Orient Reference Manual 2.1.1
Contents
1. sphere to point P on the plane is parallel o the cartesian axis Z effectively giving projection following ray from Z equals positive infinity This type of projection gives realistic view ofa distant sphere such as the moon viewed from Earth Iis azimuthal but angles and area are not generally preserved When plotting geologic data itis important that area and therefore data densities are preserved so the orthographic projection unsuitable for such purposes The net does however have ther uses such as the construction of block diagrams eg Ragan 2009 4 3 Stereographic Spherical Projection The stereographie equal angle spherical projection is widely used in mineralogy and structural geology defined geometrically by a ay passing from a point on the sphere here Z 1 through a point Pon the sphere to the projected point Pon he plane Figure 12 Note tha all points on the sphere can be projected except the point of projection itself which plots at infinity The corresponding Figure deii ofthe Figure 17 projection Poit Ponte ot stereographic also known Shee project o pont Fa the or Wall at plane stercograpbic nets Figures 16 and 17 however plot only one hemisphere Both hemispheres can be represented on net however the convention in structural geology i2. distorted on thesterengraphic Figue I3 projection An equal area projection should be used instead Sander oftvo 1948 1950 1970 Philips 1954 Badgley 1959 Tuner and Weiss alae showing 1963 Whiten 1966 Fisher etal 1987 Ragan 2099 44 Equal Area Spherical Projection The Lambert azimuthal equal area spherical projection is the correct projection to use for displaying orientation data Iis not conformal but important characteristic hat it preserves area so densities are not distorted Figure 19 As discussed in the previous Section this makes it useful for the examination of rock fabrics including the orientations of beading joints and erystallographic fabrics Billings 1942 Sander 1948 1950 1970 Phillips 1954 Badgley 1959 Tumer and Weiss 1963 Whitten 1966 Fisher etal 1987 2009 It appears widely in the geologic literature and is the most likely of these projections to be encountered in sciemific literature related to structural geology Figures Fi 19 ower 20 21 and 22 illustrate the geometric definition polar net and pare paci oe ta meridianal net respectively listes showing ck of density The term azimuthal indicates that like stereograpie and orthographic projections lines passing through the center have true direction and that its projected onto plane This distinguishes
3. orient Orientation Data Analysis Software Orient Reference Manual 2 1 1 1989 2012 Frederick W Vollmer Contents Legal Matters Installation and Software Notes 1 Introducti 2 Data and Coordinate Systems 21 Data Types 22 Coordinate Systems 23 Data Entry Circular Plots 3 Scatter Plots 32 Circular Histograms 4 Spherical Projections 41 Geometry of Spherical Projections 42 Orthographie Spherical Projection 43 Stereographie Spherical Projetions 44 Equal area Spherical Projetions 45 Projections in Orient 46 Data Symbols and Maxima 47 Contouring and Eigenvectors 48 Terminology of Spherical Projections 5 Graphs 51 PGR Graphs 6 Maps 61 Domain Analysis 7 Fault and Kinematic Analysis Appendix A Data File Format Appendix B Supported Image Formats References Legal Matters License Orient software and accompanying documentation copyright Frederick W Vollmer 1996 2007 2010 2012 They come with no warrantees or guarantees whatsoever The software is freeware and may be downloaded and used without may not be redistributed or posted online Iis not free software in the Free Software Foundation definition as 1 the author retain rights to the source code Referencing In return for fee use 1 request that any significant use ofthe software in analyzing data or preparing diagrams should be acknowledged andior referenced An acknowledgement could be I thank F
4. Geophysics and Tectonies in the 21st Century On the Cutting Edge held July 15 19 atthe University of Tennessee Knoxville thank the conveners Barbara Tewksbury Gregory Baker William Dunne Kip Hodges Paul Karabinos and Michael Wysession I thank Steven Haakon Fossen and Josh Davis discussions on spherical projections a References Allmendinger Gephart and 1989 Notes on Fault Slip Analysis Prepared for the Geological Society of America Short Course on Quantitative Interpretation of Joints and Faults November 4 amp 5 1989 55 p 1 1979 Determination of the mean principal directions of stresses given fault population Tectonophysics v 6 p T17 126 Badgley 1959 Structural methods for the exploration geologist Harper and Brothers New York 280 pp Billings 1942 Structural geology Prentice Hall New York 473 pp Billings 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 125 Bucher 1944 The stereographie projection a handy tool for the practical geologist Journal of Geology v 52 3 p 191 212 Davis 1986 Statistics and data analysis in geology Wiley 646 pp Cheeny 1983 Statistical methods in geology Allen amp Unwin 169 pp Diggle and Fisher N L 1985 Sp
5. 14 is an S pole diagram of 625 foliation planes from the Grovudalen area of Norway from Vollmer 1985 and a corresponding contour diagram Although a maxima is present there is well defined girdle pattern o indicate regional fold axis map of poles to foliation Figure 31 shows some areas of consistent orientation but the location cylindrical domains not obvious This map is generated using the Map menu commands The arrows are horizontal projections of constant length vectors so short arrows have steep plunges Mapof pols ofthe Figue 32 Map of domin eigenvectors data hin Figure gener he data a Figure 16 A plot of subdomain eigenvectors Figure 32 brings clearer picture of average data tends However visualizing which areas share a common axis is still not straightforward This map is rated using the Map gt Domain command and shows the maximum eigenvector orientations which quivalent to average poles to foliations To locate cylindrical domains a subdomain search is done to maximize the eylindsicity sum Z This is interactive combination of manual and automatic searches The automatic search proceeds by identifying subdomains that can be moved into a new domain while maintaining connectivity and increasing 2 A purely automatic search using three domains is shown Fi normalized cylindricity sum C from 0 297 to 0 784 Additional iterative manual editing and
6. converts back to 10 30 This convention can be combined with when entering a rake Data entry can be done using Orients spreadsheet interface or by importing tab delimited TSV Tab Separated Value or TXT file from Excel another spreadsheet ora text editor The File Import Data command allows import of many additional text file formats File format details are given Appendix A 3 Circular Plots Circular plots for vo dimensional orientation data include scatter plots vector mean display and circular histograms Circular plots can also be used to display the horizontal angles of lines and planes Such as lineation trends Note that for planes the dip direction is plotted the lot can be rotated 90 to display them as strikes if desired The data may be displayed as directed or undirected Undirected data plots two points at 180 The settings for circular plots are located inthe Circular Plt dialog box 3 1 Circular Scatter Plots A simple circular seater plot shows the data distribution the perimeter of a unit circle Lines may be drawn from the circle center if desired The vector mean for directed or undirected data can also be displayed 3 2 Circular Histograms Two dimensional orientation data is commonly displayed asa frequency histogram where the data count is allied for bins or sectors ofa set angular A commonly used graph is arose diagram constructed with sector radii propor
7. the computation of eigenvectors Eigenvectors are an important concept that allows the determination of the best values fora tensor such as principal stresses In the context of orientation data imagine that cach ine plotted in Figure 24 is represented by a small mass at each ofthe two points where i pies the sphere sce Figure 11 Ifyou were to spin the sphere it would have a natural tendency to spin about the axis of minimum density this is the minimum eigenvector the black point in Figure 14 Ir you were to roll the sphere it would have a natural tendency to stop with the maximum density atthe bottom this is the maximum eigenvector the white point in Figure 14 These wo vectors are exactly 90 apart and 90 from the intermediate eigenvector not shown Note that directed vectorial data such as fult slip direction is treated differently than axial data and itis important to distinguish between the two data types A mean value for directed data is calculated as normalized vector mean which may be directed upwards with a negative inclination and not by using eigenvectors Contouring directed data requires calculating densities on both hemispheres Contouring of spherical projections is done by estimating density function at points on the sphere surface and contouring that function The density functions calculated on the surface ofa sphere bback projected onto a regular grid and then contoured Orient us
8. to points on another surface commonly a plane Astronomers cartographers geologists and others have devised numerous such projections over thousands of years however two stereographic projection and the equal area projection particularly useful in for displaying the angular relationships among lines and planes in three dimensional space third projection the orthographic projection s less commonly used but is described here as its properties easily visualized These are azimuthal spherical projections projections of a sphere onto a plane that preserve the directions azimuths of lines passing through the center ofthe projection Ths isan important characteristic as azimuths horizontal angles from north strike tend ete 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 ean be uniquely defined by the orientation of the plane s pole or normal itis suffi tw describe the orientation ofa line IF only the orientation line and not its position is being considered it can be described in reference to unit sphere of radius 1 A right handed eartesian coordinate system i defined with zero a the center of the sphere A standard convention used here isto select X east Y north and Z up common alternative is X
9. agrams Phillips 1954 The phrase equal area stereogram has been used to refer to a diagram produced by equal area projection Lisle and Leyshorn 2004 however as the term stereogram is used for a diagram produced by stereographie projection the term equal areastereogram isa contradiction The phrase lower hemisphere equal area projection is clear and has a long history and priority of usage Finally itis common to see projections as Figures 8 and 9 labeled sterconets This is incorrect as projection nota net a net is a projection and most likely it s an equal arca projection Mislabeling equal arca projections stercographic projections is common Some books discuss the equal area projection ina chapter titled Stereographic Projection This is incorrect as the equal area projection is mota stereographie projection An accurate chapter title would be Spherical Projections The equal area projection and the Schmidt net have long and rich history in structural geology Mislabeling them as stereonets is wrong and disrespects that history In the United States for example the first edition of Billings 1942 discusses the use ofthe Schmidt equal area including contouring and fabric analysis Its not until the second edition of Billings 1954 that stereographie projections discussed citing Bucher 1944 5 Graphs 5 1 PGR Graphs The graph portion of Orient is used to plot data on a triangular Point Girdle R
10. andom PGR plot Iis particularly useful in map domain analysis where domains are defined in the Map portion of the program or input with the datafile Given the orientation matrix the defined Vollmer 1989 and e for n datapoints where e following Point Random Cylindeii these have the property that P G R 1 and form the basis ofa triangular plot Cylindrical data ets plot nea the top ofthe graph along P G join point or cluster distributions plot near the upper left P eindle distributions plot near the upper right and random or uniformly distributed data will plot near the bottom of the graph R Figure 10 is plot of bedding plane poles from a cylindrical fold in Ordovician graywackes Vollmer 1981 and Figure 11 isthe corresponding PGR graph These indicate a well defined girdle with distinct 7 Y Figue25 Lawer Figure 26 PGR graph of dii oot projection of aso sw in 0 Siding tom a fld n prayackes Ton For comparison a plot of ce fabric c axes digitized from Figure 7 in 1959 is shown in Figure 27 which shows a much scatered distribution and plots nearer to the bottom of the PGR graph Figure 28 Y Y gue 27 28 PGR irap of dii cssc projection of ice sw in Figure 12 1959 6 Maps Spherical projections aid in the analysis of the orientation da
11. automatic Figure 38 Itl automatic drain search 34 Final domin cootiguation after forme the suani of erative mana sod automatic Fie 17 fe ree dois maxing lt searching o fid configuration searching locates stable solution with 0 851 Figure 19 Plotting the data nd on an equal projection below left shows a clear segregation the data into m three girdle distributions three minimum eigenvectors Figue 35 Lover beepers equ projection of data 2 Wit latin poles cole coda by domain corresponding to fold axes show a Figure 36 Synoptic plot best f idles and of data shown in Fire 35 consistent rotation the map area and suggest a refolding axis plunges gently northwest Figue 7 graph ofthe mais compared othe total data set black Point Gidle Random PGR plot below lef shows the Whole area black to the three domains color Note thatthe distribution and the blue is closest a girdle Below right is data set igure 38 Data om Figue XX cola coded by dative changes in eylindricity from the cen domin is closest to point map showing the domains applied tothe Finally for comparison are contour plos of the three domains lefts the red domain right is blue and botom is green a Figue 39 Contoured lower Figure 41 Pje
12. cation of eigenvalue methods to structural domain analysis Geological Society of America Bulletin 102 p 786 791 Vollmer 1993 A modified Kamb method for contouring spherical orientation data Geological Society of America Abstracts with Programs v 25 p 170 Vollmer 1995 C program for automatic contouring of spherical orientation data using a modified method Computers amp Geosciences v 21 p 31 49 Vollmer 2011 Orient 2 1 1 Spherical orientation data plotting program wow frederiehvollmer com Vollmer 2011 Automatic contouring of two dimensional finite strain data on the unit hyperboloid and the use of hyperboloidal stereographie equal area and other projections for strain analysis Geological Society of America Abstracts with Programs v 43 5 605 Vollmer 2012 Orient User Manual 22 wwwfrederickvollmer com this document Whitten E H T 1966 Structural geology of folded rocks Rand MeNally Chicago 663 pp 2008 Theories of strain analysis from shape fabrics A perspective using hyperbolic geometry Journal of Structural Geology v 30 p 1451 1465 Additional Sources Davis Reynolds S J and Kluth 2012 Structural geology of rocks and regions 3rd edition John Wiley 839 pp Fosson 2010 Structural geology Cambridge University Press Cambridge 463 Phillips 1971 The use of s
13. chniques of modem structural geology volume 2 folds and fiches Academie Pres 700 Sande B 1970 An itodocton tothe study o of geological bodies English dition Pergatnon Press Oxford 641 from Sande 1948 1950 German elton Springer Vera Tamer fan Wei LE 1968 of menus Mare Book Company New York 545 pp 2 Twiss RL 1990 Curved slickenfibers a new brite shear sense indicator with application to sheared serpentinite Journal of Structural Geology v 1 p 471 481 Twiss RJ and Moores 2007 Structural geology 2nd edition W H Freeman New York 736 pp Van der Plijm B A and Marshak S 2004 Fart structure 2nd edition W W Norton New York 656 Vollmer 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 FW 1985 A structural study of the Grovudal fold nappe western Norway Ph D Thesis University of Minnesota Minneapolis Advisor Hudleston 233 p Vollmer 1988 A computer model of sheath nappes formed during crustal shear the Western Region central Norwegian Caledonides Journal of Structural Geology 10 p 735 743 Vollmer 1989 A triangular fabric plot with applications for structural analysis abstract Eos v 70 p 463 Vollmer 1990 An appli
14. cion s Figure 39 hemisphere equ nea projection far doin 2 Figur 40 Projection s Figure 39 for domain 3 ee Detailed Procedure The data must include X and Y coordinates for a domain search Open a data set uch as the demo 2 data set used above and a new map The general procedure to set up a search i ct the map boundary using the Map gt Page Setup command Set the number of subdomains with the Map gt Domain command Start the search by pressing the Search S button During a search use following buttons Clear C Set subdomains to 0 no domin Initialize D Set all domains to current domain 1 109 Auto Search A Grow the current domain by increasing Domain 1 9 Select the current domain from the popup menu Best B Restore best domain configuration found in this session Initialize subdomains to 1 set current domain to 2 and do an automatic search An automatic search attempts to maximize cylindricity while keeping the domains connected For each subdomain that can be moved into the current domain it locates the one that will maximize C The search proceeds until no changes will increase C The automatic search will not necessarily ind the best solution because it works stepwise from an initial and is constrained by boundary conditions but it will find a stable solution Alteram automatic search you ean edit
15. di data and isthe specialization of the author Spherical projections are used to display three dimensional orientation data by projecting surface ofa sphere or hemisphere onto a plane Lines and planes in space are considered to pass through the center of unit sphere so lines are represented by the 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 ercating Schmid stereographic used for creating Wulf nets or stereonets and orthographic projections these can be plotted on either upper lower hemispheres Point distributions are analyzed by contouring and by computing their eigenvectors axial data or vector means vectorial data Data sets and projections be rotated about any axis in space orto the principal axes For two dimensional data such as wind or current directions circular plots and circular histograms including equal area and kite diagrams can be plotted Data can be input as spherical coordinates longitude and latitude azimuth and altitude declination and inclination trend and plunge imt strike and dip or other measurements Orient is can also be used to orenalin dai analyze fault data which is represented by a plane orientation and the dir
16. e MacPaint BMP Photoshop PNG QuickTime Image SGI Image TGA When saving images itis important to make sure corect file extension is included as itis added automatically Vector Image Formats Vector based image files can be imported into veetor drawing programs such as Adobe Illustrator and AutoCAD Additionally most web browsers can display SVG Sealed Vector Graphics files Orient does most drawing internally in vector format with the exception of color maps which are bitmaps and can not be exported in vector format Therefore when exporting SVG or PDF fles the bitmap is saved separately and the bitmap must be imported separately into any drawing program Adobe Illustrator allows placing a bitmap image in an open vector drawing by sending the bitmap to the back of the drawing the vector image will overlay the bitmap Orient can save to following vector image formats with limitations noted below DXF AutoCAD Drawing Exchange Format PDF Adobe Portable Document Format SVG Scaled Vector Graphics DXF export does not support bitmaps text color or clipping of symbols PDF and SVG vector images may contain some discrepancies for example with fonts and font alignment general the most compatible vector format is SVG and this is the recommended vector format EJ Acknowledgements Portions ofthis document were prepared for Teaching Structural Geology
17. e not normally useful for undirected data 4 6 Contouring and Eigenvectors simple scater plot of data using an equal area projection may suffice forthe display of some data Sets and Orient can be used to prepare such diagrams for publications However Orient provides many additional functions manipulating and analyzing orientation data more depth Two important statistical procedures are contouring and calculating ata eigenvectors When analyzing orientation data useful procedure is to contour the data to examine it for patterns such as clusters and girdles Fisher et al 1987 Vollmer 1995 A critical point in this procedure is that density calculations must be done on the sphere prior to projection Figure 23 is contoured plot of poles to bedding from an outcrop of folded graywackes in Albany County New York from Vollmer Figure 24 Lower bemispere Figure 28 Con enisphese equ aea projection of 56 poles projection of 6 pales to obodding wh maximum and minimum genset 1981 which displays both cluster and girdle pattems The relative strength of those can be computed and ploted using the computed eigenvectors average is familiar when dealing with scalar values lke temperature Determining est value for orientation data is more complex averaging trends and plunges separately does not work Ifthe data is vectorial a vector mean can be computed but axial data requires
18. ection of slip within that plane From these data Orient can generate P Pressure and T Tension axes which are related to principal stress directions M Movement planes and slip lineas Which indicate displacement directions Spherical projections represent orientations not spacial locations Orient uses map analysis to further analyze the spacial distributions of orientation data For example in structural geology the location of domains of cylindrical folding where bedding or other layers share a common fold is oF interest domain analysis Features subdivide map region into multiple domains by maximizing an Figue 3 data from Angie cigenvalue based index 0979 data dre diia Figure 4 Subdomain orientation Figure so rom Vollmer 190 plored with contineat otia 2 Data and Coordinate Systems 2 1 Data Types Orientation data are either unit vectors referred to as vectoria or directed data unit axes referred 10 as axial or undirected data Current low directions for example are directe while fold axes are undirected Ploting contouring and statistical analysis of these data types is different Geometrically data represents either lines or planes which can be directed or undirected On spherical projections planes and lines are considered pass though the center sphere Planes are represented by th
19. efore opening the file Only one format for planes und one fo ina single file Two dimensional data only require theta value Include a type value such as SO P etc to specify multiple data types ina single file In some cases for data conversion the phi column may contain letters These special eases include centering bearings dip octants rakes and fault slip directions and are described in Chapter 2 Any additional columns are ignored by Orient Orient will also read old format Orient DAT iles When Orient saves a file it includes one line below the header that starts with Orient This isnot required Dut may include additional settings in future releases such as the angle format Currently Orient does not use the Z Station and Comment columns Example Data Files A simple data file could be Strike Dip 179 29 173 25 168 09 00 19 with map coordinates Y Strike Dip 345 1962 179 29 457 1844 25 1233 25 582 1624168 09 667 2010010 19 A ile with multiple data types Sirike Dip Trend Plunge Type moon m 141s us 140 m 80 so si L L m Appendix Supported Image Formats Bitmap Formats Orient requires Quicktime or for most bitmap export Windows versions in particular will only support BMP unless Quicktime is installed Orient can save to the following bitmap raster graphics file formats BMP IEG IPEG 2000 Imag
20. eir great circle the intersection of he plane with the unit sphere by their normal often seferred to 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 horizontal angle such strike tend or azimuth and a vertical angle such as dip plunge or inclination Two dimensional data require a horizontal angle only aailable angular measures and their definitions listed in Appendix A Orient has separate columns for lines and for planes primarily so fault ata which requires both can be entered easily Enter all plane data the plane columns and line data ine columns Unused columns can be hidden if desire 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 coordinate systems for data entry and output This conversion is normally transparent tothe user however for rotations the user should be aware of the standard coordinate system Orients standard coordinate system is right handed cartesian system defined by X Y 2 top up Standard spherical coordinates specified as longitude 0 the counterclockwise angle from X in the XY plane and colatitude the angle from 7 Alternatively coord
21. elected these options will be grayed out for the plane line P axis and T axis scs Tangent ines are drawn as short arcs staring a the piercing point and their length is specified in degrees To plot tanpent line centered on the piercing point select both hanging wall and footwall tangent lines and turn ofT one arrowhead by setting it s length to zero Appendix Data File Format Orient includes a spreadsheet interface for data entry and reads and writes tab delimited files These files normally have an extension of TSV Tab Separated Value or TXT This is a standard text readable file format with each ine of data separated by a CR Carriage Return character or LF or CRLF and individual fields separated by a TAB character ASCH control code 9 import spreadsheet data fom Excel your data must include identifying column headers The following column headers may be used Station X 7 Theta Plane Phi Plane Theta Line Phi Line Type Domain Comment Station an optional alphanumeric identifier string fora station location X Y and Z are optional numeric Locations X and Y are required for domain analysis X should be a numeric value increasing west to east and Y should be a numeric value increasing from south to north Type is an optional alphanumeric identifier defining the type of data Orient uses the Type value to assign plot symbols and calculate statistics Geological types could include for example 50 51 a
22. en in section 3 1 2 3 Data Entry Each data point must include a pair of angles specifying irs orientation in space The first angle measured n horizontal plane and the second in vertical plane For typical geological data these would be strike and dip for planes trend and plunge for ines However all common conventions are supported Two dimensional dta require horizontal angles only Before entering data select the correct data format using the Data Format command You may also Wish o hide or show appropriate columns using the Data View Options command Note that 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 and is optional Specifying type is required however if multiple data types are entered ina single file Also settings such as symbol sizes and color are saved foreach type Additional fields include station identifies ntis 2 coordinates domains and comments these are Up en Range Type listed in the Appendix X and Y coordinates are Se required for domain analysis as described later Orient does several automatic data conversions An older format used for compass readings of horizontal angles isa Bearing These are given as degrees east west of north or south for example N30W When entering data in degrees in an azimulh format such str
23. es several contouring algorithms modified or Schmidt Vollmer 1993 1995 and probability density Digele and Fisher 1985 Orient contouring and gridding options displayed in the Spherical Projection dialog box Below left a plot calculated using a modified method The density function can be displayed as a gradient map with or without overlying contours A map isa bitmap where the color value of each is mapped to he range of the density function Two or thre color gradient maps can be created using user selected colors Below right is Red Green Blue map Contours for directed data will be diferent in upper and lower hemispheres Shown below are combined gradient maps for upper and lower hemispheres right The upper hemisphere plot also inverted so the X axis in cach plot is adjacent The gradient map here maps the probability density function of magnetic remanence directions to the visible spectra The data are 107 measurements of magnetic remanence from specimens of Precambrian voleanics from Schmit and Embleton 1985 in Fisher etal 1987 4 7 Terminology of Spherical Projections The equal area projection is more correelly referred to the Lambert azimutkal equal area projection however in the context of structural geology iis usually suficiently clear to refer to it as the equal area projection and in most cases should be labeled as owe
24. here a contouring program for spherical data Computers amp Geoscience v 11 p 725 766 Fisher N L Lewis and Embleton 1987 Statistical analysis of spherical data Cambridge University Press Cambridge 329 pp Hobbs Means W D and Williams PF 1976 outline of structural geology Wiley New York 71 pp 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 and Ingerson E 1938 Structural petrology Geological of America Memoir 6 270 Lisle Rand Leyshrn 2004 Strcopaphi projection techniques fr geologist and civi gine Dad ein Cambridge University Press Carre 112 p Manda 1972 Sates of Dietional Data Academic Pres Mania and Zemroch 197 Table of maximum estimates fr the Bingham Journal of Computation and Silation v 6 p 29 34 Marshak S and 198 Basic methods of structural geology Hal 46 Philips EC 1954 The o tereoprapicprejecion i geology Edward London D D and Fiche RC 2005 Fundamentals of structural geology Cambridge University Press Cambridge 463 500 pp Ragan 2009 geology an introduction o goometical techniques th edition Cambridge University Pres Cambridge 602 pp Ramsay 1G and Huber M 1987 The te
25. ike or trend bearings are automatically converted to azimuths for example NJ0W converts 10330 A conversion is also done for plane data entered with dip octant N NE E SE S SW W or NW Enter strike fist and then he dip with dip octant The strike will then be corrected to a strike or strike lef if ibat convention is being used For example strike dip 10 30W converts 190 30 When entering fault data several conversions apply First enter the fault plane orientation Then ifthe slip tend is entered the plunge is automatically calculated IC the slip plunge is entered instead the trend is automatically calculated the plunge is nota possible value greater than the dip it will be highlighted in ed To enter the slip asa rake enter rake value inthe plunge field followed by the leer VE and the rake will be converted to a plunge By convention the rake is the clockwise angle about the upward normal ofthe plane measured from the strike with right hand thumb as upward normal rake is measured opposite from finger Figure 6 Dua enr widow Fault slip data is directed and must be entered as such Normal faults have a positive plunge inclination and reverse faults a negative plunge To assist in entering slip data use and to convert between the two For example trend plunge 10 30 gives normal slip while 10 30r converts 101190 30 which isa reverse slip 190 30
26. inates are specified dizection cosines inthis coordinate system Planes are represented by their upward normal Geographic data generally given using longitude as the horizontal angle the vertical angle is commonly latitude or colatitude Geologic data however typically specified using azimuths for horizontal angles which are measured clockwise from Y North and typically X V 7 East North Up User coordinates are typically strike and dip for planes end and plunge for lines However all common conventions are supported including dip direction declination inclination Zenith and altitude see Appendix A Orient convert among these conventions There several conventions for strike and dip By default Orient uses the common convention that the dip is to the right looking along the strike the right hand rule e g Twiss and Moores 2007 second convention where the dip the left the thumb of the right hand points down the dip referred to as Strike left This convention be selected using the Data Format command A thi convention where dip octant NE E SE ec is required is automatically converted as described in the next section Angle units can be set as degrees gradians grads or radians The format applies to all angles and is Set using the Data Format command The defaults degrees Additional discussion of spherical coordinate systems is giv
27. it fom other equal area projections which include the projection of a sphere onto conical and other surfaces however in structural geology it can usually be Figue 21 Fils Galera ne the oq nca projection ari net or Schmid nei referred to simply as an equal area projection without ambiguity The projection is also known as the Schonidt projection W Schmidt who used it in structural geology in 1925 Turner and Weiss 1963 and the meridianal equal area net s known as a Schmidt net Knopf and Ingerson 1938 Billings 1942 Sander 1948 1950 1970 Stereonets are widely used in mineralogy and their equal angle property makes them useful for certain raphical constructions such drill ole problems Rogan 2009 however they should not be used to pilot orientation data The procedures for most geometric constructions commonly used in structural identical stcreonets and Schmit nets Schmidt nets are required for unbiased data analysis and can be used to solve most common geometric problems 4 5 Projections in Orient Orient plots three types of spherical projections as upper or lower hemisphere To creat a new plot open data fle and select New Spherical Projection The settings for projections are set from the Spherical Projections dialog box Equal area projections below e are useful for examining the distribution of data points since area i
28. larly install nd run the software It not been tested on Linux systems install on Apple Macintosh systems either open the dmg file in your browser or download double click on it A window will open drag the contents into your Application folder or other suitable location To install on Microsoft Windows systems download the zip file suitable location such as your downloads folder Right click and extract the entire contents common mistake to only download the Orientexe file without the accompanying files Known Issues When saving a graph as an image different formats jpg pag bmp et will be available dependin on the operating system On QuickTime enabled systems several obscure formats are available which may not be recognized by allsoftware itis best to use standard formats see Appendix B A known problem is that the Save dialog box does not adda file extension automatically so you must insure that an image file has the correct extension jpg png bmp Tis isa bug in the current compiler that isnot fixable by me the programmer When entering fault data the spreadsheet should convert lineation pitehes to rend and plunge This i mot working correctly so Fault lineation data must be entered as trends and plunges This will be fixed ina future version 1 appreciate the reporting of bugs or other issues and will ry to correct them as time allows Future Versions Orient 3 is c
29. nd L Tor foliations and ineations Orient will remember settings assigned to the data typ Domain is used by Orient to assign structural domain from 0 to 9 Domain 0 is used to signify the map arca This is optional eni Comment is optional user entered string The angles seta plane and phi plane specify the orientations of planes and theta line and phi line specify the orientations of lines Theta is horizontal angle and phi is a vertical angle Allowable column headers are shown in Table 1 Theta Plane Phi Plane Notes Right hand rc dip i to along strike Strike len Dip is to lef along strike of dip Dip Angle from XY plane down toward 2 Theta Line Phi Line Notes Azimuth Clockwise negative angle rom Y Nowy Declination Equal to azimuth Longitude Counterelockwise positive angle from X Trend Equal to Altitude Equal t latitude Cole Angle From Z down toward XY plane Inclination Angle from XY plane down toward Z Latitude Angle from XY plane up toward 2 Nadir Angle from Z up toward XY plane Plunge Equal t inclination Zenith Equal to colatitude Table 1 Allowable column headers used to define horizontal vertical angles phi for planes and ines beta and format must be correctly set for lines should be present Angles may be in degrees gradians grads or radians however the a in Orient b
30. north Y east and Z down NED line L passing through the center of the sphere the origin will pierce the sphere at twa diametrically opposed points Figure 11 Fir of the pois Ifthe ine represents undirected axial data as opposed directed or unite ht tins vectra data such fold axis othe pole a jt pane rie rene allowable to choose either point In structural geology the conventionis 5 to choose the point on he lower hemisphere the opposite convention oor nt x its is used in mineralogy The three coordinates of point Pare known 5 direction casines and uniquely define the orientation of the line More common the rend azimuth declination and plunge inclination of the line are given Ia Figure 1 the trend ofthe line is 090 and ts plunge i Is helpful reminder designate horizontal angles using three digits where 000 north 0907 east 180 south ete and to specify vertical angles using two digits from horizontal 00 to vertical 9 Note that directed daa 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 spherical net isa grid formed by the projection of great and small circles equivalent to 6 lines of longitude and latitude Nets are commonly either meridiana polar
31. r hemisphere equai area projection figure captions Note that although less common hyperboloidal equal area and stereographic projections are useful in Structural geology as opposed to spherical projections The terminology of projections can be confusing but it is important to use correct terms for effective Scientific communication The terms stereographic projection and stereonet in particular are frequently misused Early references Sander 1948 1950 translated 1970 Phillips 1954 Badgley 1959 Tumer and Weiss 1963 Whitten 1966 Hobbs etal 1976 are careful to use correct terminology as are most current structural geology texts Marshak and Mitra 1988 Van der Pluijm and Marshak 2004 Pollard and Fletcher 2005 Twiss and Moores 2007 Ragan 2009 Note that rea projection is not the slereographie projection projection is not a type of stereographie projection Astereonet is a meridianal stercographic net and is also known as a A Schmidt net is meridianal equal An equal area net is stereonet Schmidt nets stereonet A projection of data is nora stereonet ora net a The phrase equal area stereographie projection is a contradiction like square circle An additional term that is used inthe context of spherical projections is stereogram which is used to sefer to diagrams produced by stereographie projection although it may include block di
32. rederick W Vollmer for the use of Orient 2 1 1 software A reference can be to one or more of the following see references Vollmer 1989 Vollmer 1990 Vollmer 1993 Vollmer 1995 Vollmer 2011 Vollmer 2012 The Orient software may be referenced as Vollmer 2011 Orient 2 1 1 www frederickvollmer com the user manual this document as Vollmer 2012 Orient Reference Manual 2 1 1 www frederickvollmercom Registration Please consider registering the software registration is free This helps determine usage and justify the lime spent in i s upkeep To register send an email to vollmerf a gmail com with your user name affiliation and usage You will not be placed on any mailing list or contacted again For example send me an email with something like User Frederick Vollmer Alliiaion SUNY New Paltz Geology Department Usage Undergraduate structural geology course and research No Warrantees This Sofware and any related documentation is provided as is without warranty of any kind either express or implied including without limitation the implied warranties or merchantability fitness for particular purpose or noninfringement the entire risk arising out of use or performance of the software remains with you Installation Orient is test run on Macintosh OS X 10 5 0 6 10 7 Windows and Windows 7 This includes of undergraduate students who regu
33. s for the fault plane normal may be plotted as shown below second type af tangent line isa tangent normal defined here tangent through the piercing point of parallel to This contains information identical to tangent lieation and isan alternate form of Visualization The tangent normal sense may be defined by ether hanging wall footwall movement Al four ofthese tangent lines provide identical information the choice isa matter of preference or convention Below left isa tangent normal plot with tangent normals directed towards the banging wall On the right isthe same but with fault planes plotted Although it is not necessary to plot the planes as they are perpendicular to the tangent normals it may help in visualizing the data The plot below shows the corresponding M planes and Note that the tangent lineations and angent normals shown above parallel to the M planes and are generated as rotations about the Below lef he Taxes yellow and P axes green with contoured gradient on the P axes A beach ball diagram below rieht can plotted to display the best fit nodal planes The nodal planes are calculated using the cigenveetors of the M axes and Tangent ine and beach ball plots only available for fult data with both plane and line data entered When setting the options for these plots note that the M plane data set must be s
34. s preserved Clusters of points near the edge show a similar density to clusters near the center Stereographie projections below right distort area bu preserve angular relationships The data are bedding plane normals in folded Ordovician graywackes New York Vollmer 1981 Orthographic projections below left show data as projected from infinity similar a view of the Moon from Earth Lower hemisphere projections are normally used in structural geology while upper hemisphere projections are common in mineralogy Orient plot both upper and lower hemisphere projections Below right is an upper hemisphere equal area projection Grid display and tick marks ean be turned on or off and polar grids about Z can be displayed The shown here are meridional grids drawn about the Y axis Projections can be rotated about arbitrary axes if required Below the projection has been rotated so the minimum eigenvector is parallel Z using the Graph Rotate command The data here poles to bedding planes and a second set of data representing minor fold axes has been added The equal area projection is also known as Lambert projection and the associated mer 0 known as Schmidt net The meridional grid associated with a stercograplic projection known as WullT net All of the following plots unless noted are lower hemisphere equal area projections 4 6 Data Symbols and Maxima Data symbols are
35. s to use the lower hemisphere The meridinal stereographic net is known as a sterconet or Wal ner named after the crysallographer GV Wulf who published the firs stereographie net in 1902 Whitten 1966 The stereonet is commonly used in mineralogy however the conventionis to use the upper hemisphere Itis therefore good practice clearly label all projections for example Jower hemisphere stereographie projection The projection is azimuthal so lines passing through the center of the projection have true direction these represent great circles Note that area in Figure 17 is clearly distorted the projection preserves angles is conforma but it does not preserve area An important consequence is that great circles such as meridians and small circles project as circular arcs These properties make it useful for numerous geometric constructions ia structural geology Bucher 1944 Phillips 1954 Badgley 1959 Lisle and Leyshorn 2004 Ragan 2009 The distortion of area however makes the steeographic projection unsuitable for studying rock fabrics such as multiple orientations of adding joints and crytllographic fabries Potting such data is a descriptive statistical procedure intended to identify significant clusters and other patterns Figure 18 is ower hemisphere projection of two data clusters which identical except for rotation They have identical densities the sphere
36. selected from the Data tab panel ofthe Spherical Projection dialog box Fach data type have a different symbol including fill and stroke colors These settings are saved to simplify the set up of additional plots In the diagram below left bedding plane orientations are displayed both as poles to the beds and as great circle ares Minor fold axes are displayed as red triangles plot of just poles to planes as shown on the right is referred to as an S pole or pi diagram and is generally the preferred method of displaying large amounts of data To calculate the best fit to a set oF axial data the eigenvectors calculated from an orientation matrix formed by the summed products ofthe direction cosines This gives three orthogonal vectors corresponding to the maximum intermediate and minimum moments In areas of cylindrical folding the minumum eigenvector corresponds to the fold axis Below left the minimum eigenvector and irs great circle arc is ploted This is the best it great circle for axial data Select the Data Statistics command to view the computed values Here the fold axis trends 183 and plunges 03 On the right all three eigenvectors ae displayed along with 95 confidence cones Vector mean directions mean resultant lengths and corresponding confidence cones can be ealeulated for directed data The confidence cone assumes a symmetric unimodal distribution alid for n gt gt 25 Note tha these ar
37. t s projected onto a meridian oflen the equator or pole The terms equator and pole or axis will used to referto the equivalent geometric Features on the net it is essential to remember hat they do not an absolute reference frame hats the net axis is equivalent to geographic north When used to lot data by hand an overlay with an absolute geographic reference frame north eas south et is used The projections described here are spherical projections so equal area projection is assumed to mean spherical projection Other projections are possible such as hyperboloidal projections which include equal area and stereographic byperboloidal projections Yamuji 2008 Vollmer 2011 In these projections the surface ofa nperboloid 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 and data projections illustrated were prepared using Orient 4 2 Orthographic Spherical Projection Orthographic projections are an important Family of projections in which points are projected along parallel rays as if illuminated by an infinitely distant light source Figure 12 gives the geometric definition of the orthographic spherical projection corresponding orthographic polar net is shown in Figure 13 and an orthographic meridianal net is shown in Figure 14 The projection of point Pin the
38. ta such as rock foliations but they do not show their spacial distribution To aid in spacial analysis given map coordinates Orient can plot the spacial distributions o orientation data This data can be spacially averaged and used for domain analysis For example a common problem in mapping areas of complex geological structure isto identity domains of cylindrical folding within the map area Orient provides special capabilities to search for such domains 6 1 Domain Analysis Spherical projections aid in the analysis ef the orientations of geological tru but they do not show their spacial distribution common problem in mapping areas of complex g ologie structure isto identify cylindrical domains within the arca es such as foliations Figure 29 Lower beepers equi 30 Contour pot of dats shows ares projection of ples a 625 in Figue ples fom the Grovudlen ses of Nona mes 1988 Orient provides several indexes that may be maximized including point girdle and cylindricity indexes To locate areas or cylindrical folding the cylindricity index should be maximized 2 Fora set of domains the sum of the products of the domain indexes C1 C2 C3 and the number of data points within each domain NI N Z CUNI C2 N2 is maximized Because the maximum possible value for Z is equal to N The normalized sum is C ZN Example Figure
39. tereographic projection in structural geology 3rd edition Edward Arnold London 83 Rowland S M Ducbendorfer and Schiefelbein LM 2007 Structural Analysis and Synthesis ard edition Blackwell 166 p E
40. the fault data M planes or movement planes planes containing the fault plane normal n and the slip line s The M axi m is normal the M plane Additionally P axes pressure axes and Taxes tension axes are generated these lie in the M planes at 45 from the fault planes The T axis at a 45 rotation bout m from s and the P axis is at 45 rotation These all show up as new data types in Orient and may be plotted contoured independently tangent line is defined here as the directed or undirected tangent a point on a sphere in a specified dizection where the point is the piercing point of a ine passing through the center of sphere This includes a tangent linearion whieh is drawn through the piercing point of n parallel to s When specifically used for fault data this is also referred to as slip finear tangent lincalion may be drawn indicating either hanging wall footwall displacement sense A hanging wall displacement sense uses the standard footwall reference frame for faults however a Footwall displacement sense may allow better visualization of motions on lower hemisphere projections Below let isa tangent lineation diagram showing hanging wall displacement senses tothe right is the sume using footwall displacement senses The data on these and following plots are 38 Neogene normal faults rom central Crete Greece Angelier 1979 n Irae d symbol
41. the subdomains with the mouse but only i the domains remain connected An iterative process using manual editing and automatic searching is required to locate the best possible solution 7 Fault and Kinematic Analysis Some data sets comprise planes that each contain directed or undirected line These data oflen indicate movement directions such as striae slickenside surfaces Other data such as hinge lines fold axial planes or current directions in bedding planes can also be plotted however the following focuses mainly on the kinematic analysis of faults Note lat there are numerous methods for fault analysis including diverse stress inversion techniques Orient applies a kinematic analysis based M plane or movement plane geometry as described below Fault data includes both fault plane orientations and directed slip line orientations Because the slip ine lies within the fault plane only three independent angles are required to specify this type of data Typically these angles are the strike and dip of the Fault plane and the pitch rake tend of the slip line Note thatthe lines directed and indicate the hanging wall movement soa pitch greater than 0 and less than 180 indicates a normal component and a pitch greater than 180 indicates a reverse component Chapter 2 explains how to enter this type of data Once the datas entered Orient automatically generates several planes and axes from
42. tional class frequency Figure Figue 7 Creu seat plo Unfortunately a rose diagram in this orm is not true histogram and is biased because the area displayed for a single count increases withthe radius An unbiased plot is an equal area circular histogram where each count bas an equal area and the sector area is proportional to class frequency Cheeney 1983 Figure 9 Flute amp Rose diagram with Figue 9 quale Figue 10 Kite diagram guia The whee cach count has increasing for ange bia sel re unt n arta Bis A circular polygon histogram or kite diagram Figure 10 isan altermative graph for displaying the same information In kite diagram the bin sector centers are connected by straight lines 4 Spherical Projections primary function of Orient is the creation and manipulation of spherical projections of orientation dala in particular azimuthal spherical projections that project the surface of a sphere onto 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 display and work with these projections section on nomenclature discuses terminology and common errors that occur in the 4 1 Geometry of Spherical Projections spherical projection is mathematical transformation that maps points on the surface of a sphere
43. urrently in development ILis a complete rewrite ofthe program using an open source multi platform professional compiler Free Pascal This compiler produces faster code has an advanced erapbics system offers the ability to to additional platforms and removes certain licensing issues Significant bugs will be fixed in Orient 2 however any new features will be implemented in Orient 3 only 1 Introduction Orient plotting and analyzing orientation data data can be described by an axis ora direction in space or equivalently by a postion sphere or circle Examples of dala that are represented by unit vectors vectorial or directed data or axes axial or undirected data include geologic bedding planes faults and fault slip directions fold axes paleomagnetic vectors glacial striations wind and current flow directions optical axes in quartz and ice crystals earthquake epicentes arrival directions of cosmic rays normals to comet orbital planes postions of galaxies and locations of whales in the Atlantic Ocean Orient has been written to be as general as possible to apply to wide variety data types Many examples however come from Figure 1 Lover lenispha tructural geology which requires extensive manipulation of orientation Sate pojation of ee amp structural geology which req ipulation of orientation Kam 1089 Crystallographic ates such at these net
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