Sage 2001 software

A Spatial and GeostatisticalEnvironment for Variography Isaaks & Co. 205 E. 3rd Ave. Suite 300 San Mateo, CA 94401 SAGE2001 General Purpose Software for Variography  Copyright 1999 Isaaks & Co. San Mateo, California 94401 1 Proprietary Notice Isaaks & Co. owns both this software program and its documentation. Both the program and the documentation are copyrighted with all the rights reserved by Isaaks & Co. See the License Agreement and Limited Warranty for complete information. Copyright  1998 Isaaks & Co. 205 East Third Ave. Suite 300 San Mateo CA 94401 Phone (650) 655-9051 Fax (650) 655-9443 Email [email protected] http://www.isaaks.com 2 0 TERM AND TERMINATION. 5. will perform substantially in accordance with the Documentation.0 LIMITATION OF WARRANTIES AND LIABILITIES. for a period of ninety (90) days after the initial delivery to customer hereunder (the warranty period). 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Isaaks & Co. 0 GETTING STARTED ...............................Table of Contents 1........................ 24 3............. .... ..............1 An Introduction to Variogram Modeling Using SAGE2001........................2 Output Files.........................2..........................................5......................... 22 3....................... Dips.. ..........................5............................ 19 3.....3 Cutoff..........................1 Selecting Attributes for the X....... ....... 14 3.................................. 17 3............................................................... 19 3... 16 3................................................................3 Project Title....................................0 CALCULATING SAMPLE VARIOGRAMS................2 Setup Parameters.............4...........6.........1................3 Bandwidths....... 23 3........3 Import File Delimiters...... ........ 27 4. ................................ Dip Angles.. 24 3.............1 Input File... 15 3.............2 Authorizing SAGE2001 for Unlimited Use........3 Calculating a Down-The-Hole Sample Variogram........................................................................ 10 2........................... 15 3...........5 Adding Column Headers............................. and Tolerances...............0 MODELING SAMPLE VARIOGRAMS ..................................2....2................. 17 3.............................. 22 3.................. 23 3........................................... Lags..2.......2 Rotation Conventions.. 14 3....4 Specifying Additional Constraints:............................4.................. ......................... 28 4.............................. Transforms................5 Azimuths.2..............2..............5 Customizing Azimuths................5 % of Samples.........................................0 INTRODUCTION............. 31 5 ............ 26 3........4...........6 Setting the Attribute Type................................6........ ... 10 2.... 16 3.............. 16 3.............1 Directional Increments.3 Transferring the SAGE2001 Authorization License from One Computer to Another..................4 Selecting Data Attributes and Constraints......... 26 3............................ and Output Files....................................................................1...................... .............4........ 30 4........... 21 3........6...................................... ..............2........... 25 3.......5.... 18 3.....6 Sample Variogram Estimators................2............... 20 3.2 Estimators: .... 26 3............. 8 2................2 Lag Specifications..5.......4 Log Transform.............2 Importing the Data File....................1 The SAGE2001 File Format.............3 Opening Existing SAGE2001 Files...................................... .......... .....Y. 11 2.. 27 4..........4 The Import File Grid.......................1 Title........... and/or Lag Distances. 12 3.......... 18 3........................ 22 3....................................6... .......1 Installing the Demonstration Version of SAGE2001 ......1 SAGE2001 Coordinate System and Definitions.....2 Importing Data Files......... and Z Coordinates.......1 Variogram Model Parameters by Least Squares.............. 27 4............. 26 4....6 Output Files...6........6......................... 30 4..5......... 30 4......... ...............4 Tolerances............................2......... 18 3..........2 Selecting the Sample Variogram Attribute............... . 43 6.1 Viewing Sample Variograms One at a Time...........1 Standard Conventions......................3................1 The Select Variogram Attributes & Constraints Window.................................................. 39 5..................2 Locking the Nested Structure Rotations...........6 Structure Types.1 Viewing the Report on Screen...... 34 4...4.................1 The Plot Window.... ...4............2....................................... 55 7.............1 The Print Report Window.....................2... 31 4....................... 36 4.......... 40 6.....2............. 43 6.. 39 5......2 Saving the SAG file....................2..........................4 Viewing and Printing the Sample Variogram Report.....0 VIEWING AND PRINTING REPORTS.................................5.3.......... 42 6................. 58 7....4 Re-scaling the Plot Axes........ 47 7.........................0 VIEWING AND PRINTING VARIOGRAMS .. ....................2 Printing the Report..1 The Model Sample Variograms – Setup Window........................................... ....................... ........... 34 4.......4 Overriding SAGE2001........................................................................5 Modeling the Sample Variograms.................. 31 4... 39 5.. 36 4..........................................................2 The Calculate Sample Variograms – Directions Window......4....... 32 4...2..4 Calculating the Parameters of the Variogram Model......... 46 7.........................................4...... 40 5.................. 41 6. ..... 31 4......... 34 4.. ...2....................3.............2........... 36 5... ..0 A WORKING EXAMPLE............2....................1..................................5 Printing the Plot.... ..4 Excluding Sample Variogram points....... 59 7...... 41 6........... ..........1 Opening the Print Report Window...................... 41 6..... 55 7...1 Opening the Plot Window... .........5......................................5...........2 The Plot Window............ 44 7... 46 7................................. 50 7..................3 Report Formats.......................................... ................................. 43 7. ...............2..............2 The Print Report Window......4.................... 60 6 ....... .................. 42 6.......2..........2 Custom Conventions......................................2......3 The Model Sample Variogram – Parameters Window........2..................... ........................... 44 7.........................2 Viewing Multiple Directions in One Display..............................1 Importing the Data File.................1 Adding Column Headers...................................2.. 48 7.4..............................................6 Inserting the Plot into a Report.... 57 7.........2 The Model Sample Variograms – Rotation Convention Window...................2 Calculating the Sample Variograms............ ............. ...............3 Viewing the Sample Variograms...........1. 34 4......................... 42 6............. 52 7....... 44 7.................. 32 4......... 53 7.......3 Display Options...1 Letting SAGE2001 Calculate the Variogram Model.....................4 The Parameters of the Variogram Model.............5 Weighting Scheme..................5 Interactive Variogram Modeling....................................................4..........3 Calculate Sample Variograms – Finish Window....5......2.......... ....3 Rotation Conventions.......................... .... 56 7................ ............................. .5........ .5. 64 7 ...... 63 Viewing and Printing The Variogram Model Report..........................8 The Parameters of the Variogram Model........................7... 64 Additional Postscript Output Files........4 7...5 7.. 62 The Plot Window...........6 7........... ...................5......................5........5................ 61 Interactive Variogram Modeling..7 7................... tolerance angles. etc. 8 . dip angles. vertical bands. There is no limit on the size of the input data file. • Directional sample variograms can be fully defined by user specified azimuths.0 INTRODUCTION. lag distances. SAGE2001 enables the user to easily calculate 1 to 50 or more directional sample variograms in one run and then fit a model to all of the directional sample variograms simultaneously by regression. and the pair wise relative estimators. • The input data may be transformed using the log or indicator transform. and lag tolerances • Both omni-directional and omni-directional-horizontal (all directions are parallel to a plane. possibly dipping) may be calculated. • Smaller subsets of the input data may be selected randomly from large data files. the calculation of directional sample variograms and. or by displaying multiple directions on one screen. SAGE2001 is a Windows 95/98/NT software toolkit designed for: 1. while providing the user with complete control over the calculations. • Excellent report files and summary statistics are easily generated and viewed on screen or printed for future reference. alteration types. 2. • Sample variogram estimators include the traditional average squared difference estimator. • Either two or three-dimensional data may be processed. • The selection of data may also be restricted to specific rock types. the correlogram. SAGE2001 is designed to work with many directional sample variograms at one time. one at a time. soil types. • The selection of data points may be restricted to user specified limits on each coordinate (x. SAGE2001 makes the calculation of sample variograms easy. • Down-the-hole variograms can be calculated.z) and/or to user specified limits on the variogram variable itself.y.1. • The selection of data may also be restricted by specifying a correlated variable within user specified limits. the modeling of sample variograms. Experience shows that at least 20 to 30 directional sample variograms are required to obtain a reasonably representative model of 3 dimensional spatial continuity. • Sample variograms can easily be viewed on screen. horizontal bands. 9 . The regression or fitting of the variogram model to the directional sample variograms can be controlled by the user as follows: • The sample variogram(s) may originate from one. or three-dimensional data. • Any or all of the variogram model parameters may be specified by the user. • The variogram model may consist of one or two nested structures. • The user may select one of several popular conventions for the anisotropy rotation angles or define his own rotation conventions. • A minimum number of pairs/sample variogram point may be specified. SAGE2001 can rapidly calculate the set of model parameters that minimize the average squared difference between the variogram model and all 50 directional sample variograms simultaneously. SAGE2001 will leave the user specified parameters intact while it calculates values for the remaining unspecified parameters. or more sample variograms simultaneously. SAGE2001 will also fit a variogram model to the calculated directional sample variograms by least squares or regression.Hardcopy of all graphic displays can be easily sent to the printer or clipboard. 40. For example. • Each sample variogram point may be weighted by the number of pairs. • Each directional sample variogram may be weighted by the inverse number of sample variogram points. 50. • The maximum lag distance may be specified. the user may specify the nugget and the third rotation angle. In addition to calculating directional sample variograms. • Each structure may be a spherical or exponential model. For example. two. or 50 directional sample variograms provide a far better sample of spatial continuity than the 3 or 4 directions typically calculated and modeled by other software. 40. The models of spatial continuity provided by SAGE2001 are generally far more accurate than those obtained using any other software package. Only SAGE2001 is capable of modeling 30. given 50 or more directional sample variograms. Thus. the variogram models developed by SAGE2001 are compatible and may be used with any geostatistical software package. This is because 30. 0 GETTING STARTED This section shows you how to set up the SAGE2001 software on your computer to begin calculating and modeling sample variograms. point to Programs. click Run. and click Uninstall SAGE2001. By default. The distribution disk contains files in a compressed format. • A hard disk • A 3. 2. • Follow the Setup instructions on the screen. the Setup program creates the C:\SAGE2001 directory. However. The SAGE2001 icon will be installed in a new program group SAGE2001. You cannot simply copy the files from the distribution disk to your hard disk and run the program. SAGE2001 will write the demo expiration date to the main window so you will know the number of demo days remaining.1 Installing the Demonstration Version of SAGE2001 The initial version of SAGE2001 that you install on your computer will be a demo version. You will be able to use the demo version of SAGE2001 for a period of 20 days from the date of installation with no obligations. To uninstall SAGE2001: • Click Start on the Windows taskbar. then click OKAY. you can change the name of the directory during installation. To start Setup: • Place distribution disk No. type A:SETUP in the textbox.2. or NT. To Install SAGE2001 on your computer use the program SETUP. The demo version is fully functional and can perform all of the functions that a fully licensed version can perform. 10 .EXE. This program will install the SAGE2001 executable and other files from the distribution diskettes to your hard disk. 1 in the A: drive. point to SAGE2001. The system requirements to run SAGE2001 on your computer are: • Any IBM compatible running Windows 95. You must use the Setup program that decompresses and installs the files in the appropriate directories. 98. • Click Start on the Windows taskbar.5 inch floppy disk drive. This will save the codes so that they are compatible with the Authorization Code that will be returned to you. 3. The authorization license will provide unlimited use of SAGE2001 and can be validated any time during the 20 day demonstration period. Click Save Codes. Click on the Variography à Unlock menu items as shown below. 4. 11 . At the end of the 20 day demonstration period an authorization license will be required for further use of SAGE2001. To gain unlimited use of SAGE2001 follow these steps: 1. Use a pencil or pen to record the Code Entry Number and Computer ID numbers exactly as they are displayed.2 Authorizing SAGE2001 for Unlimited Use. SAGE2001 will open the Unlock Form Window as shown below. 2.2. Store them in a safe place. com • (fax) (650) 558-9443 fax • (Telephone) (650) 558-9051 • or mail to: Isaaks & Co. 12 . 2. will send you an Authorization Code upon receipt of payment.5. Isaaks & Co. contact Isaaks & Co. the authorization license can be moved from the donor computer (this is the computer with the current license) to a recipient computer (this is the computer you are moving the license to) as described by the following steps: 1. Install a demo version of SAGE2001 on the recipient computer. 94401-4052 6. Click OKAY and the program will be authorized for unlimited use. as described above or check the SAGE2001 web page at: http://www. or fax the Code Entry Number and the Computer ID number to: • (email) ed&isaaks. Re-open the Unlock Form as shown on the previous page and enter the Authorization Code in the text box. Suite 300 San Mateo. 205 East 3rd Ave. Start SAGE2001 on the recipient computer and click the License Transfer à Start Transfer menu items as shown below.. The single user license authorizes SAGE2001 for use on one computer.com Note that the complete version of SAGE2001 and this User’s Manual can also be downloaded from this web page. 2.isaaks. Then either email. However. telephone..3 Transferring the SAGE2001 Authorization License from One Computer to Another. For the most recent price list etc. CA. Remove the diskette from the donor computer and insert it back into the recipient computer drive. 8. 3. That’s all there is to it! 13 . Start SAGE2001 on the donor computer and click the License Transfer à Transfer This License menu items as shown below. SAGE2001 will then prepare this diskette for a license transfer. Click the License Transfer à Complete Transfer menu items on the recipient computer as shown below. 5. Put the floppy diskette prepared in Step 3 into the donor computer drive.SAGE2001 will ask you to insert a floppy diskette in the recipient computer drive. SAGE2001 will copy the license from the diskette to the recipient computer. SAGE2001 will then transfer the license to the prepared diskette. 7. 4. (1989) An Introduction to Applied Geostatistics. Isaaks and Srivastava. The 0 or 360 degree azimuth lies parallel to the positive Y axis. AZIMUTH.1 SAGE2001 Coordinate System and Definitions. (This is generally interpreted to be NORTH with EAST being parallel to the X axis.0 CALCULATING SAMPLE VARIOGRAMS 3. • the Y axis runs north/south with values increasing to the north. sample variogram estimator. 14 . A useful conversion between the sine and cosine of the azimuth and the Cartesian coordinate system angle “α” or alpha (measured counter clockwise from the positive X axis towards the positive Y axis) is: sine(α) = cosine(azimuth) cosine(α) = sine(azimuth) This works for all angles α and azimuths. pages 44 to 66 is recommended. DIP ANGLES. correlogram. h-scatterplot.3. SAGE2001 is based on the conventions of the CARTESIAN COORDINATE SYSTEM. the textbook. and lag statistics etc. For example. For those who would like a detailed explanation of spatial continuity and the mechanics of calculating sample variograms. This reference will be particularly helpful in understanding the fundamental concepts of variography and terms such as separation vector. A positive dip angle is measured upwards from the horizontal while a negative dip angle is measured downwards from the horizontal. if the system of axes is oriented so that: • the X axis runs east/west with values increasing to the east. Oxford University Press. • then the Z axis will be vertical with values increasing upward. The 90 degree azimuth is parallel to the positive X axis). 015. Zone.000 NVW.92475.. 1. 1.6758.00.2 Importing Data Files. Figure1: Clicking items to open the import file dialogue box.00.5. NVW.981.2. Elevation. while 1 (one) indicates a continuous variable. 1.104872.3. East.000 The first record contains the version number.00.sag suffix.1.92402.1 The SAGE2001 File Format.473.00.104802. 15 .00.000 SVW. 0 ID. All columns must be delimited by commas in a SAG file. North. The fourth record contains the header labels for each column.104872.6840.6800.00.2.00.92475. Cu.00. The second record contains the number of columns in the data set. 3. SAGE2001 requires data files to be in a special ascii format with the file names ending with the *. The import facility in SAGE2001 makes it very easy to create a SAG file.20.2. SAGE2001-001 6 0. 1. The third record contains an indicator for each column where 0 (zero) indicates a categorical variable. The SAG format contains 4 header records as shown by the following example.00. 2. SAGE2001 will import ASCII files in FREE format with various types of delimiters. Figure 2: The standard open file dialogue box.2 Importing the Data File. click the Variography → Sample Variograms → Import File menu items as shown in Figure 1. Click the file you wish to import and then click Open.2. SAGE2001 will then open a standard Open File Dialogue Box as shown in Figure 2. To import a data file. For example. you must IMPORT your data file into SAGE2001.3.2. SAGE2001 will respond to a click on the OPEN button of the Open File dialogue box (Figure 2) by reading the import file and writing the first 5 16 .3 Import File Delimiters. 3. the original data file may be delimited as follows: • Space delimited • Comma delimited • Tab delimited • Strings may or may not be enclosed within double quotation marks 3.4 The Import File Grid. If your file is not in the SAG format. 6 Setting the Attribute Type. Columns containing variables such as Drill Hole ID. However. Figure 3: Adding column headers using the Import File Grid.5 Adding Column Headers. 3.records to a File Import Grid shown in Figure 3. 3.. East. Note that Row 1 may be used as column headers by default. Column headers may be added to each column of the import file by selecting Use row 6 for column headers in the Column Headers frame. 17 . The number of records read will be shown on the upper right corner of the grid. should be set to Categorical. SAGE2001 will initially classify each column. This will enable subsequent variogram calculations to be restricted to specific categories. and North have been typed by the user. Then type the name or column header for each column in row 6 of the grid.2. Each column of data in a SAGE2001 data file must designated as either a categorical or numerical type. Alteration Zone. Figure 3 shows a partially finished example where the column headers Sequence.2. the user may change the type by clicking on the drop down list box in row 7. Mineralogical Zone etc. Rock Type. BHID. but will have the SAG suffix appended.sag). For example.3 Opening Existing SAGE2001 Files. Elevation.sag). • X-Coordinate. Click the name of the sag file you wish to open and then click the Open button. The new file will be named with the same prefix as the import file. For example. SAGE2001 will Figure 4: Opening an existing SAGE2001 data file (*. North.Finally. only files with the suffix sag will be listed.Y. and SAGE2001 will create a new file. respond by opening up a standard Open File dialogue box. click the Variography → Sample Variograms → Open File menu items. SAGE2001 will respond by reading the selected file and report whether or not the file has been read successfully. 3. Click the drop-down-list-box arrow as shown in Figure 5. The attribute 18 . 3.1 Selecting Attributes for the X. Select the appropriate attribute from the drop down list by clicking on it. and Cu. However. and Z Coordinates. The program then advises the user to click the Next button to continue.4. the drop-down-list shown in Figure 5 contains the attributes East. click the NEXT button. 3. the imported file robson.sag.4 Selecting Data Attributes and Constraints.dat (Figure 2) would be written to disk as robson. To open an existing SAGE2001 data file (*. • Attribute#1. Select the appropriate attribute or variable from the drop down list. SAGE2001 will respond by displaying the maximum and minimum values of the attribute in the text boxes to the right.3 Calculating a Down-The-Hole Sample Variogram. Specify a new maximum or minimum if required. A new maximum and/or minimum may be specified by typing over the displayed values. This is the attribute for which sample variograms will be calculated. Specify a new maximum or minimum if required. Similarly. Specifying a proper categorical attribute for Bore Hole ID will cause SAGE2001 to calculate a down-the-hole sample 19 . Z-Coordinate. 3. select the appropriate attribute from the drop down list. select the appropriate attribute from the drop down list.4.2 Selecting the Sample Variogram Attribute. • Bore Hole ID. Specify a new maximum or minimum if required. 3.4. Figure 5: Selecting variables and constraints for sample variogram calculations.• • East has been selected from the list. Y-Coordinate. Similarly. alteration type. For example. The user wishes to calculate a sample variogram of copper (selected from the Attribute#1 drop-down-list-box) but wishes to include only those copper values with an associated arsenic value greater than 0. • Variogram values from different Bore Holes but with the same lag distance are averaged together.05.4 Specifying Additional Constraints: • Attribute#2. soil type. then the sample variogram can be considered as a directional sample variogram in the same direction as the bore holes. if all the Bore Hole samples are in the same direction.variogram. This will restrict the selection of Attribute#1 values to Lithologies 31 and 34 for the purposes of calculating sample variograms. SAGE2001 has automatically displayed all the Lithology categories in the scrollable list box to the right. etc. The result is one sample variogram where the lag spacing is generally set equal to the drill hole composite length. in Figure 5. This attribute enables the restriction of Attribute#1 values to specific categorical attributes such as rock type. and set the corresponding minimum to 0. Specify the maximum and/or minimum constraints for Attribute#2 in the text boxes to the right.05. Note that Attribute#2 is a continuous variable. The BHID ID attribute must be a categorical variable whose values are identification labels unique to each bore hole. Lithology is a categorical variable that has been selected from the Attribute#3 drop-down-list-box. Clicking the Next button will open the next window for specifying the directional parameters. 3. 20 . • All bandwidths are ignored. The directions of the down-the-hole sample variogram will correspond to a mixture of the various bore hole directions. However. The user has selected Lithologies 31 and 34 from the list of zones. suppose the input data contains both a copper and arsenic value for each sample. Additional constraints may be added to the selection of Attribute#1 by specifying a second attribute from the Attribute#2 drop-down-list-box.4. • Only samples with the same Bore Hole ID are paired. Down-the-hole sample variograms are calculated in a special way: • All tolerance angles are ignored. • Attribute#3. For example. To do this the user would select arsenic from the Attribute#2 dropdown-list-box. Dips.5 Azimuths. 225. 21 . Figure 6: Specifying Azimuths. and Tolerances. Dips. SAGE2001 is designed to calculate sample variograms in many directions simultaneously. and other tolerances for the computation of directional sample variograms. For example. and 315 degrees. Lags. 90. To facilitate the entry of the many directional parameters.3.270. 45. 180. 135. a directional increment of 45 degrees specified for the azimuth will cause SAGE2001 to calculate sample variograms in the directions given by azimuths 0. Lags. SAGE2001 requires the user to enter only the angular increments and one global unit lag distance. they are always parallel to the separation vector. or lags. Note that the horizontal bands are not actually horizontal unless the separation vector is horizontal. The total number of directional sample variograms is determined by the number of azimuth directions times the number of dip directions except for the –90 degree dip. No. 3. • Azimuth.2 Lag Specifications. Figure 7 shows the definition of the band thickness. Type in the unit lag distance appropriate for the data set at hand. This unit distance is initially applied to all directions. if the user wishes to either specify or modify specific azimuths. he can do so using the grid shown at the bottom of Figure 6. Select the dip angle increment from the drop-down-listbox. The magnitude of the largest separation vector between two sample variogram points is given by the Max.3 Bandwidths. 22 . Select the azimuth increment from the drop-down-list box. A sample variogram point at the tail of the separation vector can only be paired with sample variogram points located within the vertical and horizontal bands. 3. Note that for dip angles different from zero. For example. More accurately. these sample variograms are retained since they are useful for the SAGE2001 modeling algorithm. dips.However.5. The following text provides more details on how to respond to the text boxes shown in Figure 6. • Dip Angle. No. • Unit Distance. Although redundant. the horizontal bands always have the same dip angle and dip direction as the separation vector.1 Directional Increments. the sample variogram at an azimuth of X degrees is identical to it’s compliment at X+180 degrees. an azimuth increment of 30 degrees combined with a dip increment of 30 degrees will provide a total of 37 directional sample variograms 3. • Max. This includes dips between 90 and –90 degrees inclusive. of Lags.5. sample variograms with an azimuth of X are not symmetric to those with an azimuth of X+180 degrees and the same dip angle. The horizontal and vertical bandwidths control the horizontal and vertical tolerances allowed in the pairing of sample variogram points. Thus. Only one directional sample variogram is calculated for the –90 dip. For dip angles of 0 degrees. Type in the maximum number of lags to calculate each directional sample variogram. of Lags times the Unit Distance.5. The thick black arrow represents the separation vector. 4 Tolerances. and/or Lag Distances.) of the directional sample variograms. The tolerance angle is applied both horizontally and vertically forming a three dimensional cone whose axis is coincident with the separation vector. 60. Figure 6 shows an angular tolerance of ± 22. Angular. 3. the first column (also shaded gray) shows the dip angles (0.50. dip angles and lag distances calculated from the information entered in the Directional Increment and Lag Specifications text boxes. etc.5 degrees. -90) for the directional sample variograms. 120. Similarly. the top row (shaded gray) of the spreadsheet at the bottom of Figure 6 shows the azimuths (0. 90. SAGE2001 automatically prepares a grid or spreadsheet and populates it with the actual azimuths.5. The interior entries in the spreadsheet are the unit lag distances for each directional sample variogram. The tolerance must be specified as a fraction of the unit lag distance and must be between Figure 7: The vertical and horizontal bandthickness. • Lag. Figure 6 shows a lag of 65 units (a user edit) for the directional sample 23 . • 0. This lag will be initially applied to all directions.0 and 0.5. Type in the required lag tolerance. For example. 30. Dip Angles. Type in the required angular tolerance in degrees. -45. For example. For example.5 Customizing Azimuths.3. 6 Sample Variogram Estimators. dips. Figure 8: The final screen requiring parameters for the calculation of sample variograms. Note that the user may edit each or all of the azimuths.6.variogram with an azimuth of 60 degrees and a dip of –45 degrees.1 Title. Transforms. dip. and unit lag distances shown in the spreadsheet. This provides the user with total control over the specification of azimuth. 24 . and lag distance for each directional sample variogram. 3. 3. Type in the name of the data or project name. and Output Files. This title will appear in the reports and plots. 1 N(h) γ (h) = 1. • The Indicator Estimator.6. Z i is the sample value at location i . and σ ( + h ) is the lag standard deviation of Z i + h . γ (h) = • 1 2 N (h) N (h) ∑[Z i − Z i + h ]2 /[(Z i + Z i + h ) / 2]2 (2) i =1 The Correlogram Estimator. This estimator has exactly the same form as the standardized traditional estimator given above except that the variable Z i has been transformed to an indicator variable as follows: 25 .0 ∑ (Z i ∗ Z i+h + m ( −h ) ∗ m ( +h) ) / σ ( −h )σ ( +h ) N (h) i =1 (3) where the tail mean m( − h ) is given by: N ( h) m( − h ) = 1 N (h) ∑Z i (4) i =1 and the head mean m( + h ) is given by: N (h) m( + h ) = 1 N (h) ∑Z i+h (5) i =1 and σ ( −h ) is the lag standard deviation of Z i .2 Estimators: Click on the drop-down-list-box and select one of the following sample variogram estimators: • Standardized Traditional Estimator. i = 1. and σ Z is the global variance of Z . The equation of the standardized traditional estimator is given by: 2 γ (h) = 1 N (h ) [Z i − Z i +h ] / σ Z2 ∑ 2N(h) i =1 (1) where h is the separation vector. Z i + h is at location i + h which is separated from location i by the vector h . 2 • The Pairwise Relative Estimator. N (h) .3. This box can be used to select a random subset of the input data.6.000 or more records. • Plot. The user must supply file names for all three files before SAGE2001 will calculate the sample variograms. Specify the required cutoff to define the indicator transform as defined in the equation above. For example.3 Cutoff.5 % of Samples. 3. This file is an excellent documentation file that summarizes both the input parameters and the output lag statistics. 3. This is also an ASCII file written by SAGE2001. The file is read by SAGE2001 at the time of modeling. Note that the samples are selected randomly. .Click this check box if you wish to compute a sample variogram of Y using the transform Yi = ln( Z i ) i = 1. These are: • Report. set the % of samples to 100..6. This option is useful for very large data sets such as blast holes that may contain as many as 300.6. to select all of the samples. This file is written by SAGE2001 for the purposes of modeling the sample variograms.6 Output Files. It is an ASCII file ending with the suffix pli and contains sample variogram data. N (6) 3. The file is used to display the sample variograms on the computer screen. A value of 50 will select approximately 50 percent of the available sample data.6. Click the Finish button to begin the sample variogram calculations. SAGE2001 writes 3 files summarizing the calculated sample variograms. This file may be easily printed and filed if a permanent record of the sample variogram calculations is required • Autofit. 26 .1 if Z i ≤ cutoff Ii =   0 otherwise i = 1. The file suffix is plt. The report file written by SAGE2001 is an ASCII file with the suffix rpt.4 Log Transform. N 3. 1. C0 -. In addition to calculating directional sample variograms.the rotation angle of the first structure around the Z axis. 7. 2. 4. given 37 or more directional sample variograms.the range of the second structure in the direction of the rotated X axis.the range of the first structure in the direction of the rotated Y axis.0 MODELING SAMPLE VARIOGRAMS 4. RZ 1 -.4.the rotation angle of the first structure around the rotated X axis. 6.1 Variogram Model Parameters by Least Squares. 5. ' 12. ' 11. RX 1 -.1 An Introduction to Variogram Modeling Using SAGE2001.the range of the second structure in the direction of the rotated Z axis. 8. C2 – the coefficient of the second nested structure. ' ' ' ' ' ' 10. RY 2 -. RZ 2 -. RX 2 -. 27 . 3. AX 1 -.the nugget C1 – the coefficient of the first nested structure.the range of the first structure in the direction of the rotated Z axis.the range of the second structure in the direction of the rotated Y axis. AZ 1 -. For example. SAGE2001 can rapidly calculate the set of variogram model parameters that minimize the average squared difference between the variogram model and all 37 directional sample variograms simultaneously.the range of the first structure in the direction of the rotated X axis. AY 1 -.the rotation angle of the first structure around the rotated Y axis. RY 1 -. The parameters determined by SAGE2001 are currently limited to the following set: 1. SAGE2001 can also fit a variogram model to the directional sample variograms by least squares or regression. 9. 4. then the required rotation can be specified as either: • a left1 hand rotation of 20 degrees. 28 . ' 14. Note that a positive right hand rotation angle is the same direction as a negative left hand rotation angle around the same axis. 1 The right and left hand rules are unambiguous.1.the rotation angle of the second structure around the rotated X axis. A negative right hand rotation angle indicates a rotation in the opposite direction. AZ 2 -. However. AY 2 -.the rotation angle of the second structure around the rotated Y axis. Either one of these rotation algorithms will provide the correct result. if one requires a rotation around the Z axis so that the final rotated Y axis is at an azimuth of 20 degrees measured in the non-rotated system. the maximum number of unique variogram model parameters determined by SAGE2001 is 15. AX 2 -. For example. any subset of these parameters may be specified by the user in which case SAGE2001 will calculate values for the remaining parameters not specified by the user (if they exist).13. ' 15. coordinate transformations by rotation are not unique. • or. simple to understand. For example. Thus. SAGE2001 provides the user with a broad range of control over the modeling process from full user control to letting SAGE2001 do all the work. For example. if one wishes to rotate a coordinate system of axes to a new predetermined position.2 Rotation Conventions. Unfortunately. 4. and easily applied. a right hand rotation of 340 degrees. Then the fingers will be pointing in the direction of a positive right hand rotation. Thus. imagine grabbing the Z axis with the right hand so that the thumb is pointing in the direction of increasing Z values.the rotation angle of the second structure around the Z axis. the rotations required to get there can be defined many different ways. to rotate around the Z axis according to the right hand rule. Note that the rotation angles for the second structure are generally very different from those of the first structure. the onus is on you to determine the correct rotation algorithm for your geostatistical software. an initial rotation around the Z axis followed by a rotation around the rotated X axis followed by a rotation around the rotated Y axis is not the same rotation algorithm as an initial rotation around the Z axis followed by a rotation around the rotated Y axis followed by a rotation around the rotated X axis. This is because SAGE2001 provides many rotation algorithms in an attempt to provide variogram models compatible with all kriging and simulation packages. consider a variogram model where the rotation around the Z axis is defined as +20 degrees left. it may be next to impossible to calculate the correction. you must know the rotation algorithm of your software in order to use SAGE2001 correctly. probably defined by the author of the computer code. If one simply specifies the rotation around the Z axis in the kriging plan as +20 degrees. Each kriging and simulation program contains a specific rotation algorithm. it is easy to make the correction mentally and specify the correct rotation angle as 340 or -20 degrees to get the correct estimates. consider a kriging program written so that the rotation around the Z axis is right hand. the kriged estimates will be wrong. For example. Next. Remember the rotation algorithm will likely consist of rotations around all three axes and the order in which the rotations are applied to the axes is not interchangeable. However. For example. Thus. if the variogram rotation algorithm is more complicated. In this example. in order for a kriging program to calculate variogram values correctly. Now. one kriging program may be written so that a positive rotation angle around the Z axis is defined as left hand A second kriging program may define a positive rotation angle around the Z axis as right hand. For example.Rotations are a frequently the source of trouble. the variogram model must be defined with the identical rotation algorithm hardwired in the kriging program. 29 . Thus. Click the Sample Variogram button to open a standard File/Open dialogue box. This report is an excellent summary that can be either viewed on screen or printed 30 .1 Input File.2 Output Files. 4. • Plot. • Report. This file is used by SAGE2001 to plot the sample variograms and the model on the computer screen.pli will be shown in the box. Select the file name and then click the Open button to open the file. This file contains a detailed summary of the input parameters and the output variogram model.2 Setup Parameters Figure 9: Setting up SAGE2001 for modeling sample variograms. Click the Report button and type in a file name for the report file. 4. The azimuths and dip angles are also provided for the anisotropy axes of each structure. Only files with the extension .2. Click the Plot button and type in a name for the plot file.4.2. If two structures are required.2.3 Project Title. Type in the minimum number of pairs each sample variogram point must have to be considered in the modeling process. • Maximum Drift. • Weighting by number of pairs. Select each Structure Type from the drop-down-list-box. This text box will contain the project or report title specified previously in the sample variogram screen.4 Excluding Sample Variogram points. Select the weighting scheme from the drop-down-list box. 4.. In other words. any sample variogram point with fewer pairs than the value specified here will not be considered in determining the variogram model parameters.2. 4. Thus.6 Structure Types.0 − e -3h/P (7) • The exponential model with the traditional range T : 31 . SAGE2001 will model the sample variograms using either one or two nested structures.and kept as a permanent record of the variogram model and the input parameters to SAGE2001. this option may be useful if some of the directional sample variograms contain many more sample points than others. • Minimum # pairs.2. The options are: • No weighting. 4. then two structure types must be selected. 4. The drift is defined as the difference between the head mean and the tail mean (see Equations 4 and 5).5 Weighting Scheme. • Weighting by the inverse number of sample variogram points per direction. The structure types are: • The spherical model.2. Click the appropriate option box to select either one or two structures. • The exponential model with practical range P : γ (h) = 1. The user has the option to change the title by typing in a new one. Any sample variogram point with an absolute drift value exceeding the value specified here will not be considered in determining the variogram model parameters. SAGE2001 models all of the directional sample variograms simultaneously. e. but the second edition. The user may select one of four different standard rotation conventions or rotation algorithms2. or alternatively the user may select the Custom • 2 An abbreviated version of the rotation algorithm is provided by the two groups of 3 letters each within the brackets shown in Figure 10. RRR). (ZYX. 4. This screen enables the user to specify a rotation algorithm for the variogram model so that the model can be used with external kriging and simulation software such as GSLIB etc. note that the first edition of GSLIB (Deutsch and Journel) defined the exponential model given by (8).3 Rotation Conventions. Figure 10: Setting up the rotation conventions for the variogram model. 4.1 Standard Conventions.3. i.0 − e -h/T (8) Note that 3T = P Also. defines the exponential model given by (7).γ (h) = 1. The order of the rotations is denoted by the first 32 . However.option button and define his own custom rotation algorithm. (ZXY. The third letter indicates either a left L or right R hand rotation around the third rotation axis. However. the second letter indicates the second rotation axis and the third letter. This rotation algorithm will provide a variogram model compatible with the Vulcan geostatistical software. the Medsystem also provides several rotation algorithms from which the user must select one. The first letter indicates the first rotation axis. three letters in the brackets. for example LRL indicates the rotation directions. The Medsystem implementation is (ZXY. LRL) This rotation algorithm will provide a variogram model compatible with the Medsystem geostatistical software. RRR). Many who read this may think that the rotation algorithm for GSLIB is (ZXY. 33 . • Vulcan by Maptek. Thus. One of these options is called the GSLIB option. This appears to be an oversight in GSLIB. LRL). Maptek has implemented GSLIB in their software package. the third rotation axis. LRR). the documentation is not clear and it turns out that all GSLIB software actually executes the (ZXY. for example ZYX. • MEDSYSTEM.. LRL). The first letter indicates either a left L or right R hand rotation around the first rotation axis. LRL) option in the SAGE2001 software. to correctly use SAGE2001 variogram models in the MEDSYSTEM geostatistical software. LRL) while GSLIB is actually (ZXY. We agree that the written GSLIB documentation certainly appears to suggest the rotation algorithm is (ZXY. select the GSLIB option in the Medsystem software and the MEDSYSTEM (ZXY. (ZXY. Unfortunately. The second group of 3 letters. this option has been mislabeled or it has been implemented incorrectly. • GSLIB (ZXY. they made a slight change to the GSLIB rotation algorithm by changing the direction of the rotation around the third rotation axis. LRR) This rotation algorithm will provide a variogram model compatible with the GSLIB geostatistical software. This rotation algorithm provides a variogram model that is compatible with the SAGE2001 kriging and simulation software. The second letter indicates either a left L or right R hand rotation around the second rotation axis. However. LRR) rotation algorithm. The standard rotation conventions are as follows: • SAGE2001 (ZYX. LRL). any combination of left and right rotation directions may be selected for the three rotations. The total sum of squared differences or error SSE is also written to the screen. that the rotation algorithms (ZXZ) or (ZYZ) are valid combinations.4. When SAGE2001 has determined the variogram model parameters. which will be set to 1. the anisotropy axes of each nested structure will be oriented identically. and Exit. if you think about it you will realize that these rotations are more geologically intuitive than the older more familiar rotation algorithms.0 by default.4. Figure 11 shows the last screen controlling the variogram modeling process. Click on Fit. Besides Back. This may take a few minutes. Note that all this information is also written to the report files (*. In other words. they will be written to the screen in the appropriate text boxes. the program will open up and display a progress bar. Help.plt) files named earlier. Clicking this option button will enable the user to design his own rotation algorithm with one limitation --.4 Calculating the Parameters of the Variogram Model.3. The parameter text boxes will be blank on the screen shown in Figure 11 except for the Sill. However. A click on the Lock Rotations checkbox will provide identical rotation angles for each nested structure. so do not click on CANCEL unless you really want to exit the program. which will cause SAGE2001 to go to work and calculate the variogram model parameters. however. For example.4. Note however. The option buttons within the User defined convention frame are programmed in such a way that the user cannot select an invalid combination of axes. Note that sometimes the progress bar will appear to be stalled. 4. The azimuth and dip (measured in the original data coordinate system) of the rotated anisotropy axes for each structure are also written to the screen in the Output Anisotropy Axes frame. the direction may be either left or right as the option buttons show. However.1 Letting SAGE2001 Calculate the Variogram Model. the 34 . 4. In fact.rpt) and plot (*. it is impossible to select a (ZXX) combination.the first rotation must be around the Z axis. Finally. the user must choose from the following options: 4. it will likely continue to move at some point.2 Custom Conventions.2 Locking the Nested Structure Rotations. For example. Initially. 35 . This generally enables a better fit to the sample variogram points since the extra freedom gained by allowing individual orientations provides more degrees of freedom in fitting the model to the sample variogram points. SAGE2001 models each structure with a unique orientation for the anisotropy axes.Figure 11: The Variogram Model Parameters. mining software package DATAMINE requires identical rotation angles for all nested structures. By default. If a fix checkbox is checked. 4. if the user types the value 0. SAGE2001 will leave that parameter intact while it calculates values for any unchecked text boxes. If the user specifies all of the parameters and checks all the fix checkboxes and then clicks Fit. but will not change the Nugget. 4. C1 Decimals è type the number of decimal places required for the nugget and coefficients C1 and C2. SAGE2001 will remember the size of the plot window the next time it is opened. For an explanation of the Plot Window see Section 6.4. the hidden window can be exposed by resizing the plot window as shown in Figure 12. However. Note that SAGE2001 will not use or consider any data with a lag distance larger than Max Lag Distance. the window showing the variogram model parameters (the left window in Figure 12) will be hidden by the plot window. Note that the plot window opened by SAGE2001 may occupy the full computer screen. Simply click and drag the sides or corners of the plot window to the required size.30 in the Nugget text box.1 and Figures 14 and 15. The user may override the calculation of variogram model parameters by SAGE2001 by typing the model parameter in the appropriate text box(s) and clicking on the fix checkbox(s) immediately to the right of the text box(s). The format controlling how the variogram model will appear in the various plots and reports can be specified in the Report Formats text boxes: • C0. If this happens. • Max Lag Distance ètype the maximum distance for the separation vector h. SAGE2001 will automatically open a plot window and begin plotting the directional sample variograms and the model as shown in Figure 12. clicks the adjacent fix checkbox followed by a click on Fit.3 Report Formats.4 Overriding SAGE2001. For example.4. SAGE2001 will write the model parameters to the output files and return the identical values to the screen. • Range Decimals è type the number of decimal places for the variogram ranges. SAGE2001 will calculate values for the unchecked parameters.5 Interactive Variogram Modeling.4.4. 36 . This will be the maximum length of the X axis or h axis for all directional variogram plots. After the user has clicked Fit and the variogram model calculations are complete. SAGE2001 will then update all unchecked parameters and provide a new variogram model with a simple click on the fit button. Azimuth = 328.Figure 12: The Setup for Interactive Variogram Modeling. Viewing the directional variograms corresponding to the anisotropy axes. Dip = 24 • Rotated Y. Note that the plot window shown on the right side of Figure 11 must be closed before SAGE2001 will accept user input in the left window shown in Figure 11. For example. SAGE2001 makes it easy for the user to interactively test various variogram model parameters and model by trial and error. The right window in Figure 11 enables the user to view the current model and judge how well it fits the sample variogram points. The azimuth and dips of the anisotropy axes for each structure of the model are written to the Variogram Parameter Screen (Figure 11). the azimuth and dips of the anisotropy axes of the second structure shown in Figure 11 are: • Rotated X. The user can then type in new parameters in the appropriate text boxes and click the corresponding fix check boxes. For example. Azimuth = 60. Dip = 4 37 . Dip=-30.2. Since this example does not provide a variogram plot in the direction Az=60. Dip=-30. Azimuth = 228. • The closest directional variogram corresponding to the direction Az=328. Dip = 66 The ranges along each of these axes is also provided by SAGE2001 (Figure 11): • Range along rotated X = 329. the closest direction is Az=240. Thus.810 The directional variogram models corresponding to these directions (or nearly so) can be viewed simultaneously in the plot window by clicking on the Select multiple sets option button on the plot window (see Section 6. • The closest directional variogram corresponding to the direction Az=228. Dip=-30 is identical to the direction Az=60. 38 . Dip=+4 is Az=328. Dip=-60. Dip=0. the direction AZ=240. Dip=+24.• Rotated Z. the correct directional variograms corresponding to the azimuths and dips given above are: • The directional variogram corresponding to an azimuth of 60 and dip 24 is Azimuth=240. Make sure the correct directional variograms are selected. For example. This is because a positive dip is upward and a negative dip is downward.152 • Range along rotated Z = 118.2). Dip=+30. Dip=+66 is Az=60.153 • Range along rotated Y = 997. 5.2 The Print Report Window. 39 . Click on the Variography →Print Report menu items. SAGE2001 will open the File Open dialogue box. 5. Click on the report file you wish to open. SAGE2001 will respond by formatting the report file and opening the Print Report window. 5.1 Opening the Print Report Window. Then click on the Open button. Only files with the suffix rpt will be shown in the File Open dialogue box. Figure 13: The Print Report window.0 VIEWING AND PRINTING REPORTS. To review the report on screen. Reports may be printed one page at a time or by all pages at once.2. or type in the required magnification factor directly. click the Print all Pages button. Clicking the left arrow displays the previous page in the report while a click on the right arrow head displays the next page. To print the complete report. To print the current page. Click the Windows maximize button in the extreme upper right corner of the window. 40 . To increase the size of the report page shown in the window. select the magnification factor from the Zoom drop-down-list-box. 5.2.The Print Report window enables the user to view the report on screen or to print the report. This will maximize the window within your computer screen. click the Print Current Page button.1 Viewing the Report on Screen. 5.2 Printing the Report. A new page can be selected by clicking the tiny arrow heads at each end of the horizontal slider bar. 41 .0 VIEWING AND PRINTING VARIOGRAMS 6. SAGE2001 will respond by opening the Plot window and displaying the sample variograms. Only files with the suffix plt will be shown in the File Open dialogue box. Figure 14: The variogram plot window.1 Opening the Plot Window. SAGE2001 will open the File Open dialogue box. Click on the plot file you wish to open.2 The Plot Window.6. 6. Click on the Variography → Display Variograms menu items. Then click the Open button. This feature may be turned on and off by clicking the Auto On and Auto Off buttons. the program will immediately begin to display all of the sample variograms automatically. • Variogram Model. Click this checkbox to display the variogram model in the corresponding direction. the previous or next directional sample variogram may be manually displayed in the plot window by clicking the Next or Previous button. It does this by rotating through all of the directional sample variograms automatically.2. Note that if a variogram model 42 . Figure 15: A blow up of the Plot controls shown 6. Additional information may be plotted simultaneously with the directional sample variograms. • Connecting lines. 6. Select the directions by clicking on them.1 Viewing Sample Variograms One at a Time.6. When SAGE2001 opens the plot window. A maximum of 5 directions may be viewed at one time. The scrollable list box immediately below the option button lists the directional sample variograms that may be viewed. in Figure 14.2. Then display the directional variograms in the plot window by clicking the Graph button.2. click the Select multiple sets option button. When the Auto feature is Off. Click this checkbox to connect the sample variogram points with straight lines.3 Display Options. For example: • Show Pairs.2 Viewing Multiple Directions in One Display. To view multiple directional sample variograms simultaneously in one plot . Click this checkbox to show the number of pairs associated with each sample variogram point. Once you have re-installed the default printer driver.. 6. If the display contains multiple plots. • Click the Copy button located between the Print and Exit buttons. the clipboard image will copy exactly as it appears on the SAGE2001 screen.2. 6. Note that values for the X and Y tic-intervals must also be typed in the appropriate text boxes. title etc. This may seem totally unrelated.2. 43 . This will put a copy of the sample variogram display on the Windows clipboard.6 Inserting the Plot into a Report. The graphics display shown in the Plot window can easily be inserted into a report document using the Windows clipboard.2. this option will not be available. The printer output will also be colored if the printer is color capable. are missing. but it will probably fix the problem. • Open your report document and position the cursor at the location in the document where you wish to insert the variogram figure.4 Re-scaling the Plot Axes. Click the Apply button to re draw the plot with the new maximums and minimums. Click the Print button to print the current display in the Plot window. If the image pasted into your document from the clipboard appears truncated and some of the text such as axes labels. The re-installation of the printer driver with SAGE2001 loaded on your machine generally resolves any problems between the driver and SAGE2001. re-install the printer driver for your default Windows printer. 6. This is because the control used by SAGE2001 to copy the image to the clipboard use the Windows printer driver.5 Printing the Plot. • Press the Ctrl and V keys simultaneously.has not been fit to the directional sample variograms. the various directions will be displayed using different colors. This will copy the graphics display from the Windows clipboard to your report. The axes of the sample variogram plot may be re-scaled by typing in new maximums and minimums in the X (lag distance) and Y (variogram value) text boxes. It’s that easy! NOTE. 4 5435.00 -1.1 5987. The following sections contain an example using SAGE2001 to calculate and model sample variograms.6 5965.744 0. The original data file TEST.731 0.7.00 7.4 5435.726 0.5 332.734 20 20 20 20 20 -1.4 6324.6 5980.5 7. The data are 3 dimensional and originate from a mineral deposit.4 5435.1 5972.5 7.5 7.4 5435. The data set is called TEST.4 5435. 7. To do this click on the Variography è Sample Variogramsè è Import File drop down menu items as shown in the following Figure SAGE2001 will respond by opening the standard Windows Open File Dialogue box. This example is meant to provide an illustration of how SAGE2001 can be used to calculate and model sample variograms.1.0 324.0 A WORKING EXAMPLE. Select the file TEST.4 6324.0 339.TXT and is included with the program software.4 6324.4 6324.TXT is an ASCII text file that is space delimited and contains 10 fields of data as shown by the following 5 records: 1 1 1 1 1 DDH-01 DDH-01 DDH-01 DDH-01 DDH-01 6324.00 -1.00 -1.TXT and add column headers. SAGE2001 will respond by reading the file TEST.4 5995.5 7.830 0.0 7.1 Importing the Data File.5 347.TXT and automatically open the Import File Grid shown in the next Figure.00 -1.1 317.TXT and click Open. 44 .1 Adding Column Headers The first step is to import the file TEST. You will find this file in the same directory where SAGE2001 is installed.5 0. column 6. 10. column 4. Type the column header “Northing” in row 6. 45 . Type the column header “Lithology” in row 6. Type the column header “Depth” in row 6. Type the column header “Copper” in row 6. Type the column header “Density” in row 6. Note that the grid has been scrolled horizontally so that columns 5 to 10 are displayed in the figure. Note that all of the lithology codes are numeric. column 3. 8. Since lithology should be classified as categorical. column 9. 2. 9. column 8. Click on the Use row 6 for column headers option button in the Column Headers frame.072 data. 5. Type the column header “Elevation” in row 6. Type and/or click the following buttons: 1. This will classify the variable lithology as a categorical variable. column 7. Type the column header “Length” in row 6. Type the column header “Easting” in row 6. click on the drop down list box in row 7. Thus. SAGE2001 tells you it is displaying the first 5 rows of 5. Type the column header “Sequence” in row 6 column 1. 3. 11. column 5. SAGE2001 was not able to classify this variable as categorical. Note that SAGE2001 has automatically classified this variable as categorical because it contains letters. 4. Type the column header “BHID” for Bore Hole ID in row 6. column 9 and click categorical. 7. column 10.At the top of the grid. 6. column 2. That’s all there is to importing data files.7. Windows will respond by opening the standard Windows Save File Dialogue Box.2 Saving the SAG file. Select the required sag file and click on Open. you can open it by clicking on the Variography è Sample Variogramsè è Open File drop down menu as shown in the following figure. SAGE2001 will respond by opening the Select Variogram Attributes & Constraints window. This will create and save a file called TEST.2 Calculating the Sample Variograms. Finally. Type in the file name TEST and then click on the SAVE button. SAGE2001 will respond with the standard Open File Dialogue box. 7.SAG in the required SAGE2001 format. SAGE2001 responded by automatically opening the Select Variogram Attributes & Constraints Window. 46 . if you are at the opening window of SAGE2001 and a sag file already exists on your hard disk drive. However. click the Next button.1. When the Next button is clicked on the previous Import File Grid Window. Northing. SAGE2001 automatically selected the Easting. Type or click the follow to continue with the example exercise: 1. by specifying a minimum of 2. Thus. Click on the drop down menu list for Attribute#2 and select Length. and Elevation variables for the X.0. 2. Click on the drop down menu list for Attribute#1 and select Copper. we eliminate all samples that are shorter than 2. Length is a variable representing the length of the diamond drill core for each copper assay.5. Y. This is the variable for which sample variograms will be calculated. Then type 2.7. so there are no coordinate variables to select. 3.1 The Select Variogram Attributes & Constraints Window.0 and longer than 7. and Z Coordinate text boxes. 4. This will eliminate all copper values less than 0.0 in the Minimum text box.2.0 and a maximum of 7. Type 0.5 meters. Click on the drop down menu list for Attribute#3 and select all lithologies except -1 as shown in the figure above.0 in the Minimum text box. This 47 . This window enables the user to select the variables and constraints to use in calculating the sample variograms. SAGE2001 will respond by closing the Select Variogram Attributes & Constraints window and open the Calculate sample variograms – directions window. do not click the Bore Hole ID text box. Note that one could constrain the selection of samples by their X. dips. and/or Z coordinates.2 The Calculate Sample Variograms – Directions Window. This window is used to specify the azimuths. and tolerance parameters for calculating the sample variograms. Finally. Y. At this time we do not wish to calculate a down the hole variogram.will eliminate all samples with a lithologic code of -1 from the sample variogram calculations. click on the Bore Hole ID text box and select the variable BHID. If you wish to calculate a down-the-hole sample variogram. 48 . so for this example. click the Next button to go to the next window.2. 7. 45 or 45% of the unit lag distance. Set the Vertical Bandwidth to 25 6. Change the lag distance for the –90 Dip from 25 to 7. Note that we can also change any of the azimuth or dip angles in the grid as well as the unit lag distances Finally. Set the Horizontal Bandwidth to 16. We do this because we want to change some of the lag distances for some of the directions. 9. Type in a unit distance of 25 in the lag Specs frame.5 meters. click the Next button to close this window and open the Calculate sample variogram – Finish window.5 degrees.Type or click the following to continue with the example variogram calculations. 11. Thus. Dip Angle. 5. Leave the Azimuth and Dip text boxes in the Directional Increments frame with the values 30 and 30. Remember there is only one directional sample variogram with a dip of –90. 4. Change all lag distances for the –60 Dip from 25 to 20 meters. 10. 2. Click on the Customize Azimuth. Type in 47 for the Maximum No. of Lags. Leave the Angular Tolerance at 22. Change all lag distances for the –30 Dip from 25 to 30 meters. Use the arrow keys to move around in the grid: 1. This will provide directional sample variograms at 30 degree increments on azimuth and on dip. the total number of sample variograms will be 37. 8. Set the Lag tolerance to 0. 49 . and Unit Distance Values. 3. 7. Test. This title will appear on all the report and plot files.3 Calculate Sample Variograms – Finish Window This window requires the user to specify a few more parameters for the calculation of the sample variograms and to provide names for the output files Click or type the following to continue with the example variogram calculations.2. e. Next click on the Report button and provide a suitable name for the report file.g.rpt. We wish to use 100% of the available samples. then you must also supply the cutoff or threshold value defining the indicator in the Cutoff text box. 2. If the Indicator estimator is selected. 1.Sag. e. These will always have the suffix rpt. Type in the title Example Using Test. 3.. 4.g.7.. This box can be used to randomly select a subset of the available samples. 50 . Click on the Estimator drop down list box and select (click) on the correlogram estimator. 50%. so we leave the % of Samples box at 100. 047 of these samples were actually used to calculate the sample variograms.pli which is an ascii file that is used by SAGE2001 to calculate the variogram model. It cannot model any other type of file. When SAGE2001 has completed the sample variogram calculations. 6. note that the file is ASCII and the format is quite simple.5. Test. This will create the file Test. only 5.Sag contains 5. Click on the Plot button and type in a name for the plot files.plt.g.. 51 . Although these files are similar to the pli files they are slightly different. SAGE2001 only knows how to model pli files. it is very easy to calculate sample variograms using other software and format the output identical to a pli file. but because of the imposed constraints. The return message also indicates the actual number of samples that were used to calculate the sample variograms. Thus. For example . click on the Finish button to begin the sample variogram calculations.072 data values. For this example. e. SAGE2001 will open a progress bar and let the user know the percentage of the job completed. A return code of 0 indicates that no errors were detected during the calculations. However. Note a small message that also appears on the bottom of the Calculate Sample Variograms – Finish Window. Click on the Autofit button and type in the file name Test. Finally. the sample variogram calculations may take something like 2 or 3 minutes assuming your CPU is at least 200 Megahertz or more. Then SAGE2001 can be used to model the sample variograms. a message box will appear with the message Analysis Complete. SAGE2001 uses these files to plot the sample variograms to the computer screen. Click the message box OKAY button and SAGE2001 will respond by closing the Calculate Sample Variograms – Finish window and opening the Plot window. the file TEST. You can also open the plot window by clicking on the Display Variograms menu item as shown in the following figure.7. 52 . SAGE2001 automatically opens the Plot window when the OKAY button on the Analysis Complete message box is clicked.3 Viewing the Sample Variograms. Windows will respond by opening a standard Open File Dialogue box from which you can select a plt file and display the sample variograms using the Plot Window. 7.3.1 The Plot Window. This is the plot window that SAGE2001 uses to display the sample variograms and the model if it exists. However, for this exercise we have not calculated a model yet, so for now, we will use the plot window to simply view the calculated sample variograms. Automatic Plot Update. Probably the first thing you will notice is that SAGE2001 automatically rotates through the sample variograms by changing the plot every few seconds. To turn off the automatic rotation, click the Auto Off button. To turn it back on, click the Auto On button. You can also manually rotate through the sample variogram plots by clicking on the Previous and Next buttons when Auto rotate is off. Resizing the Window. The plot window can be resized using the standard Windows resizing methods. 1. Use the Maximize/Restore button which is the center button of the three buttons located in the extreme upper right corner of the window. This is probably the best way to increase and decrease the plot window size once you have adjusted the smaller window size to your preference. 53 2. The plot window size can also be adjusted by dragging the edges or corners of the window using the mouse. Show Pairs. Click on the Show Pairs checkbox to show the number of pairs for each sample variogram point. Connecting Lines. Click on the Connecting lines checkbox and SAGE2001 will join all the sample variogram points with straight lines. Re-scaling the Plot Axes. The axes of the sample variogram plot can be re-scaled by setting the text boxes in the lower right hand corner of the plot window: 1. Leave Minimum h = 0 and G(h) = 0. 2. Set Maximum h = 400. 3. Set Maximum G(h) = 1.5 4. Set tic-interval h = 80 5. Set tic interval G(h) = 0.25 This will re-scale the sample variogram plot as shown in the figure above. Now, as we rotate through the sample variograms, we should be noting the following: 1. Is the scale of the X-axis (max h=400) of the sample variogram plot appropriate? SAGE2001 will not use any sample variogram points at lag distances larger than a specified maximum lag distance. Thus, it is important to choose this distance appropriately. For example, if the specified length is too long, then useless sample variogram points may be included in the modeling process. This could have a negative impact on the resultant model parameters. 2. What is an appropriate minimum for the required number of pairs? View the various directional sample variogram plots and try to determine a threshold value that will eliminate spurious sample variogram points near the origin, but will also retain those points which appear to be critical to the shape of the variogram model at shorter lag distances near the origin. 54 7.4 Viewing and Printing the Sample Variogram Report. The report on the sample variogram calculations is opened by clicking on the Print Report menu item as shown by the following figure. Windows will respond by opening the standard Open File Dialogue box. Select the file test.rpt and click on the Open button. SAGE2001 will open the Print Report window. 7.4.1 The Print Report Window. 55 5.View and print the report file Test. close the window by clicking on the Close button.rpt as follows: 1. 4. Windows will respond by opening the Model Sample Variograms – Setup window. 7. 3.5 Modeling the Sample Variograms. Print all pages by clicking on the Print all Pages Button. Print the current page by clicking on the Print Current Page button. Select or scroll through the pages of the report by either moving the slider bar or by clicking on the tiny arrow heads at the ends of the slider bar. 2. The sample variogram file required for modeling purposes is opened by clicking on the Model Variograms menu item as shown in the following figure. Finally. 56 . This will increase the size of the report on the screen so it can be read. Maximize the window by clicking on the Maximize button in the extreme upper right hand corner of the window. Select 100% from the Zoom(%) drop down list box. Select 2 structures. This window collects the file names and other parameters that will control the modeling of the sample variograms. Type in the title Example Using Test. select or name the output files by clicking on the Plot and Report output file buttons. Type or click the following to continue with the example exercise: 1.pli and click Open. Select the Exp(practical range) Structure Type for each structure Now we are ready to go to the next window. 3. Similarly. 57 . Windows will respond by opening the standard Open File Dialogue box. 2.1 The Model Sample Variograms – Setup Window. 8.7. Click the Next button. Select the by pairs Weighting scheme. 4. 7. Leave the Maximum drift entry at 999999. Set the Minimum # pairs to 200 5. 6. This is such a large number that it will have no effect on the selection of sample variogram points.Sag if it does not appear in the Analysis Title checkbox.5. Select the file Test. Click on the Input file Sample Variogram button. Click on the Custom option button. Click the Z option button for the Third rotation axis. For this exercise. Click the Next button to open the Model Sample Variogram Parameters window. Click the Y option button for the second rotation axis. 3. 2.2 The Model Sample Variograms – Rotation Convention Window. This window is used to tell SAGE2001 what rotation conventions it should use to model the sample variograms. we will use the custom rotation convention ZYZ-RRR: 1.5. 58 . Leave all the direction buttons Right.7. 4. 7. C1 Decimals textbox entry to 3. Thus. To continue with the exercise.5. 2. Change the C0. Change the Max Lag Distance textbox entry to 400. type in the following: 1. 59 .3 The Model Sample Variogram – Parameters Window. This will print the nugget and the C1 and C2 coefficients with 3 decimal places in all reports and plots. it is important to choose this distance appropriately. SAGE2001 will not use sample variogram points at lag distances larger than the value specified here. This is the last window requiring input to model the sample variograms. The variogram model parameters will be written to the Model sample variogram – Parameters window. the progress bar will show some sign of activity. 60 . You should resize the plot window so you can view both the Plot window and the Model sample Variogram – Parameters window on your computer screen as shown in the following figure. SAGE2001 will open a Progress Bar and report the percentage completed. Click on the OKAY button to continue.Click Fit to begin the modeling calculations. SAGE2001 will open a message box with the message Analysis Complete. SAGE2001 will respond by opening the plot window and rotating through the directional sample variograms and their models. but is modeling the sample variograms. Note that sometimes it will appear that the program is stuck in an endless loop because the progress bar is not moving. Be patient. Eventually (within a minute or two). 2. SAGE2001 is probably not stuck in an endless loop. The movement of the progress bar from 0 to 100% can be quite sporadic and punctuated with relatively long pauses at times When SAGE2001 has finished calculating the variogram model two things will happen: 1. 00 because we have used the correlogram which has a theoretical sill of 1. and the coefficients C1 and C2 are 0. and 0. consider the second structure.517. The orientation of the anisotropy axes is: 61 . For example.1297. Note that SAGE2001 has calculated the Azimuth and Dip of the anisotropy axis for each structure. the nugget is 0. For example. Note that the sill is 1.4 The Parameters of the Variogram Model.5. The following figure shows the Modeling sample variogram – Parameters window after SAGE2001 has finished calculating the model parameters and written them to the window.0.7.353 respectively. 5.5. do the following: 1. 3.25. 2.5 Interactive Variogram Modeling.129. Click the Fix check box next to the nugget textbox. The closest directional sample variogram we have to this orientation is Az=300. Alternatively. Suppose that after examining the plot window we decide that we do not like the variogram model provided by SAGE2001. Dip=-60. You may check as many of the fix check boxes as you like. IMPORTANT – First. 7. This provides you with the option of assuming complete control over the modeling of the sample variograms. Click the Fit button. The azimuth and dip of the Rotated Y axis is 314 and -2 degrees respectively. 3. Type the value 0. The azimuth and dip of the Rotated X axis is 43 and +29 degrees respectively. SAGE2001 will calculate a new variogram model with a nugget of 0. To re-model the sample variograms and force a nugget of 0.25 in the Nugget text box. close the plot window! 2. you have the option of specifying the complete variogram model if you wish. For example. we feel the nugget is too small. The closest directional sample variogram we have to this orientation is Az=60.25 rather than 0.25. We would prefer a nugget equal to 0. Dip= 0. 4.1. The azimuth and dip of the Rotated Z axis is 229 and +62 degrees respectively. The closest directional sample variogram we have to this orientation is Az=240. you may let SAGE2001 have complete control over modeling the sample variograms or some combination whereby you share control over the modeling of the sample variograms with SAGE2001. Dip=-30. Thus. 62 . A checked fix check box will cause SAGE2001 to leave that parameter intact while it calculates values for any remaining parameters with unchecked fix check boxes. Click the directional variogram with Az = 60. Click the Select Multiple Sets option button. 2. 5. To view these directional sample variograms and their models click the following: 1. while the blue (triangles) curve is the minor axis. Dip = 0 from the list box. Click the directional variogram with Az = 300. the following figure shows the directional sample variograms and their models corresponding to the anisotropy axes of the second structure.5. The plot window can also be used to view several directional sample variograms simultaneously. 63 . 3. SAGE2001 will show the three directional sample variograms and the model using different colors. For example. Click the directional variogram with Az = 240. 4. Click the Graph button. The black curve is obviously the major axis in the above figure. Dip = -60 from the list box. Dip = -30 from the list box.6 The Plot Window.7. For example.5.5. The variogram model report should be printed and retained as a permanent record of the variogram model. Although these files duplicate the report files discussed earlier.PS.7. These files are always called ROSE. they do provide additional graphics that may be helpful in visualizing the orientation of the anisotropy ellipsoids in 3 dimensional space. Thus. they are overwritten each time SAGE2001 is run.PS.8 Additional Postscript Output Files.4. the following three figures are examples from the file ROSE. The report contains a complete description of the variogram model parameters and rotation conventions. 7. 64 . SAGE2001 also writes two additional postscript files to the working directory.7 Viewing and Printing The Variogram Model Report The variogram model report is viewed using the same procedures described in Section 7.PS and GAM. 65 . 66 . 67 .