Tensor program for fault-kinematic analysis  and paleostress reconstruction

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Answer to the most Frequently Asked Questions

Questions regularly arise from the users of Tensor programs (mostly for the Win-Tensor program). They are reported in this FAQ, with the reply that I gave. Some may seem no more relevant as the there is continuous improvement of the programme. The user might find here solutions on some of their questions. More formal guidelines are in preparation.

Dawnload the most updated pdf version of the FAQ with more answered questions.

    List of Questions
  1. Permission to use
  2. Do I need to de-install the old Win-Tensor version before installing a new one?
  3. Procedure for data input
  4. Adding a new line line to data table
  5. Digitizing module
  6. How to digitise a focal mechanism as beachball?
  7. Copy/Paste Function
  8. Saving data file under a different name
  9. Changing Subset Indexes in the Data Worksheet and transferring them to the Processing Worksheet
  10. Unknown sense of movement
  11. Faults without sense of movement
  12. Working with fracture of unknown type (X)
  13. Optimum number of data per tensor
  14. Discrimination between different subset
  15. Data filtering
  16. How the Automatic Regression works?
  17. It is mandatory to use the COMPOSITE FUNCTION or can I use anyone of the other 8 remaining functions?
  18. Focal mechanisms inversion from p-t axis data
  19. Separate data for focal mechanisms (Dos-Tensor program)
  20. Plots as in Tensor for Dos
  21. Deducing the Stresss Regime Index R' from the Stress Ratio R (in French)
  22. Plots as in Tensor for Dos
  23. Steps for the Rotational Optimization procedure
  24. Merging data sets into one single file
  25. Data validation
  26. More facts in the PDF version of the FAQ's
    Questions with their reponse
  1. Permission to use

  2. Q: I would like to ask you if it is possible to send me your stress-inverse program and to give me the permission to use it in my research and for scientific publication matters.

    R: For getting a copy of my Tensor program, I invite you to visit the Tensor web site under construction at http://users.skynet.be/damien.delvaux/Tensor/tensor-index.html (provisional address). There, on page DosTensor you will find a link to the download center for the Tensor for Dos program. In Documentation, I posted the articles related to the program (both abstract and full article as PDF).

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  3. Do I need to de-install the old Win-Tensor version before installing a new one?

  4. R: Before installing a new version, the old one will have to be removed. This can be done directly by running a first time the Win-Tensor.msi file. A message proposing two options will appear: Repair the existing file or Remove it. Select Remove. Executing a second time the same Win-Tensor.msi file will install the new version.

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  5. Procedure for data input

  6. Q: I can not understand why there is a shadow at certain boxes within de data sheet while entering new data and it is NOT taken into consideration by Win-Tensor ( no stereonet, no nothing). It is not a problem of validation. Please, explain me how to enter data, step by step, row by row. I well remember it was the same trouble with the DOS version and the No and ID labels for every row are very confusing!!!.What is the difference?

    I type data but a gray shadow starts in the "comments" and as I said this specific data in not taken into consideration.

    By the way, I suggest that every dot in the Mohr circle should have an identification number which also appears in the histogram. In this way one knows which data is not fitting and can be another way for separation or deletion.

    R: The row number is line in the left column in Excel; it is not related to a data line.

    The Data ID is linked to a particular data line and is serving to identify it. You will see the interest of the DataID relative to the Data Row, when you sort the data (double click on the top of any column).The data lines will be sorted (in ascending or descending way) according to the column selected. The DataID will be reordered as the rest of the data lines but the DataRow numbers will always remain in a Ascending way, so the relation between the Row number and the Data ID will no be the same any more.

    When you create a new file, you will first get an empty page. Start by entering the site properties. Do not forget the Outcrop Code as this will be used as a prefix for the Data ID. Once this is done, click on the first (empty, white) line of the data table. Pre-determined values will appear for some parameters. With the right arrow, move to the first orientation data to be introduced. Type successively the orientation data and move to the next (right) cell. Once the cell for entering the Slip Sense is reached, the orientation data will be displayed on the stereonets. Continue moving right by filling the cells. Once you reach the field "Comment", type eventually any text for describing the data.

    To add one more line, press the down arrow. A new like will be added and the cursor will come in the corresponding cell of the column "Type". This is the first data you might normally want to change, if a different data type than the preceding one will be entered. Repeat this operation until the end of your data. The upper stereogram is displaying the current data and the lower one, all data together. These are updated as the data are entered.

    If data has to be added to an existing file, the file has to be unlocked before. When a data file is loaded, it is not allowed to add a new file (to prevent unwanted black data lines at the bottom of the table). To unlock the file, click on "Unlock" button on the toolbar on top of the data sheet or use menu Edit > UnlockFile, or press F7. When the file is unlocked, the "Unlock" button on the toolbar appears as pressed and the Comments column in the data table is expanded.

    This procedure is effectively the same as in the Dos-Tensor version, but it is not a remaining bug. It is what I call "Controlled Data Input". If you did not like this way of working, you can type directly your data within an Excel file. To generate an empty Excel data file within the appropriate format for Tensor, create a new file within Tensor, then save it as an Excel sheet immediately after. Once the sheet has been filled with data, it can be re-opened within Win-Tensor. When loading the sheet (as for any type of datafile), Win-Tensor is controlling the format and consistency of the data. Invalid data will not be displayed the corresponding data fields will be left empty. I can expand this explanation later if you need. Once considered as valid, a data line is compiled in a standard format and the results are displayed in the columns at the right side of the Comments column. These columns are shadowed because these cannot be modified directly. Instead, these data can be copied and pasted elsewhere (in an excel sheet for example).

    For the Identification of the data in the graphics, it is a good idea. This is planned for the future developments.

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  7. Adding a new line line to data table

  8. Q:How to add a new line to data table?

    In the data table (the grid at the bottom of the Data Worksheet, active cells (which can be edited) are displayed with a white background while inactive cells (which cannot be edited) are displayed with grey background. When creating a new file, the data table is displayed with only one active line, with all cells empty. Clicking on the table will bring the focus of the cursor to that line and default values will appear.

    The data cells have to be filled successively from left to right. Moving from one cell to the adjacent one (on his right side) can be done using one of the following keys: Tab, KeyLeft or KeyDown (as this is the last active line, the downward movement will redirected to a rightward one).

    After filling the data cells of that first active line, the cursor should end up in the right-most active cell, corresponding to column "Comments". Within that cell, press KeyDown button and a new active line (with white background) will appear and the cursor will position itself to the lowermost cell of the Type column*

    * In order to facilitate data input, the cursor is positioned automatically to the Type column because this is usually the first data cell that might be changed from one input to the other. The Id is automatically generated and the Format is normally the same for the entire file. However, these can be changed if necessary (use KeyLeft to move to these cells).

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  9. Digitizing module

  10. Q: I just downloaded your latest version with the new option to digitize the PT and obtain the original fault population. This I what I needed indeed and for me it is more useful than the previous beachball with indication of extensional dieder.

    Please, be so kind and describe briefly for me the steps to follow, since I just pointed to the every P on my scanned "composed" beachball and don't now if the Ts are also to be pointed (I guess NO). And how the Program knows whether it is a compressive or extensional solution? Of course, the orientation of every P tell us about it, but there could be combinations where this could not apply (well, I am guessing!).

    R: Here is an attempt to explain the procedure to follow.

    In the Digitize window, after you define the Net center and radius (Step 1), you go to Step 2 and select the option " Focal mechanism as P and T axes ".

    Then you point to the first T axis and click on it, but maintain the left button pressed. A great circle will appear on the stereonet, whose pole is the P axis you just defined. That great circle corresponds to all areas of the stereogram which lie at 90° (orthogonal) from the P axis and contains the both T axis (tension, square) and B axis (intermediate, triangle), at 90° from each other. The P and T axes are displayed on that great circle with their location in function of the position of the mouse. Moving the mouse with the left button still pressed will circulate the P and T axes along the great circle, at 90° from each other. Once the square (digitized T axis) is adjusted to an appropriate the T axis of the scanned stereogram, releasing the left button will accept that orientation and store the data in the table.

    The advantage of this system is the possibility to associate easily a T axis with a given P axis, knowing that it should be orthogonal to the P axis, so lying on the great circle whose P axis is the pole. This limits the number of possibilities, but when a lot of data are plotted or when several T axis are plotted next to each other, it remains difficult to make the proper choice. It you make some wrong associations however, it may happen that it not possible to associate one or more of the remaining P axis with a T axis. In that case, you have to repeat the whole operation, starting with those particular P axes which you could not associate to a T axis. Working like that, after 2- trials, it should be possible in most cases to associate properly all T axes with the P axes.

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  11. How to digitise a focal mechanism as beachball?

  12. R: Here is the procedure, step by step.:
    1/ Load or paste the corresponding image with the beachball
    2/ Define the center and radius of the stereonet (= Step 1)
         a. Select mode
         b. Mark the two points in function of the mode
         c. Click on Validate
    3/ Digitize the data (= Step 2)
         a. Select the data type for the focal mechanisms
         b. Example: a focal mechanism defined as two focal planes
         c. Bring the mouse arrow over a point on the circle representing a focal plane.
         d. Press the left button and maintain it pressed (this is called a Mouse Down event).
         e. Keeping the left button pressed, move along the same focal plane on a point on the plane at about 90° from the first point.
         f. Mark that second point by releasing the left button (this is called a Mouse Up event).
         g. The first focal plane is now defined and marked on the stereogram. At the same time, a proposed auxiliary plane will appear.
         h. Keeping the left button unpressed, move the mouse pointer on a point along the auxiliary plane, again at about 90° from its intersection with the first plane.
         i. Mark that third point by pressing the left button (Mouse Down event).
         j. Keep the left button pressed while moving the pointer over the extensional dieder (the one filled in dark color). The corresponding dieder will blink as you move (this is a Mouse Move event).
         k. Mark the extensional dieder by releasing the left button (Mouse Up event).
         l. The digitalisation of the focal mechanism is now completed and the result appear in the table underneath.
    4/ For digitizing a new focal mechanism, press "New Image".
    5/ For transferring data to the Data sheet, press "Transfer".

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  13. Copy/Paste Function

  14. Q: Is there a way to copy/paste data from, for example WordPad to the tensor program?

    R: It is possible to paste data from any program, directly in the data sheet. Once the data is pasted, it will be checked for its validity.

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  15. Saving data file under a different name

  16. Q: When saving data under a different name, the input mode changes automatically from 24 to 11. This could be changed back by changing the value in the notepad, but this can´t be done in the tensor program itself.

    R: Better don't change the name of the file from the program itself.

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  17. Changing Subset Indexes in the Data Worksheet and transferring them to the Processing Worksheet

  18. Q: Once I have changed the subsets in the original file (worksheet), I expect that on processing, the indexes are carried forward or transferred accordingly so that I do not need to retype again! It doesn't seem so. I even tried to restart my computer and start the processing again and I can not see changes-do I probably need to do something to make the process automatic?

    R: What you changed in the Data Worksheet are the Input Indexes. In the Processing Worksheet, you are working with the Working Indexes. You therefore need to transfer the Input Indexes to the Working Indexes by using Menu / Data / Transfer Indexes / Input --> Working Indexes. By doing so, the Input Indexes will be copied to the Working Index column. Be aware that this will erase the previous working indexes. If you want to keep record of them before replacing them by the Input Indexes, you can copy them to the Tmp Indexes by using Menu / Data / Transfer Indexes / Working --> Tmp Indexes. This Tmp Indexes column can be used to store (copy) the indexes from the Working Index column.

    There are three different subset indexes: the Input Index that can is introduced during the data input and can be copied to the Working Index. This column is visible only in the data table of the Data Worksheet. The two other columns (Tmp and Working) Indexes are visible only in the Processing Worksheet. Like this, the original values if the subset Index is not modified during the separation procedure in the Processing Sheet.

    Be aware that, in the version of the program you have, the tree view of the subset manager is not refreshed after transferring the Input Indexes to the Working Indexes. In consequence, if new Primary Indexes are transferred (those with integer values only), they will not appear in Subset Manager. To do so, you have to save the file, close it and reopen it. This has been solved in the last version of the program.

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  19. Unknown sense of movement

  20. Q: The program won't let you fill in an "X". When you don't know the sense of the shear, the program itself decides, even with one data only, that there should be a "I".

    R: No. The program simply presents you the same sense as the previous data, to facilitate the input of series of similar data. You always have the control of the sense of movement, when this is input directly (in the case of type 1: faults with slip line). When the slip direction and sense is calculated indirectly as for pairs of conjugated fractures (type 2), movement plane and associated tension fracture and some formats for the input of focal mechanisms, the sense of movement is determined by the data you entered and you cannot modify it.

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  21. Faults without sense of movement

  22. Q: The data we collected from the field consist of 2 types:
    1- Measurements of fault planes and associated slip line WITH sense of movement.
    2- Measurements of fault planes and associated slip line WITHOUT sense of movement (since it was difficult to determine sometimes).

    The program only uses the measurements WITH sense of movement to calculate the paleostress. My question is: How can I make sure the program also uses the data from the fault planes and striations WITHOUT specified sense of movement? Via: Tools -> Options -> Default Data Values I have selected Data Type 1: Fault plane with slip line (slickenside).

    R: Effectively, the faults without sense of movement are not taken into account in the Right Dihedron module. For this one, a sense of movement is required. But this module should be used to constrain a first estimation of the stress tensor, which is used as a starting point in the Rotational Optimisation module for finer determination. If you have only data sets without slip sense, you should go directly to the Rotational Optimisation module.

    However, working with such a data set is not recommended as in fine you need to make an hypothesis on the sense of movement as otherwise, you will get two fully symmetric solutions.

    When you work with the Rotational Optimisation module using 2 different data sets, you should normally get different results as the tensor is constrained by the fault population.

    The alpha is equivalent to the Slip Deviation (SD) that I am using in Win-Tensor. It is the simple angular misfit deviation between observed and modelled slip directions. When the slip sense in known, the value of SD ranges from 0 to 180°. If no sense of movement is known, it ranges only from 0 to 90°. When the modelled and observed directions are parallel but of the opposite slip senses (hence the observed slip sense is known), SD will be close to 180° (worst). If the observed slip sense is not known, the same SD will be close to 0° (perfect fit). This explains why it is better to determine as much sense of movement in the field as possible. In practice, this is often difficult and it is also valid to work with data without sense of movement provided that enough other data have their sense well constrained. But you should not separate both types of data.

    The quality factor Confidence Level reflects this degree of confidence in the slip sense determination. A great number of data with no sense of movement will lower the final quality of the tensor.

    Q: I am happy to read that your program does work with the faults and slip data without sense of movement! I tried to check whether the program works with the 'no sense of movement' data. If you let the program do the processing this time, you will see that the paleostress regime is exactly the same as the other file, even the counting deviation histogram is exactly the same. This is where I started doubting whether the 'no sense of movement' data is considered in your program. When I read your e-mail I had another look and noticed that in the Rotational Optimisation there is a difference between the two files. Here (finally) come my questions: What does the alpha in the histogram means? Does it also have something to do with the misfit function? If you compare these 2 data files is it not strange that sigma 1, 2 and 3 are exactly the same, given the different data sets it used?

    R: In fact, the program does work with faults and slip lines without sense of movement. Nothing special has to be done for that. When you input your data, select type 1 (fault plane with slip pine) and type X for the sense of movement.

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  23. Working with fracture of unknown type (X)

  24. Q: I have difficulties when I go from the Right Dihedron to the Rotation Optimization mode to include the fracture data (with X slip R.) sense and X Confidence level) and optimize the fault and fracture data together. The problem is that I sometimes don't have enough fault data for the Tensor calculation and need to combine it with fracture data. It was possible in the previous versions of the program.

    R: This is a protection to avoid precisely using those data. A fracture of unknown type is not used in the optimisation procedure because it is not possible to determine what function has to be minimised on it. In order to avoid giving a false impression, they are excluded from the procedure. Otherwise, the stereogram can be full of fractures of unknown type which are not used to constrain the tensor.

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  25. Optimum number of data per tensor

  26. Q: How much data one can base a tensor on? We as a group feel that the more data you have, the better the tensor will be.

    R: In my own work, for about 500 stress tensors determined, I used an average of 21 data per tensor and 41 data measured in the field (some sites are polyphase). I believe that you should measure at least 20 data per site, and if possible more than 40. It is no use to measure more than 100-150 data per site, because then the data become redundant and more data did not significantly change nor improve the result.

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  27. Discrimination between different subsets

  28. Q: Is there an option to discriminate between different subsets which are both plotted in the same stereogram? By using different colours of the planes or different symbols of the poles for example?

    R: This is now possible with version 1.4.12. See documentation on Subset Management.

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  29. Data filtering

  30. Q1: How does the filtering take place? What is the statistical method used. For example: An outcrop from which the data give a perfect clock while there are actually two tensors involved. The program will filter "the sides" of the clock, while these consist of data from both tensors?

    Q2: Isn't a tensor built from data from differently orientated planes? Because when, for instance, filtering down from 300 data to 50 we noticed the orientation of the planes to be very important; the last 50 data consisted totally out of planes with the same orientation, instead of plane with all kinds of orientations, theoretically the best way to determine a tensor.

    R: The best way to determine the tensor is not the statistical way. The populations should be first filtered according to field criteria. Then you can perform further separation carefully, but controlling what you do. You can always improve the fit of the tensor by reducing the number of data you use. However, this will decrease the quality of the results. This is why I implemented the Quality Ranking system. Please refer to the documentation I gave with the program.

    If you know that two different tensors exists, but with relatively small differences, you have to start with the data you can differentiate from field criteria. Then you progressively separate the rest. When you get two slightly different tensors, they might sometimes correspond to the same tectonic stage. This is often the case when there are some components of rotation during the deformation.

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  31. How the Automatic Regression works?

  32. Q: Thanks again for your messages. Your explanation helps me a lot! As I followed your instructions on how to make subset indices in the data base, unfortunately, I got in some trouble again.. It does not seem to work in the program (or I don't understand how it works!). When I try to make subsets using ( Menu / Data / Transfer Subset Indexes / Input-->Working Indexes) I don't see the subsets in the Subset / Input-->Manager.

    I have found a way to work around this problem, which is changing the 0,0 in the WOR (under Subsets in the data table) column into 0,1 (for example), this way I can select or deselect this subset. Is this the way to (manually) divide your data into subsets? It seems to work. Apart from this I have the feeling that I am just playing around with the Rotation Optimisation without really understanding what I am doing (especially when I use the auto optimisation option). What do the 1-3, 1-4, 2 (rotation+/-20o, R+/-0.20) etc exactly mean in the Tensor optimisation & data separation section? The reason why I prefer to do this by hand is because in that case I understand and see every step I take and I seem to get lost in your program on this part, since I do not know exactly what it is calculating.

    R: For the automatic optimisation, the program performs a series of rotation, successively around the sigma 1 axis, sigma2 axis and sigma3 axis, computing the value of the function for a range of rotation angles (positive and negative) then finding the rotation angle which gives the best value of the function (minimum or maximum in function of the function selected). After rotation around the sigma 1 axis, it adjusts the tensor according to the latter rotation angle. Then the same is done around the sitma2 axis, the around the sigma 3 axis. The same principle is used for optimising the R value, by checking a range of R values at both sides of the original R value. When the 4 parameters have been optimised successively, I call this a Rotation Run.

    A Rotation Run can be performed with different precision: checking the values of the function for a rotation of max. 45°, 20°, 10°, 5°, positive and negative around a particular axis from the original tensor orientation. These are respectively Precision 1, 2, 3 & 4. When you select the mode for automatic optimisation, for example 2-4 means performing successively a rotation run with precision 2, one with Precision 3 and a lost one with Precision 4.

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  33. It is mandatory to use the COMPOSITE FUNCTION?

  34. Q: It is mandatory to use the COMPOSITE FUNCTION or can I use anyone of the other 8 remaining functions?

    R: You can use the function you want, but you have to know what you do. Function F5 is probably the best as it integrates different aspects. Function 1 and 2 only consider the deviation angle, and do not care weather the shear stress on the plane is large enough to allow the plane to slip. With function F5, you can combine different type of data: faults with slip line, tension fracture, shear fracture and compressional fractures and use them all together to constrain a tensor. With the other functions, you can use only F1 and F2 to constrain a tensor with slickenside data, F3 and F4 with shear fractures and slip planes, F8 for tension fractures and F9 for compressional fractures. The best is to try them individually on a sample data set.

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  35. Focal mechanisms inversion from p-t axis data

  36. Q:Please, consider the following questions: 1. How to calculate the true nodal plane. I see this option but not activated. Which friction ?
    2. Hot to perform the overall processing. Only after I went out of the program and tried again the same file it worked fine. What am I doing wrong?
    3. How to separate a subset of selected nodal planes?
    4. I note some filling problems in the beach balls when one the nodal planes dips less than 15° or higher that 75° or 80°.

    R:First go to Right Dihedron. In the table, all data should have a subset index 1.0. If not, reset them to 1.0 (Menu / Data / Reset Subset Indexes). Optimise the Tensor and separate the data using button next. Press it until in the Results frame, the values for Nbr and CV for Sigma 1 and sigma 3 become blue or green. The excluded data will go to subset 1.9.

    Then go to the Rotational Optimisation panel and select preferably optimization function F5. Perform automatic optimisation by clicking on AutoOptim button until the result become stable. When this is done, use option Menu/Data/Define Focal Plane. The program will separate the focal planes according to the value of function F5. The lowest the value, the better chance is that this is actually the focal plane. This function is minimising the deviation between observed and theoretical slip direction on the plane, but also minimise the normal stress and maximise the shear stress magnitude on the plane in order to favour the slip on that plane. The focal planes selected as movement plane are put in subset 1.1 and the auxiliary plane, subset 2.

    The theory and examples for this is given in Delvaux and Sperner (2003).

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  37. Separate data for focal mechanisms (Dos-Tensor)

  38. Q: How to work separate focal mechanism using F4 and option M?

    R: Working with focal mechanisms, you should use the minimisation function F5. It allows simultaneously to minimise the angular deviation between the observed and theoretical slip directions (angle alpha) and to maximise the shear stress magnitude on the focal planes. The values of this function are generally close to that of the mean deviation angle alpha. When you start the separation of the focal plane, you might want not to be too strict right from the beginning. You can then separate auxiliary from movement plane for focal mechanisms, only if the difference between the values of this function for the two planes is greater than a given value (e.g. 5). When applying the tensor to the data, the program calculates the values of the minimisation function for both focal planes of each mechanism. If the difference is greater than 5 (in this example), the plane for which the value of the function is the lowest will be considered as the potential movement plane (provided that the slip deviation alpha is lower than 30° or lower than the value fixed by the user). The other plane will be considered as the auxiliary plane. If the difference between the two values is smaller than 5° (in the present case), then both planes will still be considered as potential movement planes.

    In the resulting table, the data are presented by pairs of focal planes for the same focal mechanism. The index column is the data number (reference to the data table when you select the data for processing). The Function column is the value of the minimisation function (F5 or others). The Function difference is the difference between the two focal planes for the same focal mechanism. If the database contains only focal mechanisms (as it should do), the first plane of a mechanism has always an odd index, and the second, the next even index.

    The data in green (label = 4) are considered compatible, but with a function difference lower than the threshold. The data in Violet (label = 1) are considered as movement planes, the data in Blue (label = 2), as auxiliary planes and the data in red (label = 4) are not compatible (deviation alpha too high).

    To terminate the separation, the program classifies the data into four classes according to the labels defined above, for which you can attribute separate indexes. The data with label = 3 have to be excluded: they belong to non-compatible focal mechanism (each of them a pair of focal planes). The data with label = 1 and 2 are pairs of planes from compatible mechanisms (one is the movement plane and the other is the auxiliary plane). The data with label 4 have still to be separated into movement and auxiliary plane.

    After performing a first separation with a non-zero threshold, you have to further optimise the tensor on the remaining data, and then perform the separation again, with a smaller difference, until the difference is set to 0 (maximum one plane per each focal mechanism is kept as a potential movement plane).

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  39. Plots as in Tensor for Dos

  40. Q:While saving all created images I would like create one single plot which contains: the stereoplot, the histogram, symbols of stress axis orientations + R value and the amount of used data (n=x) in one image (e.g. all plots in Delvaux et al. 1995). But the latter two are not shown in the layout of the program and its exports.

    R:This is now possible with version 1.4.12.

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  41. Deducing the Stresss Regime Index R' from the Stress Ratio R (in French)

  42. Q:Comment expliquer la deduction de R' à partir de R pour le régime de contrainte, alors que R varie de 0 à 1.

    R:La définition de R' est une astuce pour présenter en une seule valeur le régime de contrainte tenant compte du facteur R et du type de contrainte (Extensif, décrochant ou compressif).

    Allant du plus extensif (radial extension) au plus compressif (constriction) en passant par le décrochement, on a une évolution progressive qui s'exprime par le rapport R de la manière suivante:

    • R va de 0 à 1 pour le régime extensif (d'extension radiale à extension avec composante décrochante)
    • R de 1 à 0 pour le régime décrochant (de décrochement avec composante en extension à décrochement avec composante en compression)
    • R va à nouveau de 0 à 1 pour le régime extensif (de compression avec composante décrochante à compression radiale ou constriction)

    Ce va-et-vient n'est pas très pratique pour exprimer le facteur R sous forme de diagrammes. Soit les auteurs utilisent un diagramme triangulaire, soit ils présentent les valeurs de R dans 3 diagrammes différents en fonction du régime de contrainte.

    Dans ce dernier cas, le problème si situe lorsque l'on a une population de tenseurs qui se situent à cheval sur la limite entre deux régimes. Tu dois savoir que par exemple pour la transition entre extension et décrochement, un tenseur extensif avec une valeur de R élevée est très similaire à un tenseur décrochant avec une valeur de R très élevée. A la limite, un tenseur extensif avec une valeur de R = 1 est identique à un tenseur décrochant avec une valeur de 1. Il en va de même pour la transition décrochement - compression. Un tenseur décrochant avec une valeur de R = 0 est identique à un tenseur compressif avec une valeur de R = 0. Tu peux tester cela aisément avec le programme WinTensor, en changeant la valeur de R' dans le panneau Rotational Optimisation et en regardant l'effet que cela fait sur le cercle de Mohr.

    Pour éviter cela, la valeur de R est transposée en un index composite R' allant de 0 à 3 exprimant cette évolution du plus extensif au plus compressif de manière continue.

    Il est calculé comme suit :

    • R' = R       pour le régime extensif (donc pas de changement)
    • R' = 2 - R  pour le régime décrochant (R' reste croissant du plus extensif au plus compressif, alors que R est décroissant)
    • R' = 2 + R  pour le régime compressif (juste une translation)

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  43. Inversion of focal mechanisms

  44. Q:How to compute a stress tensor from earthquake focal mechanisms?

    R:First of all, the focal mechanism data has to be defined, as Type 5, 6 or 7 according to way the focal mechanism is recorded. In particular, Type 1 (fault with slip line) has not to be confused with Type 6 (focal mechanism defined as slip plane, slip direction and sense of one of the auxiliary planes). It may look similar, but in the case of the focal mechanism, a second plane (the auxiliary plane) will be generated during data compilation. The difference will appear in the processing part of the program.

    Computing stress tensors from focal mechanisms is quite straightforward. Within the Processing Sheet, select first all data (both focal planes for all FM) and compute a preliminary tensor using Dieder. In Dieder, click on button "Next" in order to exclude one FM (two focal planes) apparently not compatible. Move then to the Optimisation pane. First optimize the tensor by clicking on button "Optimise" until the tensor stabilized. Like this, you are still working using both focal planes for each FM. Now I used the option Data/Separate Focal Mechanisms. In this, the system compares the values of the misfit function for each pairs of focal planes in order to separate actual movement planes from the auxiliary plane. We consider here that the movement plane best fit to the general tensor (has the lowest misfit value) and the auxiliary plan has the highest value of the misfit function). The decimal par of the subset index is set according to the values indicated in the drop-down box next to the labels "Movement plane" and "Auxiliary plane" in the frame "Focal plane discrimination". If the misfit function of both focal plane from the same FM have values above the specified value in the frame "Focal mechanism exclusion", they will be excluded by giving them the minor index specified. When you validate it, you remain in the subset index 1.1 with only the best-fit focal plane for every FM and some additional FM are excluded.

    The next step is to optimize the tensor using this selection (index 1.1). To finish the procedure, in is necessary to re-check the excluded FM (normally within subset index 1.9) without changing the tensor for testing if by chance, after the last optimization, some of the focal planes did not became compatible with the computed stress tensor. If not, then the process ends here. If yes, you have to re-incorporate it to the data base, re-optimize the stress tensor and check again the rejected data.

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  45. Steps for the Rotational Optimization procedure

  46. Q:After finishing the Right Dieder, I go to the Rotational Optimization (RO).

    I start with the last number of data used in Right Dieder.
    Choose the Auto-optimization mode 1 then click 'optimize'
    Choose mode 2 then click 'optimize'
    Choose mode 3 then click 'optimize'
    Choose mode 4 then click 'optimize'
    Repeat clicking 'optimize' with mode 4 until the tensor stops rotating (I guess this is what means "until the tensor is stable").
    When should I click "reject" during RO procedure? Which button should I click when working with RO? Optimize with reject or just button next?
    Should I go through this order when using auto-optimization: 1,2,3,4? Can I skip any of them for example 1 then jump to 4? What if I choose mode 1-4 then repeating mode 4 until the tensor stops rotating?

    R:The way you are using the RO procedure sounds correct. What is important is to get a stable solution, but which also gives the minimum possible value of the misfit function. It is correct to end in mode 4, but it is also good to check after that in mode 2-3 or even 4 in order to be sure that no other minima exist in the 4D space (orientation of sigma1-3 and value of R).

    Mode 1 is good for starting as it checks the whole range of possible rotation angles around the stress axes and of R values. As first the stress axes are adjusted and then the R value, a R value of 0.5 is used for finding the optimal rotation angle around the 3 stress axes (which gives the minimal value for the function). Effectively, it is when R = 0.5 that the stress axes are best defined, the magnitude difference between sigma1-2 and sigma2-3 being equal. R is fixed to 0.5 as a starting condition only in mode 1. For the other modes, the R value determined at the end of the preceding cycle is used.

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  47. Merging data sets into one single file

  48. Q:What is the most effective way to merge the datasets of two different files?

    R:Use command File/Append. This will place the data of the append file at the bottom of an existing file. Note that the header of the existing file will not be affected and that the ID of fault-slip data has to be all different.
    You can also insert the appropriate number of blank lines at the bottom of the existing data (Edit/Insert/Rows at bottom), select all the lines you want copy from a second open worksheet, copy them (Edit/Copy), position the cursor to the upper left free field in the first worksheet and paste the data (Edit/Paste).

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  49. Data validation

  50. Q:How data validation works?

    R:When you work with the database, the program validates every data lines while typing it. It may happen that when you import data, to many data lines are invalid and updating them becomes difficult. The solution is to deactivate the validation process by pressing button "Validate" on the command bar on top of the Data worksheet.

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