‘o . \c, .w\ «a J.‘ .T’HEGIC , . .... ’. a V. J g Y. J :‘l I g . ‘ t w 0 On ia>uutai\v'u.ui h 1 Ep'.‘ v 1 ——————- This is to certify that the thesis entitled A Finite Strain Study of the Baraboo Quartzite: Observation from Quartz Grain Shapes presented by James M. Raab has been accepted towards fulfillment of the requirements for Masters degree in Geology Major r @, //“‘/7yr Dr. 0.7639 MSU is an Affirmative Action/Equal Opportunity Institution MSU LIBRARIES .—:—_ RETURNING MATERIALS: Place in book drop to remove this checkout from your record. FINES will be charged if book is returned after the date stamped below. A FINITE STRAIN STUDY OF THE BARABOO QUARTZITE: OBSERVATION FROM QUARTZ GRAIN SHAPE by James Michael Raab A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Geological Sciences 1985 ABSTRACT A FINITE STRAIN STUDY OF THE BARABOO QUARTZITE : OBSERVATION FROM QUARTZ GRAIN SHAPES by James M Raab Quartz grains and pebbles of the Baraboo Quartzite are the strain markers used in this study. it is observed that the maximum finite elongation of these grains is parallel to the fold axis of the Baraboo Syncline. Petrographic observations, correlation with tension gash data, and paleocurrent directions oriented obliquely to the long axis of the strain ellipsoid suggest the grains show tectonic deformation. - i There are two models that could explain the deformation of the Baraboo Syncline. The first model involves vertical compression followed by horizontal compression. The second model is the opposite of the first model and entails an initial horizontal compression followed 2 by vertiCal flattening. The vertical flattening could be due to crustal loading from an overlying thrust sheet. Structures such as folded cleavage planes and quartz veins, and north-south oriented boudinage on the southern limb of the fold support a late stage vertical compression. ACKNOWLEDGEMENTS A special thanks goes to Dr. Cambray for sparking my interest in this structural analysis and for his guidance and assistance. .I would also like to thank Ed, Bill, Dave, and Jim for taking the time to discuss my thesis and for their helpful suggestions. I would especially like to thank my typist, field assistant, and morale booster, who also happens to be my beautiful wife, Shari, who stood by me the entire time. I am also grateful to all my new friends who have helped me out in many ways over the past few years. TABLE OF CONTENTS LIST OF FIGURES .......................................... iv LIST OF TABLES ........................................... vi INTRODUCTION .............................................. l GEOLOGIC SETTING .......................................... 5 PREVIOUS STUDY ........................................... 12 DESCRIPTION OF SAMPLES ................................... 20 Sample Sites ........................................ 20 Petrographic Descriptions ........................... 20 Cleavage ............................................ 27 ANALYTICAL METHODS OOOOIOOOOOOOOOOOOOIOOOOOOOOOOOIOOOOOOOO 30 sample Preparation 0.00.00...OOOOOOOOOOOOCOOOO.COO... 30 Analytical Procedure 0.0.0....OOOOOOOOOOOOO0.000.00... 30 RESULTS OOOOOOOOOOOC00.000.00.000.0.0...OOOOOOOOOOOIOOO... 35 Finite Strain Orientations .......................... 35 Finite Strain values 0 O O O O O I O O O I O O I O '0 I O O O O O I O I O O O O O O O 39 ReprOdUCibility Of Data 0 O O O O O O O O O O I O O O O O O O O O O O O O O O O O 42 DISCUSSION 00......OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO 45 Extension Parallel to the Fold Axis ................. 45 Deformational History 0 I 0-. O O O O O O O O O O O I O O O O O O I O O O I I O O O 48 Tectonic Implications O O O O O O O O O O O O O O O O O O O O O O O O O O O O O C O 54 CONCLUSION OOOOOOOOOOOOOOOOOOOOOO0.0.0000000000000000000.. 56 APPENDIX I.OOOOOOOOOOOOOOOOOOOO...OOOOOOOOOOOOODOOOOO.00... 58 REFERENCES OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO0.00... 62 iii Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure LIST OF FIGURES Location map of study area showing outcrop locations of Baraboo Quartzite ................ 7 Present distribution of Proterozoic red quartzites in relation to other major . Prepaleozoic tectonic features in the north- central United States ........................ ll Equal-area lower hemisphere stereoplots summarizing the orientation of stress axes from the studies of Dalziel and Stirewalt, and Riley ......................... 15 Equal-area lower hemisphere stereoplots illustrating orientations of stress axes deduced from the tension gash data of Dalziel and Stirewalt ..................... 17 Location map of study area showing sample Site locations O...OOOOOOOOOOOOOOOOOOOOOOO..0. 19 Polygonized quartz at grain boundaries ....... 24 Dust rims and quartz overgrowths ............. 24 Interfingering of quartz and phyllosilicate .. 25 Histogram of orientation difference between the long axis of quartz grains and phyllosilicate elongation ................ 26 Mesoscopic structures associated with the Baraboo Syncline ......................... 29 An example of a two dimensional Fry plot 00.000.000.000...OOOOOOOOOOOOOOOOOO0.0... 32 -Equal-area lower hemisphere stereoplots summarizing the strain orientations Of this StUdy .0...OOOOOOOOOOOOOOOOOOOOOO0.0.. 37 Flinn diagram of strain values of this StUdY 0......000......OOOOOOOOOOOOOOOOO00.0... 41 iv Figure 14. Figure 15. Figure 16. LIST OF FIGURES (Continued) Equal-area lower hemisphere stereoplot of sample LR3C showing the reproducibility Of data OOOOOOOOOOOOOOOOO0.000000IOOOOOOOOOOOO 44 Deformational model involving initial vertical flattening followed by horizontal compression ....................... 49 Deformational model involving initial horizontal compression followed by vertical compreSSion OOOOOOOOOOOOOOOOOOO00.... 52 Table Table Table Table LIST OF TABLES Precambrian stratigraphy of the Baraboo District ...................................... 8 Descriptive location of sample sites ......... 21 Composition of quartzite samples ............. 22 Comparison of terminology used for mesoscopic structures in the Baraboo QuartZite OOOOOOOOOOOOOOOOOO0000...... 53 vi I NTRODUCTI ON The Baraboo Quartzite, exposed in south central Wisconsin, has been deformed into a doubly-plunging asymmetric syncline. The proposed age of deposition (1.78 - 1.63 Ga., Van Schmus,1976) and deformation (1.63 Ga.) and geographic setting has caused same problems in correlation of Great Lakes area Precambrian stratigraphy '. The Baraboo Quartzite was rdeposited and deformed after the Penokean Orogeny (1.8 - 1.9 Ga.) and before the Keweenawan event (1.2 Ga). The time period between deposition and deformation has been termed the Baraboo Interval (Dott,1983l. This study involves the strain determination of the Baraboo Quartzite to achieve a better understanding of the Baraboo Interval deformation. ‘ . Ideally, the best' measurement of finite strain in deformed rocks is dependent upon finding strain markers of known original shape and orientation that have undergone homogeneous deformation with no volume change. However, rarely are undeformed rocks containing the same strain markers found in close proximity to their deformed equivalents. Therefore, several assumptions have to be made. As a general case, some knowledge of predeformational geometry must be assumed. The strain marker used in this study is the shape of the quartz grains in the Baraboo Quartzite. The first assumption involves the sphericity of the grains. The composition of the Baraboo Quartzite ranges from a quartz arenite to a quartz wacke. Studies of quartz grain shapes of this composition range in compacted, undeformed rocks indicate that the quartz” grains were not truly spherical, but subspherical in shape (Curray and Griffiths, 1955; Griffiths, 1967; Elliott,1970;and Holst,1982). Holst (1982) calculated an average X/z ratio of 1.26 and Currey and Griffiths (1955) determined a x/z ratio of approximately 1.35. The long dimension was usually oriented in the bedding plane. This variation must be considered when analyzing the finite strain figures measured in this work. i In addition to the shape and orientation, finite strain measurements will be affected by the behavior of the strain markers used. One assumes homogeneous deformation at constant volume in the ideal case. Quartz grains have a characteristic size and in quartz-rich sandstones should have a statistically homogeneous distribution (Fry,1979). . To obtain homogeneously deformed samples, areas that contained any anomalous features such as large quartz pebbles and thick cleavage domains were avoided. The magnitude of volume change is very: difficult to assess because there is no apparent way to quantify the volume changes that occur after deposition. Calculations by Wood (1973) show that volume changes of 15 percent or less are negligible, but greater volume changes would introduce significant errors in the strain values measured. Jank (1982) suggests that pressure solution is the major mechanism of cleavage development in the Baraboo Quartzite which indicates volume change may have occurred. The presence of quartz overgrowths indicate that material dissolved during pressure solution was redeposited, but some material may have migrated from the system. For this reason, the strain values measured have to be treated with some reservation. The two dimensional strain analysis method developed by Fry (1979) allows rapid measurement of object-object separation and is the method used in this study. From these two dimensional measurements, finite principal strain axes were obtained. The only previous deformation studies published on the Baraboo Quartzite were by Riley (1947) and Dalziel and Stirewalt (1975). Both studies examined deformation lamellae to determine stress orientations. Quartz deformation lamellae are thought to occur early in deformational history (Dalziel and Stirewalt, 1975) and therefore offer little indication of the total strain experienced during deformation. Dalziel and Stirewalt (1975) also measured strain orientations from tension gash bands. :These results differ from the deformation lamellae and are thought to occur late in the deformational history. Dalziel and Dott (1970) proposed that the Baraboo Quartzite has undergone a single continuous deformation with the various structures. merely recording stages within this continuous strain history. This study uses final quartz grain shapes to determine a finite strain pattern. Principal finite strain axes and magnitudes were determined from samples throughout the Baraboo Syncline. These results will be incorporated with other mesoscopic features to determine variations in strain patterns to derive a deformational history. This final deformational history will then be used to make certain implications about the tectonic setting. GEOLOGIC SETTING In the area surrounding Baraboo, Wisconsin, Lower Proterozoic rocks are locally exposed beneath a cover of Paleozoic rocks. These Proterozoic rocks were unconformably deposited upon silicic volcanic rocks. .The Baraboo Quartzite directly overlies the volcanics and is the most extensively exposed and thickest formation of the sequence (see Figure 1). Other metasedimentary rock units associated with- the Baraboo Quartzite include, from oldest to youngest, the Seeley Slate, the Freedom Dolomite and Iron Formation, the Dake Conglomerate, and the Rowley Creek Slate. (See Table 1_ for the Precambrian stratigraphy of the Baraboo district.) These formations have been reported in drilling and iron mining records, but have not been positively identified in ‘ outcrop (Dalziel and Dott, 1970). At Baraboo these rocks have been folded into A a doubly-plunging asymmetric synclinorium, known as the Baraboo synclinorium. The axial surface of the fold strikes east-northeast and dips steeply to the north. The geometry of the fold is such that the northern limb dips steeply to the south and in some locations is overturned, while the southern limb dips gently (20 - 40°) northward. The Baraboo synclinorium is approximately 25 A.m~mfi .upmzmr_um wee Fmp~Pao soggy .mcpuuom pmeowmoe mzocm nae promem .ewmeoUmpz .oonagmm mo more as» ea muw~uem=o ooameam Co meowumoop goguuso mewzosm more xenon to ace :ovuaoob .H mgamma H mezmpu 0:22;..." Co 395 33.5“ :52 -i can N . 0 F325 .3 a... 2.. 9:5 :1 ouvuugoso ooaaeom -Auv eowuaeopaxu 2:... z~.... mam mum mom was we: TABLE 1 PRECAMBRIAN STRATIGRAPHY _O_F_ THE BARABOO DISTRICT Rowley Creek Slate (maximum known thickness 2 149'ft.) Dake Quartzite (maximum known thickness 2 214 ft.) (Unconformity ?) Freedom Formation (minimum thickness s 1000 ft.) Seeley Slate (maximum known thickness - 370 ft.) Baraboo Quartzite (thickness over 4000 ft.) (Unconformity ?) Rhyolitic "basement" (thickness unknown) (Taken from Dalziel and Dott; 1970) miles in length and 10 miles in width and rises 700 - 800 feet above the level of the Wisconsin River Valley, forming the Baraboo Ranges. (See Figure 1). From this Figure, one can see that in the eastern closure the strike of bedding changes very abruptly, while in the western closure the change in strike of bedding is very gradual. The western half of the Baraboo Syncline contains minor folds. These fold hinges parallel the major synclinal fold hinge (Figure 1). Rb-Sr and U-Pb ages of the underlying rhyolitic complex indicates maximum age dates of 1.78 +-.02 Ga. for the Baraboo Quartzite. Intrusive plutonic rocks south of the Baraboo Syncline (Greenberg and Brown, 1984) yield a minimum age of 1.5 Ga. This interval, from 1.78 to 1.5 Ga is referred to as the Baraboo Interval. As a result of the age dating of the Precambrian succession, Van Schmus (1976) noticed that the Rb - Sr rock and mineral ages throughout the Great Lakes region were reset to 1.63 +- .03 Ga. There are no igneous rocks of this age exposed near -the Baraboo Syncline and therefore, it is proposed that the wide spread generally low grade metamorphism that occurred during the middle Proterozoic Baraboo Interval was coincident with deformation of the region. (Van Schmus, 1976, Dott,l984). Because of this proposed date of deformation, the age of the Baraboo Quartzite can be narrowed down to between 1.78 and 1.63 Ga. 10 In the subsurface, the Baraboo Quartzite is thought to exist from the Wisconsin - Iowa - Minnesota boundary, across Wisconsin and may extend as far east as the western shore of Michigan (Dott, 1983, See Figure 2). The great thickness (over 4000 feet) and areal extent of the quartzite has sparked much interest regarding its depositional setting. The deposition of a quartzose sedimentary unit over 4000 feet thick suggests that the depositional setting was a stable, slowly subsiding continental margin. This stable continental margin was located on the southern edge of Proto - North America (Dott, 1983, Greenberg and Brown,1984). The generally excepted theory is that afterthe 1.8 - 1.9 Ga.- Penokean Orogeny to the north, there was a peroid of quiescense. Uplifted Penokean plutonic and anorogenic rocks were the sources of sediment for the Baraboo Quartzite. The substantial sediment thicknesses developed during the Baraboo Interval are greater than what would 'be expected from a simple eustatic sea level rise. However, subsidence of the continental margin was thought to be slow due to the shallow water nature of most of the sediments (Greenberg and Brown, 1984). Marine transgression is thought to have begun during deposition of the Baraboo sands, because the youngest strata overlying the Baraboo Quartzite, namely the black slates and iron formation - bearing dolomite are considered to be marine. ll moor: nutrient: RID OUMTZIYII 0' 7w: wontn - «HTML use or name sun: manhunt: ourcnoes or w wro 0mm": > 3400 “I HIE suosunract rxrtwt or ouanrmcs / moo u, ISOYOPIC DATE Pnovumxs "’ II" , cannon . ' ‘ Qumran; LP—‘l‘ IMO-MIG I: 0 380 Figure 2. Present distribution of Proterozoic red quartzites in relation to other major Prepaleozoic tectonic features in the north-central United States.(N-Necedah, Wisconsin; W-Waterloo, Wisconsin: WRB-Wolf River batholith3. From Dott,(1983). PREVI OUS STUDY Baraboo Region The first and most comprehensive study of the structural geometry of the Baraboo Quartzite was done by Wiedman (1904). Wiedman was the first to correctly report the synclinal nature of the Baraboo Quartzite. Van Hise, however was the first to give a full account of the structural relationships of bedding .and cleavage. For a full discussion see Dalziel and Dott (1970). Steidtman (1910) studied the Baraboo Quartzite and noticed that some secondary structures particularly joints and cleavages, were related to the folding of the Baraboo Quartzite. He also observed that the geometry of some of the cleavage planes and joints were not indicative of a simple folding process. Steidtman noticed that the attitude of approximately 75% of the joints on the southern limb and 50% of the joints on the northern limb were oblique to the strike of bedding. The orientation of most of these joints are N608 and N30W with a vertical dip. The origin is uncertain, but a large percentage of these are probably tension controlled and related to larger structural features than the Baraboo Range (Steidtman,1910). 13 Hendrix and Schaiowitz (1964) studied cleavages in the southern limb of the Baraboo Syncline and noticed a reverse sense of shear along the bedding planes. These reverse structures are small scale planar structures whose strike approximates that of bedding but dips in the opposite direction. They observed that the reverse folds are asymmetric with steep limbs down dip suggesting that the upper beds have moved down dip relative to the lower beds. Dalziel and Stirewalt (1975) studied the quartz subfabric in the Baraboo Quartzite. They interpretted a stress history by observing the orientation of quartz deformation 1amellae.They compared their results to Riley's (1947) structural study using quartz c-axis orientations. Their combined results are illustrated in figure 3. On the scale of the syncline <33 is nearly vertical and lies in the plane perpendicular to the fold hinge . Analysis of the results from different domains of the fold are as follows: 1) in both the eastern and western closure, 01 and 02. lies parallel to the bedding plane; 2) on the fold limbs, <31 ‘is approximately parallel to the fold hinge while 03 is nearly vertical for both the steep dipping northern limb and the gentle dipping southern limb. Contrary to Riley's (1947) conclusion that the quartz subfabric in the quartzite resulted from stresses later than and unrelated to the development of the syncline, Dalziel and Stirewalt (1975) suggest that the stress system reflected by the quartz 14 Figure 3. Equal-area lower hemisphere stereoplots summarizing the orientations of stress axes from the studies of Dalziel and Stirewalt (1975), and Riley (1947). Circled numbers refer to Dalziel and Stirewalt's data, numbered dots to Riley's data. Numbers 1,2, and 3 indicate the orientations of 01 , oz ,and 03 respectively. Bedding is depicted as a solid line. The dashed line represents quartzite cleavage. .A; data from the whole syncline. B; data from the northwestern domain. C; data from the northeastern domain. D; data from the south limb. E; data from the eastern closure. F; data from the west central domain. G; data from the western closure. (From Dalziel and Stirewalt, 1975) Figure 3 l6 subfabric is related to the formation of the syncline. In addition to studying quartz deformation lamellae, Dalziel and Stirewalt (1975) observed the orientation of tension gashes throughout the syncline. These stress orientations show that the maximum stress was from a north-south direction and the least stress direction parallels the fold hinge of the syncline (Figure 4). These results differ greatly from the quartz deformation lamellae and are thought to be a late stage event (Dalziel and Stirewalt, 1975). All of these structural studies suggest a more complex deformational pattern than was initially thought. This will be discussed later in regards to a model of the total deformational history of the Baraboo Quartzite and associated Precambrian rocks. l7 Figure 4. Equal area lower hemisphere stereoplot illustrating orientations of stress axes deduced from the tension gash data of Dalziel and Stirewalt. Numbers 1,2,3 indicate orientations oftri,qé, and Us. From Dalziel and Stirewalt (1975). 18 A.m~mfi .upnzogwum new _mw~.mo Eormv .ezogm was mco.uaoop oFQEmm .cwmcoomvz .ooamgmm we more we» a, muw~ugm=o ooaagmm we meowumoop aorouao mcwzosm moan xuaum we nae eowumoom .m mgzmwm n mmauHm ,amnnnm . 9.29:? do 895 38...; 2.52 -.+I+ a=_uuma ac a_u sea ~x_tam -.4. :2» u.. 0 035.33 0323 -AMU z co_uo:upnxm z _.b. 7.~..P mam m5. mom m2 m3. DESCRIPTION OF SAMPLES Sample Sites Oriented quartzite specimens were collected from twelve localities around the Baraboo Syncline. Five collection sites are located on the steeply dipping northern limb ; two sites are near the eastern closure; one site is from the western closure; and four sites are from the gently dipping southern limb (Figure 5 and Table 2). Beds with refracted 'cleavage were sought to compare the strain as a function of varying amounts of phyllosilicates and cleavage orientation. There were only two locations that showed beds with measurable refracted cleavage. One was Lake Jerdean (which is off limits to collecting)and, the other was LaRue Quarry. Petrographic Descriptions The quartz composition of the quartzite samples collected ranged from 70 to 99 percent. The quartz occurs as medium to coarse sand size grains and sporadic rounded granules and pebbles. Pyrophyllite with minor amounts of sericite and chlorite make up between 1 and 29 percent of the quartzite while heavy minerals such as zircon, rutile and iron oxides. are accessory. (See Table 3 for a sample analysis.) These percentages were obtainedby point counting Sample Eggs Upn23 OQ32 RPR34,35,36 RR29 LNQ7 ROWll CALlO HSC26 FRIS FR17 LR1,3,4 WESTZl 21 TABLE 2 DESCRIPTIVE LOCATION OF SAMPLE SITES Location Along Hwy 154 in Narrows Creek Gorge West Baraboo Quarry off Hwy 136, 1 mi. W of Hwy 12 l/2 mi. N of Rte 33, 200 yds E of Rocky Point Rd. Along RR tracks and Baraboo R., W of Hwy 12 Netspan Quarry in Lower Narrows, W of Rte 33 E end of Rowley Rd., 100 yds N Field on B side of Beich Rd. at crest of hill as it climbs the South Range B side of Skillet Creek, 5 of Hefty Skillet Creek Cmpgd Freedom Rd, 1 mi. 5 of County Rd PF Freedom Rd., 2 mi. S of County Rd PF LaRue Quarry Western Closure, 2 mi. SW of UPN23 Sample UPN23 OQ32 LNQ7 ROWll CallO HSC26 FRlS FR17 LRl Lr3C LR3T LR4Bl LR4B3 WESTZl i Quartz 96 95 86 92 91 89 94 98 77 80 73 70 76 95 22 TABLE 3 COMPOSITION OF QUARTZITE SAMPLES g Phyllosilicate 3 4 13 22 19 26 29 23 Other (zircon, rutile, {g oxides) <1 <1 <1 <1 <1 <1 <1 <1 <1 <1 <1 <1 <1 <1 23 300-400 grains per sample. The maximum confidence interval obtained is 4% according to Pettijohn, Potter, and Siever (1973). Internal recrystallization of the quartz grains is not apparent because undulatory extinction and deformation lamellae are present. Incipient recrystallization however, is indicated by the presence of polygonized quartz at the boundaries between quartz grains (Figure 6). Dust rims of iron oxide surround some quartz grains which make it easy to identify quartz overgrowths in most thin sections (Figure 7). Sutured boundaries between quartz grains is fairly common. This indicates that recrystallization has occurred. The phyllosilicates usually have a preferred orientation throughout a thin section. This preferred orientation is parallel to the cleavage planes and is also subparallel to the overall preferred quartz grain elongation direction. Figure 9 is a histogram showing the frequency difference in quartz and phyllosilicate grain orientation. In most of the thin sections, the phyllosilicates were seen to interfinger with the quartz grains in a direction parallel to the cleavage planes (Figure 8). In rocks with less than five percent phyllosilicates, where cleavage planes are not easily discernable, phyllosilicate grains are arranged with their elongated direction parallel to the elongation direction, of the quartz grains. 24 Figure 6. Polygonized quartz at grain boundaries. Scale = 1 inch : .11 mm.. Figure 7. Dust rims and quartz overgrowths. Scale = 1 inch : .11 mm.. 25 Figure 8. Interfingering of quartz and phyllosilicates. Scale = 1 inch : .11 mm.. 26 Frequency o 5 1‘0 15 20 25 3o 35 40 Degrees Figure 9. Histogram of orientation difference between the long axis of quartz grains and phyllosilocate elongations. 27 Cleavage Dalziel and Dott (1970) describe the major types of cleavage found in the Baraboo Quartzite as: a penetrative slaty cleavage in the phyllite which' extends into the quartzite ; a fracture cleavage in the phyllite which they refer to as phyllitic cleavage ; and a closely spaced parting 'in the quartzite which they term "quartzite cleavage". This ”quartzite cleavage" is similarly known as spaced cleavage by other authors. (See figure 10 for the description of these mesoscopic structures.) ”Quartzite cleavage" will be used throughout to indicate spaced .cleavage present in the quartz-rich beds. All samples ,collected for this study contained the quartzite cleavage. Over half of the samples also contained the phyllitic cleavage while only a few contained the slaty cleavage. Jank (1982) observed that the width of the spaced cleavage planes ranged from .1 to 1 mm. with the number and width of the spaced cleavage planes increasing with increasing phyllosilicate content in the rock. Samples with wide ucleavage bands and high phyllosilicate content were avoided due to the heterogeneous nature of those samples. 28 Figure 10. Mesoscopic Structures Associated with the Baraboo Syncline (after Dalziel and Dott, 1970). NNW Plush—m axial “so .' _ .. . surfaca (cranulalion claavaoa) slum: mh em- "I'll Im an 69 (Wm ) Ttau 0‘ 51! (mt-mat) FIGURE 10 South limb SSf ANALYTI CAL METHODS Sample Preparation Each oriented specimen was cut to expose three mutually orthogonal planes. For the conglomerates, the three polished faces were analysed, but for the quartzite samples, an oriented thin section was made from each plane. Care was taken to obtain three orthogonally oriented thin sections so as to maintain homogeneity between both the quartz grain content and cleavage orientation. Eight by ten inch negative photographic prints were made directly from each thin section. The photo enlargements made it easier to determine the quartz grain centers. Analytical Procedure To determine the orientations and values of the principal strain axes, a two stage process was employed. Strain ellipses were determined for each sample. This was accomplished by computer digitizing all the quartz grain centers from the photo enlargements. The digitized sets of points were then computer analyzed using a method developed by Fry (1979). This method uses object-object separation or center to center distances to calculate relavant strain ellipses. The basis of Fry's method is to make clustering or anticlustering visible. 'One of the original digitized points 31 was placed at the center of the desired plot, retaining exact orientation. Then the positions of all the other points of the original pattern were plotted. Then a second grain center of the original pattern was placed at the center of the plot and the resulting positions of all the other grain centers were vadded to the derived plot. .This procedure was continued until all the points of the original data set had been used as the center point. The resulting pattern shows the frequency with which points in the original pattern had neighboring points at different distances‘ in different directions. (See Figure 11.) The vacancy in the center of the plot arises from the fact that any two original particles cannot come to lie closer than the sum of their radii. If the strain marker was initially spherical, this vacancy of points would give an average strain ellipse for the planar section. Care must be taken in assuming the initial distribution of grain centers because a Poisson random initial distribution will deform into a Poisson random distribution (Fry, 1979). A statistically uniform initial distribution of points can be assumed in quartz rich sandstones and quartzites (Fry, 1979). The quartz grains have a characteristic initial size, which means that the center to center separation of nearest grains is controlled by the geometric constraints of the packing. 32 ‘ .. at t 3 ~ ° ‘ : 9...:thz‘3fl J: 3.9,:.{u°3:§m .x. ‘muamw mu .. . as we. .wt°z~?”;-l*.$. O Q . .. . 0 .. :3” o‘. 3.x.“ .13§:~:‘31~“.:‘l'~. z; z, . x: :.,-{§:~. ~ '43:. M3... .Im‘v.. o.:». : a . ' a :z. m‘w 0‘} ‘QO ..‘.. a ‘90,. .0. . . w... .44 .. .~:"‘o° Roan". ’5‘ ".'°“'~‘ at. $2 $3”: ,.,.x. V O . 9 :' 3;". . . :3: s fag: W2»: K732 FIGURE 11. An example of a two dimensional Fry plot. from sample LR3C. See text for an explainat'lon. 38-3881 SNIUEIO :10 z? “988 33 Having determined the strain ellipse for all three. orthogonal thin sections, it is possible to determine both the orientations and values of the three principal axes of the strain ellipsoid (Ramsay, 1967; Siddans, 1981; and Oertel and Miller, 1979). A computer program, (PASES,obtained from Roy Kligfield), was used to make the necessary calculations as outlined by Ramsay (1969, eq. 4-23 to 4-51 and 5-4 to 5-17). This method provides objective results and is especially good for low and high strain ratios. From each ellipse, a long axis, short axis and orientation of the long axis was obtained. The three strain ellipses per sample therefore yield a total of nine data. Because the finite strain ellipsoid only requirs six terms to define its orientation and principal strain values (Ramsay and Huber,l983), the measured data exceeds the minimum data required for the solution and provides internal checks on the accuracy and consistency of the measurements obtained. (See the Appendix for a more detailed explanation of the procedure followed by the computer program PASES.) Five conglomerate samples were analyzed by the Fry method. To provide a check on the accuracy of Fry's method on conglomerates, direct length-width ratios along with the orientation of the long axis were also measured on the three orthogonal faces of the rock. Rf/ O plots (Ramsay, 1967) were made to obtain the average ellipse ratio and orientation for each face. Both sets of data were subsequently analyzed 34 using PASES.' Comparison of the results indicates that the two methods are consistent . These results are also consistent with the quartz grain shape results and therefore will be treated together in the discussion of the results. RESULTS Finite Strain Orientations The Baraboo Syncline can be divided into four inferred homogeneous deformation domains; a northern limb, a southern limb, an eastern closure, and a western closure. Figure 12 A-B are equal area lower hemisphere stereographic plots of the principal strain axes measured in the syncline. Figure 12A is a composite of all the strain data encompassing the entire syncline. From this data it is seen that even though there are strikingly different mesoscopic structures, the principal axes of strain are consistently grouped. The direction of maximum ‘elongation is gently plunging to horizontal in a direction of 250 degrees. The direction of maximum shortening plunges gently ( 30°) in a direction of 150 degrees. Figure 123 shows the orientations of the principal finite strain axes from the northern limb. The maximum principal extension closely parallels the bedding-cleavage intersection. The 2 direction is approximately perpendicular to cleavage, while the Y axis plunges steeply (80°) to the east. There is more scatter in the data for the southern limb (Figure 12C). The z axes have the greatest consistency and 36 Figure 12. Equal-area lower hemisphere stereoplots summarizing the strain orientations of this study. Stars represents the X direction, squares .the Y direction, and circles the z direction. A; data from the whole syncline. 8; data from the north limb. C; data from the south limb. D; data from the eastern closure. E; data from the western closure. 37 t. i ' WESTERN QDSURE Figure 12 38 lie in a field perpendicular to the quartzite cleavage. The scatter of X and Y may be due to the more complex folding of the western half of the southern limb. As previously mentioned, the western half of the Baraboo Syncline contains minor folds with hinges parallel to the major fold hinge. Sampling from various locations on these minor folds could lead to the scatter of data. Sample Fr 15 was taken from the southward dipping limb of the subsidiary Happy Hill Anticline while sample Fr 17 was taken from the north dipping limb. Even with the scatter, the X axes approximately parallels the fold hinge. Figure 12D shows' the Aorientations of the principal strain axes for the eastern closure. Although the X axes are consistent with the rest of the syncline, the Y and z axes vary. The 2 axis plunges 58/122, while the Y axis has an orientation of 22/358. The maximum extension closely parallels the bedding-cleavage intersection which has an average orientation of 20/268. Sample West 21 was the only sample collected from the western closure and is plotted in figure 128. The X axis plunges 55/095, while the z axis plunges 28/234. The plunge of the fold axis in the western closure approximately parallels the X direction. From these data it can be seen that the z axes lie approximately perpendicular to cleavage. This indicates that the X and Y strain axes lie in or close to the cleavage 39. plane. This is commonly reported for deformation and cleavage development (Williams,1976, Siddans, 1972, and Wood,1974). However, it is unusual that the orientation of the principal elongation axis parallels the fold hinge of the Baraboo Syncline. The X direction plunges gently to the west on both the northern and southern limbs but plunges to the east in the western closure and to the west in the eastern closure. Finite Strain Values The principal strain values were also determined in this study. These values are plotted on a Flinn diagram (Figure 13). The K21 line denotes plane strain and seperates ellipsoids of apparent flattening from those of apparent constriction. Most of the samples lie in the apparent constrictional field although a few lie in the apparent flattening field. "Apparent" has to be used, because constant volume is assumed in this figure. If volume loss occurred during deformation, the plane strain division line would have the same slope, but would shift to the right. Jank (1982) suggests that pressure solution is a major mechanism of cleavage formation in the Baraboo Quartzite, which indicates that volume change may have occurred. Assuming volume loss occurred in the Baraboo Quartzite, most of the samples would show true constrictional strain. The computer program, PASES, calculated the percentages of flattening and stretching for each sample using the following 40 equations: % flattening = (1-13 ) * 100, and the % stretching = ( 11 - 1) * 100. It is observed from these values that every sample underwent more stretching than flattening. Even the samples that fall in the field of apparent flattening were calculated to have undergone more stretching than flattening. Geological occurrences of true constrictional strains are few. In the development of cleavage, large amounts of flattening are thought to occur (Wood, 1973, 1974; Siddans, 1972). In Cloos' (1947) study of. oolites in the South Mountain fold of the Appalachians, he measured more apparent flattening than constriction. Hossack (1968) measured constrictional strains in the Bygdin Nappe and attributed it to thrusting followed by vertical compression due~ to overburden of the thrust sheet. Ramsay and Wood (1973) noticed that in rocks that have undergone pretectonic compaction, the initial deformation increments can give rise to apparent constrictive finite strains with the X axis at right angles to the tectonic X axis. However, Holst (1982) observed that depending upon the initial grain orientation, the strain magnitudes measured differed from the true simulated strain, but the strain orientations were quite accurate with respect to the true strain. It has been shown (Ramsay,l967: Elliott,l970: Mukhopadhyay,1973; Lisle,l979; Seymour and Boulter,1979: and Holst,l982) that the finite strain values determined from 41- . - south limb I - north limb G - waat closure *- aast'oloaura 1 1' ' 1'.2 'r 1'.l+ r 1.6 ' 1:8 ' 2'.o Yfl Ratio Figure 13. Flinn diagram of strain values of this study. 42 strain markers are a function of initial grain shape and the homogeneity of the sample. In experiments when the rocks underwent deformation with an axial ratio greater than 1.2, the orientation of the strain axes measured by the grain shapes coincided with the induced strain axes. The strain values, however, varied as a function of initial orientation and shape. This could also apply to two or more superimposed strains. Because this study uses grain shapes as an indicator of finite strain and since sedimentary fabrics and compaction effects of the Baraboo Quartzite are not known, the strain values measured more than likely are approximate compared to the true amount of tectonic strain, and should be treated-with some reservation. Reproducibility pf 2353 According to Fry (1979) approximately 300 quartz grains are needed to effectively produce a well defined pattern. Experimentation by the author confirmed this estimate. To achieve more reliable results, the photo enlargements were divided into six rectangular areas, each containing at least .300 quartz grains. The Fry method was applied to each area. Axial ratios and long axes orientation were averaged. These averages for each face of a sample were computer analyzed to obtain the orientation and values of the principal strain axes. Standard deviations ranged from 3 to 14 percent. This could be due to heterogeneities from one area of a thin section to another. 43 To compare the consistency of a sample, individual areas of sample LR 3C were compared. ThiS- sample was chosen because it had the most variation in orientation from the other LaRue quarry samples. The axial ratio and orientation - of the long axis for an individual area from one face was plotted against axial ratios and orientations of individual areas of the other two faces to determine the orientations of the principal strain axes. Results are plotted in figure 14. It is seen that in the 12 different runs, the principal strain axes have a fairly consistent orientation. Figure 14. Equal-area lower hemisphere stereoplot of sample LR3C showing the reproducibility of data. Stars represent 9.1. squares .represent’Az. and circles represent 7(3. ' DISCUSSION Extension Parallel pp Egg {pld Axip The results of this study show that the finite maximum extension observed in the quartz grains and conglomerates is approximately parallel to the fold axis of the Baraboo Syncline. It is clear from this and' previous studies (Dalziel and Dott, 1970, and Dalziel and Stirewalt, 1975) that the quartz grains orientation is a function of the tectonic strain. The quartz grains show a preferred orientation which is oblique to the cross stratification and ripple marks. Dalziel and Dott (1970) observed that the orientation of the pebbles and quartz grains were elongated and probably tectonically controlled. Dalziel and Stirewalt (1975) measured the orientations of stress from tension gashes in the Baraboo Quartzite. They observed maximum - extension parallel to the fold hinge. The direction of maximum shortening has an average orientation of 10/170. These results parallel the results 'from the quartz grain shapes and add support to the idea of tectonically controlled extension parallel to, the fold hinge. Rotation of the pebbles and quartz grains can not be ruled out, but is thought not to be an influential mechanism in relieving stress in the Baraboo Quartzite (Jank, 1982). 46 Nickelsen (1966) and Engelder and Engelder (1977) studied fossil distortions in Appalachianfolds and observed extension of fossils parallel to the fold axis. Engelder and Engelder (1977) suggested that axial extension is due to layer parallel shortening normal to the fold axis. This process alone will not provide maximum extension parallel to the fold axis unless it is more efficient to accommodate shortening by extension parallel to the fold axis. Most work seems to contradict that statement. Several studies (Chapple and Spang,l974: Cloos, 1947; Engelder, 1979; and Wood,1973) indicate that the maximum extension direction is nearly vertical and perpendicular to the fold axis for most upright folds. Their explanation of deformation was horizontal compressive stresses with the easiest direction of extension being vertical. Deformation involving maximum elongation parallel to the fold axis indicates that the fold history must be more complex. Spang and Groshong (1981) explained axial parallel extension as a result of two deformations. The first deformation involved a vertical maximum compressive stress followed by a second deformation ;consisting of horizontal compression . They do not mention the cause of the initial vertical maximum stress, but it was probably associated with compaction and burial. They also observed a later horizontal extension in secondary features such as tension gashes which would indicate that a late stage vertical compression had also occurred. At least two thrust 47 events are proposed for this area of the Appalachians (Perry,l978). Cloos (1947) noticed that extension parallel to the fold axis can occur in such areas as the culmination of doubly plunging folds where the fold axis is steep. This situation is observed in both the western and eastern closures of the Baraboo Syncline. Davidson (1983) measured the strain in deformed granitic rocks in Ontario, Canada that had undergone two stages of folding. He observed an extension parallel to the F1 fold axis. The F1 fold axis is approximately horizontal and trends northwest. The F2 fold axis plunges steeply to the north at approximately 70 degrees. He explained that modification of a nearly recumbent, isoclinal similar F1 fold by buckle folding and pre-existing fabric anisotropy in the granitic rocks resulted in the maximum extension being parallel to the F1 fold axis. Flinn (1956) attributed extension parallel to the fold axis as being a combination of pure and simple shear caused by thrusting. There are no known publications reporting the depth of burial or degree of compaction of the Baraboo Quartzite. Other studies (Curray and Griffiths,l955; Oriffiths,1967; Mukhopodhyay,1973; Elliott,1970: and Holst,l982) have shown that compacted, undeformed sand grains have an orientation subparallel to bedding with initial axial ratios averaging .1.30. Holst (1982) determined that this initially perferred orientation with small axial ratios had little to no effect 48 on the orientations of the tectonic strain axes. These studies along with the fact that the long dimension of the grains are oblique to paleocurrent directions indicates that the quartz grains and pebbles record the tectonic strain undergone during deformation of the Baraboo Quartzite. Deformational History Dalziel and Dott (1970) proposed that the Baraboo Quartzite has undergone a single continuous deformation which resulted in many phases of mesoscopic structural development. (See table 4 for a comparison of structures of Daziel, 1970:, Riley, 1947; and Hendrix and Shaiowitz, 1964.) Two models are proposed by the author to explain the deformational history of the Baraboo Quartzite. The first model is uniaxial flattening in the bedding plane followed by horizontal compression. which formed the syncline. The flattening stage produces disc shaped quartz grains with both the X and Y 1 directions in the .bedding plane with approximately equal values (i.e. pure flattening : see Figure 15a). If the later horizontal compression produces a flattening strain, extension would occur in all directions parallel to the axial plane of the syncline, with shortening perpendicular to the axial plane . Superimposing these two events on the quartz grains leads to a final grain shape that is elongated parallel to the fold hinge (Figure 15b). (The second model involves initial horizontal compression followed by vertical flattening. The initial stage is 7): A) VERTICAL. N ‘ FLATTENING/ <9 B) HORIZONTAL COMPRESSION N _ S /’& 7x \/ '33 3 Figure 15. Deformational model involving initial vertical flattening followed by horizontal compression. 50 NNW-SSE horizontal compression which formed the syncline. During this compressive stage, the maximum extension would be in a vertical direction and be perpendicular to the fold hinge while the intermediate strain direction would be parallel to the fold hinge. Again, if this was a flattening strain, extension would occur in both the X and Y directions (Figure 16a). A late stage vertical flattening is suggested by the asymmetry of the Baraboo Syncline and 'other' mesoscopic structures (see Table 4). Most of these later stage structures suggest that the vertical flattening may be related to an added overburden caused by thrusting from the north over the Baraboo Region (Cambray, pers. comm.). The- weight caused by the overburden produces flattening in the horizontal direction and-shortening in the vertical direction (Figure 16b). In this stage of proposed events, the direction parallel to the fold axis undergoes continuous extension. During horizontal compression, the X direction is vertical but during vertical compression, the z axis is vertical . In this case the X and 2 strain directions interchange from horizontal to vertical compression. Superposition of the two deformations causes final maximum extension parallel to the fold hinge. 51 Figure 16. Deformational model which involves initial horizontal compression followed by vertical compression. 52 A) HORlZONTAL N ' s COMPRESSION/' v B) VERTICAL COMPRESSION 0., NORTH LIMB Q / . \. / . Figure 16 umeauaoomm (do) leddlag . (nearer beddlag) Ieddlac aad beddlee plaae felleuea (erlaelpal fellaelea of eeetb llab) “ll’ Slat, cleavage. (IJlu) Ieddlaclelesy eleaeace latereeetlea (luldtllct) - m ll race (I )Mllltle Aalal pleae fellaelea real real or from allege” aertb llab eel leave (8 ') “6818. el 3'93. ‘“ Dear fracture - ‘mleueng mu:- alte cleavage later-eetlea Ieddlae/aalal plea fell-etlea/ ‘ Clo cleave“ lateneetleaqlatereectlea 1° leddlaueaart- leddlaclebear fracture “COWS I.“ halal eurfaeee of :12: elaer fglde becrela (alaerel el flea llaeeuea) Greta eleeeetlea (7) tel pleaee of aerael re felde alleleaeldee ea llaeetlea ea beddlag ‘ beddla‘ MIC”. (8 tales unla- el“ er ereulauea b.3293: Aaea of a... ereaalatleae ( ) Itrela-ellp or e Clea eleaeeae leeeree all. or reek cleavage: rereree abeer aeaee halal earfaeee ef alaer eaeerea felde L ~- Hal plaaee ef reeeeee dra‘ felde ‘ Aaea of ereeeleueaa Geese ead treqae of Aaeeofreeereedrac aad alaer cheer-ea felda cheerea or hang! felde folde r: m m ' anal earfaeee ef ee- -- -- alaer felde Aaee ef epea alaer feld- -- - sum 0 vmooa ace Jeaaee: earn-“ll“ Jelaca: «rte-fllled Jolate late :aea Illeheaeldu “lob-old“ alleleealdee mar-ta "eelae": eearta fllled teaelee peaee la beade, eeae defer-ed marks eelae: quarts fllled ladder teaelea freetaree: defer-ed aad Ireland,” fllled seal velae can: ma... Jelate Breeele aeeee Ireeela aeaee m U m All! aeewegee la qeertalte other taea 81' .eer fracturee (fl the "Ileeeaela “heel." eee “up“. Janna." ed palette" of the “neonate eeaeel". (rim froa 0mm and mum) ”hectare cleavage” ef Vea nee. c. I. Left) ead other geoloelete of 54 Tectonic Implications pf Baraboo Interval Deformation The asymmetry of the Baraboo Syncline suggests initiation of compressional forces from the north; This would cause thrusting away from the Proto-North American craton (see Ghosh, 1966). In the northern Midwest, the Baraboo Quartzite sits in a location where the basement rock is progressively-older to the north and younger to the south., This age progression southward suggests continental accretion which supports the existence of some form of plate tectonics. The elongated outcrop pattern of the Baraboo Quartzite and the correlative Souix Quartzite in Minnesota and North Dakota parallels the suture belt of the Penokean Orogeny (1.8-1.9 Ga). This area south of the Penokean Orogenic belt could represent a foreland basin which was infilled by sediment from the Orogenic belt and younger anorogenic rocks. This area was later deformed by NNW-SSE compressional forces. Forces responsible for this deformation were probably a continuation of the tectonic processes that were active during the Penokean Orogeny. The fold thrust belt of the Penokean could have been reactivated due to lithospheric plate interactions which in turn caused thrusting over the Baraboo region. The Appalachian and Cordilleran Orogenies each had several orogenic events. The Appalachian Orogeny had. three orogenic events extending over a period of approximately 300 million years. The Baraboo Interval rocks 55 were deformed around 170 million years after the Penokean Orogeny. (Other strain studies in thrust zones (Flinn; 1956, Hossack: 1968, and Engelder and Engelder; 1978) have shown extension parallel to the fold axis and also parallel to the strike of the thrust plane. These studies were conducted in the footwall of thrusts. CONCLUSI ON From this study of finite strain in the Baraboo Quartzite, it was observed that the finite elongation of the quartz grains and pebbles are parallel to the fold axis. Other reports of extension parallel to the fold axis have proposed at least two deformational events. Mesoscopic structures observed in the-Baraboo Quartzite also points to a more complex deformational history. There are two possible deformational models that apply to the Baraboo Syncline. The first model involves initial vertical compression followed by horizontal compression which formed the Baraboo Syncline. The second model entails a deformational history which is similar to Appalachian folds and involves an initial NNW-SSE horizontal compression, forming the Baraboo Syncline, followed by vertical compression due to crustal loading from an overlying thrust sheet. Most of the late stage structures found in the Baraboo Quartzite support a late stage vertical compression. Either model, however, can explain maximum elongation parallel to the fold hinge. I The tectonic setting proposed for the Baraboo Quartzite is a foreland basin located to the south of the Penokean Orogeny. Erosion of these rocks along with younger anorogenic rocks were the source of sediment for the Baraboo Quartzite. This basin was later deformed possibly as a 57 continuation -of the tectonic processes that were active during the Penokean Orogeny. APPENDI X Methodology g; 3-Dimensional Strain Program This program, given to me by Dr. Roy Kligfield is used to combine two dimensional strain data from three mutually perpendicular planes to give a complete three dimensional strain analysis. The basic tensor relationships were provided by Owens(l969, 1984) which parallel the analysis given by Ramsay(1967,p. 142- 147, p. 199-200). Provided strict adherence to a right-hand- down cartesian reference frame, the interpretation of the matrix of direction cosines, relating the principal axes of the strain ellipsoid to the reference frame, is unambiguous (Owens,l984). The solution for the eigenvectors given by Ramsay(1967) requires that the choice of sign of each direction cosine be made by inspection, which may in some instances be ambiguous (Kligfield, pers. comm.). The two dimensional data is referred to 1a right hand down reference frame which is defined by the three mutually perpendicular planes. The matrix representation of the ellipse tensor, A, referred to its principal axes, in a diagonal form is A = ‘l/RZ 0 0 l 59 where R is the axial ratio of the ellipse. This ellipse may be referred to the specimen reference axes by the tensor transformation: E=B.A.B' where B is the two dimensional rotation matrix: cos 8 -sin GI sin 8 cos 0 and B' is the transpose of B. Three such matrices, one in each reference plane, can be set Up : all a12 bll b12 Cll c12 E = " ; E = I E = XY a21 azz Y2 b21 b22 2X C21 C22 By defining scaling ratios kl‘all/ C22 7 k28 322/ bll ’ k3: cll/ b22 the two dimenSlonal ellipse tensors, (Exy'Eyz'sz) may be combined in six independent ways to derive the ellipsoid tensors of the specimen. Where there is redundant data, there could be a degree Of. mismatch between the three sections and thus the scaling ratios are used to distribute the error appropriately (Owens, 1984). The six ellipsoid tensors, two on the basis of each plane, with their internal inconsistency (level are as follows: On the basis of xy plane: * all a12 cl2 kl 5‘1'2’= a21 a22 b12*k2 C21*kl b21*k2 b22*k2 orc11*kl 60 . . Ib22*k2 ' Cll*kl Internal inconSlstency level =—b *k + C *k *100 22 2 ll 1 On the basis of yz plane: all/k2 or sz/k3 alz/kz c12/k3 5(3'4)= a21/k2 bll blZ c21/k3 bzl' b22 a /k - c /k Internal inconsistency level .l 11 2 22 3L100 all/k2 + sz/k3 On the basis of zx plane: c22 alZ/kl c12 S(5,6)= _ aZl/kl azz/k1 or bll/k3 blZ/k3 c21 b21/k3 . cll a /k - b /k Internal inconsistency level . '22 1 11 3'*100 azz/kl + bll/k3 The internal inconsistency level is the degree to which the two ellipsoids differ. Since the two dimensional ellipse tensors are symmetric, the three dimensional ellipsoid tensors, $1 to 56 are also symmetric. Each of the ellipsoid tensors are diagonalized using subroutine EIGEN, and from' the eigenvalues the following parameters can be determined: AFLINiX/y ; BFLIN-y/z ; FLINK-AFLIN-l/BFLIN-l (FLINN,1962) ARAM-ln(x/y) : BRAM-ln(y/z) : RAMX-ARAM/BRAM (Ramsay,l967) 61 The percentages of flattening and stretching are alSo determined. All six analyses are performed and the results printed out. The. best ellipsoid is then computed by averaging the components of the six ellipsoid matrices, S. REFERENCES Boulter, C.A., 1976. Sedimentary fabrics and their relation to strain analysis methods. Geology v.4 p.141-146. Cloos, E., 1947. Oolite deformation in the south mountain fold, Maryland. G.S.A. Bull. v.58 p.843-918. Curray, J.R.,and Griffiths, J.C., 1955. Sphericity and roundness of quartz grains in sediments. G.S.A. Bull. v.66 p.1075-1096. Dalziel, I.W.D.,and Dott, R.H. Jr., 1970. Geology of the Baraboo District,Wisconsin. Wisconsin Geological and Natural History survey informational circular 14, 164p. Dalziel, I.W.D.,and Stirewalt, G.L., 1975. Stress history of folding and cleavage development, baraboo syncline, Wisconsin. G.S.A. Bull. v86 p.167l-1690. Dott, R.H. Jr., 1983. The proterozoic red quartzite enigma in the north-central United States: resolved by plate collision?. G.S.A. Memoir 160 p.129-l4l. Dott, R.H. 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Cratonic sedimentation during the Proterozoic: an anorogenic connection in Wisconsin and the upper midwest. Jour. of Geology v.92 ph159-17l. ‘ Griffiths, J.C., 1967. Scientific method in analysis of sediments. McGraw-Hill Publishing Co. New York, New York, 508p. Hanna, S.S.,and Fry, N., 1979. A comparison of methods of strain determination in rocks from southwest DYfed (Pembrokeshire) and adjacent areas. Jour. of Struct. Geol. v.1 p.155-162. Hendrix, T.E.,and Shaiowitz, M., 1964. Gravitational structures in the Baraboo Quartzite near Baraboo, .Wisconsin. G.S.A. Bull. v.75 p.1045-1050. Hindeman, D.W., 1972. Petrology of igneous and metamorphic rocks. McGraw-Hill Publishing Co. 533p. Hobbs, B.E.,Means, W.D.,and Williams, P.F., 1976. An outline of structural geology. Wiley Publishing Co., New York, New York. 571p. ' ' Holst, T.B., 1982. The role of initial fabric on strain determination from deformed elliptical objects. Tectonophysics v.82 p.329-350. Hossack, J.R., 1968. Pebble deformation and thrusting in the Bygdin area (southern Norway). Tectonophysics v.5 p.315-339. Jank, M.E., 1982. Pressure solution and the development of cleavage in thhe Baraboo Quartzite. Unpublished M.S. Thesis, Michigan State University, East Lansing, Michigan. 88p. Lisle, R.J., 1979. Strain analysis using deformed pebbles: the influence of initial pebble shape. Tectonophysics v.60 p.263-277. Mukhopadhyay, D., 1973. Strain measurements from deformed ‘ quartz grains in the slaty rocks from the Ardennes and the North Eifel._ Tectonophysics v.16 p.279-296. 64 Owens, W.H., 1984. The calculation of a best-fit ellipsoid sections on arbitrary oriented planes. Jour. of Struct. Geol. v.6 p.57l-578. Perry, W.J.Jr., 1978. Sequential deformation in the Central Appalachians. Am. J. Sci. v.278 p.518-542. Pettijohn, F.J., Potter, P-E.,and Siever, ., 1973. Sand and sandstone.. Springer-Verlag Publishing Co., New York ew York, 618p. Ramsay, J.G., 1967. Folding and fracturing of rocks. McGraw-Hill Publishing Co., New York, New York, 568p. Ramsay, J.G.,and Huber, M.I., 1983. The techniques of modern structural geoa l 9e0109Y. volume 1:strain analysis. Academic Press Inc., New York, New York, 307p. Ramsay, J.G.,and Wood, D.S., 1973. The geometric effects of volume change during deformational processes. Tectonophysics v.16 p.263-277. Riley, N.A., 1947. Structural petrology of the Baraboo Quartzite. Jour. of Geology v.55 p.453-475. Seymour, D.B.,and Boulter, C.A., 1979. Tests of computerized strain analysis methods by the analysis of simulated deformation of natural unstrained sedimentary fabrics. Tectonophysics v.58 p.221-235. Siddans, 1.,1972. Review of slaty cleavage. Earth Sci. Rev. v.8 p.205-232. Spang, J.H.,and Groshong, R.H.Jr., 1981. Deformation mechanisms and strain history of a minor fold from the Appalachian Valley and Ridge Province. Tectonophysics v.72 p.323-342. Steidtman, E., 1910. The secondary structures of the eastern part of the Baraboo Quartzite Range, Wisconsin. Jour. of Geology v.18 p.259-270. Van Schmus, W.R., 1976. Early and middle proterozoic history of the great lakes area, North America. Phil. Trans. R. Soc. London v.280A, p.605-628. Van Schmus, W.R., Thurman, M.E.,and Peterman, z.E., 1975. Geology and Rb-Sr chronology of middle precambrian rocks in eastern and southern Wisconsin. G.S.A. Bull. v.86 p.1255-1265. 65 Wood, D.S., 1973. Patterns and magnitudes of natural strain in rocks. Phil. Trans. R. Soc. London v.274A p.373-382. ~