the Geoslib library is not available 2 Who can use RGeostats RGeostats can be downloaded by anyone RGeostats can be used free of charge in a non commercial use 3 The reference to RGeostats When you use this software for publication please use the following reference Renard D Bez N Desassis N Beucher H Ors F Laporte F RGeostats The Geostatistical package version number MINES ParisTech Free download from http cg ensmp fr rgeostats 4 Where can I find RGeostats The package RGeostats must be downloaded from the web site of the Centre de G ostatistique of the Ecole des Mines de Paris http cg ensmp fr rgeostats This site contains several directories such as e the user community Bo
40. ll intervals thresh i The bounds of the i interval thresh The matrix of bounds 12 7 3 Generic functions thresh print Print the contents of an object belonging to the Thresh class This function corresponds to the generic command print 12 7 4 Utilities These utilities are specific to the Thresh class They will be merely described in this manual The interested user will use the on line help for more information thresh input Define a new object of the Thresh class interactively 34 12 8 Rule An object of the Rule class contains the lithotype rule which enables the trans lation of a set of underlying random gaussian variables GRF into a categorical variable presenting several facies The lithotype rule is represented for two GRFs this 2 D space is subdivided into as many rectangular areas as facies which constitute a partition of 2 D Note that to define the areas for n facies it suffices to define n 1 edges or nodes 12 8 1 Fields An object of the Rule class presents the following fields nbnode Number of nodes equal to the number of facies 1 mode rule Type of Lithotype Rule definition 0 Standard Lithotype Rule 1 Shift the second GRF is a shifted version of the first GRF 2 Shadow a shadow is applied to the first GRF rho Correlation between the two underlying GRFs only used for standard Lithotype Rule slope Slope for the shadow calculation only used for the shadow option di
41. may have one working directory by project You launch R by typing the corresponding command or clicking the corresponding icon on Windows for example Within the R session you must load the RGeostats If RGeostats has been installed in the R distribution directory simply type library RGeostats Otherwise type library RGeostats lib loc my_ dir This information can be stored in a specific hidden file called First which is automatically started each time R is loaded in the working directory In order to create it the best solution is to enter the R session and to define it interactively by typing fix First The previous command launches a text editor The name of the text editor can also be parametrized in the First file for future use The contents of the First file could be something as First function library RGeostats lib loc my_ dir 6 2 Additional information on RGeostats When RGeostats is loaded successfully the user can check the version of the RGeostats package This information may become usefull for further discussion concerning the ability of the package to perform a given task or to describe a mysfunctioning acknowledge RGeostats The following message is displayed which may evolve with time Package RGeostats Version XX X X Date mm dd yy Geoslib Library Version XX X X Date mm dd yy Authors Didier RENARD didier renard mines par
42. nf Elevation of the plane where the shadow is calculated only used for the shadow option dsup Maximum elevation above which the relief is truncated before calculating its shadow only used for the shadow option shift Value for the shift only used for the shift option nodes Array for the characterization of the nodes The array nodes provides the definition of the nbnode nodes They are defined as a nested list Each node corresponds to a vector of the following six values 0 Type of the parent node 1 Rank of the parent node 2 Orientation with respect to the parent node 3 Type of the current node 35 4 Rank of the current node 5 Facies value A node type may be one of the following values 0 for a node defining a facies 1 for a node defining a threshold along the first GRF 2 for a node defining a threshold along the second GRF The orientation with respect to the parent node is 1 if the current node concerns values of the GRF smaller than the threshold corresponding to the parent node 2 if the current node concerns values of the GRF larger than the threshold corresponding to the parent node 12 8 2 Accessors These are the different read write accessors of some variables in the Rule class rule nbnode Number of nodes rule mode rule Type of Lithotype Rule rule rho Correlation coefficient between the two underlying GRFs rule slope Slope for the Shadow Lithotype Rule rule dinf Plane elevation
43. nge e s 1 730818 41 14 1 5 Cubic This is a covariance defined up to the third space dimension 3593 Th 3h7 4 2 4 C h C x 1 7h y where e C is the sill e ais the range 14 1 6 Cardinal Sine This is a covariance defined for any space dimension sin 4 C h Cx ale where e C is the sill e a is the practical range e s 20 371 14 1 7 J Bessel 14 1 8 K Bessel 14 1 9 Gamma This is a covariance defined for any space dimension where e C is the sill e ais the range e ais the positive exponent defined as the third parameter 42 14 1 10 Cauchy This is a covariance defined for any space dimension where e C is the sill e a is the range e ais the positive exponent defined as the third parameter 14 1 11 Stable This is a covariance defined for any space dimension ode where e C is the sill e ais the range e ais the exponent defined as the third parameter which lies within 0 2 14 1 12 Linear This is a variogram defined for any space dimension h Wn O X where e C is the multiplicative coefficient also called sill in the interface e ais the scale factor also called range in the interface 43 14 1 13 Power This is a variogram defined for any space dimension Y h C x E a where e C is the multiplicative coefficient also called sill in the interface e a is the scale factor also called range in the interface e a
44. nt Exponential exponential structure Spherical Spherical structure Cubic Cubic structure Gaussian Gaussian structure Cardinal Sine Cardinal Sine structure J Bessel Structure corresponding to the J Bessel function K Bessel Structure corresponding to the K Bessel function Gamma Gamma structure Cauchy Cauchy structure Stable Stable structure Linear Linear structure used in intrinsic case or in cases with drift 22 Power Power structure Order 1 GC Generalized Covariance of order 1 only used in the intrin sic case and in cases with drift Order 3 GC Generalized Covariance of order 3 only used for cases with linear or higher degree drifts Order 5 GC Generalized Covariance of order 5 only used for cases with quadratic or higher degree drifts Exp2dfact Factorized structure with an Exponential in 2 D and an ex ponential along the third direction Expfact Factorized exponential structure Reg1D variogram with hole effect obtained from the residuals of a ran dom function with a linear variogram to which a moving average is subtracted sill Array of sills for the current basic structure This is a square matrix with a dimension equal to the number of variables which must be definite positive In the monovariate case this sill is a single value for each basic structure The term sill is generic as it contains any multiplicative coeffi cient regardless of the fact that the covariance actually presents a
45. o 30 Fieldsr sce EA e a a g 30 ACCESE irte delirar de de de a A N 30 Generic functions o 31 Utilities vicio AAA e eee 31 ASCH format 4 aces a Re dia 31 12 6 Polygons ws scie balia BR RA AS a a 32 12 621 JPields 202 4964 ae eee RRA a 32 12 62 ACCESOS sii tae ee Seah dd BSE A R R RAR E 32 12 6 3 Generic functions 2 0 0 2 0 e 33 12 6 4 Utilities a III Se ead 33 12 6 5 ASCII format atar e alata Pe Re a 33 TAr lt Threshe ope e siae e Be ee ee ee Rae Bt 34 TATI Belda bb alii Sook aa e 34 1257 2 Accesori nil dii ee ee ee 34 12 7 3 Generic functions 2 0 2 2 0 0 2 0 0 e 34 12 74 Utilities AAA eet eo ec 34 TAa Rules eases chee ap fe Sen des e e e lp th te ee ne 35 12 81 Fields sia ite aa lait Belt ee 35 12 8 2 ACCESSOFS re dii DIL e Se A ee eed 36 12 8 3 Generic functions LL 36 12 84 Utilities a Bl ac kek EE el EEE ew se EE 37 12 8 5 ASCII format ue ie i e a 37 TsO A A ck Me lam LA LE had Ea Abd te 38 12 95 Fields i e assale he eh Ge ge GE rn a Wed 38 12 9 2 Generic functions o e e 39 12 93 Utilities ta li EA A ee amp 39 13 The graphics 39 14 Model definition 40 14 1 List of the Basic structures o 40 14 11 Nugget Effect aa A a a I 40 14 1 2 Exponential iii a ae aid 41 14 13 Spherical aaa ie a Ds e 41 14 1 4 GAUSSIAN DS RRA AL poet AA re ah i 41 TEL Cuba E E A a ee 42 14 16 Cardinal Sie ada a Pe
46. od The subsequent parameters are valid only in the case of Moving Neighborhood flag sector Specify if the Moving Neighborhood must be performed selecting samples according to the sector to which they belong flag aniso Specify if the Moving Neighborhood must be considered as anisotropic The distance from each sample to the target site must be converted into an isotropic equivalent distance before the selection algorithm is applied flag rotation Specify if the Anisotropy of the Moving Neighborhood must be rotated nmini Minimum number of samples in the Neighborhood If this number is not reached the target site is not processed nmaxi Maximum number of samples in the Neighborhood This value serves for dimensioning the arrays nsect Number of angular sectors only if flag sector is set to TRUE nsmax Maximum number of samples selected per angular sector only if flag sector is set to TRUE dmax Maximum isotropic distance coeffs Array of anisotropic coefficients only used if flag aniso is set to TRUE rotmat Rotation anisotropy matrix only used if flag aniso is set to TRUE The subsequent parameter is valid only in the case of Bench Neighborhood width Width of the vertical bench The subsequent parameters are valid only in the case of Image Neighborhood radius Radius of the image neighborhood defined in terms of grid nodes skip Skipping ratio for the selection of the Image Neighborhood For example in an
47. on line help for more information Note that the specific functions used to calculate the variograms in different conditions will not be described in this paragraph vario window Return information on the graphic window containing the graphic representation of an experimental variogram This information essentially concerns the extension of the window and its possible dilation vario model check Check if an object of the class Model and an object of the class Vario are compatible This test relies on the space dimension and optionally on the number of variables 20 12 2 5 ASCII format Format of the ASCII file for an object of the vario class Dimension of the space Number of variables Number of directions where the experimental variogram is calculated Option for the code selection 0 no selection performed on the code 1 samples are compared only if the distance between their codes is smaller or equal than the tolerance for code selection 2 samples are compared only if their codes are different Tolerance for code selection only used if the option for the code selection is set to 1 Scaling factor only used for the transitive covariogram For each direction the following parameters Flag for regular lags Number of lags Lag value Tolerance on the angles Direction coefficients vector whose dimension is equal to the space di mension Direction increments defined as increments on the grid vector whose di
48. r responds to the generic command plot db print Print the contents of a data base This function corresponds to the generic command print db read Create a data base by reading an ASCII file according to the format specific to RGeostats This function corresponds to the generic command ascii read db write Write the contents of a data base into an ASCII file according to the format specific to RGeostats This function corresponds to the generic command ascii write 12 1 4 Utilities These utilities are specific to the Db class They are merely described in this manual The interested user will use the on line help for more information db add Add new fields This command also allows the creation of new vari ables as the on the fly transformation of already existing variables this command is considered as the only transformation method within the RGeostats package It can also be used to specify the locators of the newly created fields db compare Calculate statistics count mean variance standard deviation minimum maximum between different variables within the same data base db create Create a new data base assigning its type Regular Grid or Set of Points and defining its general characteristics space dimension grid characteristics number of points 14 db delete Delete an already existing data base db edit Edit the contents of the data base This command does not include any feature for adding a n
49. rs An array of direction variograms see below The experimental directional variogram Vardir contains the following slots npas Number of calculation lags for the calculation in a direction npatot Number of calculation values This number is equal to npas for sym metric structural tools variogram and equal to 2 npas 1 for asymmetric structural tools covariance pas Lag value tol Tolerance on the distances defined as a percentage of the lag value flag regular Flag set to 1 if the lags are defined regularly as multiples of the parameter pas When set to 0 the lags are calculated using the parameter breaks as thresholds on distances breaks Array giving the thresholds applied on distances in order to derive the lags codir Vector defining the direction for experimental structural tool size Dimension of the variogram arrays sw Array containing the weights attached to each variogram lag hh Array containing the average distance attached to each variogram lag gg Array containing the average value of the structural tool attached to each variogram lag 18 12 2 2 Accessors These are the different read write accessors of some variables in the class vario calcul Type of calculation of the experimental structural tool vario by sample Way the variogram calculation is performed vario ndim Space dimension vario nvar Number of variables vario ndir Number of directions for the calculation of experimental struc
50. s in their own domain of activity without having to bother writing lines of code However these packages do not allow the user to modify the code in order to test new ideas or algorithms This is the reason why starting in late 1990 s some researchers started introducing some algorithms in the framework of the R package This was initiated with the GEFA package developed for the fisheries community which uses geostatistical techniques to forecast the fish density by species and age The user could benefit from all the advantages due to the large number of contributors of R developers combined to the procedures established by the researchers of the Centre de G ostatistique As usual with writing packages using the R interpreted language the GEFA package needed to be strongly improved for improving the calculation speed This usually involves writing pieces of the package in using a compiled language such as C or C For that reason the package RGeoS was created in the year 2001 containing a set of R objects to manipulate data parameters and results The package RGeoS is based on a library of geostatistical code written in C and C called Geoslib Recently the package RGeoS has been renamed RGeostats during the year 2014 to better explain its contents and avoid conflict with packages with similar names The main characteristics of the RGeostats package is to perform geostatistical operations simultaneously on several p variab
51. s long as they belong to a given direction up to an angular tolerance 12 2 1 Fields The Vario class contains the following slots calcul the type of structural tool by sample the way the calculations are performed When set to TRUE a sample seed is selected and the corresponding sample variogram is cal culated by comparing the seed to any other sample according to distance and angular selection criteria The final variogram is obtained as the av erage of the sample variograms When set to FALSE the variogram is calculated in the classical way ndim Space dimension nvar Number of variables used for the calculation of the experimental struc tural tool opt code Option concerning the use of the code during the calculation of the experimental structural tool 0 samples are compared whatever the value of the code if defined 17 1 two samples can be compared if the code variable is defined and the dif ference of the code values at samples is smaller than the parameter tolcode 2 two samples can be compared if the code variable is defined and the code values at samples are different scale Scale value tolcode Tolerance for code used when opt code is defined and equal to 1 means Array of the means of the variables under consideration They are used for the Poisson variogram calculation vars Array of variances of the variables under consideration They are used for the graphic representations vardi
52. the anisotropic case this value will serve as the reference isotropic range e the third parameter it must be provided even if not necessary for the given structure For each basic drift function e the type see the appendix for the list of the drift functions Per basic structure e the square matrix of sills which should be definite positive its dimension is equal to the number of variables 12 4 Neigh The Neigh class contains the information of the neighborhood which defines the selection of the active samples used in the estimation or the simulation of a target site This neighborhood belongs to one of the following three characteristics e Unique neighborhood where all samples are systematically selected for each target site e Moving Neighborhood where only a selection of active samples is chosen which moves with the location of the target site e other neighborhoods which are defined specifically for some applications such as Image Neighborhood used when processing information defined on a Regular Grid Bench Neighborhood where all the samples belonging to a horizontal slice called a bench are systematically selected for all the target sites which belong to this slice 12 4 1 Fields An object of the class Neigh contains the following fields ndim Space dimension type Type of neighborhood according to the following list 26 0 Unique Neighborhood 1 Bench Neighborhood 2 Moving Neighborho
53. the site http cran r project org If available for your Operating System it is easier to install directly the ded icated binary version Otherwise one can always download the source code configure it and compile it Then please follow official information provided on the site The installation requires the Administrator rights 5 2 Required package The package Rcpp is required and can be downloaded from the CRAN web site 5 3 Additional contributions Moreover some additional contributions can be downloaded from the same site such as maps and mapproj which are only necessary in some parts of the package RGeostats and will be only needed upon request Each extension comes as an archive file 5 4 Installing an additional contribution When installaing a package one may choose between e installing it as a permanent extension of R this operation requires the Administrator rights as the RGeostats add on package is written on the directory where R distribution is installed The installation is performed by typing R CMD INSTALL mypack e installing it as a personal extension this is the case when an extension often varies This installation does not require the Administrator rights The package is installed on a user s dedicated directory say my_ dir by typing R CMD INSTALL mypack library my_ dir 6 Getting started with RGeostats 6 1 Loading the package You must first start R in a working directory You
54. tural tools not allowed for writing vario opt code Option concerning the use of the code during the calculation of the experimental structural tool vario tolcode Tolerance for the use of the code during the calculations vario means Array of means of the variables vario vars Array of variances of the variables vario vardirs Array of directional variogram calculations not defined for writing These are the different read write accessors of some variables in the Vardir class vardir npas Number of lags vardir npatot Number of calculated values vardir pas Lag value vardir tol Tolerance on distance vardir flag regular Flag specifying if regular distances are considered or if lags are calculated using thresholds defined using the breaks parameter vardir codir Direction definition vector vardir size Dimension of the variogram arrays vardir sw Array of weights not defined for writing vardir hh Array of distances not defined for writing vardir gg Array of variogram values not defined for writing These are the different read write accessors of some arrays in the class 19 varioli j k 1 The experimental structural tool in the direction i for the pair of variables j and k and for the lag l The output is a list composed of three element sw weight hh distance and gg structural tool varioli j k The experimental structural tool in the direction for the pair of variables j and k for all
55. zonal anisotropy main direction 49 Count of Basic structures 1 NA 1 1 Nugget Effect 2 Exponential Spherical Gaussian Cubic Cardinal Sine J Bessel K Bessel Gamma 10 Cauchy 11 Stable 12 Linear OANA I W I 13 Power 14 Order 1 GC 15 Cosexp 16 Exp2dfact 17 Expfact Rank of the basic structure 1 17 2 Sill 0 000000 NA 1 Anisotropy Def n y n y Anisotropy rotation Def n y n n Anisotropic Ranges 1 0 000000 NA 1 Anisotropic Ranges 2 0 000000 NA NA Model characteristics Space dimension 2 Number of variable s 1 Number of basic structure s 1 Number of drift function s 1 Number of drift equation s 1 Covariance Part Exponential Range 1 000 Sill 1 000 Anisotropy 1 2 1 1 000 N A Total Sill 1 000 Drift Part Universality Condition 50 When reading model from an ASCII file using the model read procedure the range in the Y direction should be set to NA again But the NA string cannot be read instead it must be replaced by the conventional string 999 0 as demonstrated in the following ASCII file corresponding to the model entered interactively above Model 2 1 0 000000 0 000000 General parameters 1 Number of basic covariance terms 1 Number of drift terms 2 1 000000 0 000000 Covariance characteristics 1 Anisotropy Flag 1 000000 999 0 Anisotropy Coefficients

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