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User Manual - Frederick Vollmer

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1. i i A gt T i I imagery Date 9 20 2013 41 45 47 477 N 74 09 22 32 W elev 456m eyealt 485m Figure 7 2 Example data from the file Sky Top viewed in Google Earth Example data types are SO bedding red S1 cleavage blue J joints green and a lineation L magenta 7 4 Orientation Fields and Domain Analysis Spherical projections aid in the orientation analysis of data but they do not show their spacial distribution Therefore Orient provides tools for analyzing the spacial variation of orientation data including orientation fields and structural domain analysis Orientation fields are a way to look for regional patterns in data by defining eigenfoliations and eigenlineations on a grid over the area Vollmer 1990 One method is to define discrete subdomains that include all data within them for example a one kilometer square area A second method is to apply a weighting function to produce area smoothed orientation values For example a common problem in mapping areas of complex geologic structure is to identify cylindrical domains within the map area Ramsay 1967 Figure 7 3 is an equal area lower hemisphere 49 projection of poles to foliations from the Doverfjell mountains Norway and Figure 7 4 is a modified Kamb contour plot of the data Their spacial distribution 1s shown in Figure 7 5 plotted using the Orientation Map command 180 Figure 7 3 Lower hemisphere equal area projection of poles t
2. 23 Figures 4 10 4 11 and 4 12 illustrate the geometric definition polar net and meridianal net respectively The term azimuthal indicates that like stereographic and orthographic projections lines passing through the center have true direction and that it is projected onto a plane This distinguishes it from other equal area projections which include the projection of a sphere onto conical and other surfaces however in structural geology it can usually be referred to simply as an equal area projection without ambiguity The projection is also known as the Schmidt projection after W Schmidt who first used it in structural geology in 1925 Schmidt 1925 Turner and Weiss 1963 and the meridianal equal area net is known as a Schmidt net Knopf and Ingerson 1938 Billings 1942 Sander 1948 1950 1970 sei ii z LLAIN HHN f UT TPES l l iSoTuu amawa nATE EHT SHE QO aaa ry ey Figure 4 10 Geometric definition of Figure 4 11 Polar equal area Figure 4 12 Meridianal equal the equal area projection net or Billings net area net or Schmidt net The Schmidt net Figure 4 12 is not a stereonet Figure 4 6 The stereonet is constructed using the stereographic projection Bucher 1944 Figure 4 5 and should not be used for plotting data Figure 4 8 Schmidt nets are required for unbiased data analysis and can also be used to solve most common geometric problems encountered in structural geology 4 5
3. 2 3 Data Entry Each data point must include a pair of angles specifying its orientation in space The first angle is measured in a horizontal plane 0 and the second in a vertical plane 0 For typical geologic data these are strike and dip for planes and trend and plunge for lines However all common units are supported Table 2 1 Two dimensional data require horizontal angles only Before entering data select the desired data format using the Data Orientation Units command You may also wish to hide or show appropriate columns using the View Data Columns command Separate columns are used for planes and for lines so make sure the required columns are visible The Type column can contain any alphanumeric identifier for example SO and S1 are often used in geology to designate bedding and cleavage This is optional but is required if multiple data types are entered in a single file All settings such as symbol sizes and color are saved for each type Additional data attributes include station identifiers location coordinates domains and comments Table 2 2 Orient does several automatic data conversions If data is entered as a bearing with compass quadrants it is automatically converted to a numerical azimuth Bearings are given as degrees east or west of north or south for example N30W will be converted to 330 A conversion is also done for planes in strike and dip or strike left and dip formats if a dip octant N NE E SE S
4. Figure 1 3 Upper and lower hemisphere equal area projection of directed data magnetic remanence directions from Precambrian volcanics with modified Kamb contours at 20 density data from Schmidt and Embleton 1985 in Fisher et al 1987 Data can be input as spherical coordinates longitude and latitude azimuth and altitude declination and inclination trend and plunge strike and dip or other measurements Orient does kinematic analysis of fault data which is represented by a plane and the direction of slip within that plane by generating P and T kinematic axes tangent line diagrams Figure 1 4 and beachball plots Figure 1 5 Spherical projections represent data orientations but not spacial locations Orient therefore includes orientation maps to analyze spacial distributions of orientation data such as the location of domains of cylindrical folding in polydeformed regions Figures 1 6 and 1 7 Orient can plot the distribution of data globally Figure 1 8 and integrates with internet maps like Google Maps and with Google Earth 180 Figure 1 4 Lower hemisphere equal area slip tangent plot of 38 normal faults from Crete Greece Each data point is defined by both a plane and a directed line data from Angilier 1979 4 4 l i i n a ff ff a r T il ee ee ee a ee ee ll Figure 1 6 An axial orientation field of eigenfoliation dip lines derived from 625 foliation planes Dovrefje
5. 1979 Determination of the mean principal directions of stresses for a given fault population Tectonophysics v 56 p T17 T26 Badgley P C 1959 Structural methods for the exploration geologist Harper and Brothers New York 280 pp Barnes J W 1995 Basic geologic mapping 3 Edition Open University Press Milton Keynes UK Billings M P 1942 Structural geology Prentice Hall New York 473 pp Billings M P 1954 Structural geology 2nd edition Prentice Hall New York 514 pp Bingham C 1974 An antipodally symmetric distribution on the sphere Ann Stats v 2 p 1201 1225 Bucher W H 1944 The stereographic projection a handy tool for the practical geologist Journal of Geology v 52 n 3 p 191 212 Cheeney R F 1983 Statistical methods in geology George Allen amp Unwin London 169 p Davis J C 1986 Statistics and data analysis in geology Wiley 646 pp De Sitter L U 1956 Structural Geology McGraw Hill Book Company Inc London New York Toronto 552 p Dutch S 2015 Converting UTM to latitude and longitude or vice versa www uwegb edu dutchs usefuldata utmformulas htm accessed 27 April 2015 Cheeney R F 1983 Statistical methods in geology Allen amp Unwin 169 pp Diggle P J and Fisher N I 1985 Sphere a contouring program for spherical data Computers amp Geoscience v 11 p 725 766 Donn W L and Shimer J A 1958 Graphic methods in structural geology Appleton
6. 8432 12 12922 30 141 15 S1 spaced 8466 08 12865 40 138 02 8492 01 12872 00 140 09 L Table 2 4 Example of a more complex Orient data file as displayed in a spreadsheet such as Microsoft Excel or LibreOffice with an initial file comment data locations multiple data types and data comments See Tables 2 1 and 2 2 for other possible column headers Tutorial 2 Plotting Spreadsheet Data Open a spreadsheet program such as LibreOffice or Microsoft Excel and enter the data shown in Table 2 My Orientation data file Strike Dip Trend Plunge Type O60 65 SO 10 45 SO 40 60 SO 310 60 SO 280 70 SO 90 40 FH 330 55 S1 Table 2 5 Example of an Orient data file for Tutorial 2 Enter this into a spreadsheet such as LibreOffice or Microsoft Excel Save the file using a standard format csv tsv ods xls or xlsx as Tutorial 2 Open the file in Orient using the Open icon or File Open command Press the Spherical Projection icon and you should get a plot as in Figure 2 1 If you have previously modified settings however they will still be in effect The Help Restore Defaults command can be used to reset all settings to default 11 180 Figure 2 1 Lower hemisphere equal area projection Figure 2 2 Equal area scatter plot as in Figure 2 1 of Tutorial 2 data from Table 2 5 after removing the Schmidt net and assigning colors to the data symbols
7. Vollmer F W 1995 C program for automatic contouring of spherical orientation data using a modified Kamb method Computers amp Geosciences v 21 p 31 49 Citation for the PGR plot or automated structural domain analysis Vollmer F W 1990 An application of eigenvalue methods to structural domain analysis Geological Society of America Bulletin v 102 p 786 791 Citation for use of the Orient software Vollmer F W 2015 Orient 3 a new integrated software program for orientation data analysis kinematic analysis spherical projections and Schmidt plots Geological Society of America Abstracts with Programs v 47 n 7 p 0 Citation for Orient 3 0 2 software Vollmer F W 2015 Orient 3 0 2 Spherical projection and orientation data analysis software www frederickvollmer com Citation for the Orient 3 0 2 User Manual this document Vollmer F W 2015 Orient 3 0 2 Spherical projection and orientation data analysis software user manual www frederickvollmer com il An acknowledgement such as I thank Frederick W Vollmer for the use of his Orient software Frederick W Vollmer s Orient software was used to prepare figures or even Orient was used to prepare figures is greatly appreciated Registration Please consider registering the software registration is free This helps determine usage and justify the time spent in it s upkeep To register send an email to vollmerf gmail com with your us
8. points of four different types of geologic data bedding cleavage joints and slickenside lineations For web map access select one of the locations and choose a websites from the Data Show Location menu The selected web map will display the location of the data point you can then zoom in or change display options as needed In order to display orientation data symbols as well as location Orient writes KML files for Google Earth so orientation symbols and complete data sets can be viewed Open the Preference Dialog by clicking on its icon select the Orientation Map Settings option and the Symbols pane Select the data types from the pulldown menu and check just one symbol for each data type For J check Strike select a strike line with two ticks and set Stroke Color to light green For L check Line select an arrow symbol and set Stroke Color to magenta For SO check Strike select a strike line symbol and set Stroke Color to red For S1 check Strike select a strike line with a tooth and set Stroke Color to red Press OK when done 48 Save the file as Sky Top klm using the File Export to Google Earth KML command Double click on it to open in Google Earth The location that I can see from the window in my university office should come into view with the data symbols Figure 7 2 For a quicker demonstration there 1s a copy of the resulting file in the Example Data folder a ___ Google Earth OD alsel ol e 8 2 as METT
9. 1 Introduction Orient is a fast professional easy to use spherical projection and orientation data analysis program In 1986 Orient introduced modified Kamb contouring automatic contouring on the sphere Figure 1 1 PGR Point Girdle Random diagrams orientation fields and automated structural domain analysis Vollmer 1988 1989 1990 1993 1995 Orient 3 brings a new level of accuracy and speed with many new tools including interactive data analysis coordinate conversions digitizing and integration with applications such as Microsoft Excel LibreOffice Adobe Illustrator InkScape and Google Earth Orient is for plotting and analyzing orientation data data that can be described by an axis or direction in space or equivalently by a position on a sphere or circle Examples of data that are represented by unit vectors directed or axes undirected include geologic bedding planes fault planes fault slip directions fold axes paleomagnetic vectors glacial striations current flow directions crystallographic axes earthquake epicenters cosmic ray arrival directions comet orbital planes positions of galaxies whale migration paths and the locations of objects on the Earth Orient has been written to apply to a wide variety data types however many examples come from structural geology which requires extensive manipulation and analysis of orientation data 180 180 Figure 1 1 Lower hemisphere equal area Figure 1 2 Circular f
10. Century Crofts Inc New York 180 p Fisher N I Lewis T and Embleton B J 1987 Statistical analysis of spherical data Cambridge University Press Cambridge 329 pp Fosson H 2016 Structural geology 2 Edition Cambridge University Press Cambridge 463 pp Hills E S 1963 Elements of structural geology Chapman amp Hall London 483 p Hobbs B E Means W D and Williams P F 1976 An outline of structural geology Wiley New York 571 pp Howarth R J 1999 Measurement portrayal and analysis of orientation data and the origins of early modern structural geology 1670 1967 Proceedings of the Geologists Association v 110 p 273 309 57 Kamb W B 1959 Ice petrofabric observations from Blue Glacier Washington in relation to theory and experiment Journal Geophysical Research v 64 p 1891 1909 Knopf E B and Ingerson E 1938 Structural petrology Geological Socity of America Memoir 6 270 Pp Lisle R J and Leyshorn P R 2004 Stereographic projection techniques for geologists and civil engineers 2nd edition Cambridge University Press Cambridge 112 pp Mardia K V 1972 Statistics of Directional Data Academic Press Mardia K V and Jupp P E 2000 Directional statistics John Wiley amp Sons Ltd Chichester UK 430 p Mardia K V and Zemroch P J 1977 Table of maximum likelihood estimates for the Bingham distribution Journal of Statistical Computation and Simulation
11. HW 228 amp ID Station Strike Dip Trend Plunge q 1 1 10 0 10 0 2 2 20 0 20 0 3 3 30 0 30 0 4 4 40 0 5 6 F 8 9 10 11 12 13 ES PS Strike Dip 40 0 40 0 Figure 1 10 Display of data in spreadsheet and spherical projection The data point can be selected in either window and will be highlighted in the other window Next open the Preferences Dialog by clicking its icon Select the Spherical Projection option from the pulldown menu and the Data Symbols Panel Check the Great Circle box Figure 1 11 and press OK The projection will update to show great circle arcs for each of the data points Selecting multiple rows of data in the spreadsheet will display the calculated maximum and minimum eigenvectors and display them on the spherical projection Figure 1 12 A common calculation required for geologic data analysis is to determine the intersection between two planes such as bedding and cleavage to find the predicted fold axis To do this in Orient select the two planes the result is displayed in the status bar and plotted on the spherical projection Figure 1 12 Finally click on the Circular Histogram icon to display a circular histogram or rose diagram of the data Figure 1 13 By default the data is displayed as undirected data and planes are displayed by their strikes BOK Orient Preferences BOO SP untitled Ea FA Q aa 0 Data Symbols Spherical Projection Symbols Data type De
12. Stroke Color for S D1 S D2 and S D3 to red green and blue respectively giving the map in Figure 7 15 55 As a final step prepare lower hemisphere equal area modified Kamb contour plots Section 4 7 of the three domains Figures 7 16 7 17 and 7 18 180 180 Figure 7 16 Lower hemisphere equal area Figure 7 17 Projection as in Figure 7 16 for midified Kamb contour plot of poles to domain 2 green domain in Figures 7 10 to foliation for domain 1 red domain in Figures 7 15 7 10 to 7 15 contoured at 20 180 Figure 7 18 Projection as in Figure 7 16 for domain 3 blue domain in Figures 7 10 to 7 15 56 Acknowledgements Portions of this document were initially prepared for Teaching Structural Geology Geophysics and Tectonics in the 21st Century On the Cutting Edge held July 15 19 2012 at the University of Tennessee Knoxville which rekindled my enthusiasm for completing this new version of Orient I thank the conveners Barbara Tewksbury Gregory Baker William Dunne Kip Hodges Paul Karabinos and Michael Wysession I thank Eric Erslev Steven Wojtal Haakon Fossen Josh Davis Yvette Kueiper Peter Hudleston Robert Bauer and Dazhi Jiang for discussions at various times Thanks to beta testers and bug reporters Emily Lubicich City College of New York Chistopher Gahn SUNY New Paltz Ben Michael Frieman Colorado School of Mines and Tammy Xinran He Colorado School of Mines References Angelier J
13. centered at latitude longitude 0 0 X is out Y is right Z is at the top and the plot should appear as in Figure 4 25 To center the projection at latitude longitude 41 764 74 156 open the Rotate Projection dialog Figure 4 31 Set Z as the Axis enter 74 157 into the Angle edit box and press Apply The projection 1s now centered at 0 74 157 Then set Y as the Axis enter 41 764 into the Angle edit box and press Apply The projection is now centered at 41 764 74 157 Tutorial 7 Rotations Open the file Vollmer 1981 from the Example Data folder any of the csv tsv ods xls or xlsx versions is fine in Orient and click on the Spherical Projection icon If not already done remove the Schmidt net from the background Click on the Preferences icon and locate the Net pane under the Spherical Projection settings Uncheck both Axes and Net Next in the Labels pane change the Increment to 90 the Offset to 14 and the Size to 12 In the Spherical Projection settings restore the projection to Lower hemisphere and Local coordinates In the Symbols pane uncheck Symbol for the SO data type and check both Contour and Gradient Click on the gradient paint picker and select the BCYR Blue Cyan Yellow Red preset Finally in the Contours pane set Levels to 5 This gives modified Kamb contours at 20 density levels and the plot should appear as in Figure 4 34 Use the Rotate Projection command to open the Rotate Pro
14. data row containing latitude longitude coordinates and choose a website from the Data Show Location menu 7 3 Google Earth Integration The program Google Earth is an invaluable tool in numerous areas and has become a widely used tool in geologic mapping Google provides an interface using KLM Keyhole Markup Language files that can contain geographic coordinates viewing instructions and many other details Orient uses this interface to display outcrop locations and symbols for orientation data measurements Symbols are selected from the Preference Dialog Orientation Map Settings Symbols pane where various symbols can be selected as well as color size and line width The symbol size is set in meters in the KML length edit box and the width in the KML width edit box To save the file use the File Export to Google Earth KML command Double click the resulting file to open in Google earth Tutorial 10 Web and Google Earth Integration This tutorial covers internet web maps such as Google Maps as well as Google Earth integration Open the file Sky Top from the included Example Data folder any of the provided file formats is fine csv tsv ods xls or xlsx This is a demonstration file with simulated geologic data for use in this tutorial You may wish to use the View Data Columns command to close some of the unused columns The file contains the latitude longitude coordinates of one marker location and eight simulated data
15. usages of latitude and longitude for data input A geologist typically records data locations expressed as Cartesian coordinates such as UTM Universal Transverse Mercator or as latitude and longitude pairs as well as collecting orientation data at that location Therefore it is necessary to determine whether a latitude longitude pair is meant as the location of a data point or 1f it is the data point itself The convention adopted here is that atitude longitude or lat long refer to a data point location and that atitude sphere longitude sphere or lats longs refer to the data point to be plotted on a spherical projection There is unfortunately more than one convention for strike and dip including two contradictory ones both called the right hand rule e g Ragan 2009 A distinction must be made so by default Orient uses the convention that the dip is to the right looking along the strike e g Pollard and Fletcher 2005 Twiss and Moores 2007 A second convention where the dip is to the left the thumb of the right hand points down the dip Barnes 1995 is referred to in Orient as strike left or strikel This convention can be selected using the Data Orientation Units command A third convention using a dip octant N NE E SE etc is automatically converted to one of the above as described in Section 2 3 Finally dip and dip direction are another common way of giving the orientations of plane which is also supported
16. 0 coordinate system in Orient Figure 4 29 Equal area projection of earthquake Figure 4 30 Equal area projection of earthquake epicenters as in Figure 4 25 centered at 90 0 epicenters as in Figure 4 25 centered at 90 0 the Polar coordinate system in Orient the Antipolar coordinate system in Orient 33 The standard settings provide views of data along all coordinate axes however it is also possible to select a view along an arbitrary axis using the Rotate Projection command The Rotate Projection dialog is shown in Figure 4 31 ANLO Rotate Projection Axes X Out Y Right 2 Top Longitude Sphere 0 0 Latitude Sphere 0 0 Angle W Premuliply Data type CO z Eigenvector Maximum a ee aS a XE _ Apply wed slabs mi Figure 4 31 The Rotate Projection dialog showing the settings for a rotation of 74 156 about the Z axis which is currently at the top of the projection For example to produce a projection centered at latitude longitude 41 764 74 156 first set the coordinate system to Equatorial 0 Figure 4 25 The projection is now centered at 0 0 with X out Y right and Z top Set Z as the Axis enter 74 157 into the Angle edit box and press Apply The projection is now centered at 0 74 157 Then set Y as the Axis enter 41 764 into the Angle edit box and press Apply The projection is now centered at 41 764 74 157 Figure 4 32 Equal area projection of earthquake epicenters as in F
17. Maxima and Eigenvectors Spherical orientation data is characterized by either directed unit vectors or undirected axes in space The concept of a mean value is familiar when dealing with scalar values like temperature Determining such a value for orientation data is more complex averaging trends and plunges separately does not work As with circular data a useful measure is the vector mean the center of mass for directed data The procedure for finding the mean is similar to that for directed circular data A data point on a unit sphere can be represented by three coordinates which are its direction cosines If we designate this point as the vector x xX X2 X3 then the mean vector is the averaged sum with mean resultant length R x 24 and mean direction the normalized mean vector o xR Axial data requires the computation of eigenvectors an important concept that gives best fit values or moments of inertia for tensors such as the principal stresses of a stress tensor In the context of orientation data imagine that each line passing through the center of the unit sphere is represented by a small mass at each of the two points where it pierces the sphere If the sphere were spinning it would have a tendency to spin about the axis of minimum density this is the minimum eigenvector If 1t were rolling it would have a tendency to stop with the maximum density at the bottom this 1s the maximum eigenvector the interm
18. ORIENT Orient 3 0 2 Spherical Projection and Orientation Data Analysis Software User Manual Copyright 1986 2015 Frederick W Vollmer Contents Legal Installation Introduction Tutorial 1 Quick Start Data and Coordinate Systems 2 1 Data Types 2 2 Coordinate Systems 2 3 Data Entry 2 4 Spreadsheet Integration Tutorial 2 Plotting Spreadsheet Data 2 5 Digitizing Data Circular Plots 3 1 Scatter Plots 3 2 Circular Histograms 3 3 Frequency Polygons 3 4 Circular Mean Tutorial 3 Circular Plots Spherical Projections 4 1 Geometry of Spherical Projections 4 2 Orthographic Projection 4 3 Stereographic Projection 4 4 Equal Area Projection 4 5 Maxima and Eigenvectors 4 6 Confidence Cones Tutorial 4 Scatter Plots 4 7 Contouring Tutorial 5 Contour Plots 4 8 Coordinates and Rotations Tutorial 6 Geographic Coordinates Tutorial 7 Rotations 4 9 Terminology of Spherical Projections 4 10 Schmidt Plots Kinematic Analysis Tutorial 8 Kinematic Analysis Orientation Plots 6 1 PGR Plot D oON NN 13 15 15 15 17 18 19 20 20 21 22 23 24 26 26 2 31 31 36 37 37 38 39 42 45 45 Orientation Maps 7 1 Latitude Longitude UTM Conversion Tutorial 9 UTM Conversion 7 2 Google and Web Maps Integration 7 3 Google Earth Integration Tutorial 10 Web and Google Earth Integration 7 4 Orientation Fields and Domain Analysis Tutorial 11 Domain Analysis Acknowledgem
19. P on the as a stereonet or Wulff net plane The projection 1s azimuthal so lines passing through the center of the projection have true direction these represent great circles Note that area in Figures 4 6 and 4 7 is clearly distorted the projection preserves angles is conformal but it does not preserve area An important consequence is that great Ze circles such as meridians and small circles project as circular arcs These properties make it useful for numerous geometric constructions in structural geology Bucher 1944 Phillips 1954 Donn and Shimer 1958 Badgley 1959 Lisle and Leyshorn 2004 Ragan 2009 As was recognized by Walter Schmidt in 1925 the distortion of area makes the stereographic projection unsuitable for studying rock fabrics such as crystallographic axes bedding joint and foliation measurements Plotting such data is a descriptive statistical procedure intended to identify significant clusters girdles and other patterns Figure 4 8 1s a lower hemisphere stereographic projection of of 2048 directed data points on a spherical Fibonacci grid Swinbank and Purser 2006 The points have equal densities on the sphere except at the very center but are distorted in stereographic projection Figure 4 8 Lower hemisphere stereographic Figure 4 9 Lower hemisphere equal area projection of 2048 directed data points on a projection of 2048 directed data points on a spherical Fibonacci grid Swinbank and Purser
20. SW W or NW is given The strike or strike left will be corrected if necessary For example a strike dip pair entered as 10 30W will be converted to 190 30 2 4 Spreadsheet Integration Data entered into the Orient spreadsheet can be saved in several spreadsheet formats tab separated values tsv comma separated values csv OpenDocument spreadsheet ods Microsoft Excel xls and Excel Open Office XLM xlsx These are all compatible with most spreadsheet programs including Microsoft Excel and LibreOffice Orient can also read all of these formats allowing users to enter data files into Microsoft Excel LibreOffice or other spreadsheet software The only requirements are that the data have a header row consisting of headers listed in Tables 2 1 and 2 2 and that any initial comment lines start with two slashes Table 2 3 gives a simple example and Table 2 4 gives a more complete example The simplest possible file would be a list of horizontal angles such as trends or azimuths for two dimensional analysis Three dimensional analysis also requires vertical angles such as dips or plunges The included folder Example Data has numerous examples of compatible files Open them in Excel or LibreOffice to examine them they are used in the following tutorials Column Header Abbreviation Notes ID N Integer identification number for data point Station Alphanumeric stat
21. To prepare the plot for presentation it is good to simplify it and focus on the data so change some of the settings as follows From the spherical projection window press the Preferences icon Under Spherical Projection in the Net pane turn off both Net and Axes Press Preview to see the result In the Labels pane set the Increment to 90 the Offset to 14 and the Size to 12 Next assign different colors to the data types In the Symbols pane select data type SO bedding click on the data symbol icon and assign the Fill Color blue Select data type S1 cleavage and assign its fill color to green and FH a fold hinge yellow Press Preview and the plot should be as shown in Figure 2 2 Now add great circles to represent the planes In the Symbols pane select data type SO again and check the Great circle box Then select data type S1 check the Great circle box and set the Stroke Color to green Figure 2 3 A plot of planes represented by their great circles is a p beta diagram With a lot of data this type of diagram becomes crowded and loses any statistical significance but for a small number of points it can help with visualization A plot with planes represented by their poles is a pi diagram or S pole diagram and is preferred over a P diagram as a better statistical representation 12 180 Figure 2 3 Equal area plot as in Figure 2 2 with Figure 2 4 Equal area plot as in Figure 2 3 with planes represented as great circl
22. al distribution is a familiar model for scalar data Using these models confidence cones can be drawn around either the mean direction or the eigenvectors Fisher et al 1987 Three models are used in Orient to draw confidence cones the Fisher distribution for rotationally symmetric directed data the Watson distribution for rotationally symmetric axial data and the Bingham distribution for non rotationally symmetric axial data Each of these can be set at confidence levels of 90 95 or 99 Figure 4 15 1s an example of 99 confidence cones using the Bingham distribution for the folded bedding data Note that because of the strong girdle pattern in this data the confidence cone radii about the minimum eigenvector are small while the maximum is strongly elliptical within the girdle This shows that the minimum is well constrained while the position of the maximum within the girdle is less well defined 180 Figure 4 15 Bedding data as in Figure 4 13 with 99 Bingham confidence cones The axes are colored as in Figure 4 14 Tutorial 4 Scatter Plots Open the file Vollmer 1981a from the Example Data folder any of the csv tsv ods xls or xlsx versions 1s fine in Orient and click on the Spherical Projection icon If not already done remove the Schmidt net from the background Click on the Preferences icon and locate the Net pane under the Spherical Projection settings Uncheck both Axes and Net Next in the Labels pa
23. an For SL P check Visible uncheck Contour and Gradient and set the Symbol Fill color to red In the Kinematics pane check Beachball The resulting plot is shown in Figure 5 6 44 6 Orientation Plots 6 1 PGR Plot A triangular PGR Point Girdle Random eigenvalue plot is particularly useful when a summary diagram is required of numerous data sets On the PGR plot a single point summarizes the type of orientation data distribution among point or cluster girdle and random or uniform distributions The PGR plot is also used in map domain analysis where domains are defined in the Orientation Map portion of the program by maximizing the total cylindricity index Given the orientation matrix eigenvectors Ej 2 and E for n data points where the magnitudes gt gt 3 the following are defined Vollmer 1989 Point P n Girdle G 2 n Random R 3 n Cylindricity C P G these have the property that P Gt R 1 and form the basis of the triangular PGR plot Cylindrical data sets plot near the top of the graph along the P G join point distributions plot near the upper left P girdle distributions plot near the upper right G and random or uniformly distributed data will plot near the bottom of the graph R Figure 6 1 is a plot of bedding plane poles from a cylindrical fold in Ordovician graywackes Vollmer 1981 and Figure 6 2 1s the corresponding PGR graph These indicate a well def
24. ation of a three dimensional structure Phillips 1954 Following Bucher 1944 equal area stereogram is a contradiction 4 10 Schmidt Plots The Schmidt net Schmidt 1925 was widely used in structural geology Billings 1942 Knopf and Ingerson 1938 Turner and Weiss 1963 prior to the introduction of the stereonet Bucher 1944 Billings 1952 Phillips 1954 however it 1s common to see spherical projection scatter plots Section 4 4 and contour plots Section 4 7 mislabeled as stereonets As they are not stereonets Figure 4 7 what they actually represent and the projection used to make them 1s unclear The equal area projection and the Schmidt net have a long and important history in structural geology mislabeling them as stereonets does not give due credit In 1925 Schmidt recognized that the stereographic projection was not suitable for orientation data analysis and invented the Schmidt net 90 years ago Although diagrams produced using Schmidt s equal area method Schmidt 1925 are ubiquitous in structural geology and tectonics no succinct term exists for them The term Schmidt plot therefore is suggested for a lower hemisphere Lambert azimuthal equal area spherical projection of three dimensional orientation data such as foliation planes joints slickensides magnetic vectors crystallographic axes fold axes and lineations Vollmer 2015 These plots which are often contoured e g Figures 4 17 and 4 18 have been in comm
25. axes respectively and fault kinematic analysis can therefore done by examining populations of P and T axes using moment tensors Marrett and Allmendinger 1990 When fault data is entered in Orient normally a strike and dip for a fault plane and a trend and plunge for a slip lineation Orient automatically generates M planes P axes and T axes An extension 1s added to the data type indicate each of the five data elements Table 5 1 Data Type Extension Data Element 3 Plane fault slickenside or shear plane L Line slip direction slickenline or shear direction M M movement plane P P shortening axis T T extension axis Table 5 1 Data type extensions automatically generated for kinematic data Each of these extended data types can be plotted and analyzed independently For kinematic analysis the P and T axes are contoured Section 4 7 and their maximum values and scatter determined by eigenvector analysis Section 4 5 Figures 5 3 and 5 4 and for the construction of beachball diagrams Figure 5 5 270 180 Figure 5 3 Lower hemisphere equal area projection of poles to M planes green P shortening axes red and T extension axes blue for data in Figure I2 4 180 180 Figure 5 4 Lower hemisphere equal area Figure 5 5 Projection as in Figure 5 3 with modified Kamb contour plot of the fault data contours on the T extension axes from Figure 5 2 with 10 density contours on t
26. be given as lower hemisphere equal area projection Note that other spherical equal area projections exist such as the cylindrical equal area projection Snyder 1985 Additionally hyperboloidal equal area and stereographic projections exist and are used for some geologic data Yamaji 2008 Vollmer 2011 For brevity and to avoid ambiguity the succinct name Schmidt plot has been proposed Vollmer 2015 Section 4 10 37 Early references Schmidt 1925 Billings 1942 1954 Bucher 1944 Sander 1948 1950 1970 Phillips 1954 De Sitter 1956 Donn and Shimer 1958 Badgley 1959 Turner and Weiss 1963 Hills 1963 Whitten 1966 Ramsay 1967 Hobbs et al 1976 are careful to use correct terminology as are most current structural geology texts e g Marshak and Mitra 1988 Van der Pluijm and Marshak 2004 Pollard and Fletcher 2005 Twiss and Moores 2007 Ragan 2009 Fossen 2016 Note that e The equal area projection is not a type of stereographic projection e Astereonet or Wulff net is a stereographic net Figure 4 7 e A Schmidt net or equal area net Figure 4 12 is not a stereonet e Scatter plots and contour plots are not stereonets e The phrase equal area stereonet is a contradiction e The phrase equal area stereographic projection is a contradiction The term stereogram was defined as a diagram produced by stereographic projection Bucher 1944 however the term was previously used to refer to a planar represent
27. ctor for S D1 S D2 and S D3 and set the fill and stroke colors the same The result should be as in Figure 7 12 Note that the three domains show well defined girdles Turning off the data symbols give Figure 7 13 which suggests refolding of earlier folds about a northwest plunging axis Next open a PGR Point Girdle Random plot using the PGR Plot icon he data spreadsheet window In the Preferences dialog PGR Plot Symbols pane set the Symbol Fill Color for S to white and then for S D1 S D2 and S D3 to red green and blue respectively and increase the symbol sizes to 16 The resulting PGR plot Figure 7 14 shows the relative changes in cylindricity from the whole area to the three domains Note that domain 2 green has the strongest point distribution and domain 3 blue has the strongest girdle distribution 54 270 180 Figure 7 12 Lower hemisphere equal area Figure 7 13 Synoptic plot of best fit girdles and projection of data from Figure 7 3 with foliation axes of data shown in Figure 7 12 poles color coded by domain and the great circle normal to the minimum eigenvector drawn for each domain _ i Ko pon Ld H if R x Figure 7 14 PGR graph of the three domains compared to the total data set white Figure 7 15 Data from Figure 7 5 color coded by domain To clean up the map turn off the display of the maxima in the Orientation Map Maxima pane turn off display of data type S symbols and set Strike on with
28. de or the counterclockwise angle from X in the XY plane and that o is the colatitude the angle from Z However there are numerous ways to specify the same information with two angles typically specified by the scientific discipline such as geology geography or astronomy e g Fisher et al 1987 Mardia and Jupp 2000 Planes are represented by their normal or pole Alternatively coordinates can be specified by three direction cosines in this coordinate system which are the coordinates of points on a unit sphere In Orient the user can specify 9 and for lines and planes according to their data or discipline Table 1 Geographic data are generally given using longitude as the horizontal angle the vertical angle 1s commonly latitude or colatitude azimuth and altitude are used in astronomy Geologic data however are typically specified using azimuths for horizontal angles measured clockwise from North Y and dips or plunges for vertical angles measured down from horizontal the XY plane Geologic angles are typically strike and dip for planes or trend and plunge for lines Orient supports all common conventions Table 1 and converts among them Column Header Abbreviation Plane 0 Horizontal orientation angle of plane Strike Clockwise from North Y dip is to right along strike Strike left strikel Clockwise from North Y dip is to left along strike Dip direction dipdir Azimuth of dip line Vertical orientation angle of plane Ang
29. des sets the number of calculated grid points the default of 100 gives 10000 calculated nodes A value of 30 is the approximate minimum for acceptable contours but Orient is very fast so there is little to be gained by decreasing this from 100 Increasing this for example to 200 gives little additional detail In the Spherical Projection Contours panel select either Contour levels the default or Contour interval If levels is selected enter the number of levels for example 10 for contours at 10 density or 5 for contours at 20 density If Contour interval is selected then enter the Interval and the Minimum and Maximum Contours Finally check Fill contours to fill the contours using the Gradient fill Figure 4 21 illustrates contouring with Gradient on and Figure 4 20 with Gradient and Fill contours on With the gradient option on the density is calculated at each pixel on the default page size this is approximately a half a million pixels For comparison with the scatter plots in Figures 4 13 4 14 and 4 15 Figure 4 23 is a modified Kamb contour plot of the same bedding data 29 180 180 Figure 4 21 Modified Kamb contour plot of data Figure 4 22 Modified Kamb contour plot of data shown in Figure 4 16 with contours at 10 shown in Figure 4 16 with contours at 10 density and the Gradient option on density and the Gradient and Fill contours options on 0 180 Figure 4 23 Lower hemisphere equal area projection of poles
30. e System Preferences and the Security amp Privacy option Under General select Allow apps downloaded from Anywhere On Windows unzip the zip file zip using the Extract All option and drag the Orient folder to any desired location The Orient folder contains the Orient application Orient exe and a Resources folder which is required Make sure to entirely extract the Orient folder from the zip file this is the most common installation problem On Linux unpack the gzip file tgz and copy the Orient folder to any desired location The Orient folder contains the Orient application orient and a Resources folder which is required An application icon orient png is included in the Resources folder if desired for installation The Example Data folder should also be copied for use in the tutorials After installing a new version you may wish to reset the preferences using the Restore Defaults command in the Help menu This will clear any options that may have changed and set them to default values The preferences are stored in the file Orient3 xml which is located in the folder Orient in your operating system s application preferences folder To deinstall simply delete the Orient application folder and optionally delete the preference folder No other files are installed on your computer No administrative permissions are required to install Orient and it is possible to keep a copy on a thumb drive to run on any computer
31. e angle between the pole and slip line Arrows are tangent lines that show the displacement sense of the hanging wall with respect to the footwall Two additional kinematic axes can be defined within the M plane at 45 from the lineation Figure 5 1 These are commonly referred to to as the P axis and T axis terms derived from first motion studies in seismology however they should not be confused with stress axes Rather P is an incremental shortening axis and T is an extension axis 39 Figure 5 2 A lower hemisphere equal area s ip linear or pole tangent line diagram of a population of 38 Neogene normal faults from central Crete Greece The arrows through the fault pole projections show the displacement sense of the hanging wall with respect to the footwall data from Angelier 1979 180 Figure 5 3 A lower hemisphere equal area s ip tangent line diagram of the data shown in Figure 5 2 The arrows through the slip lineation projections show the displacement sense of the hanging wall with respect to the footwall data from Angelier 1979 The arrows drawn though the lineation and the fault normal are tangent lines directed lines tangent to a projected point on a sphere In Figure 5 1 tangent lines are drawn through the lineation and the fault pole projections to show the placement sense of the hanging wall with respect to the footwall They can be viewed as instantaneous rotation vectors about the M axis The term s ip l
32. e directed turtle data Figure 3 1 using 24 15 bin sectors the same size as in Figures 3 3 to 3 6 Figure 3 7 Circular frequency polygon plot or kite diagram of the directed turtle data shown in Figure 3 1 using 24 15 Figure 3 8 is an example of an undirected circular frequency polygon using the joint data Figure 3 2 also using 24 15 bins To illustrate the effect of bin size on circular histograms Figure 3 8 1s the same data plotted using 12 30 bins 17 180 180 Figure 3 9 Circular frequency polygon diagram of the joint data as in Figure 3 8 but using 12 30 sector bins Figure 3 8 Circular frequency polygon plot or kite diagram of the undirected joint data shown in Figure 3 2 using 24 15 sector bins 3 4 Circular Mean A simple measure of location or best fit to circular orientation data is the mean direction which 1s calculated as a vector sum For directed data the two sums are calculated arctan S C Since the mean resultant length approaches 1 as orientations converge it is common to cite the sample circular variance V 1 A which is 0 when all the orientations are identical For undirected data the same calculation is done however 9 is doubled prior to the summation and the result is halved For details of statistical measures 18 and tests for circular orientation data see Mardia 1972 Cheeney 1983 Davis 1985 Fisher et al 1987 and Mardia and Jupp 2000 Tutor
33. e of a hyperboloid is projected onto a plane These are used in the context of strain analysis and are unlikely to be confused with the more common spherical projections Figure 4 1 Definition of the point P on the unit sphere that defines the orientation of the undirected line L The line is trending toward X east and it s plunge is The Y coordinate axis north is into the page 4 2 Orthographic Projection The orthographic projection is an important projection in which points are projected along parallel rays as if illuminated by an infinitely distant light source Figure 4 2 gives the geometric definition of the orthographic spherical projection A corresponding orthographic polar net is shown in Figure 4 3 and an orthographic meridianal net in Figure 4 4 The projection of point P in the sphere to point P on the plane is parallel to the Cartesian axis Z effectively giving a projection following a ray from Z equals positive infinity This type of projection gives a realistic view of a distant sphere such as the moon viewed from Earth It is azimuthal but angles and area are not generally preserved When plotting geologic data it is important that area and therefore data densities are preserved so the orthographic projection unsuitable for such purposes The net does however have other uses such as the construction of block diagrams e g Ragan 2009 21 ice eRRew Pes be bay Figure 4 2 Geometric defin
34. ediate eigenvector is exactly 90 from the other two As an example Figure 4 13 is a lower hemisphere equal area scatter plot of bedding plane normals represented by points on the lower hemisphere The orientation tensor or scatter matrix Mardia and Jupp 2000 is given by 1 Ti T xx m i l the averaged sum of the unit orientation vectors times their transpose The eigenvectors of this matrix are determined and plotted In Figure 4 14 the maximum eigenvector is a red circle the intermediate green and the minimum blue In cylindrical folds the minimum eigenvector of poles to bedding gives the fold axis and a great circle drawn perpendicular to the minimum eigenvector gives the best fit through the plane poles Figure 4 14 0 180 180 Figure 4 13 Lower hemisphere equal area Figure 4 14 Projection of data as in Figure 4 13 projection or scatter plot of 56 poles to bedding in with maximum red intermediate green graywacke Albany County New York data from minimum blue eigenvectors and great circle to the Vollmer 1981 minimum eigenvector 25 For details of statistical measures and tests for spherical orientation data see Mardia 1972 Cheeney 1983 Davis 1985 Fisher et al 1987 and Mardia and Jupp 2000 4 6 Confidence Cones There are a number of models for distributions of spherical orientation data Mardia 1972 Fisher et al 1987 and Mardia and Jupp 2000 By analogy the Gaussian or norm
35. ell and adjacent Trollheimen ranges The map of foliations Figure 7 5 shows some areas of consistent orientation but the location of cylindrical domains is not obvious Click on the Orientation Map icon to display a map of the foliation data then in the Orientation Map window click on the Preferences icon In the Orientation Map Extents pane uncheck Auto scale and enter the coordinates 890 150 and 1010 300 for the minimum and maximum map extents To view the data uncheck all symbols in the Maxima pane and check only Strike in the Symbols pane The result should appear as in Figure 7 5 To set up the domain search uncheck Strike in the Symbols pane and check Strike in the Maxima pane In the Field pane the Method should be Subdomain and Directed should be unchecked Enter 12 and 15 for the number of subdomains The coordinates are UTM based in meters so this gives one square kilometer subdomains The resulting map should be as in similar to Figure 7 6 except that the strikes are not projected Press OK when done To begin the domain search select the Domain Search command form the Graph menu Figure 7 9 Press Jnitialize to set all subdomains to 1 then press Search to grow domain 2 Change the search domain to 3 and press Search again The result is should in Figure 7 10 which has a cylindricity index c 0 738 There are some edge effects particularly where domain 1 wraps around the other two Move the mouse over the map to see in
36. ents References History ii 47 47 47 48 48 48 49 53 of of 60 Legal License Orient software and accompanying documentation are Copyright 1986 2015 Frederick W Vollmer They come with no warrantees or guarantees of any kind The software is free and may be downloaded and used without cost however the author retains all rights to the source binary code and accompanying files It may not be redistributed or posted online It is requested that acknowledgment and citation be given for any usage that leads to publication This software and any related documentation are provided as is without warranty of any kind either express or implied including without limitation the implied warranties or merchantability fitness for a particular purpose or non infringement The entire risk arising out of use or performance of the software remains with you Citation Orient is the result of countless hours of work over three decades It 1s released for free in the hope that it will be useful for scientific and educational purposes Commercial institutions should contact the author with details of the intended use In return for free use any significant use of the software in analyzing data or preparing diagrams must be cited in publications presentations reports or other works One or more of the following should be cited as appropriate Citation for the modified Kamb contouring method automatic Kamb contouring on a sphere
37. er name affiliation and usage You will not be placed on any mailing list or contacted again other than my response with a thank you For example send me an email with something like User Dr Frederick Vollmer Affiliation SUNY New Paltz Geology Department Usage Research on joint orientation analysis Catskill Mountains NY fault kinematics in the Hudson Valley fold and thrust belt Teaching an undergraduate structural geology course with approximately 35 students per year If you are specific about the type of project this can help me in developing future releases If you are using Orient in a teaching environment I am interested to know the course and approximate number of students 1V Installation Orient is compiled tested and debugged on Macintosh OS X Windows and Linux Macintosh OS X 10 5 to 10 10 Windows XP 7 and 8 and Linux distributions testing and debugging done in Ubuntu only should all run without problem On Macintosh OS X double click the disk image file dmg and drag the Orient application to your Applications folder or other desired location If you get the App Can t Be Opened Gatekeeper alert message when double clicking on the Orient icon right click or control click on the icon choose Open and click the Open button at the next dialog warning to launch Orient Gatekeeper in OS X 10 7 to 10 10 must be set to allow applications other than from the Mac App Store to be opened To do so open th
38. es best fit great circle and pole given by the minimum eigenvector of SO bedding Finally add the SO maxima In the Maxima pane select the SO data type and check Visible For this plot just add the Minimum eigenvector which gives us a best fit fold axis Uncheck the Symbol for both the Maximum and Intermediate eigenvectors For the Minimum eigenvector check the Symbol and Great circle checkboxes and set their colors to red Figure 2 4 2 5 Digitizing Data When digital data files or text listings of orientation data are not available data can be digitized from scanned images of spherical projections or maps To digitize a spherical projection from a suitable source image insure that the image is undistorted that is circular and that the north point is unrotated An image editing program such as Adobe Photoshop or GIMP can remove distortion and rotate the image if necessary Open the image in Orient using the File Open Image command which will display the Digitizing Window Figure 2 5 File types tiff jpg png and bmp files are supported Click on the Digitize icon to display the Digitize Dialog Figure 2 6 Select the correct options for the spherical projection the projection options are stereographic equal area or orthographic in either upper or lower hemisphere one hopes that the original author correctly specified these Select the data type line or plane and press OK A prompt will ask for three points on the perim
39. es drawn from the center and with symbols on the perimeter Figures 3 1 and 3 2 Figure 3 1 1s a circular scatter plot of the orientations of 76 turtles after laying eggs data from Gould cited in Mardia and Jupp 2000 an example of directed circular orientation data In order to better visualize overlapping data points the opacity of the data point symbols is set to 50 Figure 3 2 is a plot of the means of two joint sets from each of 24 counties in central New York data from Parker 1942 This data is plotted as strike azimuths an example of undirected data Figure 3 1 Circular scatter plot of the orientations of Figure 3 2 Circular scatter plot of the means of two 76 turtles after laying eggs Gould s data from joint sets from each of 24 counties in central New Mardia and Jupp 2000 York data from Parker 1942 3 2 Circular Histograms Two dimensional orientation data is commonly displayed as a circular frequency histogram where the data count 1s tallied for bins or sectors of a set angular width A commonly used graph 1s a rose 15 diagram constructed with sector radii proportional to class frequency an equidistance rose diagram Figure 3 3 shows an example for directed data Unfortunately such a diagram is biased and not a true histogram because the area displayed for a single count increases with the radius An unbiased plot is an equal area circular histogram where each count has an equal area and the sector area 1s propor
40. eteorological Society v 132 n 619 p 1769 1793 Turner F J and Weiss L E 1963 Structural analysis of metamorphic tectonites McGraw Hill Book Company New York 545 pp Twiss R J 1990 Curved slickenfibers a new brittle shear sense indicator with application to a sheared serpentinite Journal of Structural Geology v 11 p 471 481 Twiss R J and Unruh J R 1998 Analysis of fault slip inversions do they constrain stress or strain rate Journal of Geophysical Research v 103 p 12205 12222 Twiss R J and Moores 2007 Structural geology 2nd edition W H Freeman New York 736 pp Van der Pluijm B A and Marshak S 2004 Earth structure 2nd edition W W Norton New York 656 p Vollmer F W 1981 Structural studies of the Ordovician flysch and melange in Albany County New York M S Thesis State University of New York at Albany Advisor W D Means 151 p Vollmer F W 1985 A structural study of the Grovudal fold nappe western Norway Ph D Thesis University of Minnesota Minneapolis Advisor P J Hudleston 233 p 58 Vollmer F W 1988 A computer model of sheath nappes formed during crustal shear in the Western Gneiss Region central Norwegian Caledonides Journal of Structural Geology v 10 p 735 743 Vollmer F W 1989 A triangular fabric plot with applications for structural analysis abstract Eos v 70 p 463 Vollmer F W 1990 An application of eigenvalue methods to structural domai
41. eter of the projection after entering these a circle will be drawn over the projection If the circle is a reasonable fit proceed to digitize the points which will appear in the Data Window spreadsheet If not the circle can be reinitialized or distortion of the image may need to be removed Spurious data points can be deleted in the spreadsheet as necessary If digitizing needs to be interrupted save the file and reopen the file and image later to resume To change data type lines or planes reopen the Digitize Dialog select the desired one press enter and continue digitizing 13 Digitizing orientation data from a map is similar Make sure the image 1s undistorted and that the X and Y directions are orthogonal with north to the top The X and Y coordinate scales do not need to be equal but they must each be scaled linearly within the map area If necessary remove any distortion using an image editor Select Map as the source the correct element line or plane and press OK There will be a prompt for two points with known coordinates to define the area and coordinates If the result is satisfactory begin digitizing the elements by clicking on a start point and then an end point The coordinates entered into the spreadsheet will be the center point between the two points 6 0 0 digitize tiff B00 Digitize E a Q a P e Projection symbol Source Spherical projection rd Map symbol Projection Equalarea si E Frame Hemisphere Lo
42. ext in the Histogram pane select the Equidistant plot Figure 3 6 and then the Frequency polygon Figure 3 8 to compare plot types 19 4 Spherical Projections A primary function of Orient is the creation and manipulation of spherical projections of orientation data in particular azimuthal spherical projections that project the surface of a sphere onto a plane This chapter discusses mathematical concepts related to spherical projections in particular the geometry of several common projections and the spherical nets which are commonly used to display and work with these projections A final section on nomenclature discuses terminology and common errors that occur in the literature 4 1 Geometry of Spherical Projections A spherical projection 1s a mathematical transformation that maps points on the surface of a sphere to points on another surface commonly a plane Astronomers cartographers geologists and others have devised numerous such projections over thousands of years however two the stereographic projection and the equal area projection are particularly useful for displaying the angular relationships among lines and planes in three dimensional space A third projection the orthographic projection 1s less commonly used but is important for some applications and is easily visualized These are azimuthal spherical projections projections of a sphere onto a plane that preserve the directions azimuths of lines passing through
43. f subtracting a subdomain from one domain and adding it to the search domain will increase the index It can only do so if both domains remain connected The user can manually edit domains moving the mouse over the map will display subdomain information in the status bar and clicking on a subdomain will add it to the search domain if possible The constraint that the domains remain connected can cause edge effects and vacant subdomains may also effect connectivity The general procedure is to do a search on a desired number of domains then manually edit them and search again to see if a better solution 1s found Once the search is completed pressing OK will assign domains to each of the data points The domains are added as attributes of the data use the View Data Columns to view the Domain column Extended data types are formed by appending domain extensions D1 to D9 to the data type so each domain can be plotted independently for example on a spherical projection 52 Tutorial 11 Domain Analysis Open the file Vollmer 1985 included Example Data folder any of the provided file formats 1s fine csv tsv ods xls or xlsx This is the data displayed in Figures 7 3 to 7 7 625 foliation planes from the Doverfjell mountains Norway While folds are clearly present the spherical projections Figure 7 3 and 7 4 do not display a girdle pattern that would indicate cylindrical folding there are spectacular sheath folds in the Doverfj
44. fault B M Symbol M Visible Ci M Great circle _ Directed E Ray Kinematics Ci C Polyline Ci Contour Gradient Preview Cancel i Teee Figure 1 11 The Orient Preferences Dialog showing spherical Figure 1 12 The projection after checking projection data symbol options the Great circle option OOO SP untitled 0o0o0o0oooaaaa a00 CH untitled ho HAAR S 0 0 ie Trend 182 Count 2 Figure 1 13 The projection after selecting all data points the minimum blue and maximum red eigenvectors are displayed Figure 1 14 Circular histogram of the data displayed in Figure 1 7 2 Data and Coordinate Systems This chapter defines the orientation data types that Orient can analyze including specification of the angles and coordinates used to describe them There are numerous ways of describing an orientation including latitude longitude trend inclination strike and others There are also many possible coordinate reference frames the basics are described here with more detail for those needing it in Section 4 8 The main goal of this chapter however is to get the user quickly started by explaining how to enter data Often it is simplest to enter the data directly into Orient s spreadsheet however Orient can read and write files compatible with spreadsheet software such as Microsoft Excel and LibreOffice and for many workers this is a better option Finally Section 2 4 explains how data can be d
45. formation about each subdomain Clicking on one will change it to the current search domain if all domains remain connected Edit the domains by selecting a search domain and clicking on the map When done go back to the dialog and search on each domain again If the domains are stable they will not change Figure 7 11 shows a stable solution with C 0 851 an improvement over the previous value Press OK when done 53 Figure 7 10 Initial automatic domain search Figure 7 11 Final domain configuration after formed by grouping the subdomains of iterative manual editing and automatic Figure 7 6 into three domains maximizing searching to find a stable configuration This cylindricity This configuration has a configuration has a cylindricity index C cylindricity index C 0 738 0 851 The map will now be cluttered with symbols as the three new domains are plotted in addition to the field Before cleaning up the map open a spherical projection by clicking on the Spherical Projection icon in the data spreadsheet window and then the Preferences dialog In the Spherical Projection Net pane uncheck Axes and Net and in the Labels pane set Increment to 90 Offset to 14 and Size to 12 as in previous tutorials In the Symbols pane for data type S uncheck Visible Then for data types S D1 S D2 and S D3 the new data types set the Symbol Fill Color to red green and blue respectively In the Maxima pane select only the Minimum eigenve
46. formatted to plot the data on a spherical projection and is not the one for this tutorial This data is a set of 14 229 earthquake epicenters between 1980 and 1990 with magnitudes greater than 4 5 data from NOAA Next open the UTM Conversion Dialog Figure 7 1 select Latitude longitude to UTM WGS 1984 and UTM latitude zone Press OK and the conversion is done Finally select View Data Columns and check Zone Easting and Northing if not already checked UTM grid zones and coordinates should all be displayed If you want to get a taste of Tutorial 9 select one of the earthquake data rows and select Data Show Location Google Maps Satellite As this is a global data set you may need to zoom out before determining where you are 47 7 2 Google and Web Maps Integration A large number of internet web sites offer access to maps including street maps topographic maps and terrain maps by entering search terms or geographic coordinates Google Maps 1s perhaps the most well known of these Orient includes integration with a number of these sites including Google Maps ACME Mapper which has many topographic maps Bing Maps Nokia HERE OpenStreetMaps and others If a data file contains latitude and longitude coordinates these can be opened directly from Orient If the data contains UTM coordinates they must first be converted to latitude longitude as covered in Section 7 1 To see the location displayed in your default browser select a
47. gration with mapping websites and integration with Google Earth Orient is designed to plot the spacial distributions of orientation data and has the capability of calculating orientation data fields that can be used to study regional tends and to do structural domain analysis For example a common problem in mapping areas of complex geological structure 1s to identify domains of cylindrical folding Orient provides unique capabilities to automatically search for such domains Vollmer 1990 7 1 UTM Latitude Longitude Conversion Orient includes UTM to latitude longtitude and latitude longtitude to UTM conversions Snyder 1987 Dutch 2015 Conversion among 14 datums including WGS 1984 an NAD 1983 is available The Data UTM Conversion Dialog Figure 7 1 can be accessed when there are either easting northing coordinates or latitude longitude coordinates Select the conversion and the desired datum The hemisphere can be specified using the UTM grid zone or by hemisphere aC UTM Conversion Conversion Latitude longitude to UTM 4 Datum WGS 1984 B Hemisphere UTM latitude zone be Cancel OK Figure 7 1 UTM latitude longitude conversion dialog Tutorial 9 UTM Conversion Open the file World Earthquakes 1980 1990 Map from the included Example Data folder any of the provided file formats is fine csv tsv ods xls or xlsx Note that the file World Earthquakes 1980 1990 Sphere is
48. he P shortening axes Figure 5 6 Lower hemisphere equal area beachball diagram showing the P shortening and T extension quadrants using the data shown in Figure 5 3 Tutorial 8 Kinematic Analysis Open the file Angelier 1979 from the Example Data folder any of the csv tsv ods xls or xlsx versions in Orient and click on the Spherical Projection icon If no settings have been previously 42 modified the projection will look as in Figure 5 7 The Help Restore Defaults command can be used to reset the preferences if desired To remove the Schmidt net from the background click on the Preferences icon and locate the Net pane under the Spherical Projection Settings Uncheck both Axes and Net Next in the Labels pane change the Increment to 90 the Offset to 14 and the Size to 12 Next go to the Symbols pane Note that there are 5 data types displayed in the Data type pulldown list Select SL P check Visible then select SL T and check Visible At this point all data type elements should be displayed with a symbol as in Figure 5 8 The first step is to prepare a pole tangent line or slip linear plot In the Symbols pane uncheck Visible for all the elements except SL S so only the poles to the fault planes are displayed Now go to the Kinematics pane and check Tangent lines The resulting plot is shown in Figure 5 2 Figure 5 7 Lower hemisphere equal area scatter Figure 5 8 Projection as in Figure 5 7 after turning
49. ial 3 Circular Plots Open the file Gould from the Example Data folder any of the csv tsv ods xls or xlsx versions is fine in Orient and click on the Circular Histogram icon If no settings have been previously modified the projection will look as in Figure 3 4 The Help Restore Defaults command can be used to reset the preferences if desired This is an example of directed circular orientation data The default display is an equal area circular histogram or rose diagram In the Circular Histogram Symbol pane this data type is displayed as Default as none was specified in the file Check Directed so this data will be treated as unit vectors instead of axes Next in the Histogram pane select the Equidistance plot Figure 3 4 and then the Frequency polygon Figure 3 5 to compare plot types Next open the file Parker 1942 This is an example of undirected circular orientation data They are treated as circular instead of spherical data because although joints are planar only the strikes were reported Note that because these are planes recorded by strike the direction plotted should be specified as Strike otherwise the plane s normal would be plotted Reset the Histogram to equal area There are two data types in this file J1 and J2 In the Symbols pane select J1 and set the Histogram Fill Color to red and uncheck Symbol for both data types J1 and J2 and uncheck Directed The resulting plot should be as in Figure 3 5 N
50. igitized from scanned images of spherical projections or maps 2 1 Orientation Data Types Orientation data are either unit vectors directed data or unit axes axial or undirected data Current flow directions for example are directed while fold axes are undirected Plotting contouring and statistical analysis of these data types is different Geometrically data represents either lines or planes On spherical projections planes and lines are considered to pass though the center of a unit sphere Planes are represented by either their great circle the intersection of the plane with the unit sphere or by their normal often referred to as the plane s pole Unit vectors or axes in three dimensions can be specified by their coordinates on the surface of the unit sphere these are the direction cosines However it is more common to specify just two independent angles a horizontal angle such as strike trend or azimuth and a vertical angle such as dip plunge or inclination Two dimensional data require a horizontal angle only Available angular measures and their definitions are listed in Table 1 and discussed in Section 2 2 Orient has separate columns for lines and for planes this allows data that contains both such as kinematic data Chapter 5 to be entered as well Unused columns can be hidden if desired by opening the Data Columns Dialog from the View Menu Angle units can be specified as either degrees 0 to 360 degrees gradia
51. igure 4 25 centered at latitude longitude 41 764 74 157 34 In examining some data sets such as crystallographic axes it may be desirable to produce a plot whose axes are related to the distribution such as the eigenvectors Fisher et al 1987 Figure 4 33 shows the Rotate Projection dialog with settings to rotate a data set to the maximum eigenvector BOM Rotate Projection Axis Maxima HA Axes X Right Y Top Z Out Trend 0 0 Plunge 0 0 Angle 41 764 W Premuliply Data type 50 Eigenvector Maximum KA Apply Undo C Revert oK ee e ARDA Figure 4 33 The Rotate Projection dialog showing the settings for a rotation to center the projection on the maximum eigenvector of the SO data type E Figure 4 34 is a lower hemisphere equal area modified Kamb contour plot of poles to bedding data shown in Figure 4 13 which is then shown rotated the maximum Figure 4 35 intermediate Figure 4 36 and minimum Figure 4 37 eigenvectors Figure 4 34 Lower hemisphere equal area Figure 4 35 Contour plot as in Figure 4 34 modified Kamb contour plot of poles to bedding rotated to the maximum eigenvector of the data from Figure 4 13 with contours at 20 density 35 Figure 4 36 Contour plot as in Figure 4 34 Figure 4 37 Contour plot as in Figure 4 34 rotated to the intermediate eigenvector of the data rotated to the minimum eigenvector of the data The final topic in this section is data rota
52. ike 180 Figure 7 9 The Mi Project Length scale 1 0 Domain Search dialog box Preview Cancel Figure 7 8 Orient Preference dialog showing the Orientation Map Symbols pane The options shown are to project strike lines as in Figure 7 6 Line is the direction of a line or of the plane normal 0 Dip line is the opposing direction 0 180 and used to display a plane s dip direction Strike is the plane strike 8 90 and Strike is the opposing direction 8 90 Only Line and Dip line can be projected To display a projected strike symbol select Dip line and the strike symbol shaped like a sideways T Figures 7 6 and 7 8 The Length scale scales the length of the symbol The KLM settings are for the display of data in Google Earth Section 7 3 To conduct a domain search define the extents of the map area in the Extents panel select the Subdomain Method in the Field panel along with the number of subdomains Then use the Domain Search command which displays the dialog shown in Figure 7 9 This is used to maximize the orientation index using an automated search process The Value is the current value of the index and N is the number of points used to calculate it Domains are numbered from 1 to 9 zero represents an unassigned domain Clear sets all subdomains to zero nitialize sets all domains to the search domain Search will attempt to grow the search domain The search process iteratively checks to see i
53. inear has been used for a tangent line drawn through the fault pole using this reference frame Marshak and Mitra 1988 Figure 5 2 shows a slip linear diagram of a population of 38 Neogene normal faults from central Crete Greece data from Angelier 1979 The term tangent lineation has been used for the tangent line drawn through the fault pole showing the placement sense of the footwall with respect to the hanging wall Twiss and Unruh 1998 Twiss and Moores 2007 However the reference frame used in Figures 5 1 and 5 2 for slip linears is compatible with the definition of fault slip as a displacement vector of the hanging wall with respect to the footwall and has priority so is the default setting Since Orient offers both conventions the term pole tangent line tangent line through the projected fault pole is used to include both slip linear and tangent lineation reference frames A second type of tangent line can be drawn through the slip lineation within in the M plane This is referred to here as a slip tangent line tangent line through the projected slip line drawn though the projected lineation towards or away from the pole to the fault Figure 5 1 This contains the same information as a pole tangent line Note that many spherical projections of fault data in the literature show ticks or arrows parallel to the trend of the slip lineation which 1s not the same The P and T axes Figure 5 1 indicate shortening and extension
54. ined girdle with a distinct maximum R 180 Figure 6 1 Lower hemisphere equal area Figure 6 2 PGR graph of data shown in Figure modified Kamp contour plot of poles to bedding 6 1 from a fold in Ordovician graywackes Albany County New York data from Vollmer 1981 45 A contour plot of ice fabric c axes Kamb 1959 is shown in Figure 6 3 which shows a much more scattered distribution and plots nearer to the bottom of the PGR graph Figure 6 4 Finally a plot of fold axes associated with the bedding data in Figure 5 1 is shown in Figure 6 5 and the associated PGR plot in Figure 6 6 showing a strong point cluster R f l Figure 6 4 PGR graph of data shown in Figure 6 3 Figure 6 3 Lower hemisphere equal area modified Kamb contour plot of ice c axes data from Kamb 1959 R Figure 6 5 Lower hemisphere equal area modified Figure 6 6 PGR plot of fold axis data in Figure Kamb contour plot of minor fold axes associated 6 5 showing strong point cluster with the bedding data in Figure 6 1 46 7 Orientation Maps Spherical projections aid in the analysis of the orientation data such as rock foliations but they do not display their spacial distribution Understanding the spacial relationships of orientation data is often one of the primary goals of a geologist particularly a structural geologist A number of tools are provided in Orient to assist with spacial analysis These include coordinate conversions inte
55. ion identifier Zone Alphanumeric zone such as UTM grid zone Easting East X X or easting coordinate of data location Northing North Y Y or northing coordinate of data location Elevation Z Elevation of data location Latitude lat Latitude of data location D D M or D M S Longitude long Longitude of data location D D M or D M S Plane 0 Horizontal orientation angle of plane from Table 2 1 Plane 0 Vertical orientation angle of plane from Table 2 1 Line Horizontal orientation angle of line from Table 2 1 Line o Vertical orientation angle of line from Table 2 1 Type Alphanumeric data type such as SO or S1 Label Alphanumeric label Domain Integer identification number for domain Comment Alphanumeric comment Table 2 2 Column headers used to specify data attributes in Orient The header or its abbreviation 1s used in data files to identify a column of data See Table 2 1 for orientation data angles Strike Dip 230 24 018 54 141 15 Table 2 3 Example of a simple Orient data file as displayed in a spreadsheet such as Microsoft Excel or LibreOffice with strikes and dips of planes See Tables 2 1 and 2 2 for other possible column headers 10 Example of an Orient 3 data file in a spreadsheet this is a file comment 2015 05 04 Easting Northing Strike Dip Trend Plunge Type Comment 8452 05 12885 05 230 24 SO approximate 8456 03 12825 03 018 54 SO overturned
56. ition of the Figure 4 3 Polar orthographic Figure 4 4 Meridianal orthographic spherical projection Point net orthographic net P on the sphere is projected to point P on the plane 4 3 Stereographic Projection The stereographic or equal angle spherical projection is widely used in mineralogy and structural geology It is defined geometrically by a ray passing from a point on the sphere here Z 1 through a point P on the sphere to the projected point P on the plane Figure 4 5 The corresponding stereographic nets are shown in Figures 4 6 and 4 7 Both hemispheres can be represented on the net however the convention in structural geology is to use the ower hemisphere The meridinal stereographic net is known as a stereonet Bucher 1944 Billings 1954 Donn and Shimer 1958 Badgley 1959 or Wulff net named after the crystallographer G V Wulff who published the first stereographic net in 1902 Whitten 1966 The stereonet is commonly used in mineralogy however the convention is to use the upper hemisphere It is therefore good practice to clearly label all projections for example lower hemisphere stereographic projection STIRS OLE MSC CHS suas cranneee ee Le COTON HS OX a AZ Figure 4 5 Geometric definition of the Figure 4 6 Polar stereographic Figure 4 7 Meridianal stereographic projection Point P on the net stereographic net also known sphere is projected to point
57. jection dialog Figure 4 33 Set Axis to Maxima Data type to SO and Eigenvector to Maximum to produce Figure 4 35 Intermediate for Figure 4 36 and Minimum for Figure 4 37 4 9 Terminology of Spherical Projections The stereographic projection was known to the Greeks Hipparchus and Ptolemy and was given its present name by Francois d Aguilon in 1613 The Lambert azimuthal equal area projection was invented by Lambert in 1772 Snyder 1985 In 1925 Walter Schmidt recognized that the stereographic projection was unsuitable for orientation data analysis due to its distortion of area Figure 4 8 and introduced the equal area projection for fabric analysis Rejecting the stereographic or Wulff net used by mineralogists Schmidt introduced the equal area net or Schmidt net as well as data contouring The stereonet Bucher 1944 Billings 1954 Donn and Shimer 1958 Badgley 1959 was introduced for use in structural geology in North America by Walter H Bucher Bucher 1944 Bucher defined stereonet as a contraction of stereographic net and stereogram as a diagram produced using the net These are constructed using the stereographic projection and are therefore not equal area The equal area projection 1s correctly referred to as the Lambert azimuthal equal area projection Snyder 1985 although in the context of orientation data analysis it is usually referred to simply it as the equal area projection The projected hemisphere should also
58. l Projection icon to display the default Schmidt net Figure 1 9 The toolbar icons in the spherical projection window are Save As Find Zoom In Zoom Out Zoom Fit and Preferences Save As will save the image to a graphics file there is also a separate Export Vector Graphics command in the File menu for Adobe Illustrator and Inkscape compatible vector images Begin entering numbers into the strike and dip columns and the spherical projection will automatically update to display them The ID number is automatically incremented although a different number can be entered To identify individual measurements click on the Find binoculars icon in the spherical projection window In this mode any selected data point will be highlighted in the other window a colored bar in the spreadsheet and a selection icon in the spherical projection window Figure 1 10 To only display data items selected in the spreadsheet turn on the Plot Selected option in the Graph Menu In this case only the selected data will be displayed on the spherical projection Turn this off before continuing the tutorial ANNO untitled ANGO SP untitled BS et78 amp s amp h aaa g i D Station Strike Dip Trend Plunge U Ww 0 i es el M ele eje a L Pd eIl a p Figure 1 9 The Orient Data Window with the spreadsheet for data entry and display and a Spherical Projection displaying the default Schmidt net ANOA untitled ANAO SP untitled BAOF amp
59. le from XY plane down toward Z Line 0 Horizontal orientation angle of line Azimuth Clockwise angle from North Y Declination Equal to azimuth Longitude Sphere Counterclockwise angle from X Trend Equal to azimuth Line Vertical orientation angle of line Altitude Equal to latitude Colatitude Angle from Z down toward XY plane Inclination Angle from XY plane down toward Z Latitude Sphere Angle from XY plane up toward Z Nadir Angle from Z up toward XY plane Plunge Equal to inclination Zenith Equal to colatitude Table 2 1 Column headers used to specify orientation data formats in Orient The header or its abbreviation is used in data files to identify a column of data A plane requires two header such as strike and dip A line also requires two header such as trend and plunge To convert between units or to set the default units for data entry open the Data Orientation Units Dialog from the Data Menu This will set the orientation data units entered in the spreadsheet and will convert any preexisting values to the new format For example a common conversion is from strike and dip to dip and dip direction The data will be saved in the new format Note that data files contain the format opening a saved file will always have the format as saved Due to the standard use of geographic locations typically from GPS Global Positioning System positioning of data points in geology Orient requires a distinction between two
60. ll mountains Norway data from Vollmer 1990 180 Figure 1 5 Lower hemisphere equal area beachball diagram of data in Figure 1 4 showing quadrants of P shortening red and T extension cyan kinematic axes Figure 1 7 PGR Point Girdle Random diagram showing the variations in orientation data symmetry and scatter among structural domains defined from the data in Figure 1 6 Figure 1 8 Upper hemisphere equal area projection of 14 229 earthquake epicenters 1980 1990 an example of directed data plotted by latitude and longitude data from NOAA Tutorial I Quick Start Open the Orient application to display the data entry spreadsheet the main data display area Figure 1 9 By default columns for ID Station Strike Dip Trend and Plunge are displayed The ZD is an integer that should be unique for each measurement Station is any alphanumeric string to identify the measurement to see all available columns select the menu command View Data Columns these additional columns will be covered later Measurements for planes should be entered in the strike and dip columns and ines in the trend and plunge columns Use the mouse to examine the icons in the toolbar from left to right these are Open Save As Spherical Projection Circular Histogram PGR Plot Orientation Map and Preferences Most of the controls in Orient have tooltips or help hints displayed when the mouse is over the control Click on the Spherica
61. n In Figure 4 1 the trend of the line is 090 and it s plunge is It is a helpful reminder to designate horizontal angles using three digits where 000 north 090 east 180 south etc and to specify vertical angles using two digits from horizontal 00 to vertical 90 Note that directed data such as fault slip directions may have negative upward directed inclinations An important tool for plotting line and plane data by hand and for geometric problem solving is a spherical net A spherical net is a grid formed by the projection of great and small circles equivalent to lines of longitude and latitude Nets are commonly either meridianal or polar that is projected onto a meridian often the equator or a pole The terms equator and pole or axis will be used to refer to the equivalent geometric features on the net it 1s essential to remember that they do not have an absolute reference frame that is the net axis is not equivalent to geographic north When used to plot data by 20 hand an overlay with an absolute geographic reference frame North East South etc is used Ragan 2009 The projections described here are spherical projections so equal area projection 1s assumed to mean equal area spherical projection Other projections are possible such as hyperboloidal projections which include equal area and stereographic hyperboloidal projections Yamaji 2008 Vollmer 2011 In these projections the surfac
62. n analysis Geological Society of America Bulletin v 102 p 786 791 Vollmer F W 1993 A modified Kamb method for contouring spherical orientation data Geological Society of America Abstracts with Programs v 25 p 170 Vollmer F W 1995 C program for automatic contouring of spherical orientation data using a modified Kamb method Computers amp Geosciences v 21 p 31 49 Vollmer F W 2011 Automatic contouring of two dimensional finite strain data on the unit hyperboloid and the use of hyperboloidal stereographic equal area and other projections for strain analysis Geological Society of America Abstracts with Programs v 43 n 5 p 605 Vollmer F W 2015 Orient 3 a new integrated software program for orientation data analysis kinematic analysis spherical projections and Schmidt plots Geological Society of America Abstracts with Programs v 47 n 7 p 0 Vollmer F W 2015 Orient 3 User Manual www frederickvollmer com this document Vollmer F W 2015 Orient 3 Spherical projection and orientation data analysis program www frederickvollmer com Whitten E H T 1966 Structural geology of folded rocks Rand McNally Chicago 663 pp Yamaji A 2008 Theories of strain analysis from shape fabrics A perspective using hyperbolic geometry Journal of Structural Geology v 30 p 1451 1465 59 History 3 0 2 2015 09 28 e Fixed Preferences Dialog list spacing Optimized contour line segment joining f
63. ne change the Increment to 90 the Offset to 14 and the Size to 12 26 In the Symbols pane Data Type SO should be selected and the Symbol checkbox checked Set the Fill Symbol Color to yellow At this point the plot should look as in Figure 4 13 To add eigenvector maxima select the Maxima pane check Visible then under Intermediate eigenvector check Symbol and under Minimum eigenvector check Great circle Set the great circle Stroke to black and the Stroke Width to 2 Set the Symbol Size to 16 for each The plot should now look as in Figure 4 14 To add confidence cones as in Figure 4 15 check Confidence cone and turn off the maxima symbols which in this case hide the confidence cones Increase the Stroke Width to 2 for the cones and set the Confidence to 99 4 7 Contouring A simple scatter plot of data using an equal area projection Figure 4 13 or with maxima displayed Figure 4 14 may suffice for some data sets However since the first use of lower hemisphere equal area projections for displaying orientation data Schmidt 1925 they have commonly been contoured to bring out underlying patterns such as girdles or point clusters Figure 4 16 Fig 2 Granit Uhligstal Figure 4 16 Early examples of contoured lower hemisphere equal area projections A Crystallographic fabric in a sample of granite Schmidt 1925 B Crystallographic axes in a sample of ice Kamb 1959 Schmidt 1925 devised a method to hand c
64. ns 0 to 400 gradians or radians 0 to 27 radians Orient stores all numbers internally as radians which are transparently converted to user units This is a global preference that sets how angles are read from files and user input and stored in files There is no mechanism to determine this from file input so this should only be done if all files share the same format or to convert files from one format to another Degrees is the default value and will not normally need to be changed 2 2 Coordinate Systems Orient is designed to be used with all types of orientation measurements and coordinate systems and converts to and from user coordinates for data entry and output The user does not normally need to be concerned about the underlying coordinate system except in the case of rotations or selecting different geographic coordinates Section 4 8 Orient uses a standard right handed spherical coordinate system defined with default axes X Y Z Right Top Up In geologic usage these normally correspond to East North Up which conforms to map coordinate systems using Easting Northing Elevation Section 4 8 explains how the default coordinates can be changed to any other orientation such as global geographic Orient has 13 standard coordinate systems which can be modified by rotations about any axis Spherical coordinates are specified by two angles O theta and o phi The standard mathematical definitions are that 0 is the longitu
65. o 625 foliation planes from the Doverfjell Mountains Norway data from Vollmer 1985 Figure 7 5 Orientation map of foliation strikes of the data shown in Figure 7 3 50 180 Figure 7 4 Modified Kamb contour plot of the data shown in Figure 7 3 with contours at 20 density aa ie ace cab fF EY eS Hee Fy ee eee ee ae a a ae a See sS rT Ar a ot amp Sh Sa CMS eS FL 2 A A Lt M Mewes 4 A A E a a oe Se F aa ECIN eee Pe YA A hg et Pee Fk eR RK EFM KAY EF BBE A Oe RA TPR FR A B A Pee b T a ee oe ee ee a BS ot ag oft og Be Oy A A op o ter xee Lx OS Sh a oe oe Figure 7 6 Subdomain orientation field of eigenfoliation strikes generated from the data shown in Figure 7 3 The strike tick marks represent the horizontal projection of the dip line LNSS gt NN SSS Ne _ Ay Ww Ne Bee Ser Pa p a ek z Pa A Ff a a a a eee Se nn en ee M F l i i l ffi Lees 4 met Fd ae eT eet Y d Figure 7 7 Weighted orientation field of eigenfoliation dip lines generated from the data shown in Figure 7 3 The arrows represent the horizontal projections of the dip line The geometry of the structure defined by the foliations is not obvious Figure 7 6 is a subdomain orientation field defined on a one kilometer grid Note that the number of data points within each subdomain varies and that each has a discrete boundary Figure 7 7 i
66. ogy North at the top and East at the right however it is easily configured for other common geographic or spherical coordinate systems which is the first topic covered in 1n this section The second topic covered here 1s coordinate system rotation or projection rotation In some cases it 1s useful or necessary to view data in a more specialized coordinate system for example centered over a specific location or chosen parallel to the data eigenvectors The third topic 1s data rotation which may be required for a number of reasons such as paleomagnetic fold tests or rotation of paleocurrent measurements back to horizontal The primary coordinate system is selected in the Preferences dialog in the Spherical Projection Projection panel Figure 4 24 In addition to the Projection and Hemisphere pulldown menus there is an Orientation option where six geographic coordinate systems can be selected Polar Antipolar Equatorial 0 Equatorial 90 Equatorial 180 and Equatorial 270 and six spherical systems XY ZX YZ YX XZ and ZY planes Additionally there are checkboxes for inverting the projection about the Y and X axes These are used for example to produce plots like Figure 1 3 a plot of directed magnetic data displayed on both hemispheres These options provide views along any of the three axes in either direction The Axes display changes when these are modified so the current coordinate system 1s clear for example X Right Y Top Z Ou
67. on use in structural geology tectonics and related disciplines since their introduction by Walter Schmidt in 1925 38 5 Kinematic Analysis Some data comprise planes that contain lines These data may indicate movement along faults or shear directions such as striae on slickenside surfaces Other data such as hinge lines in fold axial planes or current directions in bedding planes also have that characteristic however this section deals only with the kinematic analysis of faults and shear zones Numerous methods exist for the determination of stresses strains or displacements from populations of faults Orient implements a kinematic analysis based on M plane or movement plane geometry Angelier 1979 Marshak and Mitra 1988 Twiss and Unruh 1998 Marrett and Allmendinger 1990 Twiss and Moores 2007 Although the term fault is used here the kinematic analysis can be applied to shear zones if the displacement directions can be determined As the slip lineation lies within the fault plane the displacement direction must lie in the plane containing the lineation and the pole to the fault this plane is the M plane Figure 5 1 shows the geometric relationships with the M plane shown in gray 0 270 180 Figure 5 1 Lower hemisphere equal area projection of a normal fault with a slip lineation red pole to the fault blue and the M axis or movement axis green the M plane is shown in gray Directions P and T bisect th
68. ontour orientation data using percentages This method or variants of it is still used Ragan 2009 although it is generally superseded by computerized methods Vollmer 1995 Ragan 2009 Schmidt contouring however suffers in that it does not correctly take into account the sample size Kamb 1959 therefore introduced a method using binomial statistics giving a greater statistical validity to the contours Kamb 1959 Vollmer 1995 A problem with both the Schmidt and Kamb methods in addition to being hand contouring methods is that the density calculations are done on the projection plane after projecting the data points from the sphere causing distortion Therefore in 1986 the modified Kamb method which calculates density directly on the sphere was introduced in Orient see figures in Vollmer 1988 and 1990 Vollmer Zh 1995 An alternative method using probability density estimation on the sphere is given by Diggle and Fisher 1985 Orient implements the modified Kamb modified Schmidt Vollmer 1995 and probability density methods Figure 4 17 1s a lower hemisphere equal area scatter plot of crystallographic axes of ice data digitized from Kamb 1956 although not all points could be resolved which is shown contoured using the modified Kamb method at 36 with 20 contours in Figure 4 18 This is the data and contour levels that were used to hand contour Figure 4 16B 180 Figure 4 17 Lower hemisphere equal area sca
69. or vector export Optimized data grid scrolling Fixed Linux About display Optimized messaging Fixed crash when non Roman Unicode characters are in user name A workaround is to run Orient from a thumb drive with only Roman characters in file and folder names Work on User Manual 3 0 1 0 2015 05 30 e Fixed bug importing dip direction 3 0 0 77 2015 05 01 e First release of Orient 3 Complete rewrite with numerous fixes and upgrades tested in 77 pre release versions Compiled tested and debugged on Macintosh OS X Windows and Linux 2 1 2 2012 10 31 e Last release of Orient 2 1 0 0 1986 e First release of Orient 1 Introduced modified Kamb contouring PGR plots and automated domain analysis see Vollmer 1988 and 1990 for example plots created in Orient 1 60
70. plot of fault data in Figure 5 2 showing fault off display of the Schmidt net and showing the P normals white slip lines red and M planes shortening magenta and T extension cyan axes green with Schmidt net Next prepare modified Kamb contour plots of the P shortening and T extension axes Uncheck Tangent lines in the Kinematics pane and open the Symbols pane Uncheck Visible for SL S For SL P check the following Visible Symbol Contour and Gradient Modify the defaults as follows Set the Symbol Fill color to white and the Symbol Size to 6 Click on the gradient color picker and select YR yellow red from Preset Next go to the Contours pane and set Levels to 5 to give modified Kamb contours at 20 density The resulting plot is shown in Figures 5 9 43 180 180 Figure 5 10 Projection as in Figure 5 10 with Figure 5 9 Lower hemisphere equal area ao he exiencion aes modified Kamb contour plot of the fault data from Figure 5 2 with 20 density contours of the P shortening axes To prepare a contour plot for the T extension data uncheck Visible for SL P For SL T check Visible Symbol Contour and Gradient Set the symbol Fill color to white and the Symbol Size to 6 Click on the gradient color picker and select CB cyan blue from Preset The resulting plot is shown in Figure 5 10 Finally to prepare a beachball diagram uncheck the SL T options for Contour and Gradient and set the Symbol Fill color to cy
71. requency polygon plot of the modified Kamb contour plot of ice means of two joint sets from each of 24 counties in crystallographic axes with contours at 10 central New York plotted as undirected strikes density an example of undirected axial data data data from Parker 1942 from Kamb 1959 Spherical projections Figure 1 1 are used to display three dimensional orientation data by projecting the surface of a sphere or hemisphere onto a plane Lines and planes in space are considered to pass through the center of a unit sphere so lines are represented by two diametrically opposed piercing points Planes are represented by the great circle generated by their intersection with the sphere or more compactly by their normal Spherical projections include equal area used for creating Schmidt nets stereographic used for creating Wulff nets or stereonets and orthographic projections these can be plotted on either upper or lower hemispheres Point distributions are analyzed by contouring and by computing eigenvectors of undirected data or vector means of directed data Figure 1 3 is an example of directed data plotted on both upper and lower hemispheres Data sets and projections can be rotated about any axis in space or to principal axes For two dimensional data such as wind or current directions circular plots and circular histograms including equal area and frequency polygon diagrams can be prepared Figure 1 2 180 180
72. s a weighted orientation field where each grid node is generated as a weighted sum of all other data points This map shows the horizontal projection of the dip lines with steeper dips displayed as shorter lines Structural domain analysis Vollmer 1990 is done by attempting to maximize a quantity or index related to the given problem Orient provides several indexes that may be maximized including point girdle and cylindricity indexes To locate areas of cylindrical folding the cylindricity index is maximized C amp 283 n Where g is the orientation matrix eigenvalue for n data points and gt 2 gt 2e3 For a set of domains the sum of the products of the domain indexes C1 C2 Cs and the number of data points within each domain nj no n3 Z Cyn Con Czn is maximized Because N yer Ne Nes the maximum possible value for Z is equal to n The normalized sum is C Z n 51 The settings for the Orientation Map command are in the Preferences Dialog Orientation Map panels For each data point or field value it is possible to plot a symbol in four directions Line Dip line Strike and Strike 180 Figure 7 8 ONN Orient Preferences OO DomainSearch Orientation Map red Symbols Index Cylindricity Value 0 0 Data type tS N 0 Clear C Line KML length 3 0 Initialize 1 E M Dip line KML width 3 Search 2 Hd C Strike a EE Cancel j COK 4 O Str
73. spherical Fibonacci grid Swinbank and Purser 2006 showing density distortion 2006 showing lack of density distortion For plotting fabric data the equal area projection with no density distortion Figure 4 9 should be used instead Schmidt 1925 Sander 1948 1950 1970 Phillips 1954 Badgley 1959 Turner and Weiss 1963 Whitten 1966 Ramsay 1967 Hobbs et al 1976 Fisher et al 1987 Van der Pluijm and Marshak 2004 Pollard and Fletcher 2005 Twiss and Moores 2007 Ragan 2009 Fossen 2016 4 4 Equal Area Spherical Projection The Lambert azimuthal equal area spherical projection is the correct projection to use for displaying orientation data It is not conformal but an important characteristic is that it preserves area so densities are not distorted Figure 4 9 As recognized by Walter Schmidt in 1925 see Section 4 3 the equal area projection should be used for the examination of rock fabrics including the orientations of bedding joints and crystallographic axes Schmidt 1925 Sander 1948 1950 1970 Phillips 1954 Badgley 1959 Turner and Weiss 1963 Whitten 1966 Ramsay 1967 Hobbs et al 1976 Fisher et al 1987 Van der Pluijm and Marshak 2004 Pollard and Fletcher 2005 Twiss and Moores 2007 Ragan 2009 Fossen 2016 The equal area projection appears widely in the geologic literature and is the most likely of these projections to be encountered in scientific literature related to structural geology
74. t is displayed for local coordinates 31 KO Orient Preferences Spherical Projection Settings Projection Orientation EquitorialO Axes X Out Y Right 2 Top Kinematics C Invert about Y _ Invert about X kammas AERE E eee Preview f Cancel x Wi Ma Figure 4 24 Preferences dialog Spherical Projection Settings pane displaying the options for an equal area upper hemisphere projection centered at latitude longitude 0 0 Note the Axes display here X Out Y Right Z Top gives the current position of the coordinate axes Figures 4 25 to 4 30 are equal area projections of 14 229 earthquake epicenters with magnitudes greater than 4 5 from 1980 to 1990 data from NOAA plotted on the six standard geographic coordinate systems Figure 4 25 Upper hemisphere equal area projection of 14 229 earthquake epicenters with magnitudes greater than 4 5 from 1980 to 1990 centered at latitude longitude 0 0 the Equatorial 0 coordinate system in Orient data from NOAA 32 Figure 4 26 Equal area projection of earthquake epicenters as in Figure 4 25 centered at 0 90 the Equatorial 90 coordinate system in Orient Figure 4 27 Equal area projection of earthquake Figure 4 28 Equal area projection of earthquake epicenters as in Figure 4 25 centered at 0 180 epicenters as in Figure 4 25 centered at 0 90 the Equatorial 180 coordinate system in Orient the Equatorial 27
75. the center of the projection This is an important characteristic as azimuths or horizontal angles from north strike trend etc are standard measurements in structural geology geophysics and other scientific disciplines The orientations of lines and planes in space are fundamental measurements in structural geology Since planes can be uniquely defined by the orientation of the plane s pole or normal it is sufficient to describe the orientation of a line If only the orientation of a line and not it s position 1s being considered it can be described in reference to a unit sphere of radius R 1 A right handed cartesian coordinate system is defined with zero at the center of the sphere A standard convention used here 1s to select X Y Z East North Up see Section 4 8 for alternative conventions A line L passing through the center of the sphere the origin will pierce the sphere at two diametrically opposed points Figure 4 1 If the line represents undirected axial data as opposed to directed data such as a fold axis or the pole to a joint plane it is allowable to choose either point In structural geology the convention is to choose the point on the lower hemisphere P the opposite convention is used in mineralogy The three coordinates of point P are known as direction cosines and uniquely define the orientation of the line More commonly the trend azimuth or declination and plunge inclination of the line are give
76. tion The principal is the same as projection rotation however the rotations are applied to the data The data can be rotated about any of the coordinate axes or about an arbitrary axis of any orientation Figure 4 38 oe Rotate Data Axis Z HH Axes X Right Y Top 2 Out Trend 0 0 Plunge 0 0 Angle 20 0 Fa j l y Ts a Fa i k Apply Unde Cancel x Figure 4 38 The Rotate Data dialog allows rotation of the data about any of the coordinate axes or about an arbitrary axis of any orientation Tutorial 6 Geographic Coordinates Open the file Earthquakes with Continents from the Example Data folder any of the csv tsv ods xls or xlsx versions is fine in Orient and click on the Spherical Projection icon The projection will be extremely cluttered Open the Preferences dialog and select the Spherical Projections Symbols pane For the data type CO uncheck Symbol check Polyline and check Directed For the data type EQ set the Symbol Size to 1 the Stroke and Fill Colors to red and the Stroke and Fill Opacities to 50 Check Directed Select the Net pane uncheck Axes and check Net For the Y axis uncheck both Major and Minor Great circles and Small circles For the Z axis check Major Great circles and Major Small circles and set both Stroke Colors to a very light gray 36 Select the Projection panel set the Hemisphere to Upper Hemisphere and the Orientation to Equatorial 0 The projection is now
77. tional to class frequency Cheeney 1983 Mardia and Jupp 2000 Figure 3 4 Figures 3 5 and 3 6 are examples for undirected data 180 Figure 3 3 Equidistance rose diagram of the directed turtle data shown in Figure 3 1 The increasing area for larger bin counts results in an area bias so this is not a true histogram 300 270 240 180 Figure 3 5 Equidistance rose diagram of the undirected joint data shown in Figure 3 2 The increasing area for larger bin counts results in an area bias so this 1s not a true histogram 300 270 240 180 Figure 3 4 Equal area circular histogram or rose diagram of the directed turtle data shown in Figure 3 1 Each count has an equal area removing area bias 300 270 240 180 Figure 3 6 Equal area circular histogram of the undirected joint data shown in Figure 3 2 Each count has an equal area removing area bias 16 Each of these plots is drawn with 24 bins or 15 sectors The selection of bin size will change the appearance of the diagram an example is shown for circular frequency polygons in Section 3 3 3 3 Circular Frequency Polygons A circular frequency polygon Howarth 1999 or kite diagram Davis 1986 is an alternative graph for displaying the circular orientation data In a circular frequency polygon diagram the bin sector centers are connected by straight lines to form a polygon Figure 3 5 is a circular frequency polygon diagram of th
78. to bedding green from Figure 4 13 with modified Kamb contours at 20 density and minor fold axes cyan 30 Tutorial 5 Contour Plots Open the file Vollmer 1981b from the Example Data folder any of the csv tsv ods xls or xlsx versions in Orient and click on the Spherical Projection icon If not already done remove the Schmidt net from the background Click on the Preferences icon and locate the Net pane under the Spherical Projection settings Uncheck both Axes and Net Next in the Labels pane change the Increment to 90 the Offset to 14 and the Size to 12 If still on from the previous tutorial turn off eigenvector and confidence cone display in the Maxima panel The Help Restore Defaults command can be used to reset all preferences if desired In the Symbols pane two data types are available F minor fold axes and SO bedding Set the F Symbol Fill Color to cyan and SO Symbol Fill Color to light green For SO check both Contour and Gradient Click on the gradient paint picker and select the YOR Yellow Orange Red preset Finally in the Contours pane set the Levels to 5 This gives modified Kamb contours at 20 density levels and the plot should appear as in Figure 4 23 4 8 Coordinates and Rotations The rotations used for projection and data display are normally transparent to the user and the default settings are sufficient in most cases The default coordinates are local coordinates commonly used in geol
79. tter Figure 4 18 Lower hemisphere equal area plot of crystallographic axes of ice data from modified Kamb contour plot of data from Figure Kamb 1956 4 17 using 30 with contours at 2c Compare with Figure 4 16B An alternate and perhaps preferable choice for selecting contours is to contour the density distribution at equal levels Fisher et al 1987 Figure 4 19 is a modified Kamb contour plot of this data contoured at 20 density 5 equally spaced levels over the density distribution Figure 4 20 is a probability density contour plot also contoured at 20 density 28 2 0 180 180 Figure 4 19 Modified Kamb contour plot of data Figure 4 20 Probability density contour plot of from Figure 4 17 at 30 with contours at 20 data from Figure 4 17 with contours at 20 density 5 equally spaced levels over the density density 5 equally spaced levels over the density distribution distribution The settings related to contouring are in the Orient Preferences Dialog on the Spherical Projection Contours and Gridding Panels Gridding is the first step in contouring in which the density calculations are done In this panel select the Method Modified Kamb or Probability density Modified Schmidt is not recommended Normally Weighting should be left at the default setting Exponential Sigma at the default 3 and Calculate kappa checked Details for these settings can be found in Vollmer 1995 and Diggle and Fisher 1985 The number of nodes No
80. v 6 p 29 34 Marrett R and Allmendinger R W 1990 Kinematic analysis of fault slip data Journal of Structural Geology v 12 p 973 986 Marshak S and Mitra G 1988 Basic methods of structural geology Prentice Hall 446 p Parker J M 1942 Regional systematic jointing in slightly deformed sedimentary rocks Geological Society of America Bulletin v 53 p 381 408 Phillips F C 1954 The use of stereographic projection in structural geology Edward Arnold London 86 pp Pollard D D and Fletcher R C 2005 Fundamentals of structural geology Cambridge University Press Cambridge 463 500 pp Ragan 2009 Structural geology an introduction to geometrical techniques 4th edition Cambridge University Press Cambridge 602 pp Ramsay J G and Huber M I 1987 The techniques of modern structural geology volume 2 folds and fractures Academic Press 700 pp Sander B 1970 An introduction to the study of fabrics of geological bodies 1st English edition Pergamon Press Oxford 641 p Translated from Sander 1948 1950 German edition Springer Verlag Schmidt W 1925 Gefugestatistik Tschermaks Mineralogische und Petrographische Mitteilungen 38 p 392 423 Snyder J P 1987 Map projections a working manual United States Geological Survey Professional Paper 1395 383 p Swinbank Richard and Purser R James 2006 Fibonacci grids a novel approach to global modeling Quarterly Journal of the Royal M
81. wer hemisphere 14 Coordinate Symbol center z _ Reinitialize Element Panen PS Se ee i Cancel Ok pe Figure 2 6 The Digitize Dialog showing options for digitizing orientation data from images F 6 125 c ones Loc i 2 uc Figure 2 5 An image of a spherical projection opened in the Digitize Window 14 3 Circular Plots Circular plots for two dimensional orientation data include scatter plots circular histograms and circular frequency polygons Davis 1985 Fisher et al 1987 Cheeney 1983 Howarth 1999 Mardia and Jupp 2000 Circular plots can also be used to display the horizontal angles of lines and planes such as lineation trends For planes it is possible to plot the strike direction dip direction or the azimuth of the plane normal The data may be directed or undirected Undirected data plots two points at 180 or can be plotted on a double angle modulo 180 plot The settings for these plots are in the Orient Preferences Dialog using the Circular Histogram selection 3 1 Circular Scatter Plots A simple circular scatter plot shows the data distribution on a circular plot normally the perimeter of a unit circle Cheeney 1983 Mardia and Jupp 2000 Directional rays may be drawn from the circle center or symbols plotted on the perimeter The vector mean for directed or undirected data Section 3 4 can also be displayed There are many variations on scatter plots Orient implements ray plots with lin

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