FaultFoldForward v. 6
by Richard W. Allmendinger © 2012
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Table of Contents
Introduction!.....................................................................................................................3 Disclaimer!........................................................................................................................4 Interactive Features and Differences with Previous Versions!...................................5 Program Layout!..............................................................................................................6 Using FaultFoldForward!................................................................................................8 Making a New Model!.............................................................................................................................8 Modifying Your Model!........................................................................................................................10 Modifying Your Plot!............................................................................................................................11 Saving and Importing an Old Model!.................................................................................................12 Making more complicated models using pictures and ad hoc beds!............................................12 Ad Hoc Beds!................................................................................................................................13 Using Pictures!..............................................................................................................................14
Selected References!....................................................................................................16
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Introduction FaultFoldForward is a program for FaultFoldForward is an update of the both Macintosh and Windows operating forward modeling part of my venerable systems that allows you to create forward FaultFold program for Macintosh and Windows computers. The older program, models of area balanced cross sections. The FaultFold v. 4 and 5, no longer works unprogram allows you to specify either similar der Windows 7 or Mac OS X 10.7 or parallel fault-bend folds {Medwedeff (“Lion”). This new program works with 1986; Suppe 1983; Suppe 1990; Woodward all recent versions of Mac and Windows operating systems. Eventually, we will 1989}, and produces fault-propagation folds produce updated versions of the program using trishear kinematics {Allmendinger that also incorporate and update the in1998; Allmendinger 2000; Cardozo 2003; Erverse modeling functions of the original slev 1991; Hardy 1997a; Hardy; Zehnder FaultFold. 2000}. Sections can have multiple faults and each fault can have multiple bends in it. Individual faults can be either normal or reverse. The program also calculates strain at evenly spaced intervals in a section. Surprisingly complicated sections can be simulated (Fig. 1):
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Figure 1. Example of a complicated sequence of faults simulated with FaultFoldForward. The active fault is in black and inactive faults in red. Several generations of growth strata are in orange. Ellipses are shaded by magnitude of strain. Diagram is unretouched PDF output from FaultFoldForward. This is the same section as appears in colored format on the title page.
While FaultFoldForward offers considerable power for constructing forward models of cross sections that are area balanced, it has several limitations that may reduce its suitability for simulating any particular deformation. A few of these include: • Multi-bend kink fault-bend folds like those described by Medwedeff and Suppe {%Medwedeff 1997} cannot be produced with the program. Kink -3-
axes due to the active ramp do not refract across higher level inactive ramps. Thus, bed thickness is not preserved across higher ramps. In general, you are better off using similar folding over multi-bend ramps. • Kink-style fault-propagation folds {Suppe 1990} cannot currently be produced with the program (though we hope to introduce this capability in future versions. • It is possible to enter parameters that will result in at least local area loss or gain. For example, if you have a kink ramp off of a decollement higher than 30° the program will warn you but will allow you to go ahead with the model. • Small errors in area calculations accrue to to rounding, offsets by faults, etc. • Probably many other things that I am forgetting right now!
Disclaimer FaultFoldForward is distributed on an "as is" basis without any warranty, explicit or implicit. The author will not be liable for direct, indirect, incidental, or consequential damages resulting from any defect in this software or this user’s manual. Furthermore, I make no systematic effort to inform all users of either bug fixes or upgrades. The program is upgraded periodically; write to us for details. The algorithms in FaultFoldForward were written by Richard W. Allmendinger, based on the theory published in {Allmendinger 1998; Allmendinger 2000; Hardy; Jin 2006; Suppe 1983; Suppe 1992; Williams 1983; Zehnder 2000}. There are many other publications about these topics (see the further reading list at the end), but the list above are the ones whose theory I relied upon. I distribute the program FaultFoldForward to non-commercial users without charge in the interest in scientific communication (and because I don’t want to have to worry about whether someone pirated the program every time I see a plot produced by it in a journal or at a meeting!). I grant permission for people to distribute one copy of the program and the user’s manual to other non-commercial users, but only free of charge and accompanied by this page. This program may not be sold or offered as an inducement to buy any other product. Commercial users, please contact me for details. I do not distribute copies of the source code in order to protect me from unauthorized changes for which we might be blamed later. Please do not ask. If you have scientific questions about any of the procedures, I will provide copies of the individual subroutines for your inspection.
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I have tried to make the program as bug free as possible (after all, we use it for our own research), but errors may remain. I am always interested in errors people have found or suggestions for improvement. Please write with your comments or suggestions. Thanks for your interest. I hope your find the program useful. Any names herein that refer to other software are trademarks of, and/or copyright by, their respective owners/companies.
Interactive Features and Differences with Previous Versions FaultFoldForward has numerous differences with previous versions. Many of these are due to use of a different development environment and the modern interface enabled by that environment. This version has a much higher degree of interactivity, better display of various parameters, etc. Some of the interactive features include: • clicking and dragging in the plot cross section tab will measure distance and angle • control/right clicking in the cross section tab of the window will display the plot menu are a contextual menu • option-clicking on an ellipse will open up the info tab and display highlight the ellipse in the strain list box as well as writing the strain for that ellipse to the history panel. • any selected ellipse will be highlighted with a yellow halo in the plot window. you can deselect all ellipses by option clicking in the cross section tab (not on any ellipse), or by choosing deselect all from the edit menu. • the Strain listbox in the Info Tab is sortable by column so you can sort by, say, stretch and select all ellipses that have a stretch greater than a certain value. • You can turn on or off the plotting of any bed by toggling the checkbox for it in the bedding listbox. • Normally, the coordinates read in the units and in the direction of the axes displayed on the screen (positive to the right and up). However, if you hold down the shift key while moving/dragging the mouse in the window, you will see displayed the coordinates and lengths in pixels in the screen's native coordinate system (positive to the right and down). Likewise, this version has capabilities that the old version lacked: • There is no longer any limit on the length of beds. All arrays should resize automatically.
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• Scans of existing cross sections can be imported as .png, .jpg, .tiff, or .pdf format using File:Open:Picture. These can be rescaled and moved around with the Digitize:Picture Scale & Position menu choice and the transparency controlled with a slider in the appearance tab of the Inspector. Plotting is turned on or off completely with the Plot:Picture menu choice. • Right now, the program can read and write text files (as well as saving plots as PDFs), but eventually it will have a native binary file format. I want to see what format makes the most sense and is most comprehensive for the eventual functionality. It should read and write the old FaultFold text files.
Program Layout The main program window has two tabs: selecting “Cross Section” will display the forward model you are working on (Figure 2a). Whenever the mouse moves over the plot area, its position is shown at the left side of the status bar at the bottom of the window. Clicking and dragging in the plot area draws a line between the initial mousedown position and the current position; this can be used to measure lengths and angles, which are displayed in the status bar. The coordinates and lengths are shown in the current coordinate system (positive to the right and positive up) which is displayed in light
Click and drag the mouse in the plot area to measure lengths and angles, which are shown here Status of the current model is displayed here. You can copy text from any of these fields Mouse cursor position updated as you move over the plot area
Figure 2a. The Cross section tab of the main window. -6-
Bedding Info list box. You can turn on or off plotting of a bed by toggling the checkbox in this list.
History Text area. This editable text area records the history of your model. You can add your own notes to this box just by clicking and typing, and text can be copied/pasted from/to this box.
Strain Info list box. Data on all strain ellipses are listed here. Columns can be sorted by clicking on the headings. Select one or more lines in the list box and the corresponding strain ellipses will be highlighted on the plot in the Cross Section tab
Figure 2b. The Info tab of the main window.
gray. If you want to see the screen coordinates — always in pixels, with 0, 0 at the upper left corner and positive to the right and down — hold down the shift key while moving or dragging the mouse. The coordinate system scale and position of the origin (0, 0) can be set at any time by choosing Set Scale and Origin in the Model Menu. The Info Tab (Figure 2b) has three sections. On the left is a scrolling text area that contains a history of all of the models you have run since you started up the program. This field is completely editable: you can jot down your own notes here, erase information that you don’t need, and copy and paste text information from or to this box. On the right hand side are two list boxes: at the top is a list of all of the beds in the model. You can control which beds are plotted by toggling the checkbox in the corresponding bedding row. The bottom list box contains a listing of all of the strain ellipses in the model. If you select one or more lines in this box, the corresponding ellipses in the plot will be highlighted in yellow. You can sort the list by clicking any column in the box. Finally, you can select any or all of the rows and then copy tab delimited text data to the clipboard. These data can be pasted into spreadsheet programs or other programs for further analysis and plotting.
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Using FaultFoldForward Making a New Model To start a new model, choose “New” from the File Menu. Doing so will completely erase whatever model may previously have been plotted. The characteristics of a new model is controlled by settings in two different places. The most basic settings, and those that you are likely to change relatively infrequently are set in the Model tab of the Inspector Palette (Figure 3), a floating window that you can make visible by choosing it from the Windows Menu. The parameters in the New Model group box, especially the length of beds, spacing between points on a bed, and slip increment can markedly affect your model run times. With the settings shown in Figure 3, each bed will be a polygon of 500 vertices. If Figure 3. The Model tab of you have a total slip of 100, the model will be recalcuthe Inspector Window lated 50 times (a slip increment of 2 units). If you were to change the bed point spacing and the slip increment to 1 each, you would increase the number of calculations by a factor of 4. The calculations would be marginally more accurate but usually not enough to merit the increased processing overhead. One could further increase the speed by unchecking strain and particle paths if you were sure that you wouldn’t need those later on. In my experience, particle paths are seldom used by strain is frequently used so the defaults shown in Figure 3 are my preferences. Turning on or off strain and particle paths only has an effect if done before a new model run. You cannot, for instance, turn on strain midway through a model run. You can set the default backlimb kinematic fold model to either parallel or similar folding. If you choose the latter, you should also specify an oblique shear angle. This angle, commonly referred to as alpha in the literature is given as the deviation from vertical. Figure 3 shows a shear angle of zero, which means that the shear planes will be vertical. By convention, antithetic shear planes — those which dip opposite to the dip of the fault — are positive and synthetic shear planes are negative. Finally, you also specify the default characteristics of trishear fault propagation folding here. The linear, sine, and center concentrated fields are all as described in Zehnder and Allmendinger {%Zehnder 2000}; corrections to a typographical error in the sine field in that reference are given in Hardy and Allmendinger {%Hardy}. The backlimb kinematics and the trishear zone can be change in mid-model using the Modify -8-
Model command Model Menu.
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More common features of new models, which are likely to change with each model, are specified in the New Model dialog box (which in Mac versions of the program appears as a sheet window, sliding down from the title bar of the main menu). Most of the entries in this box are reasonably selfFigure 4. The New Model dialog box. explanatory. Positive values of all angles (dips) are inclined downwards to the left in the plot area. If you want to model a normal fault, both the slip and the P/S ratio should be negative; clicking the “normal” radio button, both of these values will be made negative automatically. Likewise, if you make either the P/ S ratio or the Slip value negative, the normal radio button will automatically be selected. If you check the “Ramp up…” button, your model will have a decollement at the level given by the “Y =” value in the preceding line; otherwise, the fault will have a constant dip downwards below the initial coordinates of the tip line. Additional bends in the fault can be added after the slip is completed by selecting Modify Model from the Model menu. If you want a fault that has multiple bends before any displacement at all has occurred — that is essentially an infinite P/S prior to the start of deformation — then check “Initial multi-bend fault”. After you click Okay, the program will wait for you to draw the fault and display a small dialog box Figure 5. Small reminder that you are still drawing a fault. (Figure 5) to remind you that you are still in faultdrawing mode and that you should double click to identify the tip line and exit from fault drawing mode. While in fault-drawing mode, every mouse click will be interpreted as a vertex on the fault. Drawing the fault happens in a different thread than the main program; if you mistakenly forget to double click for the tip line and run the model before you are finished by selecting cmd-R (Mac) or ctl-R (Windows), the program will automatically kill the thread and assume that the last clicked vertex is tip line.
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Beds are added to the model in the panel on the right hand side of the New Model dialog box (Figure 4). You can add beds by clicking the “Add Bed” button or simply press return/enter on your keyboard while editing a line and a new bed will be added automatically. If you make no entry in the Dip column, the dip for that bed will be assumed to be zero. If you mistakenly press return after the last bed, simply delete that line before pressing “Okay”. Once the new model has been defined, it will be displayed on the screen. To run the model, choose “Run” from the Model Menu. If you want to terminate a model run before it has reached the full slip specified in the New Model dialog, just click the mouse. Running a model happens in a separate thread so that you can change what to plot while the model is running (e.g., turn on or off display of ellipses, for example); however, you should do this via key commands (cmd- or ctl-E in the case of ellipse plotting) because if you use the mouse to make a menu selection, the program will interpret the click to mean stop the run early. If this happens, you can just choose Run again from the Model Menu to complete the run. Finally, if your model has run to the specified slip and you want to continue with the same parameters, simply choosing Run again will not work because the model has already reached the specified slip. In that case, you have two options: The easiest is simply to choose “Continue” from the Model Menu (cmd- or ctl-K); the model will then be run by the same increment of slip as the initial increment. For example, if you set the total slip to be 100 units in the New Model dialog, running the model will result in 100 units of slip, choosing Continue once will result in another 100 units of slip (i.e., 200 units total) and each subsequent time you choose Continue, you will get 100 more units. This is an excellent way to produce growth strata, for example, with even increments of slip. The other way to continue running the model with more total slip is to choose Modify Model from the Model Menu and then enter a new value for the slip. Modifying Your Model After your model has stopped running, you may modify it in three different ways: (1) Change the parameters for the active fault, (2) add one or more beds, or (3) as a new fault in a different part of the sections. To change the parameters for the current active fault, use the Modify Model dialog (Figure 6) which you access from the Model Menu. Note that you can change several characteristics including the backlimb kinematics and the type of trishear propagation. The Display increment
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Figure 6. The Modify Model dialog box.
determines how often the screen is refreshed during a model run. It does not change the slip increment, but will make a model run come to conclusion faster because the program will not have to take time to redraw the screen. Another way to modify an existing model is to add new beds to it. Doing so simulates growth strata deposition during deformation and you can reproduce many of the classic growth strata geometries with FaultFoldForward. To add beds select “Add Beds” from the Model Menu and you will get the dialog box shown in Figure 7. A new bed will already be added and the cell for specifying the top ready to receive input. Like the bedding part of the New Model dialog, you can just press return to enter another bed, or use the Add bed button. For your reference, all of the beds are displayed in this dialog. Beds that are added after the start of deformation are referred to as “growth strata” in the Inspector, where they can be assigned a different color and/or line weight. Finally, you can add a new fault to your existing section by choosing “Start New Fault” from the Model Menu. This dialog (Figure 8) works exactly like the left side of the New Model dialog. The fault can be normal or reverse, ramp up from a decollement, or you can draw it with initial multiple bends. A section can have only one active fault. Once you click Okay the previously active fault is re-digitized with a spacing between vertices of two and it deforms passively just like beds. Old faults can never be reactivated once you have drawn a new fault. To “reactivate” along the same trace as the old fault you will have to define a new fault with the exact same trace as the old fault. This can be done surprisingly successfully, albeit somewhat tediously!
Figure 7. The Add Beds dialog box.
Figure 8. The Start New Fault dialog box.
Modifying Your Plot At any time during you use of the program, you determine what gets plotted by making selections in the Plot Menu. If an item is checked in the menu, it will be plotted (assuming it has be calculated -- e.g., particle paths will not be plotted if they have not been calculated, even if they are checked in this menu).
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Colors, line widths, etc. are controlled by the “Strain” and “Appearance” tabs of the Inspector Window (Figures 9a and b). Note that here you can specify that ellipses be colored according to their strain magnitude by checking the box “Color fill by strain magnitude. If you want to have the fill but not the outline, just set the line weights to zero for both normal ellipses and every 5th ellipse. The color scale for the magnitude at present is hardwired and cannot be changed. To change any of the other colors, click on the color box to the right; a standard system color picker will be displayed. Changes in the Inspector are instantaneously reflected in the plot window Saving and Importing an Old Model Models can be exported to disk as a text file by selecting “Export:Forward Model” from the File Menu. Such text files retain all strain information but any special formatting beyond the default colors and line widths is not retained. You can read back into the program any file that you have exported. Doing so will erase whatever plot is currently on the screen, though not the ad hoc beds. The import and export text file formats are the same as those used by earlier versions of FaultFold and so should be interchangeable. Eventually, the program will have a native binary file format which will capture the exact state of the program, including all formatting, etc. The program capabilities need to stabilize further before implementing a permanent file format
Figure 9. (a) The Strain tab and (b) the Appearance tab of the Inspector.
Making more complicated models using pictures and ad hoc beds FaultFoldForward can create surprisingly complicated structural models from very simple starting geometries with layer-cake stratigraphy (e.g., Figure 1). Normally, forward model beds are linear with constant dip, even thought he earth is considerably more complicated than that. In the real Earth, beds pinch out or have other pre-existing complicated geometries. Thus, in addition to forward model beds (i.e., what you enter in the New Model or Add beds dialog boxes) the program offers a second type of bed, ad hoc beds, which provide a unique solution with multiple applications:
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Ad Hoc Beds
Ad hoc beds are beds in the same coordinate system as the forward model beds that the program keeps track of. Unlike forward model beds, ad hoc beds are never deformed when running a model. Ad hoc beds are entered by drawing polygons on the screen. These polygons can be as complicated as you like, can have gaps or breaks, and can start and end wherever you want on the screen. You can at any time convert ad hoc beds into forward model beds, and forward model beds can be duplicated as ad hoc beds. Some potential uses of ad hoc beds include: • Provide a frame of reference for comparing two forward models. In this case, you would run the first forward model, then convert it to ad hoc beds, then run the second ad hoc model. For example, in figure 10, a forward model was run with a slip increment of 2. It was then converted to ad hoc beds (colored red) and the same model was run again with a slip increment of 10 (in black) in order to see how slip increment influences fold shape.
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Figure 10. Example of using ad hoc beds to compare the results of two different model runs. The red beds were run with a slip increment of 2 and the black beds with a slip increment of 10.
• Provide a mechanism for producing more complicated starting models. In this case, one can simply draw on screen the starting geometry (or tracing on screen an imported picture such as a photograph, seismic section, or pre-existing cross section; see the section on Pictures, below). For example, the two plots below (Figure 11) show a more complicated geometry draw on the screen as ad hoc beds (a simple rift scenario with some beds trun-13-
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cated below a gentle angular unconformity), converted to a forward model, and then reactivated as a high angle reverse fault. 400
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Figure 11. Example of using ad hoc beds to enter a more complicated bed geometry (left side), which can then be converted to, and deformed as, a forward model (right side).
Ad hoc beds have a variety of other uses but these cover two of the most frequent. Using Pictures
FaultFoldForward can read in existing graphics files as .png, .tif, .jpg, or .pdf format by selecting “Open:Picture” from the File Menu. These pictures can be of just about anything, but realistically they are most likely to be a photograph of an outcrop, scan of a seismic line, or some previously published cross section and/or reconstruction. By default, the picture is placed at the top of, and scaled to the width of, the window, and is displayed at 50% transparent. The transparency can be controlled, from completely transparent to completely opaque, by the slider in the Appearance Tab of the Inspector (Figure 9b). This is convenient because it is easiest to trace over a part of a picture when it is partly transparent. You can move the picture around and shrink or expand it to suit your needs by choosing “Picture Scale and Position” from the Digitize Menu. The resulting dialog box (Figure 12). Note that if you click the “fit window width” radio button the picture will be returned to its default position at the top of and with the current width of the drawing area. Although you can set the offset of the picture from its current to its new position, you may find it easier to check “set offset by clicking and dragging the mouse”. Once you click Okay, the dialog box will not disappear but will remind you to click and drag. Click on the exact point that you want and drag it to the Figure 12. Scaling and repositioning a picture point that you want it to be once repositioned. As -14-
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soon as you release the mouse button, the picture will be redraw in its new location and the dialog box will disappear. A particularly convenient work flow is to position the picture where you want, and then set the scale and origin of the model. To set the scale, first click and drag on a known distance in your model and note the number of pixels displayed in the status bar. Then select “Set Scale and Origin” from the Model Menu. In the Set Scale and Origin dialog, to produce Figure 13, I entered 253 pixels = 25000 units (meters) and set the origin with the mouse by clicking at the east (right) end of the section.
Figure 13. A picture repositioned and scaled, and then with the scale of the model and the origin set according to the scale on screen in the picture.
Pictures and ad hoc beds combined allow you to develop powerful and complicated models to study. They will acquire even more utility when inverse modeling returns to the program.
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Acknowledgments The PDF classes included in this program are from pdfFile by Toby W. Rush Copyright © 2004. I would like to thank Néstor Cardozo, Alan Zehnder, Ernesto Cristallini, and Stuart Hardy for their contributions and collaborations over the years.
Selected References Allmendinger, R. W., 1998, Inverse and forward numerical modeling of trishear faultpropagation folds: Tectonics, v. 17, no. 4, p. 640-656. Allmendinger, R. W., 1999, Propagation-to-slip ratio and fold style in fault-propagation folds: perspectives gleaned from trishear modeling, in Geological Society of America Abstracts with Programs: . Allmendinger, R. W., 2004, Evaluating uncertainty in balanced cross-sections: A critical step for relating thrust-belts to plateau uplift: Geological Society of America Abstracts with Programs, v. 36, no. 5, p. 49. Allmendinger, R. W., Cardozo, N. C., and Fisher, D., 2012, Structural Geology Algorithms: Vectors & Tensors: Cambridge, England, Cambridge University Press, 289 pp. Allmendinger, R. W., and Shaw, J. H., 2000, Estimation of fault propagation distance from fold shape: Implications for earthquake seismicity: Geology, v. 28, no. 12, p. 1099-1102. Allmendinger, R. W., Zapata, T. R., Manceda, R., and Dzelalija, F., 2004, Trishear kinematic modeling of structures, with examples from the Neuquén Basin, Argentina, in McClay, K., ed., Thrust tectonics and hydrocarbon Systems: Tulsa, American Association of Petroleum Geologists, Memoir, p. 356-371. Cardozo, N., 2005, Trishear modeling of fold bedding data along a topographic profile: Journal of Structural Geology, v. 27, no. 3, p. 495-502. Cardozo, N., 2008, Trishear in 3D: Algorithms, implementation, and limitations: Journal of Structural Geology, v. 30, p. 327-340, doi: 10.1016/j.jsg.2007.12.003. Cardozo, N., and Aanonsen, S., 2009, Optimized trishear inverse modeling: Journal of Structural Geology, v. 31, no. 6, p. 546-560. Cardozo, N., Bawa-Bhalla, K., Zehnder, A. T., and Allmendinger, R. W., 2003, Mechanical models of fault propagation folds and comparison to the trishear kinematic model: Journal of Structural Geology, v. 25, no. 1, p. 1-18.
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Cardozo, N., Jackson, C. A. L., and Whipp, P. S., 2011, Determining the uniqueness of best-fit trishear models: Journal of Structural Geology, . Cristallini, E. O., and Allmendinger, R. W., 1999, Pseudo-3d Numerical Analysis of the Trishear Fault-propagation Fold Model: Geological Society of America Abstracts with Programs, v. 31, no. 7, p. 127. Cristallini, E. O., and Allmendinger, R. W., 2001, Pseudo 3-D modeling of trishear faultpropagation folding: Journal of Structural Geology, v. 23, no. 12, p. 1883-1900. Cristallini, E. O., and Allmendinger, R. W., 2002, Back-limb trishear: A kinematic model for curved folds developed over angular fault bends: Journal of Structural Geology, v. 23, no. 2, p. 289-296. Cristallini, E. O., Giambiagi, L., and Allmendinger, R. W., 2004, True 3-D trishear: A kinematic model for strike-slip and oblique-slip deformation: Geological Society of America Bulletin, v. 116, no. 7/8, p. 938-952, doi: 10.1130/B25273.1. Erslev, E. A., 1991, Trishear fault-propagation folding: Geology, v. 19, no. 6, p. 617-620. Erslev, E. A., and Mayborn, K. R., 1997, Multiple geometries and modes of faultpropagation folding in the Canadian thrust belt: Journal of Structural Geology, v. 19, no. 3-4, p. 321-335. Erslev, E. A., and Rogers, J. L., 1993, Basement-cover geometry of Laramide faultpropagation folds, in Schmidt, C. J. and others, eds., Laramide basement deformation in the Rocky Mountain foreland of the Western United States: Boulder, Colorado, Geological Society of America, p. 125-146. Finch, E., Hardy, S., and Gawthorpe, R., 2003, Discrete element modelling of contractional fault-propagation folding above rigid basement fault blocks: Journal of Structural Geology, v. 25, no. 4, p. 515-528. Fischer, M. P., and Wilkerson, M. S., 2000, Predicting the orientation of joints from fold shape: Results of pseudo–three-dimensional modeling and curvature analysis: Geology, v. 28, no. 1, p. 15-18. Hardy, S., 1995, A method for quantifying the kinematics of fault-bend folding: Journal of Structural Geology, v. 17, no. 12, p. 1785-1788, doi: 10.1016/0191-8141(95)00077-Q. Hardy, S., 1997, A velocity description of constant-thickness fault-propagation folding: Journal of Structural Geology, v. 19, no. 6, p. 893-896. Hardy, S., and Allmendinger, R. W., in press, Trishear: A review of kinematics, mechanics, and applications, in McClay, K. and others, eds., Thrust fault related folding: Tulsa, Oklahoma, American Association of Petroleum Geologists.
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Hardy, S., and Ford, M., 1997, Numerical modelling of trishear fault-propagation folding and associated growth strata: Tectonics, v. 16, no. 5, p. 841-854. Hardy, S., and McClay, K., 1999, Kinematic modelling of extensional fault-propagation folding: Journal of Structural Geology, v. 21, p. 695-702. Hardy, S., and Poblet, J., 1995, The velocity description of deformation, Paper 2: Sediment geometries associated with fault-bend and fault-propagation folds: Marine and Petroleum Geology, v. 12, p. 165-176. Hardy, S., Poblet, J., McClay, K., and Waltham, D., 1996, Mathematical modelling of growth strata associated with fault-related fold structures, in Buchanan, P. G. and Nieuwland, D. A., eds., Modern developments in structural interpretation, validation and modelling: London, The Geological Society, p. 265-282. Jin, G., and Groshong, R. H. J., 2006, Trishear kinematic modeling of extensional faultpropagation folding: Journal of Structural Geology, v. 28, p. 170-183. Johnson, K. M., and Johnson, A. M., 2002, Mechanical models of trishear-like folds: Journal of Structural Geology, v. 24, no. 2, p. 277-287. Medwedeff, D. A., 1989, Growth fault-bend folding at southeast Lost Hills, San Joaquin Valley, California: American Association of Petroleum Geologists Bulletin, v. 73, no. 1, p. 54-67. Medwedeff, D. A., and Suppe, J., 1997, Multibend fault-bend folding: Journal of Structural Geology, v. 19, no. 3-4, p. 279-292. Mitra, S., and Mount, V. S., 1998, Foreland basement-involved structures: American Association of Petroleum Geologists Bulletin, v. 82, no. 1, p. 70-109. Molinero, J., Colombo, F., and Hardy, S., 1996, Disposición geométrica profunda de los materiales terciarios en el corte del río Najerilla (Sector Riojano de la cuenca del Ebro): Geogaceta, v. 20, no. 4, p. 792-795. Patton, T. L., and Fletcher, R. C., 1995, Mathematical block-motion model for deformation of a layer above a buried fault of arbitrary dip and sense of slip: Journal of Structural Geology, v. 17, no. 10, p. 1455-1472. [NO STYLE for: Hardy 2001]. Rodgers, D. A., and Rizer, W. D., 1981, Deformation and secondary faulting near the leading edge of a thrust fault, in McClay, K. R. and Price, N. J., eds., Thrust and nappe tectonics: London, Geological Society of London, p. 65-77. Shaw, J. H., and Shearer, P. M., 1999, An elusive blind-thrust fault beneath metropolitan Los Angeles: Science, v. 283, p. 1516-1518.
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