SeisImager2D Manual v3.3
SeisImager2D Manual v3.3
SeisImager2D Manual v3.3
Version 3.3
Pickwin v. 4.0.1.5 Plotrefa v. 2.9.1.6
October 2009
Table of Contents
1 2 3 INTRODUCTION..................................................................................................... 7 INSTALLING THE SOFTWARE .......................................................................... 9 THE PICKWINTM MODULE ............................................................................... 21 3.1 FILE MENU......................................................................................................... 23 3.1.1 Open SEG2 File ........................................................................................ 23 3.1.2 Save SEG2 File ......................................................................................... 24 3.1.3 Open SEG2 File (SmartSeis) .................................................................... 24 3.1.4 Open McSeis-3 File................................................................................... 24 3.1.5 Open OYO 160MX (SEG1) file ................................................................. 24 3.1.6 Open First Break Pick File ....................................................................... 25 3.1.7 Save First Break Pick File ........................................................................ 25 3.1.8 Print Window Display............................................................................... 27 3.1.9 Print Preview ............................................................................................ 27 3.1.10 Page Setup ................................................................................................ 28 3.1.11 Group (File list) ........................................................................................ 29 3.1.11.1 Make File List ................................................................................... 30 3.1.11.2 Open File List ................................................................................... 33 3.1.11.3 Save File List (text)........................................................................... 35 3.1.11.4 Save File List (XML)........................................................................ 35 3.1.11.5 Show File List ................................................................................... 36 3.1.12 Last Four Files Opened ............................................................................ 36 3.1.13 Exit ............................................................................................................ 37 3.2 EDIT/DISPLAY MENU ......................................................................................... 37 3.2.1 Undo.......................................................................................................... 37 3.2.2 Redo .......................................................................................................... 38 ...................................................................................... 38 3.2.3 Select Trace [ 3.2.4 Select All Traces ....................................................................................... 39 3.2.5 Selected Traces ......................................................................................... 41 3.2.5.1 Reverse Polarity .................................................................................... 42 3.2.5.2 Kill ........................................................................................................ 42 3.2.5.3 Delete .................................................................................................... 43 3.2.6 Time Shift Traces ...................................................................................... 44 3.2.7 Correct Shot Time ..................................................................................... 45 3.2.8 Automatic Shift.......................................................................................... 47 3.2.9 Correct S-wave.......................................................................................... 51 3.2.10 Filter ................................................................................................... 54 3.2.11 Truncate Traces (Shorten Record Length) ............................................... 56 3.2.12 Resample Data .......................................................................................... 57 3.2.13 Edit Source/Receiver Locations, Etc......................................................... 58 3.3 VIEW MENU ....................................................................................................... 59
............................................................................. 60
........................................................................................ 61
3.3.5 Show Traveltime Curves [ ................................................................... 64 3.3.6 Axis Configuration .................................................................................... 65 3.3.7 Pre-trigger Shift [...................................................................................... 66 3.4 PICK FIRST ARRIVALS MENU ............................................................................. 67 3.4.1 Pick First Breaks ................................................................................. 67 Audio/video clip of First Break Picking Procedure.......................................... 68 3.4.2 Linear Velocity Line ........................................................................... 68 3.4.3 Delete All Velocity Lines........................................................................... 69 3.5 SURFACE-WAVE ANALYSIS MENU .................................................................... 69 3.6 OPTION MENU ................................................................................................... 69 3.6.1 Dimension Size.......................................................................................... 70 3.7 HELP MENU ....................................................................................................... 70 3.7.1 Version Info. (Pickwin) (A) ....................................................................... 70 3.8 ADDITIONAL TOOL BUTTONS AND HOT KEYS ................................................... 71 3.8.1 Increase Amplitude Tool Button and Hot Key ............................... 71 3.8.2 3.8.3 3.8.4 3.8.5 3.8.6 3.8.7 3.8.8 3.8.9 3.8.10 4 Decrease Amplitude Tool Button and Hot Key
Increase Horizontal Axis Tool Button and Hot Key Decrease Horizontal Axis Tool Button and Hot Key Increase Vertical Axis Tool Button and Hot Key Decrease Vertical Axis Tool Button and Hot Key Draw Traveltime Curve Tool Button X Tool Button Page Up Tool Button Page Down Tool Button
TM
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THE PLOTREFA
MODULE ............................................................................ 78
4.1 FILE MENU......................................................................................................... 78 4.1.1 Open Plotrefa File (Traveltime Data and Velocity Model) ...................... 79 4.1.2 Append Plotrefa File................................................................................. 80 4.1.3 Save Plotrefa File ..................................................................................... 82 4.1.4 Open .bpk Files (Field First Breaks) ........................................................ 83 4.1.5 Open .pik files (SIPT2 First Breaks)......................................................... 84 4.1.6 Open .lpk Files (SIPQC Output)............................................................... 84 4.1.7 Import Elevation Data File....................................................................... 84 4.1.8 Open Borehole Data File.......................................................................... 86 4.1.9 Save Traveltime Curves (DXF Format).................................................... 86 4.1.10 Save Velocity Model (DXF Format) ......................................................... 87
4.1.11 Save velocity file as the SurferTM format (.txt) .......................................... 87 4.1.12 Save analysis result as text format (.txt) ................................................... 88 4.1.13 Print .......................................................................................................... 89 4.1.14 Print Preview ............................................................................................ 89 4.1.15 Page Setup ................................................................................................ 90 4.1.16 Exit Program............................................................................................. 91 4.2 TRAVELTIME CURVE MENU ............................................................................... 92 4.2.1 4.2.2 4.2.3 4.2.4 4.2.5 Exit Edit Mode .................................................................................... 92 Modify Traveltimes (All Shots) ........................................................... 94 Modify Traveltimes (Individual Shot Only) .............................................. 96 Shift a Traveltime Curve ........................................................................... 96
Calculate Traveltime Difference Curve .............................................. 97 Audio/video clip of Difference-time Curve Calculation .................................. 98 4.2.6 Check Reciprocal Traveltime.................................................................... 98 4.2.7 Correct Reciprocal Time Automatically ................................................... 99 4.2.8 Connect Common Source Traveltime Curves ......................................... 101 4.2.9 Delete a Traveltime................................................................................. 105 4.2.10 Correct Traveltime Curve For Shot Offset ............................................. 105 4.2.11 Display .................................................................................................... 107 4.2.12 Common Source <-> Common Receiver................................................ 111 4.2.13 Reverse Survey Line................................................................................ 113 4.3 VELOCITY MODEL MENU ................................................................................ 114 4.3.1 Define Bottom Layer ............................................................................... 115 4.3.2 Plot Velocity Labels [ .............................................................................. 117 4.3.3 Set Location of Velocity Labels............................................................... 118 4.3.4 Highlight Velocity Labels [ ..................................................................... 119 4.3.5 4.3.6 4.3.7 4.3.8 4.3.9 4.3.10 4.3.11 4.3.12 4.3.13 4.3.14 4.3.15 4.3.16 4.3.17 4.3.18 4.3.19 4.3.20 4.3.21 Color Shading [ ............................................................... 120 Color <-> Monochrome [ ....................................................................... 125 Automatic Contour Interval [ .................................................................. 126 Manual Contour Interval ........................................................................ 126 Show Cell Boundaries [ .................................................................... 127 Show Layer Boundaries [ ........................................................................ 127 Show Sources [ ........................................................................................ 129 Axis Title (Elevation or Depth) ............................................................... 129 Reverse Legend [ ..................................................................................... 129 Modify Layer Boundary (Point by Point) ......................................... 131 Modify Layer Boundary (by Segment) .................................................... 131 Straighten Layer Boundary..................................................................... 133 Modify Velocities (by Mouse) ................................................................. 133 Modify Velocities (by Dialog Box).......................................................... 135 .................................................................................. 135 Exit Edit Mode Enable Surface Topography Modification [ ........................................... 136 Smooth..................................................................................................... 137
4.3.22 Extend Velocity Model to Remote Sources ............................................. 139 4.3.23 Modeling ................................................................................................. 145 4.3.23.1 Generate New Velocity Model ....................................................... 146 4.3.23.2 Add Random Noise to Traveltime Data.......................................... 147 4.3.23.3 Convert Synthetic Data to Observed Data .................................. 148 4.4 VIEW MENU ..................................................................................................... 151 4.4.1 Axis Configuration (Manual).................................................................. 151 4.4.2 Axis Configuration (Automatic) [............................................................ 152 4.4.3 Apply Custom Axis Configuration .......................................................... 152 4.4.4 Save Current Axis Configuration............................................................ 152 4.4.5 4.4.6 4.4.7 4.4.8 Show Traveltime Curves [ Show Velocity Model [ Show Time-term [ Show Raypath [ ................................................................. 153 ...................................................................... 153
4.4.9 Scale .......................................................................................... 155 4.5 TIME-TERM INVERSION MENU ......................................................................... 156 4.5.1 Assign Layer 2 Arrivals .......................................................................... 157 4.5.2 Assign Layer 3 Arrivals .......................................................................... 159 Audio/video clip of Layer Assignments ......................................................... 160 4.5.3 Do Time-term Inversion.......................................................................... 161 4.5.4 Clear Layer Assignment.......................................................................... 161 4.6 RECIPROCAL METHOD MENU .......................................................................... 162 4.6.1 Layer Assignment.................................................................................... 165 Set up T (1/2T(ab) calculated automatically) [ .................................. 165 Audio/video clip of Setting up T ................................................................... 166 4.6.3 Set up T (1/2T(ab) set manually) ............................................................. 167 4.6.4 Delete All T Curves................................................................................ 167 4.6.5 Show T(ab) Line [ .................................................................................. 167 4.6.6 Set Velocity Line ..................................................................................... 168 Audio/video clip of Setting Velocity Line...................................................... 169 4.6.7 Adjust Velocity Line ................................................................................ 170 4.6.8 Decimal Places of Velocity Label ........................................................... 172 4.6.9 Delete All Velocity Lines......................................................................... 172 4.6.10 Calculate Delay Times............................................................................ 172 Audio/video clip of Delay Time Determination ............................................. 177 Audio/video clip of Reverse-shot Delay Time Determination ....................... 179 Audio/video clip of Entire Delay Time Calculation Process.......................... 179 4.6.11 Modify Delay Time (Times) .................................................................... 180 4.6.12 Modify Delay Time (Velocities) .............................................................. 180 4.6.13 Calculate Velocity Model From Delay Time Data ................................. 181 4.7 RAYTRACING MENU ........................................................................................ 185 4.7.1 Execute.................................................................................................... 185 4.7.2 Delete Theoretical Traveltimes............................................................... 186 4.6.2
4.7.3 Show RMS Error ..................................................................................... 186 4.8 TOMOGRAPHY .................................................................................................. 186 4.8.1 Generate Initial Model............................................................................ 188 4.8.2 Inversion (With Default Parameters)...................................................... 190 4.8.3 Convert into Layered Model ................................................................... 192 4.8.4 Inversion (Set Parameters Manually)..................................................... 193 4.9 OPTIONS MENU ................................................................................................ 197 4.9.1 Dimension size ........................................................................................ 197 4.9.2 Units [...................................................................................................... 198 4.9.3 Edit Title.................................................................................................. 198 4.10 ADDITIONAL TOOL BUTTONS........................................................................... 198 4.10.1 5 5.1 5.2 5.3 5.4 5.5 Scroll Tool Buttons: .................................................................... 198 APPENDICES ....................................................................................................... 202 APPENDIX A - FUNDAMENTALS OF SEISMIC REFRACTION ............................... 202 APPENDIX B - THE TIME-TERM METHOD ......................................................... 217 APPENDIX C - THE RECIPROCAL TIME METHOD .............................................. 221 APPENDIX D - THE TOMOGRAPHIC METHOD ................................................... 232 APPENDIX E - RECOMMENDED READING ......................................................... 255
Introduction
Welcome to SeisImager/2DTM! SeisImager/2D is an easy-to-use, yet powerful program that allows you to: Read in and display your refraction data. Control how your data is displayed. Make changes/corrections to your data files and save them. Pick first breaks and save them. Invert your data for a velocity section. Output a travel-time plot, velocity section, and other graphics.
SeisImagerTM is the master program that consists of four modules for refraction and surface wave data analysis. The individual modules are PickwinTM, PlotrefaTM, WaveEqTM, and GeoPlotTM. The Surface Wave Analysis WizardTM is not a separate module but automatically calls on specific functions from Pickwin, WaveEq, and GeoPlot. Pickwin and Plotrefa are the modules used for refraction analysis, making up the program called SeisImager/2DTM. Pickwin is the first break picking module and Plotrefa is the main analysis program. Though we touch on some refraction theory in this manual, this is not meant to be a treatise on seismic refraction. It is assumed that the user has a reasonable grasp of the main principals of seismic refraction, especially those behind the specific analysis techniques employed by this software. Please see the recommended reading list (Appendix E) for some good primers on seismic refraction theory and inversion techniques. SeisImager/2D is a very powerful refraction package. It offers three separate inversion techniques: the time-term method, the reciprocal method, and tomography. Both the time-term and reciprocal methods are based on delay times (see Appendix C for a discussion of this all-important concept). The main difference between the two is the method by which the delay times are calculated. In the time-term method, the delay times are calculated automatically (via a linear least-squares inversion technique). In the reciprocal time method, the delay times are calculated manually. Each technique is different, and which technique you should use depends on the goals of the survey and the character of the data. SeisImager/2D also contains many ancillary tools that we hope you will find useful. Section 2 describes the software installation process. Section 3 describes the process of picking first breaks with Pickwin. Section 4 describes in detail the various inversion techniques available in Plotrefa. Appendix A provides an overview of seismic refraction theory. Appendices B, C and D describe some
of the particulars of the three inversion algorithms. Appendix E provides a list of references for further reading on seismic refraction. A separate booklet of examples, SeisImager/2D Examples, is available for download on our ftp site at ftp://geom.geometrics.com/pub/seismic/SeisImager/. Please visit our site often for manual updates and free updates of the software. Although this manual can be printed, it was designed as an online resource. It will be updated on a semi-regular basis, and a current version will always be available for download on our ftp site. Be sure to display the bookmarks in your PDF reader to simplify navigation. There are embedded audio/video clips that you may find useful (be sure to turn up the volume). The manual makes liberal use of color, so if you elect to print it, using color is highly recommended. Finally, we are very interested in your constructive criticism of both this manual and the software itself. Please contact us at seismicsales@mail.geometrics.com with any comments you might have. Note: All screens in this manual were captured in Windows XP Home Edition. If you are running a different version of Windows, some dialog boxes may look slightly different than they appear here.
2. Double-click on the file named SeisImager.msi (or SeisImager_1009.msi) to install the software. The Welcome to the SeisImager Setup Wizard window will appear as follows. a. If you are presented with the option to Repair SeisImager or Remove SeisImager as shown below, the installer has detected an older version. Select Remove SeisImager and click on Finish, then Close after the uninstall process is complete. Double-click again on the file SeisImager.msi to install the new version as described in Step 2b.
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b. If an older version is not detected, you will be presented with the installer as shown below. Click on Next, indicate the directory for installation (the default directory is recommended), click on Next, Next, and Close. It is not necessary to reboot the PC after completing the installation.
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3. To copy the SeisImager manuals to your hard drive (~125 MB), select the folders SeisImager2D_Manual and SeisImagerSW_Manual on the CD and copy them to your hard drive in the desired location. Note that the SeisImager2D_Manual folder contains .avi video clips that must reside in the same location as the files SeisImager2D_Manual_vX.X.pdf and SeisImager2D_Examples_vX.X.pdf (where X.X is the current version). You will need Adobes freeware program Acrobat Reader to view the manual files. If you need this program, go to the Adobe website to download the latest version compatible with your operating system. 4. To register the software, go to the Start menu, under All Programs, SeisImager to find the SeisImager Registration program as shown below. If you are using the software on a trial basis in demonstration mode, skip to Step 5. Open the register and email the keyword shown to support@geometrics.com with your order number and seismograph serial number (if you purchased the software with a seismograph) and we will reply with a registration password to enable the version of the software you have purchased. Once received, enter the password into the password field and click OK.
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The programs enabled by the password will be reported in a series of messages. For example, as shown below, for purchase of SeisImager/2D Standard and SeisImager/SW-2D, the register reports that SeisImager/2D Standard, SeisImager/SW-2D, and GeoPlot Standard are registered. Click OK to accept each message.
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After these messages have appeared, the register will also reflect the programs that have been registered, as shown below.
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Typically, installing an upgrade of the software does not require reregistration, but if you are upgrading from a version older than April 2007, you will need to re-register. 5. Once installed, the program modules can be opened directly through the desktop icons shown below or through the links in the SeisImager Start menu folder.
SeisImager/2D consists of the Pickwin and Plotrefa modules. SeisImager/SW-1D consists of the Pickwin and WaveEq modules. SeisImager/SW-2D consists of the Pickwin, WaveEq, and GeoPlot modules. The Surface Wave Analysis Wizard is not a separate module but automatically calls on specific functions from Pickwin, WaveEq, and GeoPlot to walk you through the analysis process. All of the icons will be shown regardless of which program(s) have been purchased or will be used. To begin using the software, double-click the Pickwin module icon. If you have installed for the first time or upgraded from a version older than April 2007, a prompt will ask you to set the language as shown below. Choose English.
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For registered installations, upon selection of the language, the module opens and is ready for use. As well, the other registered modules are ready for use. For unregistered installations running in demonstration mode, proceed to Step 6. 6. If you are using the software in demonstration mode, after selecting the language you will be presented with the registration dialog box as shown below. Leave the password field empty and click OK.
Detection of no password and the number of available run-times will be reported as shown below. Click OK.
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After running the software in demonstration mode, if you later purchase the software, refer to Step 7 on how to enter your registration password. 7. To enter your password after running the software in demonstration mode, go to the Start menu, under All Programs, SeisImager to find the SeisImager program as shown below. Open the Registration register and email the keyword shown to support@geometrics.com with your order number and seismograph serial number (if you purchased the software with a seismograph) and we will reply with a registration password to enable the version of the software you have purchased. Once received, enter the password into the password field and click OK.
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Once the software is registered (refer to Step 4 for a full description of the process), the data input dimensions of the demonstration version will be updated to reflect the limits of the program purchased. Click OK.
This completes the description of all possible registration pathways. As mentioned previously, the Lite version of SeisImager/2D comes free with all seismograph purchases, so if you have purchased SeisImager/SW with a
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seismograph, you are also entitled to the Lite version of SeisImager/2D. If you do not already have a license of SeisImager/2D, Lite or otherwise, but would like to order a copy, please contact us at seismicsales@geometrics.com or support@geometrics.com. A general recommendation when using SeisImager/2D is to close and reopen the software modules or open a second instance of the software modules to start new, separate analyses. The programs are efficient and quickly launch so this is easy to do, and will prevent complications when data processing. Regarding making report graphics and documenting your data processing, it is handy to have a screen capture program such as HyperSnap from Hyperionics (www.hyperionics.com). Bitmap screen captures can be quickly and easily made at the desired stages of processing and saved for import to Microsoft Office or other programs.
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PlotRefa
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Note: Never over-write raw field data. Always save edited data with a different file name from the raw data.
Click on the
The user-interface of Pickwin consists of a series of menus along with a toolbar. We will now discuss in detail the various menus of Pickwin.
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3.1
File Menu
Click on File to reveal the File menu:
3.1.1
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Find the folder your data resides in and open it. SEG2 files from Geometrics seismographs have a .dat extension, so this is the default, and only .dat files will be displayed. Choose the file you want to read in by double clicking on it. If there are already data in memory, you will be presented with the following dialog box:
Generally you will be reading in a new file, but you may also append records together. The append option is discussed in depth in Section 3.2.8.
3.1.2
3.1.3
3.1.4
3.1.5
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This is identical to that described in 3.1.1. It is used to open data acquired with the Oyo 160MX seismograph. There is no particular file extension for 160MX files.
3.1.6
First break pick files that have been picked with Pickwin have a .vs extension. Choose the file you want to read in by double clicking on it.
3.1.7
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Choose a file name and press Save. The extension will default to .vs.
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3.1.8
3.1.9
Print Preview
To preview the window display of Pickwin for printing, choose Print preview(V). You will see a preview of the window display that will be printed:
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To print this display, press Print. To close this display, press Close.
3.1.10
Page Setup
To set up a page for printing, choose Page set up(R). You will see the print dialog box for your computer:
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Adjust the properties for printing or click OK to print the current window display of Pickwin.
3.1.11
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3.1.11.1
Make File List To make a group, choose Make file list in the submenu. Choose the files you wish to group my holding down the CTRL or SHIFT key and clicking on them.
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Press OK:
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If the source and receiver positions are included in the data files, click both boxes in the above dialog box (default). The geometry will be automatically read from the file headers. The following table will then be displayed:
If you read the geometry directly from the shot file headers, then the geometry information displayed in the table should be ignored. However, this is a good place to confirm the shot records you have included in the group (see the ID column). If you want to delete one of the files in the group, click the appropriate box in the Edit column and press the Delete button. Press OK to continue If the geometry data were not read from the shot file headers, this dialog box will allow you to set up the survey geometry. For each file, enter the source position, the location of the first receiver, and the receiver interval. For refraction applications, you may ignore the # of aux column. Use the Next and Back buttons to scroll up and down through the shot record IDs. Ignore the Setup and Set # of aux buttons. Note: The above dialog box assumes constant geophone spacings. If you have variable geophone spacings, and the geometry data were not recorded in the shot record files, you may enter the geometry information under Edit source/receiver locations, etc. in the Edit/Display menu. This must be done on a file-by-file basis read in the file, fill in the geometry information, and save the file back out as a SEG-2 file. It is generally advisable to set the geometry parameters in the field and record them in the shot file headers.
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3.1.11.2
Open File List Once you have created a group, you may save it for future retrieval in .txt or .xml format (see below). To open a group, select Open file list. You will be presented with the following dialog box:
You can append file groups in the same way you can append individual files (see Section 3.2.8). Choose New file or Append to present data and press OK:
Choose the appropriate group file (the default file format is .xml). If the file is in .xml format, you will see the geometry dialog box:
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This is an opportunity to modify the geometry or to delete shot files from the group. Press OK to display the first shot record in the group. If the group file is in a .txt format, you will be presented with the following dialog box:
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Prefix: Some seismographs put some sort of prefix before the file ID number, e.g., FILE2001.SG2. When the group file is in text format, you must enter any prefix manually. If there is no prefix (Geometrics seismographs), leave the prefix field blank. Extension: Different seismographs use different file extensions, such as .dat or .sg2. Enter the correct extension. Digits: Enter the number of digits in the file ID number. Finally, indicate whether or not the source and receiver positions should be read from the file headers or not. Press OK, and you be presented with the geometry menu, as above. Press OK again to display the first shot record in the group. In general, .xml format tends to be the most convenient. Once you reach the data display, you may now page through all of the shot and tool buttons. This is extremely records in the group using the convenient in the first break picking process.
3.1.11.3
Save File List (text) Choose Save file list (text) to save the group as a text file.
3.1.11.4
Save File List (XML) Choose Save file list (XML) to save the group as a .xml file.
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3.1.11.5
Show File List Select Show file list to display the geometry menu:
3.1.12
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3.1.13
Exit
To exit the Pickwin module, choose Exit (X). You will see the following dialog box:
3.2
Edit/Display Menu
Note: Be sure to do any trace editing before picking your first breaks. Click on Edit/Display to reveal the Edit/Display menu:
3.2.1
Undo
To undo the last command performed, click on Undo. Or, press the Undo tool button . The last command performed by Pickwin will be undone.
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3.2.2
Redo
To redo a command that was undone, click on Redo. Or, press the Redo tool button . The last command that was undone will now be redone.
3.2.3
Select Trace [
Certain operations can be performed on individual traces. It is therefore necessary to choose which traces you wish to perform these certain operations on. Specifically, a trace must be selected before it can be reversed in polarity, killed, or deleted. To enable individual trace selection, click on Select trace. Alternatively, you may enable/disable trace selection by pressing the button. tool
Select a trace for editing by clicking on it. The trace will change from black to red when it is selected.
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3.2.4
Alternatively, you can press the button and then drag your mouse over some or all of the traces. This is a convenient way to select a group of traces:
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3.2.5
Selected Traces
When a trace or traces are selected for editing, the selected trace(s) can have the polarity reversed, killed, or deleted:
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3.2.5.1
Reverse Polarity To reverse the polarity of a selected trace(s), click on Reverse polarity from the sub-menu:
Note that the polarity of the group of traces selected earlier has now been reversed.
3.2.5.2
Kill To kill a selected trace(s), click on Kill trace(s) from the sub-menu:
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The selected trace(s) will now be killed (zeroed), as shown above. 3.2.5.3 Delete To delete a selected trace(s), click on Delete trace(s) from the sub-menu:
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3.2.6
Choose an amount of time (in milliseconds) to shift the record and click OK. The record me be shifted in a positive or negative time direction. In the example shown below, a negative 100 msec shift has been applied.
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Note: A positive (+) value will shift the record to the left and shorten the record time of the traces. A negative (-) value will shift the record to the right or increase the record time of the traces.
3.2.7
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To correct the shot time, choose Correct shot time in the Edit/Display menu. (notice that point-shot mark is now displayed in the editing status mode in the upper left-hand corner). Position the cursor along the time record to where you would like to set the correct time of the shot and click. The time-position of the cursor is shown at the bottom of the window. The traces will be adjusted for the corrected shot time, as shown below:
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3.2.8
Automatic Shift
Some styles of surveying require the ability to append shot records together. For instance, if the goals of your survey require more channels than are available, you may overcome this by laying out several individual spreads end-to-end, and re-occupying some or all of the shot points. As an example, suppose you wish to do a 48-channel, 5-shot spread, but you only have a 24channel seismograph available. You may simulate this through the following procedure: lay out the left half of the spread (all 24 of your channels), do your five shots as if the entire 48-channel spread is on the ground, pick up the 24-channels and moving them over to the right half of the spread, redo your 5 shots.
Once this has been completed, you have acquired the exact same data that you would have required had you laid out 48 channels all at once and simply done 5 shots.
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When conducting more than one shot at the same location, the physical properties of the earth can be altered, leading to slight differences in local velocities. This, in turn, can lead to a slight difference in traveltimes to equivalent geophone stations between the first and subsequent shots. This is especially true when using explosives. To account and correct for this, it is best to overlap one or two geophones when acquiring data in this fashion. The Automatic shift in SeisImager/2D can then be used to correct for any change in traveltimes from one occupation to the next. This is demonstrated in the following example. Read in the first half of the spread. Next, read in the second half. You will be asked if it is new data, or if you would like to append it to the present data:
Choose Append to present data. Next, you will be presented with the following dialog box:
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If you need to correct the source location (read from the SEG-2 file header), you may do so here. The component number is used to keep different spreads separate, and will automatically increment each time you append a new file. In this case, the component number defaulted to 2. You may append up to 10 files. Note: The Change check box must be checked for any changes you make in the above menu to actually take effect. Press OK and the next file will be appended to the first:
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If we zoom in, we can see that stations 1410 and 1420 overlap:
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Note that there is a slight time shift between the two. To eliminate this, select one of the overlapping traces (the red trace shown above), and then select Automatic shift:
The second spread has been shifted in time to correspond with the first.
3.2.9
Correct S-wave
When doing a shear or S-wave survey, it is common practice to do reversepolarity shots in order to facilitate the identification of shear wave arrivals. It is useful to overlay reverse-polarity shots from the same shot point. This can be done by reading in the first shot, and then appending the second, resulting in an overlay like the one shown below:
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Ideally, the first shear wave arrival times will be identical for both records. However, it is often the case that they are not one is often shifted slightly in time. This is quite common when the shear wave source consists of a long plank of wood or other non-point source. To correct the S-waves to coincide at the same arrival times, click on Correct S-wave in the Edit/Display menu:
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A cross-correlation of the oppositely-polarized traces will be done in an attempt to better align first breaks. An example of the effect is shown below:
Before correction
After correction
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3.2.10
Filter
Filters can be used to remove noise caused by wind, traffic, and other sources. You may apply high-cut filters and low cut filters. To apply a 1000 Hz highcut filter, press CTRL-H. Each subsequent press of CTRL-H will multiply the corner frequency by 0.8, so that the second press applies an 800 Hz filter, the third press applies a 640 Hz filter, and so on. To set a 5 Hz low cut filter, press CTRL-L. In a similar fashion to that described above, each subsequent press increases the corner frequency by 1.5. Below is an unfiltered record with some high-frequency noise in the early part of the record:
Here is the same record after applying a 512 Hz high-cut filter (four presses of CTRL-H):
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55
Here is the same record after applying a 38 Hz low-cut filter (six presses of CTRL-L):
To disable all filters and return to the raw data, press the
tool button.
3.2.11
56
Click on a default truncation of 1024, 2048, 4096, 8192, or 16384 samples to truncate the traces to the respective record length. Clicking on Arbitrary can specify an arbitrary truncation of a trace. If an arbitrary truncation of a trace is chosen, the following dialog box will be displayed:
Type the desired data length or number of samples for the traces. Click OK and the traces will be truncated or shortened accordingly.
3.2.12
Resample Data
To resample data, click on Resample data. From the sub-menu, click on one of the default re-sampling options: Every other, Every 4th, or Every 8th. This can be useful if the data has been over sampled and you wish to make the data files smaller.
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3.2.13
58
Edit the geometry of the survey by clicking in a box and typing in the new value. If you change the Group interval or First geophone coordinate, you must press the Set button to affect the change. Only six geophones are displayed at a time. Use the Back and Next buttons to scroll through the geophones. Click OK when changes are complete.
3.3
View Menu
Click on View to reveal the View menu:
Many of the features in this menu are toggle switches clicking on them either enables (signified by a [ next to the selection) or disables the feature. Most toggle switch items also have buttons on the tool bars, and all work the same way. In the discussion below, toggle switches are identified by a [ and their tool bar button, if they have one.
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3.3.1
Normalize Traces [
When traces are normalized, the maximum amplitude of each trace will be equalized. Lower amplitude traces (those farther from the source) will be turned up so that their maximum amplitude is equal to that of higheramplitude traces. This has the effect of optimizing the appearance of the first breaks across the record, and is recommended when picking first breaks. An example of normalized traces is shown below, followed by a record with normalization disabled.
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3.3.2
Clip Traces [
The Clip traces feature is useful in preventing adjacent traces from interfering with each other and obscuring the first breaks. An example of clipped traces is shown below.
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3.3.3
Trace Shading [
In addition to the positive-shaded trace display used in the previous examples, you may also shade negative amplitudes, or seismic traces may be displayed as simple wiggle traces. The trace style may be changed via the Trace shading sub-menu or with the appropriate tool buttons shown above. An example of negative amplitude shading is shown below, followed by a wiggle-trace plot.
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3.3.4
Select the number of traces you wish to display. Note that whatever is chosen, trace number 1 will be the first trace displayed. For instance, if you choose 12, traces 1-12 will be displayed. If Arbitrary is selected, the following dialog box will appear:
3.3.5
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3.3.6
Axis Configuration
To change the display of the time (horizontal) axis or the distance (vertical) axis, click on Axis configuration. The following dialog box will appear:
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The functions of most of the parameters in the above dialog box are selfevident or can be deduced by simple trial and error. Configure the axes to your liking and click OK when finished .
3.3.7
Pre-trigger Shift [
If you have recorded pre-trigger data (accomplished by setting a negative delay on the seismograph), you may choose whether or not to display it. In the example below, the pre-trigger data is displayed, and the shot or zero time is indicated by the vertical tan line.
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The pre-trigger shift setting can also be controlled from the Axis Configuration dialog box.
3.4
3.4.1
67
Once Pickwin has automatically picked the first arrivals, these picks may be manually adjusted. Simply position the mouse at the desired location and click. The first break pick will be updated. Repeat until you are satisfied that the first breaks have been assigned correctly to all traces.
3.4.2
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3.4.3
3.5
3.6
Option Menu
Click on Option to reveal the Option menu.
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3.6.1
Dimension Size
Click on Dimension size in the Option menu. A dialog box will appear with options to change the maximum samples and traces allowed to be displayed by the Pickwin module.
Note: A password is required to upgrade the maximum samples and traces displayed by Pickwin. Email (seismicsales@mail.geometrics.com), fax (408954-0902), or call us (408-954-0522) to upgrade your software.
3.7
Help Menu
Click on Help to reveal the Help menu:
3.7.1
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3.8
3.8.1
The Increase amplitude tool button increases the amplitude of all of the traces. The up arrow key () on the keyboard accomplishes the same thing.
3.8.2
The Decrease amplitude tool button decreases the amplitudes of all of the traces. The down arrow key () on the keyboard accomplishes the same thing.
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3.8.3
The Increase horizontal axis tool button increases the length of the horizontal (time) axis. The right arrow key () on the keyboard accomplishes the same thing.
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3.8.4
The Decrease horizontal axis tool button decreases the length of the horizontal (time) axis. The left arrow key () on the keyboard accomplishes the same thing.
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3.8.5
SHIFT
The Increase vertical axis tool button increases the length of the vertical (distance) axis. Pressing the up arrow key () on the keyboard while holding down the SHIFT key accomplishes the same thing.
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3.8.6
SHIFT
The Decrease vertical axis tool button decreases the length of the vertical (distance) axis. Pressing the down arrow key () on the keyboard while holding down the SHIFT key accomplishes the same thing.
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3.8.7
3.8.8
X Tool Button
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This tool button exits from whatever editing mode you might be in. For instance, if you choose Draw velocity line, you are in an edit mode. In order to exit that edit mode (so you can, for instance, select traces), you must press the button.
3.8.9
3.8.10
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Click on the
Like Pickwin, the user-interface of Plotrefa consists of a series of menus along with a toolbar. We will now discuss in detail the various menus of Plotrefa.
4.1
File Menu
Click on File to reveal the File menu:
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4.1.1
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Find the folder your data resides in and open it. Plotrefa files from Pickwin have a .vs extension, so this is the default, and only .vs files will be displayed. Choose the file you want to read in by double clicking on it. You will see a traveltime plot like the one below:
Note: Initial Plotrefa files written by Pickwin are traveltime files only. As you advance through the interpretation, the Plotrefa file will have additional data added to it, such as elevations, layer assignments, and a velocity model.
4.1.2
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Next, click on Append Plotrefa file. You will be presented with a dialog box like the one shown below:
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The two files will be appended together as shown above. You many append any number of files. Note: Appending must be done before creating a velocity model. You may not append velocity models, only traveltime plots.
4.1.3
82
Choose a file name and press Save. The extension will default to vs.
4.1.4
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4.1.5
4.1.6
4.1.7
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The left column is the geophone location, and the right column is the elevation. You may read in this elevation file and incorporate it into your velocity model. Click on Import elevation data file and double-click on the appropriate file (there is no default extension for elevation files). The elevation profile will be displayed:
After interpreting your data and calculating the velocity structure, it will be drawn relative to the elevation profile, as shown below:
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4.1.8
4.1.9
Choose the appropriate options and press OK. The file will default to a .DXF extension.
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4.1.10
4.1.11
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4.1.12
SP 1 2 3 4 5 6 7 Geo 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
X-loc 70.00 98.00 109.00 123.00 135.00 148.00 176.00 100.00 102.00 104.00 106.00 108.00 110.00 112.00 114.00 116.00 118.00 120.00 122.00 124.00 126.00 128.00 130.00 132.00 134.00
Layer 2 3.14 3.14 3.49 3.89 2.15 4.94 4.94 3.14 3.43 4.11 4.49 4.28 2.70 3.30 3.45 4.77 3.21 3.67 3.76 4.01 2.87 2.26 2.39 2.36 2.01
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4.1.13
Print
To print the window display of Plotrefa, choose Print, press CTRL-P, or press the Print tool button computer: . You will see the print dialog box for your
4.1.14
Print Preview
To preview the window display of Pickwin for printing, choose Print preview(V). You will see a preview of the window display that will be printed:
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To print this display, click Print. To close this display, click Close.
4.1.15
Page Setup
To set up a page for printing, choose Page set up(R). You will see the print dialog box for your computer:
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Adjust the properties for printing or click OK to print the current window display of Plotrefa.
4.1.16
Exit Program
To exit the Plotrefa module, choose Exit program (X). You will see the following dialog box:
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4.2
4.2.1
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Also, if you double-click on a traveltime, the shot location and depth for that traveltime curve will be displayed and can be edited if necessary:
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You may also draw a velocity line on your traveltime plot by clicking on the tool button and clicking and dragging your mouse. The velocity of the line will be displayed dynamically at the top of the display. Right click to set the velocity line:
If you are in an edit mode (for instance, modifying traveltimes), clicking and dragging the mouse will alter your data, depending on the specific edit mode you are in. To get out of edit mode, choose Exit edit mode, or press the tool button.
4.2.2
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While holding the button down, drag the cursor to where you want the traveltime to be, and release:
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4.2.3
Now, only traveltimes on that particular curve can be selected for modification. Note above that the cursor is pointing to a traveltime that is coincident with a traveltime on another curve. But only the one in the highlighted curve can be modified. Click and drag the traveltime as described above. Note: You will notice that the curve is no longer highlighted. This feature turns itself off after adjusting one traveltime, i.e., all traveltimes are accessible after the first one is modified. You must choose Modify traveltimes (individual shot only) again to highlight another curve.
4.2.4
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You may also shift an entire traveltime curve. Choose Shift a traveltime curve, click and hold on the curve of interest (it will change colors), and drag it to the new position:
The entire curve highlighted in the previous section has been moved to a later time.
4.2.5
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In the example above, the blue curve represents the difference time curve for the highlighted traveltime curves. Note that the crossover point for the red curve is clearly delineated by the difference time curve. This is an extremely useful tool when crossover points are difficult to determine. To remove the difference time curve, simply press the tool button.
4.2.6
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should recheck your traveltimes. Velocity models calculated from data exhibiting poor reciprocity are likely to be invalid. Plotrefa will check reciprocity, where appropriate, automatically. Simply choose Check reciprocal traveltime, and the program will examine the traveltimes and calculate reciprocity between shots in which the conditions of reciprocity are met.
In the example above, the reciprocity has been reported for the three interior shots. Both the absolute and percent errors are reported. The reciprocity report will be saved to a file called reciprocity_check.txt in the same folder in which your data are stored. Note: Reciprocal times are calculated only for shots that are within the geophone spread. For this reason, it is recommended that the shots at the end of the spread be located between the two end phones at either end of the line. For instance, with a 24-channel spread, the left end-shot would be between geophones 1 and 2, and the right end shot would be between geophones 23 and 24. SeisImager/2D will interpolate to calculate the reciprocal times at the shot locations.
4.2.7
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If the data quality is such that you cannot get better that a 5% reciprocity error, it is sometimes helpful to have the program correct the data. This, of course, is no substitute for picking the data correctly. It should only be used when true reciprocity cannot be achieved, because of difficulty in picking first breaks. The program will iteratively shift the traveltime curves to spread the reciprocity error out as evenly as possible, and this will sometimes yield a better answer than if left alone. To correct the reciprocal times, choose Correct reciprocal time automatically:
The traveltimes will be shifted to minimize the errors, and a table of total error versus iteration number will be displayed. Press OK, and a new reciprocity report will be shown:
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Note: The amount of confidence in the resulting model should be inversely proportional to the level of correction required. A model calculated from modified data is always suspect.
4.2.8
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The highlighted traveltime curve needs to be adjusted in time before doing so. Otherwise, the final interpretation will include an artifact due to a sudden and false jump in traveltime at that location. In the figure below, the highlighted traveltime curve has been moved down to better agree with its commonsource data:
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After manually correcting where necessary, you may connect the traveltime curves:
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You now have a traveltime plot that should be exactly the same as the one you would have achieved had you laid out the geophones once, and occupied all of the shot points once. At this point, it should be obvious why overlap is highly desired when using multiple spreads. As shown in Section 3.2.8, this same step can be accomplished in Pickwin. Where you do it is a matter of preference. But no matter how you do it, overlapping geophones is essential to correct for inconsistencies at the shot.
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4.2.9
Delete a Traveltime
You may delete a traveltime by choosing Delete a traveltime and clicking on it:
4.2.10
105
Input the source location (long the line), depth, and offset (perpendicular to the line), and the traveltimes will be corrected, using the near-surface velocity, to what they would be if the source were on the surface at zero perpendicular offset. In the example below, the center shot of the data set shown above has been corrected for a 2-meter offset:
The geophones closest to the shot are most affected by this correction (compare to uncorrected data).
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4.2.11
Display
The display contains a sub-menu which allow you to control various display parameters of the traveltime plot. All of these choices are toggle switches; you simply click on them to turn them on or off. If you have done your layer assignments, you may color-code them by choosing Show layer assignments:
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If you would like to differentiate the shot gathers, you may color them different colors. Just click on Color traveltime curves:
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You may choose whether or not to connect the sources to the near geophones. Below is the same plot without the source lines drawn:
Note: Source lines are only shown for shots within the geophone spread. If you have traced rays through your velocity model, the traveltime plot will default to displaying both the observed and theoretical data:
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If you wish to only see the theoretical data, click on the Show observed data toggle switch:
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4.2.12
111
To convert this to a common receiver gather, click on Common source <-> common receiver:
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4.2.13
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4.3
The Velocity Model menu allows you to edit a velocity model and control its appearance. A velocity model can be generated synthetically with the modeling module (discussed in Section 4.3.23), or it may be calculated from seismic data. A velocity model generated from the data set above will be used for purposes of illustrating the features of this menu.
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4.3.1
The program automatically assigns a thickness to the bottom layer of an interpreted velocity model. But in a refraction survey, there is insufficient information to actually determine the thickness; it is therefore assigned arbitrarily. However, by drawing the bottom layer with a certain thickness, it can give the impression that this thickness is known. It is therefore sometimes desirable to manually define the base of the bottom layer. One way to deal with this is to determine the maximum thickness of the bottom layer. You can estimate this by assuming a maximum velocity for the layer below it, and using a crossover distance equivalent to the greatest shotgeophone distance in your survey (i.e., you just missed seeing the next layer). Then compute the maximum depth from
depth = xcross / 2 (vn + 1 vn / vn + 1 + vn ) ,
where xcross is the assumed crossover distance, Vn is the velocity of the bottom layer, and Vn+1 is the assumed maximum velocity.
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Once you have computed a maximum depth, you may modify the base layer to reflect this. In the velocity model below, the assumed maximum thickness has been drawn on the model (red line).
This is accomplished by clicking on manually in the sub-menu, and then clicking at various points along the line with the mouse. You must start outside the left edge of the velocity model, as shown above. To complete the process, click outside the right edge of the velocity model (see cursor above:
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4.3.2
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4.3.3
The location of velocity may be set manually, or the program can set it automatically. To set it manually, simply click and hold on the center of the label, drag it to the desired location, and release:
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Note: A small red line will appear under the label to indicate that you have actually grabbed it with the mouse.
4.3.4
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4.3.5
Color Shading [
If you have done a tomographic inversion, your velocity model will not consist of discrete layers of constant velocity like those discussed so far, but will instead resemble that shown below:
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In a tomographic inversion, the velocity model is divided into velocity cells. In the above model, the velocity for each cell is displayed. This is the default setting for tomographic inversions, and is enabled by pressing the button. tool
To create a more aesthetically-pleasing velocity model, you may wish to contour the velocities. Choose Contour (no lines), or press the button to contour the data: tool
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If you would like to include the actual contour lines, choose Contour (with lines), or press the tool button:
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If you have a layered model (defined as seven layers or less), like the one below,
and you would like to remove the colors, choose No shading, or press the button:
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tool button.
Note: Only layered models can be displayed in this manner; tomographic models cannot.
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4.3.6
If you wish show your velocity model in shades of gray, choose monochrome:
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4.3.7
4.3.8
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4.3.9
4.3.10
127
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4.3.11
Show Sources [
If you wish to show where the sources are located, click on Show sources:
4.3.12
4.3.13
Reverse Legend [
You may reverse the legend to put high velocities at the top and low velocities at the bottom, or vice versa. Simply click on Reverse legend to toggle between the two:
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4.3.14
To change the geometry of the velocity boundaries on a point-by-point basis, click on Modify layer boundary (point by point), or press the tool button. The individual velocity cells will be displayed. You may change the depth of any layer by clicking on a cell intersection and dragging the red dot to the desired depth:
4.3.15
131
In addition to moving individual points, you can also grab an entire segment of a boundary and move it. Choose Modify layer boundary (by segment). Click on one end of the segment you wish to move. A red dot will be displayed. Now, click on the other end:
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4.3.16
The layer segment will be a straight line between the two points.
4.3.17
133
Enter the desired velocity, and press OK. Now, click on the cells or click and drag your mouse over the region you wish to alter the velocity:
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4.3.18
Indicate the layer, distance range, and new velocity, and press OK:
4.3.19
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4.3.20
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4.3.21
Smooth
The layer boundaries and velocity transitions can be smoothed. To smooth layer boundaries, choose Layer boundaries from the sub-menu:
137
With all three of the above smoothing operations, each time you click, a little more smoothing occurs. For instance, in the above model, the layers were smoothed twice. In the one below, it has been smoothed five times:
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4.3.22
139
140
This can be demonstrated by running the ray tracing routine through the above velocity model:
Note that no theoretical traveltimes have not been computed for the remote sources. We must extend the velocity model to include them. To extend the velocity model, choose Extend velocity model remote sources to reveal the following dialog box:
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The distance values will default to the locations of the farthest remote shots. The number of cells generally defaulted to zero. Press OK, and the model will be extended to include them:
At this point you may refine the model as usual using the tomography module, and the remote sources will be included in the analysis. In this particular case, 142
since the topography is significant, a tomographic analysis is the best approach. We use the above model as the intial model and invert:
Note now that theoretical data have been calculated for all sources, including remote ones. The travel times outside of the spread are calculated from extrapolated velocities and should be ignored.
143
At this point, you can trim down the result to show only the zone within the geophone spread:
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4.3.23
Modeling
Plotrefa includes the capability of creating a custom velocity model for forward modeling purposes. You may create a simple layer-cake initial model, and then customize it further using the editing techniques discussed above. Once you have completed your model, you may use the ray tracing routine (discussed in Section 4.7) to compute theoretical traveltimes for the model.
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4.3.23.1
Generate New Velocity Model To make a new velocity model, choose Generate new velocity model to reveal the following dialog box:
Specify the necessary parameters, press OK, and a velocity model will be created with default velocities:
You may now customize the model as needed using the tools in the Velocity model menu. Below is a customized version of the initial model:
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4.3.23.2
Add Random Noise to Traveltime Data If you calculate synthetic traveltimes using the Raytracing menu, you may add random noise to them. Below are the synthetic traveltimes generated for the model above:
Choose Add random noise to traveltime data to reveal the following dialog box:
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Indicate the [standard deviation] noise range in milliseconds, and press OK:
Your data will now have a random noise component superimposed on it. 4.3.23.3 Convert Synthetic Data to Observed Data It is often useful to convert synthetic traveltime data calculated from a synthetic model into observed data. This basically tricks the program into thinking that the synthetic data is actually real data, allowing you to treat it as such. This is a necessary step if you wish to invert this synthetic data and compare the resulting model to the original input model. This forward/inverse modeling can be very useful in testing the capabilities of the various inversion techniques on various types of seismic models. For instance, if you wanted to test the fault-detecting ability of tomography, you might follow the following steps: 1) Create a faulted velocity model. 148
2) Use the Raytracing menu to calculate the synthetic traveltimes. 3) Add a reasonable level of random noise to you data. 4) Convert the synthetic data into real data. 5) Do a tomographic inversion of the real data. 6) Compare the initial model to the calculated model 7) The new synthetic data will now be displayed along with the observed data (below).
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4.4
View Menu
Click on View to show the View menu:
This menu gives you control over various display parameters. It allows you to configure the axes, determine which graphics to view, and set the scale.
4.4.1
The X-axis will always be in units of length (set in the Options menu, discussed in Section 4.9.2); the units of the Y-axis will depend on what is 151
being displayed when you choose to customize the axes. If the velocity section is displayed, the Y-axis will be in units of length. If the traveltime plot is displayed, the Y-axis will be in units of time. You may also control the number of traveltime curves that are displayed. Experiment with the various parameters to see their effects.
4.4.2
4.4.3
4.4.4
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4.4.5
4.4.6
4.4.7
Show Time-term [
As will be discussed in future sections, the time-term and reciprocal methods modules are based on the concept of time-terms or delay times. The calculated delay times are use in conjunction with the associated velocities to generate the velocity/depth section. If you would like to view the delay times, click on Show time-term, or press the tool button. The delay times will be presented in a plot similar to the one shown below:
4.4.8
Show Raypath [
If you have run your model through the ray tracing routine (discussed in Section 4.7), and you would like to view the ray paths, click on Show
153
raypath, or press the tool button. A ray path diagram similar to that shown below will be displayed:
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4.4.9
Scale
There are several ways to set the scale of your output. If you click on Scale, you will see the following sub-menu:
Choose from any one of the scales listed, or click on Option and enter whatever scale you want. Alternatively, you may increase/decrease the scale by pressing the or tool buttons, respectively.
If you would like to change the aspect ratio, click on Vertical exaggeration and enter the desired ratio.
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4.5
We will now discuss the first of three inversion techniques. Which technique you employ will depend on the goals of your survey. In a fashion consistent with what we have done so far, each menu item for each technique will be discussed individually. Examples of each of the three interpretation techniques are given accompanying examples booklet. The Time-term technique employs a combination of linear least squares and delay time analysis to invert the first-arrivals for a velocity section. It is a good approach for lower-budget, simple refraction surveys, in which refractor detail is of lesser importance than gross velocities and depths. A good example might be a rippability survey. These types of surveys are typified by 12 or 24 channels, with as few as two shots per spread. The answer usually does not need to be a detailed one, and minimizing the time between fieldwork and the deliverable to the client tends to trump all. A brief explanation of the time-term technique is given in Appendix B. The general flow of the time-term technique is displayed in the flow chart below:
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Assign Layers
Invert Data
Tomographic Inversion
Raytracing
4.5.1
157
158
4.5.2
159
Note: When travel times from different shots coincide at a hinge point, it can be difficult to assign layers to both travel time curves. When this happens, the best remedy is to display a partial traveltime plot at any one time, as discussed in section 4.10.1.
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4.5.3
Do Time-term Inversion
Once all of the layers have been assigned, you are ready to invert the data for the velocity section. Click on Do Time-term inversion. The inversion error will be displayed:
Note: The message above does not indicate a failure. It is reported every time you do a time-term inversion. It is simply a measure of the quality of the least-squares inversion. Generally, a matrix inversion error of 1.5 or less is acceptable. If it is larger, you might want to re-examine your picks and/or layer assignments. Press OK and the velocity section will be revealed:
4.5.4
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4.6
The Reciprocal method of interpretation is a powerful technique for solving more complex refraction problems. It works best with highly redundant data (many shots), 24 channels or more per shot, and requires a far greater degree of input from the interpreter compared with the time-term method. This technique can provide a refractor depth beneath each geophone, provided a delay time for that geophone can be determined. This, in turn, requires overlap to calculate a delay time for a particular refractor for a particular geophone, you must have an arrival from that refractor from opposing directions. This has implications for how the data are acquired in the field, and will be discussed in further detail below. The general flow of a reciprocal time inversion is shown in the following flow chart:
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Assign Layers
Tomographic Inversion
Raytracing
If you are doing a simple rippability survey, the reciprocal method is overkill. You will do a lot more work and yield a marginally more useful answer. But if you are trying to image a fault or a buried stream channel, this technique can often provide a superior image. To learn more about the reciprocal method, see Redpath (1973), and Palmer (1980, 1981, 1990). Below is an example of a refraction record that nicely lends itself to interpretation by the reciprocal method:
Overlap
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Note the redundancy of the data. This is very important, because the reciprocal method makes much use of the scatter of the data about a best-fit line in this type of interpretation, this is considered signal, not noise. It yields crucial information about the geometry of the refractor. But scatter about the best-fit line can have several other sources, not the least of which is errors in picking. For this reason, redundancy, achieved through numerous shots, is critical. It helps you to separate real structures from artifacts due to picking errors. Note also the region of overlap. It is over this segment of the geophone spread where delay times can be calculated. Outside of this zone, the reciprocal method will not provide a solution. We will now step through each of the items in the Reciprocal Method menu.
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4.6.1
Layer Assignment
Layers are assigned as discussed in Sections 4.5.1 and 4.5.2. The Reciprocal Method menu differs from Time-term in this regard, allowing up to 5 layers to be interpreted.
4.6.2
165
Note: The reduced traveltime curve will be parallel to the first traveltime curve that you click on. In the example above, the two end-shots were chosen (right shot first), and the reduced traveltimes are shown in purple. The T(ab) line is shown in black (about 110 msec).
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4.6.3
Enter the T(ab) value, and press OK. The reduced traveltimes will be calculated and presented as shown in the previous section.
4.6.4
4.6.5
167
You may choose whether or not you want to display the T(ab) line on the traveltime plot. Simply click on Show T(ab) line to toggle it on or off.
4.6.6
168
169
4.6.7
170
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4.6.8
If you are working in units of kilometers, you will probably want to display velocities to at least one decimal point. Click on Decimal places of velocity label and choose the desired number of decimal places.
4.6.9
4.6.10
172
Now you must indicate the portion of the curve to compute delay times for. Like the velocity line, this should include only the region of overlap. Click on the left-most traveltime within the region of overlap, on the traveltime curve parallel to the reduced traveltime curve:
173
You will be presented with the delay times for that shot:
174
You should do this for all opposing shots that have reasonable overlap, and for each pair, you should calculate the delay times for both shots in the pair. To do so for the above shot pair, we will calculate the reduced traveltimes again, but this time we will click on the left shot first:
Note that the slope of the reduced traveltime curve is now in the opposite direction -- the reduced traveltimes are the same as they were before, but reversed. The delay times for the left end-shot shot can now be calculated from the differences between the left shot times and the reduced traveltimes. Simply follow the procedure detailed above for the right end-shot. An alternative process for determining delay times is as follows: 175
After setting the velocity line, press the velocity label to select the velocity line:
176
To calculate delay times for the right shot, click on Delay time, and then choose the segment of overlap on the traveltime plot parallel to the reduced traveltimes and click. The delay times for the right shot will be calculated and displayed:
177
To calculate the delay times for the left shot, right click on the velocity label to bring up the above menu again, and choose Reverse:
Position the cursor on the T(ab) line, and click. The velocity line will be reversed:
178
Select the new velocity line, right click, and choose Delay times. The delay times for the left shot will be calculated and displayed.
179
4.6.11
4.6.12
Enter a velocity value, and then click on the cells you wish that velocity to be assigned to:
4.6.13
Choose a smoothing level (generally 2 or 3), and press OK. The velocity model will be calculated and displayed:
181
Note that the solution is limited to the zone of refractor overlap (45 to 180 feet). At the beginning of this section, it was noted that in order to calculate a delay time for a refractor at a geophone, a refracted arrival is needed at the geophone from opposing directions. Note that in this data set, the first few arrivals from the end shots are direct arrivals. Hence this condition is not met toward the ends of the geophone spread, and delay times cannot be calculated. How can we make maximum use of the geophone spread? We must do offset shots. The idea of offset shots is to move the shot far enough off the end of the line such that all of the first arrivals from that shot are refracted arrivals, including those nearest the shot. The distance from the offset shot to the nearest geophone should be equal to or greater than the crossover distance at that end of the line.
182
Above is our data set again. The left end-shot is at 31 feet. The crossover distance for that shot is at about the third geophone, or 45 feet. That means the crossover distance is about 15 feet. So we want our offset shot to be at least 15 feet to the left of the left-most geophone (it is generally best to add 50% to account for any deepening of the refractor). At the right end, the crossover distance is about 25 feet. So we want to do a shot at least 25 feet to the right of the far right geophone.
183
Above is the same data set with the addition of offset shots at 3 feet and 233 feet. The new information gained from the offset shots is indicated. We now have overlap over the entire spread, and can calculate delay times for all 48 geophones for these two shots.
We now have a velocity model that covers the entire geophone spread.
184
4.7
Raytracing Menu
Click on Raytracing to reveal the Raytracing menu:
As discussed in earlier sections, Plotrefa may be used to calculate theoretical traveltimes for any velocity model, real or synthetic. This is very useful for pre-survey planning, and for assessing the validity of an interpretation by either the time-term or reciprocal method.
4.7.1
Execute
To calculate the synthetic traveltimes, simply click on Execute. The traveltimes will be calculated and displayed along with the observed data, along with the RMS error:
185
4.7.2
4.7.3
4.8
Tomography
186
Tomographic inversion is the third interpretation technique provided by Plotrefa. This method starts with an initial velocity model (generally generated by a time-term inversion), and iteratively traces rays through the model with the goal of minimizing the RMS error between the observed and calculated traveltimes. Tomographic inversion is generally best used when velocity contrasts are known to be more gradational than discrete, when strong horizontal velocity variations are known to exist, and in extreme topography. All of these cases can lead to erroneous results with the previous two interpretation techniques, depending on the severity. The typical flow of a tomographic inversion is shown in the flow chart below:
Invert Data
Velocity Section
187
4.8.1
The chosen parameters for the initial model should bracket the possibilities. You can get an idea, for instance, of the minimum and maximum velocities from the raw traveltime curves. From these and crossover distances, an idea of maximum depth of the lowest layer can be estimated. Note: By far the most important parameters to get right are the minimum and maximum velocities. If these do not bracket the actual velocities, the inversion will not converge. If you are setting these values manually, always err on the conservative side the maximum velocity can be 20-30% higher than the real maximum, but it should not be lower. Similarly, the minimum velocity can be somewhat lower than the true minimum, but it should not be higher. In any case, the best way to generate the initial model is to do a quick timeterm inversion of the data. Then, open the above dialog box and check the Use layered model as initial model checkbox. This overrides all of the other settings in the dialog box, including the minimum and maximum velocities. If you have done a reasonable time-term inversion, the minimum and maximum velocities from this should provide a good tomographic inversion. After doing the inversion, you may change the minimum and
188
maximum velocities and re-invert if necessary. See the tomography examples in the examples booklet.
Once you have entered the necessary parameters, press OK, and you will be presented with the initial velocity model:
189
4.8.2
190
To see the agreement between the calculated and observed data, display the traveltime curves by pressing the tool button:
191
4.8.3
You must provide the number of layers and the velocities you wish them to have. The program will divide the tomogram into the number of layers you specify, and the boundaries between them will divide layers having bulk velocities matching the specified velocities. Ideally, if you had done a layered interpretation from the start, this is what it would have looked like. In the above example, examination of the traveltime curves quickly indicates a two-layer case with approximate velocities of 300 and 1000 feet per second. Entering this information into the above dialog box yields the following:
192
This procedure can be useful in improving the quality of any layered inversion, particularly when layer assignments are difficult. See the examples booklet. Note: If you wish to keep the tomographic inversion, you must save the Plotrefa file before you convert to a layered model.
4.8.4
193
Number of iterations: The number of iterations defaults to 10. In general, the better the initial model, the less iterations required to arrive at an acceptable solution. If you are unsure about the quality of the initial model, you might want to compensate by increasing the number of iterations. Note: the number of iterations setting applies to each inversion, and subsequent inversions are cumulative. For example, if this parameter is set to 10, and after 10 iterations you decide to change one of the inversion parameters and run the inversion again, the cumulative number of inversions will be 20. Number of nodes: Tomography divides the velocity model into cells of constant velocity, and then traces rays through the model (see Appendix D). The number of nodes defines the density of rays the more nodes, the more
194
rays (and the longer the inversion takes). The corner of each cell is a node. In addition, there can be nodes along the sides of each cell. The number of nodes per side is what we refer to when we talk of the number of nodes. In the cell shown below, the number of nodes is one.
Horizontal/Vertical Smoothing: It is generally desirable to apply some smoothing of the cell velocities, for two reasons: 1) it tends to produce a more pleasing velocity plot, and 2) it removes the inevitable small-scale velocity artifacts that might otherwise be interpreted as real. On the other hand, if you have extremely high-quality, redundant data, you may want to avoid smoothing so as not to obscure small-scale variations. In most cases, the default values will be suitable. Smoothing is accomplished by applying a three-term, weighted moving-average filter to the velocity cells. Smoothing in the horizontal and vertical directions is done independently. Number of smoothing passes: This parameter controls the number of times the weighted average is applied in any one direction. You may run the same filter more than once. The more passes, the more smoothing. Smoothing weight: This is the weight of the center term in the moving average. The basic filter equation is as follows:
V 2 = W 1V 1 + W 2V 2 + W 3V 3
195
The default value of 0.5 for W2 therefore weights the center term twice as much as the other two. Note: The larger the smoothing weight, the less the model will be smoothed. A smoothing weight of one will result in no smoothing at all. You may set the number of smoothing passes to zero if you wish not to smooth the model. Number of layers to be smoothed: This applies to vertical smoothing only. Since the resolving capabilities of any geophysical technique, including seismic tomography, tend to decrease with depth, it is often desirable to smooth the bottom layers more than the top layers. This parameter determines the number of layers from the bottom of the model to be smoothed. For instance, if the tomogram has 15 layers, setting this parameter to five will result in the bottom five layers being smoothed. Minimum/maximum velocity: See above for explanation. If the match between observed and calculated data is poor, it may be that the minimum and maximum velocities need to be decreased and increased, respectively. You may change them in this dialog box and do the inversion again. Note: If you used the time-term model as your initial model, the minimum and maximum velocities in this dialog box will match those of the time-term inversion until you override them. Velocity vs. depth: In any surface refraction inversion technique, including tomography, it must be assumed that velocity increases with depth. However, this is not true in surface-to-borehole and borehole-to-borehole tomographic surveys. If you are doing a borehole survey, de-select Velocity does not increase with depth. Note: If you de-select the above parameter, run an inversion, and then decide to run a second inversion, be sure to de-select the parameter again, as it is selected by default.
196
4.9
Options Menu
Click on Options to reveal the Options menu:
4.9.1
Dimension size
You must make sure that the program is dimensioned large enough for the data set you are working with. Setting the values too small will result in errors. On the other hand, it is best not to set them much bigger than you really need, because memory is set aside to accommodate these dimensions. It is best to set them large enough, but not much larger than required. Note: In order for changes to become effective, you must check the Change dimension size checkbox.
197
Note: The maximum allowable dimensions are displayed, and are a function of which version of SeisImager/2D you purchased. If you choose to upgrade, we can provide a password that will increase the maximum dimension sizes.
4.9.2
Units [
Click on the units you would like shown on your traveltime plots and velocity sections.
4.9.3
Edit Title
Clicking on Edit title will reveal the following dialog box:
Enter the title you wish to have displayed on your output, and press OK.
4.10
4.10.1
198
The left-most two shots (shot one and shot two) are displayed. We may buttons to scroll through the spread. Pressing the now use the button once will display shots two and three:
199
The number of shots added or removed with each press of the button is always one less than the total number of shots displayed. If we display three shots at a time, as shown below,
pressing the
200
201
5
5.1
Appendices
Appendix A - Fundamentals of Seismic Refraction
A simple two-layer velocity model along with its associated traveltime curve is shown below. We will use this figure as a basis for discussing the fundamental principals underlying the seismic refraction technique. Note: This appendix discusses the very basics of seismic refraction, and is not intended to be a complete treatment of the subject. For more in-depth discussions, see the recommended reading list in Appendix E.
202
Traveltime (T)
Crossover distance xc
e S lo p
=1
/V 2
Traveltime Curve
=1 S lo pe /V
1
xc
Distance (X) x
ic
Velocity Model
h V1
ic
c V2 travels at V2
The break in slope of the above traveltime curve, which occurs at the crossover distance, marks the point at which traveltimes refracted from V2 overtake direct arrivals traveling through V1. The equation for the first segment T1 is simply
203
T1 = X / V 1
(Equation 5.1-1)
ac cd df T2 = + + V1 V2 V1
ac = df = h cos(ic) .
Substituting, we get
T2 =
cd 2h + V 1 cos(ic) V 2
(Equation 5.1-2)
204
Now,
tan(ic) =
or
bc de = h h
bc = de = h tan(ic) .
Referring back to the figure,
cd = x bc dc = x 2h tan(ic)
x 2h tan(ic) 2h T2 = + V 1 cos(ic) V2
(Equation 5.1-3)
205
Rearranging,
2h 2h tan(ic) x T2 = + V 1 cos(ic) V2 V2
1 tan(ic) x T 2 = 2h + cos( c ) 1 2 V i V V2
V 2 V 1 sin(ic) x T 2 = 2h + c 1 2 V V i cos( ) V2
Equation 5.1-4
206
V1 sin(ic) = V2
Equation 5.1-5
207
x cos(ic) T 2 = 2h + V 2 sin(ic) V 2
and from Snells Law (Equation 5.1-5), we substitute V1 for V2sin(ic):
T 2 = 2h
cos(ic) x + V1 V2
Equation 5.1-6
208
since
1 sin 2 (ic) x T 2 = 2h + V1 V2
Equation 5.1-7
V1 sin(ic) = V2
so
V 1 sin (ic) = V 2
2
209
T 2 = 2h
V 1 1 V 2 V1
x + V2
V 12 1 2 x V2 T 2 = 2h + V1 V2
V 2 2 V 12 x V 22 T 2 = 2h + V1 V2
V 2 2 V 12 2 V x T 2 = 2h + V1 V2
210
V 2 2 V 12 x T 2 = 2h + V 1V 2 V2
2 h V 2 2 V 12 Ti = V 1V 2
Equation 5.1-8
2h cos(ic) Ti = V1
Equation 5.1-9
V1 ic = sin V2
1
211
TiV 1 1 h= 2 cos(sin 1 V 1 / V 2)
Equation 5.1-10
h=
1 TiV 1V 2 2 V 2 2 V 12
Equation 5.1-11
Using Equations 5.1-10 or 5.1-11, we can calculate the depth by measuring Ti, V1, and V2 from the traveltime graph. Alternatively, the crossover distance can be used in lieu of the intercept time. At the crossover distance xc, T1=T2, so we can equate Equations 5.1-1 and 5.18:
xc 2h V 2 2 V 12 xc T1 = = + = T2 V1 V 1V 2 V2
xc xc 2h V 2 2 V 12 = V1 V2 V 1V 2
212
xc 1 1 = 2h V 1 V 2
V 22 V 22 V 1V 2
V 2 2 V 12 xc V 1V 2 = 1 2h 1 V 1 V 2
1 1 1 V 1 V 2 h= xc 2 V 2 2 V 12 V 1V 2
1 1 V 1V 2 1 V 1 V 2 xc h= 2 2 2 V2 V1
213
V1 V2 V 1V 2 1 V 1V 2 V 1V 2 h= xc 2 2 2 V 2 V1
V 2 V 1 V 1V 2 1 V 1V 2 h= xc 2 V 2 2 V 12
1 (V 2 V 1) h= xc 2 V 2 2 V 12
Squaring both sides,
1 (V 2 V 1) 2 h = x c 4 V 2 2 V 12
2 2
214
(V 2 + V 1)(V 2 V 1)
Substituting,
(V 2 V 1) 1 h2 = xc 2 4 (V 2 + V 1)(V 2 V 1)
2
1 (V 2 V 1) 2 h = xc 4 (V 2 + V 1)
2
1 (V 2 V 1) xc h= 2 (V 2 + V 1)
Equation 5.1-12
Equations 5.1.11 and 5.1.12 are the most basic equations in seismic refraction, relating layer thickness to the traveltime curve. Although valid only for constant layer thinkness, understanding them and where they came from are essential to understanding seismic refraction in general. The above can be extended to any number of layers. See Repath (1973) for a good example of a four-layer case.
215
The derivation for a smoothly varying thickness with flat interfaces is much more complex, and beyond the scope of this discussion. A good treatment of the varying thickness case is also provided in the above-mentioned reference.
216
5.2
ic
z V1
ic
S1 =
1 V1
1 S2 = V2
217
S2 sin(ic) = S1
Referring back to the derivation in Appendix A (see math leading up to Equation 5.1-6), the total traveltime t from source to receiver is then
t = 2 S 1 cos(ic) z + xS 2
Now, if we define
c = 2 S 1 cos(ic) ,
then
t = 2cz + xS 2 .
218
The above example assumes that the refractor is parallel to the ground surface. If we expand this to the general case non-parallel, curved surfaces, as shown below we end up with three unknowns rather than two, e.g. z1, z2 and S2.
source
receiver
ic
V1
ic
V2
Now, we have
t = cz1 + cz 2 + xS 2 .
219
Generalizing, we get
tj =
c
k =1
jk k +
xjs2
cm 3 cmn
x1 z1 t1 x2 z 2 t 2 x3 z3 t3 = x4 t 4 z n xm s2 t m
where m = number of traveltimes, and n = number of receivers (depths to be calculated). We can now solve the matrix for z1zn and S2.
220
5.3
Referring to the figure above, and following the derivation of Equation 5.1-6 in Appendix A,
cos(ic) x T 2 = 2h + V1 V2
221
TAP
hA cos(ic ) AP hP cos(ic ) + + V1 V2 V1
and
TBP
hB cos(ic ) BP hP cos(ic ) + + V1 V2 V1
We define
222
Substituting,
hB cos(ic ) BP hP cos(ic ) + + V V V1 1 2
or
t0 =
AP BP AB 2hP cos(ic) + + + V2 V2 V2 V1
AB = AP + BP .
Substituting,
2hP cos(ic) t0 = V1
223
to is twice the time required for the seismic energy to travel from P to P. We call t0/2 the delay time:
DT =
t 0 hP cos(ic) = V1 2
Equation 5.3-2
224
Reduced Traveltimes We will now examine the concept of reduced traveltimes. Computing reduced traveltimes is useful because it tends to remove the effect of changing layer thickness on the traveltime curve, and allows a better measurement of velocity. As will be seen, it also allows the computation of delay time and hence, refractor depth.
x
A P ic hA ic ic hP B ic hB
Referring to the above figure, we define TAP (the reduced traveltime at point P for a source at A) as TAP. This is represented by the red arrow. Upon examination, it should be apparent that a plot of T vs. x, since all that changes with the position of P is the length of the ray traveling at V2, will be roughly linear, unaffected by changes in thickness of the layer. Further, its slope will be 1/V2. Mathematically, TAP can be expressed as follows:
T ' AP = TAP
Equation 5.3-3
225
Rearranging, we get
The above equation allows a graphical determination of the T curve. Refer to the figure below.
TAB
TAB
1/2TAB
The traveltime curves represent what you would expect to see from a velocity stucture in which the thickness of layer 1 varies with x. TAB is known as the reciprocal time. We have drawn in TAB, which is the first term in Equation 5.3-4.
226
( TAP TBP )
2
,
TAB
TAB
1/2TAB
Now, using Equation 5.3-4, we can draw the reduced traveltime curve by adding TAP-TBP/2 to the TAB/2 line:
227
TAB
TAB
1/2TAB
x
The slope of T is 1/V2. Delay Time We now have everything we need to calculate the delay time at point P. Combining Equations 5.3-1
T ' AP = TAP
228
We see that
t0 T ' AP = TAP . 2
Combining with Equation 5.3-2
t 0 hP cos(ic) = V1 2
we get
T ' AP = TAP
hP cos(ic) V1
Equation 5.3-5
TAP
2hP cos(ic) x + V1 V2
Equation 5.3-6
229
T ' AP =
hP cos(ic) x + V1 V2
Equation 5.3-7
hP cos(ic) DTP = V1
Substituting into Equation 5.3-7 yields
T ' AP = DTP +
x V2
x DTP = T ' AP V2
Equation 5.3-8
230
DTPV 1 hP = cos(ic)
Equation 5.3-9
231
5.4
Source
lij sj
Receiver R e
232
Definition:
s=
s = slowness v = velocity lij = raypath
1 v
ti =
dX = s ( X )dX X ( X ) X
ti = s j lij
j =1
We end up with M simultaneous equations (one for each traveltime), and N unknowns: t1 = l11s1 + l12 s2 + +l1N s N t 2 = l21s1 + l22 s2 + +l2 N s N t3 = l31s1 + l32 s2 + +l3 N s N
t M = lM 1s1 + lM 2 s2 + +lMN s N
233
Rapaths
2 x1 + x 2 = 11 4 x1 + x 2 = 17 6 x1 + x 2 = 23
Unknowns are x1 and x2. In matrix notation, we get:
11 2 1 x1 AX = 4 1 x = 17 = Y 6 1 2 23
(AX=Y)
234
f 3 = 6 x1 + x2 23
or
f1 2 1 x1 f A = 4 1 = 2 6 1 x1 f 3 x 1
f1 x2 f 2 x2 f 3 x2
E = ( AX Y ) ( AX Y ) = AX Y
T
Minimize
dE = 2 AT ( AX Y ) = 0 dX
and solve for X:
(A A)X = A Y
T T
235
2 x 1 + x 2 = 11 4 x 1 + x 2 = 17 6 x 1 + x 2 = 23
and solving,
11 2 1 x1 2 4 6 2 4 6 T A A X = 17 = A Y 1 1 1 4 1 1 1 1 = x 23 6 1 2
T
56 (A A)X = 12
T
12 x1 228 = = AT Y 3 x2 51
X = AT A
So x1 = 3 and x2 = 5.
236
Example 2:
2
slowness A 2 B 0.5
C 1
D 1.5
5 raypaths:
A B 1
3 C 2 4 D 5
237
Observed traveltimes:
t1 t2 T = t3 = t4 t 5 2 2.5 2 +1 3 = 1 + 1.5 2.5 0.5 + 1.5 2 2 + 1.5 2 4.949747
2 + 0.5
Equation to be solved:
LS =
1 1 0 1 0 1 0 0 1 0 1 0 2 0 0
238
Normal equation:
4 1 T L LS = 1 2 1 1 2 s1 12.5 2 0 1 s2 4.5 T = =LT 0 2 1 s3 5.5 1 1 4 s4 11.5
S T = (s 1
s2
s3
s4 ) = (2 0.5 1 1.5)
Jacobian matrix requires ray-path Ray-path can not be calculated with out a velocity model Can not solve at once Must use non-linear Least Squares method
y (Z ) = x1Z x2 e Zx3
y ( z1 ) x1 y ( z 2 ) x 1 A= y ( z m ) x1
y (z1 ) x2 y ( z 2 ) x2 y ( z m ) x2
y ( z1 ) x3 z1 y (z 2 ) z 2 x3 = y ( z m ) z m x3
e Z1 x 3 e Z 2 x3
e Z m x3
x2 Z1e Z1 x3 x 2 Z 2 e Z 2 x3 Z m x3 x2 Z m e
239
1)
Calculate theoretical value Y0 for initial value X0. Y0 (Z ) = Y (Z , X 0 ) Calculate residuals (Y) between theoretical value Y0 and observed value Y.
2)
3)
(A A)X = A Y
T T
4)
5)
6)
240
Example 3:
True solution:
x1 1 X = x2 = 2 x 1 3
z 0 1 2 3 4 5 6 7 8 9 10
y(z) -2 0.26421 1.729329 2.900426 3.963369 4.986524 5.995042 6.998176 7.999329 8.999753 9.999909
241
Partial differentiation:
y =Z x1
y = e Zx3 x2
y = x2 Ze Zx3 x3
Initial model:
x1 2 X 0 = x2 = 3 x 2 3
Jacobian matrix A:
y ( z1 ) x1 y ( z 2 ) A0 = x1 y ( z11 ) x1
y ( z1 ) x2 y ( z 2 ) x2 y ( z11 ) x2
y ( z1 ) x3 z1 y ( z 2 ) z 2 x3 = y ( z11 ) z11 x3
Z1 x3
e Z 2 x3
Z11 x3
1 - 0.1353352832 - 0.0183156389 - 0.0024787522 - 0.0003354626 - 0.0000453999 - 0.0000061442 - 0.0000008315 - 0.0000001125 - 0.0000000152 - 0.0000000021
0.4060058497 0.1098938333 0.0223087696 0.0040255515 0.0006809989 0.0001105958 0.0000174621 0.0000027008 0.0000004112 0.0000000618 0
Observed data:
Y T = (- 2.0000
0.264241 1.729329 2.900426 3.963369 4.986524 5.995042 6.998176 7.999329 8.999753 9.999909
242
Residual vector:
Y = Y0 Y
Y0T = (- 1.0000 1.3298 2.2157 3.0921 4.0356 5.0133 6.0049 7.0018 8.0007 9.0002 10.0001 )
Solve:
(A A )X
T 0 0
T = A0 Y0
Get:
1.0016 X 0 = 1.0021 1.2162
243
X 1 = X 0 X
In second calculation,
Correction is:
- 0.001 X 1 = 0.002 - 0.179
244
Residuals are:
RMSE2 =
Y2T Y2 = 0.0122 0 11
Summary:
Simultaneous equations:
LS = T
L(S )S = T
Initial model
S0
Raytracing
L0
Then,
T0 = T O T0C = T O L0 S 0
Calculate correction:
L0 S 0 = T0
Correct model:
S1 = S 0 + S 0
Tk = T O TkC = T O Lk S k
Lk S k = Tk
S k +1 = S k + S k
246
Use diagonal:
n 2 li1 i =1 LT LS = 0 0
l
i =1
2 i2
n 0 ti li1 s1 i =1 s n 0 2 = ti li 2 = LT T i =1 s n n m 2 t l lim i im i =1 i =1
t ij t i Ti c i =1
n
Li = lij
j =1
l
i =1
ij
Ti = tij
j =1
Example 4:
From example 2:
LS =
1 1 0 1 0 1 0 0 1 0 1 0 2 0 0
247
Initial model:
T S0 = (1 1 1 1)
Calculate residuals:
RMSE:
T T T RMSE0 = = 2.44949 5
s j =
t
n i =1 n i =1
l ij Li
ij
248
Second iteration:
2.5 2.65533 - 0.1553 3 2.90533 0.09467 T1 = T T1c = 2.5 2.75888 = - 0.2589 2 2.50888 - 0.5089 4.9497 4.12132 0.82843
RMSE: T T T = 1.02243 5
RMSE1 =
249
General Summary:
Source
Ray path
Receiver Cell
Node
250
4 3 8 2 5 9 2 10 1 4
251
252
253
254
5.5
Crice, Doug, Shear Wave Techniques and Systems. ftp://geom.geometrics.com/pub/seismic/ShearWaves.pdf Caswell, Brad, Seismic profiling aids well location.* ftp://geom.geometrics.com/pub/seismic/Literature/s-tr162.pdf Dobecki, Tom L., Seismic shear waves for lithology and saturation.* Dobrin, Milton B., Introduction to Geophysical Prospecting, 629 p. 1976. Gorin, Stephen R., and Robert H. Gilkeson, Use of the seismic refraction technique to optimize monitoring well locations at hazardous waste sites.* Haeni, F.P., Application of seismic-refraction techniques to hydrologic studies, USGS TWRI Book 2, Chapter D2. 1988. ftp://geom.geometrics.com/pub/seismic/Literature/s-tr54.pdf Jackson, Don, Rip instead of drilling and blasting, reprinted from Coal Age.* Langston, Robert W., High resolution refraction data acquisition and interpretation.* Laymon, Douglas E., and Robert H. Gilkeson, Application of seismic refraction methods to evaluate regional ground-water resources.* Palmer, Derecke, The generalized reciprocal method of seismic refraction interpretation, Society of Exploration Geophysicists, 104 p. 1980. Redpath, Bruce B. Seismic refraction exploration for engineering site investigations, Explosive Excavation Research Laboratory, Livermore, California. 1973. ftp://geom.geometrics.com/pub/seismic/Literature/s-tr2.pdf Sirles, Phil C., and Andy Viksne, Site-specific wave velocity determinations for geotechnical engineering applications.*
* Available in hardcopy form from Geometrics. Visit our literature page for a complete list of available references. http://www.geometrics.com/LitForm/litform.html
255
INDEX
Add Random Noise to Traveltime Data, 147 Adjust Velocity Line, 170 Append PlotRefa File, 80 Apply Custom Axis Configuration, 152 Assign Layer 2 Arrivals, 157 Assign Layer 3 Arrivals, 159 Audio/video clip of Delay Time Determination, 177 Audio/video clip of Difference-time Curve Calculation, 98 Audio/video clip of Entire Delay Time Calculation Process, 179 Audio/video clip of First Break Picking Procedure, 68 Audio/video clip of Layer Assignments, 160 Audio/video clip of Reverse-shot Delay Time Determination, 179 Audio/video clip of Setting up T, 166 Audio/video clip of Setting Velocity Line, 169 Automatic Contour Interval, 126 Automatic Shift, 47 Axis Configuration, 65 Axis Configuration (Automatic), 152 Axis Configuration (Manual), 151 Axis Title, 129 Calculate Delay Times, 172 Calculate Traveltime Difference Curve, 97 Calculate Velocity Model From Delay Time Data, 181 Check Reciprocal Traveltime, 98 Clip Traces, 61 Color <-> Monochrome, 125 Color Shading, 120 Color Traveltime Curves, 108 Common Source <-> Common Receiver, 111 Connect Common Source Traveltime Curves, 101 Convert Into Layered Model, 192
Convert Synthetic Data to Observed Data, 148 Correct Reciprocal Time Automatically, 99 Correct Shot Time, 45 Correct S-wave, 51 Correct Traveltime Curve For Shot Offset, 105 Decimal Places of Velocity Label, 172 Decrease Amplitude Tool Button, 71 Decrease Horizontal Axis Tool Button, 73 Decrease Vertical Axis Tool Button, 75 Define Bottom Layer, 115 Delay Time, 228 Delete a Traveltime, 105 Delete All T Curves, 167 Delete All Velocity Lines, 69, 172 Delete Theoretical Traveltimes, 186 Delete Trace, 43 Dimension Size, 70, 197 Do Time-term Inversion, 161 Draw Traveltime Curve Tool Button, 76 Edit Source/Receiver Locations, 58 Edit Title, 198 Enable Surface Topography Modification, 136 Execute, 185 Exit Edit Mode, 92, 135 Exit Edit Mode Tool Button, 76 Exit Program, 37, 91 Extend Velocity Model to Remote Sources, 139 File Menu, 23 Filter, 54 flow chart, 21, 156, 162, 187 Fundamentals of Seismic Refraction, 202 Generate Initial Model, 188 Generate New Velocity Model, 146 Highlight Velocity Labels, 119 Import Elevation Data File, 84 Increase Amplitude Tool Button, 71
256
Increase Vertical Axis Tool Button, 74 Increase Horizontal Axis Tool Button, 72 Inversion (Set Parameters Manually), 193 Inversion (With Default Parameters), 190 Kill Trace, 42 Layer Assignment, 165 Linear Velocity Line, 68 Manual Contour Interval, 126 Modify Delay Time (Times), 180 Modify Delay Time (Velocities), 180 Modify Layer Boundary (by Segment), 131 Modify Layer Boundary (Point by Point), 131 Modify Traveltimes (All Shots), 94 Modify Traveltimes (Individual Shot Only), 96 Modify Velocities (by Dialog Box), 135 Modify Velocities (by Mouse), 133 Normalize Traces, 60 Number of Traces Shown, 64 Open bpk Files, 83 Open First Break Pick File, 25 Open lpk Files, 84 Open McSeis-3 File, 24 Open PlotRefa File, 79 Open SEG2 File, 23 Open SEG2 File (SmartSeis), 24 Page Setup, 28 Page Setup, 90 Pick First Breaks, 67 Plot Velocity Labels, 117 Pre-trigger Shift, 66 Print, 89 Print Preview, 27, 89 Print Window Display, 27 Raytracing, 185 Reciprocal Time Method, 221 Recommended Reading, 255 Redo, 38 Reduced Traveltimes, 225
Resample Data, 57 Reverse Legend, 129 Reverse Polarity, 42 Reverse Survey Line, 113 Save Current Axis Configuration, 152 Save First Break Pick File, 25 Save PlotRefa File, 82 Save Traveltime Curves (DXF Format), 86 Save Velocity Model (DXF Format), 87 Scale, 155 Scroll Tool Buttons, 198 Select All Traces, 39 Select Trace, 38 Set Location of Velocity Labels, 118 Set up T (1/2T(ab) calculated automatically), 165 Set up T (1/2T(ab) set manually), 167 Set Velocity Line, 168 Shift a Traveltime Curve, 96 Show T(ab) Line, 167 Show Cell Boundaries, 127 Show Layer Assignments, 107 Show Layer Boundaries, 127 Show Observed Data, 110 Show Raypath, 153 Show RMS Error, 186 Show Sources, 129 Show Time-term, 153 Show Traveltime Curves, 64 Show Traveltime Curves, 153 Show Velocity Model, 153 Smooth, 137 Source Lines, 109 Straighten Layer Boundary, 133 Time shift traces, 44 Time-term Method, 217 Tomographic Method, 232 Tomography, 187 Trace Shading, 62 Truncate Traces, 56 Undo, 37 Units, 198 Version Info, 70
257