geoFractal: User Manual - FracMan
Contents
1. Pow z 26 e Error No text of specified style in document 6 2D Gridded Data The analysis of 2D gridded data displays five graphical layouts that are computed using default parameters with other data types geoFractal allows the user to change these parameters The graphical interface for 2D gridded data is shown below 0 F clon 005 01 015 02 0 5 03 20 Gridded CDF Graph A er cae 4727 to lor Fi clio nes 2D Gridded Histogram Pn Graph p 4 Histagram f e Spectral Density of Sleeve Friction a n z0 w 2 40 _ T 1 el UL 1 UIE UL Uu Ls 20 Gridded amp eostatlstics PIU aC um Sleeve Fr Y 25 2 gridded Spectre Lienztv ot Sleeve Frieticm 2 0 1 2 2 4 5 I 5 35 Isi L 1 al 8 157 05 u L 2 z 6 6 12 12 c nD La E 16 7 F RY ff 17 cuc geoFractal displays 2D gridded data as plot of the x location versus the y location The data has been grouped into bins specified by the user as the amount of rows and amount Error No text of specified style in document e 27 of columns the data will be group into The value of the data type within unique2. Zaj Mass Fractal gt 524 3 2D Data Geostati 5 p 3 5 ERES T m 10 4 Eu 4 gt n oe i i D 2 4 8 10 T c d Bux Size m x e gt I 5 T AAS pr 22 Error No text of specified style in document geoFractal displays 20 data as graphically as the x location versus the y location with the value of the data type displayed as a gradationally colored circle Values for the data are assigned a color value The grading color is shown at the top portion of the graph covering the full range of data values The second graphics displays the data as a CDF graph The data type is plotted against percentile This graph can be modified to a CCDF graph and a curve of type normal log normal power law or exponential curve can be fit to the data The final graph displayed for borehole data is the geostatistical analysis this analysis describes the spatial correlation between observations in terms of a second order moment defined as yh EK xE h where x z is the value of some parameter at a location z x z h is the value of the parameter at some location a vectorial distance h from z is the mathematical expectation of the quantity in braces and yh is the semivariance h is sometimes referred to as the ag or the ag distance The plot showing the semivariance func
3. Fearcern Fercenj 0 1 10 tain D 1 10 1 107 Trace Length Trace Length View 2 log log View 3 log linear The final graph displayed for borehole data is the geostatistical analysis this analysis describes the spatial correlation between observations in terms of a second order moment defined as Error No text of specified style in document 19 y h 1 E x z x z y where x z is the value of some parameter at a location z x z h is the value of the parameter at some location a vectorial distance h from z is the mathematical expectation of the quantity in braces and yh is the semivariance h is sometimes referred to as the ag or the ag distance The plot showing the semivariance function vs the lag is termed the variogram or semivariogram The lag is the distance or separation between data points and the semivariogram is a measure of the spatial correlation The user must specify a model type to fit a curve to the data The model types available are Spherical Exponential Gaussian Power or de Wijs The mathematical formulae for these models can be found in most geostatistical texts for example Journel A G and Ch J Huijbregts 1978 Mining Geostatistics Academic Press The standard deviation or the sum of squares error is displayed to guide the user as to how well the model with the parameter values displayed fits the empirical semivariogram The parameters for each model can be comp
4. Error No text of specified style in document e 39 Baecher Analysis PDF Edit Parameters Fractal for Windows iz Ef x File Edt View Help 2 POF of Fracture Count B Poisson distribution 5 statistics 0 1 0400533 level of Cm Analysis PDF x pen 4 Histogram 58 Box Fractal Dimension ne Mass Fractal Analysis P GA Baecher Analysis CDF Baecher Analysis PDF E View Previous View Chart Layout Edit Parameters rit Weippe Fercent of Total im Export Chart 5 New Window 0 Print 2 Amt of Fracture Centers in Cell datasets in workspace 2 Histogram Settings Range Baecher Analysis PDF I asinum Increment __ 220204060068 pm Fracture Centers in Cell 40 Error No text of specified style in document 8 Gridding Data Irregularly spaced data can be gridded by specifying the new grid size the origin of the grid and the amount of cells The user should also specify if the grid value is an average minimum maximum or count When analyzing borebole or 2D data the option to grid the data is found in the edit menu under view edit data Fractal for Windows File Edit View Help zB e Mats Tame Tim Strats Gridding Data nix dep em aM dala meine in Haie
5. Upon selecting Extract Data the chart plane displays the data as a graph y location versus x location with the intensity of the data label region shown as a shaded block Import Gridded Data Data Description e g Test 204 Data Type 2D Gridded Data 20 3ridded Data Label Conductivity Sleeve Friction amp mt of 50 Amt of Columna 29 x Spacing 1 Y spacing 1 A Origin Y T Extract Data from File x Select User Parameters Data Extraction Sequence From Column Read Sleeve Friction Dats Row Definition v Wo Test in Lines 8 Amb Les fas kn Text at the B eginning af a Data Line Number of Data Columns C Test Any Place in Data Line Apply Use Parameters Sequence Fead Sleeve Friction from Column 3 3 columns in 1250 rows Conteats of File mth Highlighted D ata Block Extract Daa Help 0 000528859 zi Fracture Trace Data Fracture Trace Data requires data grouped into two endpoints These endpoints are connected by geoFractal to create a traceplane map Data can be loaded as a F2D file a text file TXT comma delimited file CSV and space delimited file PRN F2D files are Error No text of specified style in document e 9 created in FracWorks95 by sampling fracture sets with traceplanes to create fracture trace maps The user is prompted to give the
6. AF F View Data Ef x E Tip Stress Depth Tip Stress s 1 mm T D 10 2 3 40 13 61 0 055 1981 0 055 _ D 2 24 35 012 0 24 3 2555 0 145 4 2533 0 21 5 2651 024 2081117171 CI J B 2402 0 305 0 8 E 2224 0 345 1 AHU 8 16 93 0 42 3 1715 0 455 _ Borehole Data Depth Chart arid Data Cancel Help 5 datasets in workspace 2 Change Data Grid gt New Grid Size Start Grid at Amt of Cells auto selected if left blank Grid Value Average C Masimum Minimum Count Error No text of specified style in document 41 Index 8 24 25 26 32 44 Irregularly spaced point data 1 2D etidded 9 29 Beacher uy ED 40 Borehole dat cen u Uie aa 7 Irregularly spaced one dimensional data 1 diniens ee a io eo otov odit 2 37 40 4 20 21 25 30 35 CDF 4 20 21 25 30 35 40 Changing parameters Edit parameter eese ERE RE CORE M 18 d oed t 18 Chart asso a dedu bes 14 C hiisSquate tuya uuu uuu aus 41 Curve Fit Exponential etek 21 25 30 35 21 25 30 35 Normal cn detract al 20 21 25 30 35 Power dtes
7. Error No text of specified style in document The first graphical interpretation of the data is represented as data type versus depth The data points are connected to show the general trend of the data The second graphic displays the cumulative density function CDF of the data as data type versus percentile This graph can be easily altered to show a CCDF graph This option as well as the option to change the scale linear log linear log log linear log is found in the toolbar To fit a curve to the CDF or CCDF function the user must decide if the data is most accurately fit using a normal log normal power law or exponential curve Statistics are calculated for the user to access the fit The third graphic displays a histogram of data type versus percent of total Interval range and increment spacing can be changed under the edit parameter option in the popup menu To fit a curve to the histogram the user decides on the appropriate curve type and checks the statistics The fourth graphic shows the CDF of spacing as data spacing versus the percentile The graph can be displayed as a CDF or CCDF graph A normal log normal power law or exponential curve can be fit to the data Customize Charts CDF Graph CDF Graph Ferrer e Fercenie I led U 2 4 D 10 12 14 U 2 4 0 10 12 14 Length Trace Length Default View View 1 linear log CDF Graph T CDF Graph
8. as is typical of image logs core or scanlines 2 Irregularly spaced point data on two dimensional surfaces This type of data might represent single values determined at non systematic locations such as wells 3 Gridded data This data represents some parameter value assigned to an area represented by a cell in a finite rectangular grid Gridded data can be imported directly into geoFractal or irregularly spaced two dimensional data can be converted into a grid according to various user selected options 4 Fracture trace data These traces might represent interpretations of lineaments outcrop mapping or top of reservoir structure maps For each one of these four fundamental data types geoFractal performs a number of analyses to describe the population statistics and to assess how well alternative spatial models characterize the data Population statistics are displayed on the screen and may be optionally saved in ASCII files The populations themselves are characterized by statistical distributions typically by frequency histograms and cumulative probability graphs The data underlying the graphs and the graphs themselves may be exported into formats readily accessible to graphics or word processing programs There are three broad categories of spatial analyses that geoFractal carries out 1 Uncorrelated Poissonian processes 2 Fractal box dimension mass dimension and self affine dimension and Error No text of specified sty
9. fracture trace data 15 Mass Fractal Analysis This analysis compares the distance from a specified origin on the studied region to the number of fracture centers found within the distance from the origin The user has the option to modify the origin for this analysis and the interval range for the analysis of various radii The calculation method depends on the method chosen to count fractures four options exist fracture centers whole fractures fracture intersections and fracture density P21 The graph is then fit to a linear function or to a power function geoFractal displays the statistics to allow the user to make the best fit The Mass Fractal dimension is computed by determining how much of some parameter is a region of a particular size One of the original uses of this dimension was to examine the spatial scaling of mass in the universe in which planets suns etc are essentially points with a scalar value of mass associated with them The calculation started with Earth at the center and looked at how much mass was contained in spheres of ever Increasing radius The same type of calculation is performed on the fracture data Again the user has options on whether the fracture center points traces or other parameters are examined geoFractal allows the user to specify a central starting point and the radius of the inner and outer circles as well as the number of circles between them The results are plotted as the Log mass v
10. oe Edo eot au usu uama Qui ds EUER CE HE Ou CEPR ah s aT UU 17 Z Borehole Dati ITO ii 16 S81 2 7 Fr S 22 02D Gridded Di s unsi ua kasu ass 27 Practice Trace Dto cao SO t 31 o Griddi b pru jr anu 41 43 Table of Contents e ii 1 Introduction geoFractal Welcome to geoFractal geoFractal is a tool to characterize fracture data in ways that it is typically acquired Although it contains many sophisticated algorithms to evaluate the fractal properties of fractures it also makes it possible to evaluate alternative models including uncorrelated stochastic spatial and geostatistical processes geoFractal has been designed to run efficiently on most modern computers operating under the Windows family of operating systems Future releases will expand geoFractal to other widely used platforms geoFractal s intuitive user interface makes it possible to interactively test the data and view the results One of the benefits of the software is that upon import of a data file all of the analyses are automatically carried out using default parameters The user can immediately view the results 1 1 Overview of Program Structure The highest level of geoFractal focuses on the type of data There are four data types currently supported These are 1 Irregularly spaced one dimensional data such
11. of Tip Stress data points in this set Borehole Data a CDF Graph 1D Semivarioqram Setup istics Histogram New Lag Range iz COF of Spacing us 9 Geostatistics Min lag value has lag value Amt af Lage Uniformly in lag space Semi anagram Cloud Lag datasets in workspace 2 The user define the lag values in terms of the minimum lag the maximum lag and the number of lags The lag width is equal to max lag min lag number of lags The default lag interval is arithmetic but the user may wish to specify the lags as uniform in log space if the object is to test the self affine fractal model The semivariogram cloud model displays all of the raw lag pairs rather than just the mean value for each lag class Error No text of specified style in document e 21 2D Data The analysis of 2D data displays four graphical layouts that are computed using default parameters These parameters can be adjusted to better fit the specific data The graphical interface for 2D data is shown below lt D Deta 7r ctiani Patio 117 114 20 Data CDF Graph 9 o UT T T 3 2 eto v 20 Data Histogram fig qed 1104 n Ealio 5 60 ES m 10 e COF Graph Histogram m p 38 Box Fractal Dimension 4 Mass Fractal Analysis Geostalistics us E nz 1 14 on Maj Fractal Dimension
12. type options Fractal for Windows Edit View Help Y b 2 EN A 92 Se F 3 F GF 5 amp lt S g 2 Q A S S xe 9 2 Error text of specified style document 5 3 4 Opening Files geoFractal for Windows recognizes four types of data borehole one dimensional data two dimensional data that does not follow a regular gridded structure two dimensional data that is gridded and fracture trace data Files are opened by selecting Open under the file menu and then choosing a file that contains one of the four types of data Once the file has been opened the user must specify the data type before viewing the data Hew Fractal Data C 2D gridded data C 2D x u z data __ Cancel Cancel Fracture trace 6 Error No text of specified style in document Borehole Data Borehole data requires two data fields depth of borehole and related data Data can be loaded as a text file TXT comma delimited file CSV or a space delimited file PRN The data description and data type are prompted by geoFractal after borehole data has been chosen as the data type To extract the data the user must select the columns that contain the depth and related data Upon selecting Extract Data the chart plane displays the data as a graph data label versus depth Data 1D borehole Data Data Description 9 Test
13. 1 1 5 2 Tez 21 3713 Trace Length 14104 signif level 0 1441 20803 Filliriy E dit Fit Region OK 2 Histogram Cancel es V Show Fit Info Chart li Histogram 20 1 deles in var 535 Percent of Total reise Length feiss Uk M ota U zit 4 1 z poy ase cum To Y sar plese RAL Delon aid e H H L The third graphic displays histogram of data type versus percent of total Interval range and increment spacing can be changed under the edit parameters option in the popup menu To fit a curve to the histogram the user decides on the appropriate curve type and checks the statistics geoFractal next analyzes the fracture trace data to find the box fractal dimension For a thorough discussion on calculating the fractal box dimension see Barton C C and P R La Pointe 1995 Fractal in the Earth Sciences Plenum Press Chapter 8 The graph displays the box size versus a count of the fractures in doubly logarithmic axes The Box fractal model may a useful model for the spatial pattern of the traces if the points lie on straight line There are three methods used to count the fractures fracture centers whole fractures and random points on fractures The Fracture Centers option creates a set of fracture trace centerpoints and computes the Box dimension of this set The
14. Analysis 13 data paints in this set defeult local mask region used o Box Fractal Dimension x S 4P Histogram map Mest Vi 08 Fracta Dimensicn I es Mass Fraclal Analysis Previous View Baecher Analysis Chart Layout Baecher Analysis PDF 110 ET Mane Ie c Fil Curve E F snort Charl 10 sl T T Mew Windows amens Pant _ 1 1 17 1 10 1 10 Box 5156 datasets in warkspacas ze Settings for Fractal Dimension Analysis Bux 1202 Maximum 13930 amem Box Frecture Irers Inerement Handom Fonts POL E ws Calculation Use Locel Mask UN peut Use Global Mask MAC gt z7 Shas Mack Calculate 1 5 x v An w Stet 36 e Error No text of specified style in document Box Fractal Dimension Fit Curve Dialog Fit Curve Power Function w Straight Line n Ants Least Power Functian he K E CE EE E 18131157 504 Cover Frac Random P 2471 9195 12 05848 3635 zin OA if zi Select Fitting Box Fractal Dimension e HE m C TL UT T T T t T po n e Rendam Pointe _ ed Corer Frac pres kr b st wn and drea ET use The fifth type of analysis performed on the
15. BHZ AF orehole Llata Label e g Landuchyiy Tip Stress i Extract Data File Data Source Extrection Secuence Select User Parameters data fron text file rom Column Head 2 Amt Lines To Skip hi Number Columns Tp Stress t Text In Data Lines Cancel T ext at the Beginning Data Line Test Any Place in Line et Columns Amply leer Parameters Sequence Head Depth tron Lclumn 1 i Data block contains Read Tip Stress from Column 2 4 columna n 24 rows Contents of File with Highlighted Data Block 55 19 611 120 24 35 145 25 552 210 25 33 240 26 101 309 24 027 n 22 23 220 18 331 gt 17 157 Extract Data Cancel 20 Data Error text of specified style in document e 7 20 data requires three data fields the x and location and related data Data can loaded as a text file TXT comma delimited file CSV or a space delimited file PRN After the data description and data type are prompted by geoFractal after 2D data has been chosen as the data type To extract the data the user must select the columns that contain the location information x and y and the location of the related data Upon selecting Extract Data the chart plane displays the data as a graph y location versus x location with data label intensity shown as variou
16. Random Points option is very similar except that one or more random points are selected along the trace Both options are primarily useful for determining model generation parameters for example for a Discrete Fracture Network model The Whole Fracture option calculates the minimum number of boxes to cover the whole fractures as it is done in the reference in the preceding paragraph This is probably the best option for comparing 1D and 2D scaling properties of fracture data sets since the Box dimension of fracture intersection points in a 1D sample like a borehole should be exactly 1 0 less than the Box dimension of the trace pattern in 2D The slope of the line is equal to the Box fractal dimension for all options To calculate the Box dimension the User must specify the geometry of the calculation grids In essence the grid begins at the smallest values of X and Y data and extends to the maximum grid size as shown in the figure the minimum or starting grid size is also displayed in the lower left hand corner of the larger square to visually indicate the two extreme grid sizes The user also needs to specify the number of grid cell sizes in between these two extreme values To restrict the calculation to a subregion of the data set the user should define a local or global mask and apply it Error No text of specified style in document e 35 Fractal tor Windows _ xf File Edit view Help 25828 Bos Dimension
17. am 12 i C 5 4 7 Oo gi EU aL CL Fractal Dimension me 5 10 15 CDF Giap Histogram ff Blox Fractal Dirrension z A la f i 5 Mass Fractal Analysis _ Mass Fractal Analysis ef Baecher Analysis CDF 150 a Bache Analysis PDF E l ui D m D m L m CDF Graph CA PLNS az L b P rali Baecher Analysis PDF f p 2 EH l f f 14 I 13 20 I 40 s of Con ers 1 22 E S s e CL 1 Tx J RE u Frecture Certers in Fracture trace data is displayed as a trace map The data is imported as paired endpoints which are connected to show the length and orientation of the fracture along a plane The first graphical display shows the map as referenced to the x location and y location of each endpoint 32 Error No text of specified style in document The second analysis consists of a graph which plots the data type against percentile The graph can be easily altered to show a CCDF graph This option as well as the option to change the scale linear log linear log log linear log is found the toolbar To fit a curve to the CDF or CCDF function the user must decide if the data is most accurately fit using a normal log normal power law or exponential curve Statistics are calcul
18. arid Lines General amauununananananaanaananaananananananananaanaq Tanssanssmunansuansauusuaussausansaussauu sanas Range and Division Tick Marks 0 000000 Maximum 1 000000 Major arid interval 0 200000 Number of minor ticks aa within a major grid Show ticks Tick style Dutside avout Chart Settings Continued View Previous Wew COF CCOF Chart Layout Edit Parameters Fit Curve Export Chart Mew window Print Change the axis scaling and representation The user can define the minimum and maximum values for the axis the major and minor grid intervals and whether and how the tick marks are displayed Error No text of specified style in document 15 General Page 1 Scale Major Grid Lines Show major arid lines Style Solid Y Thickness 0 254000 mm Both major and minor grid lines can be displayed The user can amunuunnuuunanunaananananananananamanananananananana Chart Layout Chart Settings Continued Scale View Line Marker Previous View COF CCOF Minor Grid Lines Show minor grid lines Style Solid Chart Layout Edit Parameters Fit Curve Thickness 0 205200 mm Export Chart Color CHANGE New Window Print defi
19. as installed in the Start menu and click the geoFractal icon OR From Explorer open the geoFractal program folder and double click the geoFractalWin exe file 2 3 Uninstalling geoFractal Should you wish to uninstall geoFractal the steps for uninstalling are explained below TO UNINSTALL geoFractal Click the Start button and select Control Panel from the Settings menu Double click the Add Remove Programs icon 2 Error No text of specified style in document From the list in the Add Remove Programs window select geoFractal and click OK Follow any further directions should they appear 3 The geoFractal User Interface 3 1 Basic Layout The main window for geoFractal contains a viewing window and a control window The program is run through a series of commands found in popup menus and from the main menu and tool bar The following display shows the various sections of the basic layout Error No text of specified style in document e 3 Tool Main Menu goiat Dataset Info Bar Fractal for Windows File Edit View Help oh Data Type Tip Stress Borehole Data mS 4 24 data paints in this set a SDE Graph Tip Stress Histogram 0 10 20 ai ii Dataset Plane 4 CDF of Spacing a Tree View Geostatistics a 0 2 0 4 0 6 Borehole Data Depth Chart n datasets in workspace 2 Workspace Info 3 2 Main Menu Graph Info Chart Plane Th
20. ated for the user to access the fit Fractal for Windows i Inl x File Edit view Help 2582 M 6 PDF of Trace Length 18 data points in this Trace Data CDF Graph 3n Histogram x e Histogram 00 Fractal Dimensicn e 58 Mass Fraclal Analysis 15 Baecher Analysis CDF 4 Baecher PDF Previous view x 10 Chart Layout Edit Parameters O 5 Fit Curve Export Cart 0 5 1 1 Print Trace kength 1410 1 datasets in workspac 2 i Modify Histogram Settings Fange Histogram i 700 Increment Update 0 0 5 1 1 5 2 CERERI Trace Length 1031 Percent of otal Error No text of specified style in document 33 Histozram Fit Curve ractal for Windows D x Edi Help Ex 4 POF cf Trace Lencth 13 data peirts in tars Fl NE Ed Fah Histogram EN Hiz ogram fea COF Boede POF Wie Prev n vig m Char Ft Parameters i E Fit Curve Espcr Dialog Fit Curve Parameters Function LogMaormal Dist Normal Distr Loghormal Distr a Exponential Distr oem B 3785 deviation 05448 Function From Parameters D 5
21. bin displays as a color determined on a gradational color scale The second analysis consists of a CDF graph which plots the data type against percentile The graph can be easily altered to show a graph This option as well as the option to change the scale linear log linear log log linear log is found in the toolbar To fit a curve to the CDF or CCDF function the user must decide if the data is most accurately fit using a normal log normal power law or exponential curve Statistics are calculated for the user to access the fit The third graphic displays a histogram of data type versus percent of total Interval range and increment spacing can be changed under the edit paramenters option in the popup menu To fit a curve to the histogram the user decides on the appropriate curve type and checks the statistics Version 1 0 of geoFractal allows the user to calculate the power spectrum of the gridded data For more information on the calculation and use of the power spectrum of 2D fracture data see La Pointe P R and C C Barton 1995 Fractals in Petroleum Geology and Earth Processes Plenum Press Chapter 12 Essentially the data is distributed in a self affine fractal manner in 2D is the power spectrum plots as a straight linen in doubly logarithmic axes The exponent of this line is not the self affine fractal dimension but is related to it as explained in the reference above in the special case where the line is appr
22. data a descriptive name and then enter the column numbers of the desired data After the columns are reset the data can be extracted to create a trace map on the Chart plane Create Hew File Cata Description 9 Test 2 4 Cata Label 9 Conductrvity Fracture Trace Data Type Fracture Trace Cancel i Extract Data from File Data Extraction Sequence Select User Parameters From Column Read Dats Row Definition Al No Test in Data Lines Text at the Beginning 2 of a Linc fe Humber of Data Columns C Test Any Place in Data Line Te TIT Apply User Parameters Sequence Fead 1 from Columr 2 Fead 71 trom Lolurnr 3 Fead xz from Columr 4 Fead 72 from Columr 5 gt Data block contains 8 columns in 929 rows Conteats of File with Highlighted D ata Black Extract Dara 10 e Error text of specified style in document 1 1R7TF rf 4 ASSAF 3 1 19 3 DIR R nSATFE 12 2111 05 3 635E 03 1 2138 05 3 8217E403 Cancel 2104 05 2 7476 03 1 2115E D5 2 7953E403 2115 05 2 7953 03 1 72130E 05 2 9346 03 213 05 2 9346 03 1 72147E 05 319712 02 2147 05 3 1971 03 1 2152 05 3 3263 03 E 1 1780E 05 4 2960E 03 1 1955E 05 4 5388E403 1 17352 405 A 9133F 05 1 177RF 05 18382 n3 3 5 Graphical Interface Whe
23. e lag is termed the variogram or semivariogram The lag is the distance or separation between data points and the semivariogram is a measure of the spatial correlation The user must specify a model type to fit a curve to the data The model types available are Spherical Exponential Gaussian Power or de Wijs The mathematical formulae for these models canbe found in most geostatistical texts for example Journel A G and Ch J Huijbregts 1978 Mining Geostatistics Academic Press The standard deviation or the sum of squares error is displayed to guide the user as to how well the model with the parameter values displayed fits the empirical semivariogram The parameters for each model can be computed using a minimum likelihood estimator MLE or can be directly specified by the user Semivariogram analysis be used to examine both the second order spatial correlation in the data and also the self affine fractal properties see for example Burrough P A Nature 294 240 242 1981 Examples of applying variogram analysis to fracture pattern attributes can be found in La Pointe P R and J A Hudson 1985 Geological Society America Special Paper 199 geoFractal s semivariogram models makes it possible to test several of the most common functions that exhibit second order stationarity geoFractal also makes it possible to evaluate the self affine fractal model This is done by computing the empirical variogram and displaying it on doubly
24. e main menu lists operations that can be performed by the fractal program Each of the four options File Edit View and Help results in additional menu options To choose an option from the geoFractal main menu highlight the desired option by pointing with the mouse and clicking the left mouse button The file menu is used to open new projects close and save projects export files and print The edit menu controls the chart properties The view menu moves the on screen layout to a separate screen previous or next viewing options and changes cumulative curves between CDF and CCDF graphs geoFractal help and information about the geoFractal is located in the help menu 4 Error No text of specified style in document Edit View Help Edit View Edt View 7 0 Open Chart Layout Ctrl L window Fractal Help About Fractal Close View Edit Data Chri E Previous eee Close All Parameters Save 5 c CDF CCDF switch iia E dit Mask Region E part Import Power Frint Ctrl F Print All Quit 3 3 Toolbar Options The toolbar provides shortcuts to frequently used functions All of these functions are also found within the main menu The toolbar contains commands to open new files save existing projects print charts edit parameters view data edit the chart create a new window and toggle between various chart
25. ede p o mna ues 6 Comma delimited file CSV 7 8 9 10 PD Tile NEMO TRECE 10 Space delimited file PRN 7 8 9 10 Text HIe Du mM 7 8 9 10 PDF 40 Poisson oi hom Uto 40 41 Of i um u ay cbe Power TUDCUO uuu a te E to rade era 40 POW CES PCC FUITE 30 40 Second order 21 25 32 Self affine dimension 2 Self affine fractal 22 23 25 26 30 32 22 25 32 Semivariogram 22 23 25 26 32 40 Semivariogram 15 225 255 32 Stationary geostatistical processes 2 Toolbqt oie 5 T 11 2 hu PHP 4 Error text of specified style in document 43
26. eo n 21 25 30 35 DG th CHOPIS oboe don 30 Edit 4 er 21 File 4 Fractal 22 25 30 32 37 40 Fracture intensity Fracture 52 a un 37 40 Fracturedensity P21 u usa 40 Random points od d ood ds 37 Whole Fractures 37 40 Fracture Trace 10 33 Trace Tape t oa atu ut ames 11 34 Grdadme Data zo eb IE 44 Help 4 N 21 30 37 2 Kolmogorov Smirnof test 41 I66qr PUNCION s uuu u u 40 4 icd u 3 Mass dimension ur uu u ul nun u Susu 2 40 Mass Fractal Analysis 40 Mass Fractal dimension 40 testes edunt ve sien 40 WAT PAA AO acceso TT 23 Minimum likelihood estimator 22529592 Model types dE Wika a umu uamata 22792 22 32 e iUe todo 22232 DOWEL 22 32 Splierical sm ni 22 32 Su
27. f the data has no spatial correlation a horizontal power spectrum a box dimension equal to 2 0 and a mass dimension equal to 2 0 geoFractal grids the fracture trace data and estimates the mean data density as a function of grid cell size Next it creates a PDF and CDF for a Poisson process that has the same mean density for the same grid cell size and compares it to the actual results For the PDF a Chi Square test is performed to check the goodness of fit For the CDF a Kolmogorov Smirnof test is carried out Test statistics are reported for both tests The statistics are somewhat sensitive to the grid cell size chosen Grid cells that are too large or too small will produce useless results 38 e Error No text of specified style in document Fractal For Windows El Baecher Histogram datasets in workspace Feira Analysis lil I l errentile Ta m Graph Baecher Analysis POF Baecher Analysis CDF Edit Parameters a Box Fractal Dimension Fractal Analysis 24 Baecher Analysis CDF IN ci CDF Percentile D 2 4 Amt of Fracture Jer For Daechrer n Edit Parameters s Baecher Analysis PDF of ES n B B Amt of Fracture eners in Cel
28. fy the layout general page x axis y axis x scale y scale gridlines line and marker The windows are displayed under the edit menu or as a popup menu in chart layout Error No text of specified style in document 13 Chart Layout Chart Settings CDF Graph L hart Layout 2 Change the graph title add subtract a frame change font or change plot background Automatic jue Changes the page size and margins not Implemented In current version Change the title of the axis the location of the axis and axis style or the font style Solid 0 508000 14 Error text of specified style document Chart L 1 Scale arid Lines Line Marker General Page Kass Scale abel Percentile Type F aq E Linie Style Solid Thickness 0 508000 mm Lalor mM CHANGE Order of values Battom to top to bottom Axis location Left Right Label fort a hBci dL Annotation fort CHANGE 1234557890 A IS Line YAMS Tick Marks YScae GridLines General Page Range and Division Minimum 0 000000 10 000000 Major grid interval 2 000000 Number of minor ticks within a major qrid Show ticks Tick style Dutside 2 Scale Marker Yami Line Axis Page
29. geoFractal Geostatistical and Fractal Analysis for Spatial Data User Manual Version 1 0 September 2000 Prepared by Paul LaPointe Anna Burago Kuantsai Lee Bill Dershowitz FracMan Technology Group Golder Golder Associates Inc 2000 geoFractal Manual doc LICENSING geoFractal was developed by Golder Associates Inc Redmond WA Any permission granted for the use of this software includes the express condition that all liability and responsibility for the results obtained from use of this software 1s exclusively that of the individual user or organization Golder Associates makes no warranty of the accuracy functionality or application of this software Users entire remedy shall be limited to refund of the purchase price This software may not be incorporated into any commercial product without written authorization from the copyright holders Information in this document is subject to change without notice and does not represent a commitment on the part of Golder Associates Inc The software described this document 15 furnished under a license agreement The software may be used or copied only in accordance with the terms of the agreement It 1s against the law to copy the software on any medium except as specifically allowed in the license agreement No part of this document may be reproduced or transmitted 1n any form or by any means electronic or mechanical including photocopying recording or informati
30. ics K 5 statistics 01327 signif level 352415310 Edit Fit Region Percentile C n eff fede vl Show Fit Info an Chart Cancel Select Fitting Region x Borehole Data CDF of Spacing 0 8 T B Daa AHAA D 0 4 gaH _ T wn Remove 0 Cancel 2 3 4 5 g Data Spacing 1 10 2 2 v Show Fit Marker n The Chart NE select unselect a point use left click select unselect a set of points press left button and drag the mouse Help Error No text of specified style in document e 17 4 Borehole Data The analysis of borehole data displays four graphical layouts that are computed using default parameters These parameters can later be adjusted to better fit the specific data The graphical interface for borehole data is shown below Tit Stress 12 20 30 10 HL CDF Graph Ju E 2 1 17 i r ZJE i M L1 HHHH LL IEEE i f T ii Eorehole Depth Chart isi 1 1 12 15 Stress 5 0 BENE Borehole Histogram CDF Histogram CDF of Spacing m 15 Ceostatistics ac 11 T 5 J Borehole Geostatistics _ Borehole CDF of Spacing 1 5 dai 1 4 T E d RI 0 4 U 11 Usa Ud US Ub i Lag 0 2 2 ai 4 E ata Spacing 10 2 18
31. laying it on doubly logarithmic axes If the empirical variogram plots along a straight line then a self affine fractal model isprobably a useful representation of the spatial correlation in the data The slope 6 of this line is related to the self affine fractal dimension by D 2 2 where D is the self affine fractal dimension Error No text of specified style in document e 23 The calculation of the semivariogram for irregular 2D data requires the specification of several parameters These include the minimum and maximum lags the number of lags and the mean direction and angular tolerance of the lags Journel A G and Ch J Huijbregts 1978 Mining Geostatistics Academic Press is a good reference for this calculation geoFractal displays a menu that allows the user to specify the angle and shows the results in a graphical form for easy checking The example shown below shows a direction specified as 30 from east west Only data pairs that are within this green angular window will be included in the semivariogram calculation 24 e Error No text of specified style in document ZD S5enivariaogiram Setup lew Lag Range Win lag value 0 lag vale L ATE Amt af lags 10 Log Space L ag Directions Include gids From 3 degrees d grees Aleulake Setup Directional Senivarnogam Enter numbers below NEN move dals in the display MN mui lu cha
32. le in document e 1 3 Second order stationary geostatistical processes Each type of analysis allows the user freedom to specify salient calculation parameters Since default graphs are rarely of sufficient quality for report reproduction or publication geoFractal contains many options for customizing the appearance of the graphical output These options are both flexible and intuitive This manual first explores options and operations common to all four analyses These options are such things as graphical customization and file manipulation Next the manual describes operations and procedures specific to each of the four data types The final section contains thoughts on how to analyze spatial data or to organize and complete a project involving spatial data analysis Successful completion of such projects requires more than knowledge of geoFractal 2 Installing geoFractal 21 What You Will Need geoFractal can be installed on any PC compatible computer which operates with Microsoft Windows 95 98 2000 and NT 2 2 Installing and Initializing geoFractal Similar to many current programs a simple step by step interface is used for installing geoFractal onto your system TO INSTALL geoFractal Insert the Installation CD into your computer and click the geoFractal Folder Select the Setup exe icon and follow the prompts to complete installation TO START geoFractal Click the Start button and locate the folder to where geoFractal w
33. logarithmic axes If the empirical variogram plots along a straight line then a self affine fractal model isprobably a useful representation of the spatial correlation in the data The slope 6 of this line is related to the self affine fractal dimension by 2 where D is the self affine fractal dimension The calculation of the semivariogram for irregular 2D data requires the specification of several parameters These include the minimum and maximum lags the number of lags and the mean direction and angular tolerance of the lags Journel A G and Ch J Huijbregts 1978 Mining Geostatistics Academic Press is a good reference for this calculation geoFractal displays a menu that allows the user to specify the angle and shows the results in a graphical form for easy checking The example shown below shows a direction specified as 30 from east west Only data pairs that are within this green angular window will be included in the semivariogram calculation 30 e Error No text of specified style in document 7 Fracture Trace Data The analysis of fracture trace data displays seven graphical layouts that are computed using default parameters with other data types geoFractal allows the user to change these parameters The graphical interface fracture trace data is shown below Error No text of specified style in document 31 26 Fracture Trace CDF Graph J 8 7 10 gt 34 Ds z Histogr
34. n data is imported into geoFractal all relevant analyses are carried out using default parameters The User is presented with a standard tree structure which can be expanded or collapsed An example of the graphical interface for fracture trace data is shown below Error No text of specified style in document 11 26 Fracture Trace 2 9 gt _ m 1 0 n l S ti 12 16 T c PE TN 52 5 D E F 1 Trace c a e d CL E ampl2b 1 4 Box Fractal Dirrension 08 Mass Fractal Analysis 4 Baecher Analysis CDF i M B aeche Anale POF E 2 m L Fractures Centers CDF Graph gt 0 E Loki ral Baecher Analysis POF 411 33 12 20 gt 40 Arm of Con Coll 2 e J j s ji All 0 10 zx 3L 40 Fracture Certers in ell 12 e Error No text of specified style in document CDF Graph Bax Fractal Dimension ICO Histogram 5 race Lech Mass Fractal Analysis 18 3 6 Chart Options All graphical displays in geoFractal can be modified according to color scale labels marker style line style grid line thickness and frequency The following figures show all windows associated with chart parameters There are nine tabs that define the options available to modi
35. ne the colors of these lines their thickness and their style General Page 1 Scale A line 15 often the result of a regression or similar calculation performed on the data The user may change the line color thickness or style General Page 1 Scale Markers are symbols denoting data points The user can change marker color size and style arid Lines Draw curve through data points Style Solid Thickness 01 2 7000 mm Color CHANGE Axis Grid Lines XScale Line Marker Scale amaumumunananananananasaananaananaanananaq Line Marker Show data points Style CIRCLE F adius 0 Color mI CHANGE 16 Error No text of specified style in document 3 7 Editing Fit Data Under each edit parameter option the user has the option to modify data points by omitting outliers This is done by highlighting the data to be removed and right clicking the mouse to display the remove option Data can be re added by the same procedure The process of adding and removing data effects the curve chosen to fit the data statistics are automatically adjusted to the resulting change CDF of Spacing Fit Curve Dialog Fit Curve gt Parameters function Marmal Distr Borehole Data CDF of Spacing c co c e mean 0 0496 deviation oo 41 Function From Parameters Statist
36. on storage and retrieval systems for any purpose other than the licensee s personal use without the express written permission of Golder Associates Inc Copyrights for this software techniques and documentation are reserved by Golder Associates Inc 2000 Table of Contents i Table of Contents EICOHSIHD c EM aa n usu y I i Idntroduction 10 800 P PUHCIUL i er t i iu 1 LI Overview of Program SIYICINY6eL l u i u u ve TEE ERR POE 1 2 Installine q u una nana uu Mes 2 hat You WIE NeGU tos avia euo ER Ex us gaa 2 2 2 Installing and Initializinp oeoF ractal ia aaa Venue aaa 2 2 5 Uninstalling 2 agreements 3 Dal ce 3 2 eee 4 3 9 Toolbar Options wis 5 De COINS 6 S5 Graphical 11 9 0 T 13 3 7 Editme Fit Data Dub EDU eee e Uu PEE
37. oximately horizontal there is no spatial correlation in the data Spectral analysis often benefits from detrending and filtering the data A satisfactory discussion of these pre processing stages is beyond the scope of the manual Most texts on signal processing contain sufficient information on these issues to enable the casual analyst to utilize these options 28 e Error No text of specified style in document Edit 2D Gridded Data x 20 Gridded Data Sleeve Friction 0 05 01 1 15 1 2 1 25 TETTE RE 30 p of Feature Error text of specified style document 29 The final graph displayed borehole data is the geostatistical analysis this analysis describes the spatial correlation between observations in terms of a second order moment defined as yh EK xE h where x z is the value of some parameter at a location z 2 is the value of the parameter at some location a vectorial distance h from z E is the mathematical expectation of the quantity in braces and yh is the semivariance h is sometimes referred to as the ag or the ag distance The plot showing the semivariance function vs th
38. riye Ihe EE gt directio range ands L LECCO that willbe used Far ett Td A semivallagrarms shaded in green Angle Fom Ses Upper Bound 30 degrees LLLEEEELELLLI 8111111111311 0 5 Lower Bound Ar n 5 7 2 111 17 degrees s EEEEEEEER 1 Update T Semivariogram 1 U aan T Ai Pi Cancel B ob i D 17 m 2 GJ D 5 10 5 Lac Distance Error No text of specified style in document 25 Creoststistics Fit Curve Im Fractal for Windows IBl x oehoe D ata zh 2 2D Data 2D Data Geostatistics 4524 PDF Graph n i Curre 2D Gridded Data H Trace 102 e TU eee E a 21 F s m Select Model
39. s Log radius If this plot is a straight line then a mass fractal model may be a useful model for the data An alternative to using a single circle center is the multiple centers option The user is free to select the starting points for this calculation with a mouse or to allow the program to select a user specified number of random starting points The calculation is carried out for the circles surrounding each point and the results for all of these starting points is displayed See La Pointe P R in C C Barton C C and P R La Pointe 1995 Fractals in Petroleum Geology and Earth Processes Plenum Press Chapter 3 for the estimation of the fractal dimension from multiple starting points The Mass Fractal dimension probably is most for assessing the scaling properties of fracture intensity and for fluid flow If the intersection points option is selected then the result is akin to a 2D lattice percolation problem for which it is known that critical percolation occurs when the mass fractal dimension is approximately equal to 1 89 The sixth and seventh types of analysis for fracture trace data are the CDF for Beacher Analysis and the PDF for Beacher Analysis The Baecher analysis focuses on whether the spatial pattern in 2D conforms to a spatial Poisson process The hallmark of such a process is that there is no spatial correlation in the data This can also be assessed through the semivariogram which should be a horizontal line i
40. s shades at the data location Create New File Data Type 2D X y data Data Data Description e g Test BH204F 20 data Llata Label e g L 5nductieru Friction Extract Data from File Llata Source Secuence Select User Parameters rom Column Asad 4 Amt Lines Skip il Number OF Columns Cancel Y 3 Faction Ratio iv data fron text file No Test In Data Lines Text at the Beginning of 3 Data Line Test Any Place in Dala Line Seat Apply leer Parameters Sequence Head tron Lalumr 1 Head Y Calumr 2 Read Friction Ratio kom Column 3 Data block contains 3 columns n 200 rows d Contents of File with Highlighted Bata Black 0 05 1 27 0 009 0 1 5 25 0 026 0 15 1146 0 044 0 2 22 05 0 105 2443 114 0 3 25 J 107 3k 24480 nna Extract Data Cancel 2D Gridded Data 2D gridded data requires three data fields the x and y location and related data Data can be loaded as text file TXT comma delimited file CSV or a space delimited file PRN 8 Error No text of specified style in document After the data description and data type are prompted by geoFractal 2D gridded data has been chosen as the data type To extract the data the user must select the columns that contain the location information x and y and the location of the related data
41. tion vs the lag is termed the variogram or semivariogram The lag is the distance or separation between data points and the semivariogram is a measure of the spatial correlation The user must specify a model type to fit a curve to the data The model types available are Spherical Exponential Gaussian Power or de Wijs The mathematical formulae for these models canbe found in most geostatistical texts for example Journel A G and Ch J Huijbregts 1978 Mining Geostatistics Academic Press The standard deviation or the sum of squares error is displayed to guide the user as to how well the model with the parameter values displayed fits the empirical semivariogram The parameters for each model can be computed using a minimum likelihood estimator MLE or can be directly specified by the user analysis can used to examine both the second order spatial correlation in the data and also the self affine fractal properties see for example Burrough P A Nature 294 240 242 1981 Examples of applying variogram analysis to fracture pattern attributes can be found in La Pointe P R and J A Hudson 1985 Geological Society America Special Paper 199 geoFractal s semivariogram models makes it possible to test several of the most common functions that exhibit second order stationarity geoFractal also makes it possible to evaluate the self affine fractal model This is done by computing the empirical variogram and disp
42. uted using a minimum likelihood estimator MLE or can be directly specified by the user Semivariogram analysis can used to examine both the second order spatial correlation in the data and also the self affine fractal properties see for example Burrough P A Nature 294 240 242 1981 Examples of applying variogram analysis to fracture pattern attributes can be found in La Pointe P R and J A Hudson 1985 Geological Society America Special Paper 199 geoFractal s semivariogram models makes it possible to test several of the most common functions that exhibit second order stationarity geoFractal also makes it possible to evaluate the self affine fractal model This is done by computing the empirical variogram and displaying it on doubly logarithmic axes If the empirical variogram plots along a straight line then a self affine fractal model isprobably a useful representation of the spatial correlation in the data The slope 6 of this line is related to the self affine fractal dimension by D 2 2 where D is the self affine fractal dimension 20 e Error No text of specified style in document Editing 5emivariogr ams Borehole Data View Char aynl Wiers Edit Late Pale Gnd it Curve qo at C emt aro3ram Enmen smar TIT fI racks gun E T peer g at oie 2 g pu io File Edit View Help GE amp USERS dn gt Semivaragram
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