Evolution and geometry of the Jura mountains
Transcription
Evolution and geometry of the Jura mountains
The Geometry and Evolution of the Jura Mountains: Fernschub mechanics Tabea Kleineberg 03.10.2013 Paper for the excursion “Geländeseminar Alpen” led by Prof. Dr. Janos Urai, Institute of Structural Geology, Tectonics and Geomechanics and Prof. Dr. Ralf Littke, Institute of Geology and Geochemistry of Petroleum and Coal at the RWTH Aachen University. 2 The Geometry and Evolution of the Jura Mountains: Fernschub mechanics Tabea Kleineberg 319001 ABSTRACT .......................................................................................................................................3 1. GEOLOGICAL SETTING..................................................................................................................4 2. STRATIGRAPHY AND EVOLUTION OF THE JURA MOUNTAINS.......................................................5 2.1 BASEMENT .......................................................................................................................................5 2.2 THE SEDIMENT COVER ........................................................................................................................5 2.2.1 The basal décollement within the Triassic evaporites ...........................................................7 2.3 EVOLUTION OF THE JURA MOUNTAINS ..................................................................................................7 2.4 PALINSPASTIC RECONSTRUCTION ..........................................................................................................8 3. STRUCTURES................................................................................................................................9 3.1 EVAPORITE-‐RELATED FOLDS .................................................................................................................9 3.2 THRUST-‐RELATED FOLDS .....................................................................................................................9 3.3 TEAR FAULTS ..................................................................................................................................10 4. FERNSCHUB HYPOTHESIS........................................................................................................... 11 4.1 MECHANICS ...................................................................................................................................11 4.1.1 Kinematics ...........................................................................................................................12 4.1.2 Critical taper ........................................................................................................................13 4.2 LABORATORY EXPERIMENTS ...............................................................................................................14 5. CONCLUSION ............................................................................................................................. 15 6. LITERATURE............................................................................................................................... 16 3 The Geometry and Evolution of the Jura Mountains: Fernschub mechanics Tabea Kleineberg 319001 Abstract The Jura Mountains, representing the most external part of the Alpine chain at its North-‐western front, are divided into three parts, all featuring different structural styles, ranging from plain plateaux in the external and Tabular Jura to a well developed fold-‐train in the internal Jura. The Jura Mountains formed in the latest stage of the Alpine orogeny in Upper Miocene/ Lower Pliocene times and are closely linked to the Molasse Basin. Its basement is comprised of metamorphic rocks and is decoupled from the sediment cover by a basal décollement. Folding and thrusting is restricted to the sedimentary cover rocks, pointing to a thin-‐skinned fold-‐and-‐thrust tectonics, which require very low basal friction. When shortening in the subalpine Molasse reached the Jura, the décollement in the Triassic Evaporites sheared off into the foreland generating the thrusts and folds of the Jura Mountains. This process is called the Fernschub hypothesis by BUXTORF (1916) and it is, at the present day, the most broadly-‐acknowledged theory for the formation of the Jura Mountains. Its essence and mechanics will be discussed in this paper. 4 The Geometry and Evolution of the Jura Mountains: Fernschub mechanics Tabea Kleineberg 319001 1. Geological Setting The Jura Mountains are located in Central Europe, in the Northwest of Switzerland and in the East of France in front of the Western Alpine arc. Their length amounts to 370 km with a maximum width of 75 km (BECKER, 2000). Figure 1 shows the structural map of the Jura arc, with its division into the internal, external and Tabular Jura highlighted in different shades of grey. In the south, the Jura Mountains are linked with the Alpine front of the Prealps, however, in the northeast they are separated from the Alpine chain by the tertiary Molasse Basin which is up to 50 km wide close to the eastern termination of the Jura Mountains northwest of Zurich. The Molasse Basin correlates to an Oligo-‐ Miocene foredeep, that developed in front of the Alpine orogen (SOMMARUGA, 1998). The crucial features along the western and northern border are the Tertiary rifts of the Bresse Depression and the Upper Rhine Graben (BECKER, 2000). The Rhine and Bresse Graben are associated with the Eocene and younger, West-‐European rift system. The Jura overthrusts the Bresse Graben in the west, and the Tabular Jura in the north (SOMMARUGA, 1998). Both rifts were active during the Eocene to Miocene, before Jura folding commenced (AFFOLTER ET AL., 2004). The remaining areas along the northern margin of the Jura folds belong to the Tabular Jura; the more or less unfolded, locally block faulted and non-‐decoupled sedimentary analogue of the folded Jura cover (BECKER, 2000). 001 A[ Sommaru`a:Marine and Petroleum Geolo`y 05 "0888# 000 023 Figure 1: Structural sketch of the Jura Mountains (SOMMARUGA, 1998). Fig[ 1[ Tectonic sketch of the Jura arc showing main structural units[ Legend] PHS Plateau de Haute!Saone^ IC Monts^ Fe Ferrette^ AR Aiguilles Rouges^ MB Mont Blanc[ Modi_ed from Sommaruga "0884#[ Ile Cre⇣ mieu^ AM Avants! 5 The Geometry and Evolution of the Jura Mountains: Fernschub mechanics Tabea Kleineberg 319001 2. Stratigraphy and Evolution of the Jura Mountains The Jura Mountains are a foreland fold-‐thrust belt, where the structural components involve a relatively thin sediment cover; approximately 2 km thick in the Internal Jura, deformed above a basal décollement within the Middle and Upper Triassic evaporites (Figure 3) (AFFOLTER ET AL., 2004). The Mesozoic and Cenozoic rocks are folded at variable degrees and detached from the gently 1-‐5° SE dipping pre-‐Triassic basement, illustrated by Figure 3 (SOMMARUGA, 1998 and BECKER, 2000). By contrast with the deformed Jura cover, the molasse fill of the foreland basin was left virtually un-‐ deformed by Alpine deformations (Figure 3) (AFFOLTER ET AL., 2004). 2.1 Basement The crystalline basement is composed of medium-‐to-‐high grade metamorphic and plutonic rocks, which were deformed during the Hercynian orogeny. The surface of the basement, including some Permo-‐Carboniferous troughs, is not strongly accentuated. Nowhere is it exposed in the Jura and Molasse Basin (BECKER, 2000). It is characterized by two major unconformities, one below the Carboniferous and the second below the Triassic (SOMMARUGA, 1998). Its tectonic style, the depth and geometry and its internal deformation are still uncertain (BURKHARD, 1990). Some moderate basement elevations, however, are proven along the Vuache fault system, the eastern border zone of the Bresse Depression, the southern rim of the Permo-‐Carboniferous Trough of northern Switzerland and in the Oyonnax region of the southern Jura Mountains. The depth of the basement varies from more than 7 km below sea level in front of the Aar massif to more than 4 km above sea level 20 km further to the southeast (Figure 3) (BECKER, 2000). 2.2 The sediment cover The sediment cover of the Jura Mountains reaches maximum thicknesses of 1.5 km in the north, approximately 2 km in the centre and more than 3 km in the south (BECKER, 2000). It is separated from the basement by an evaporite layer (Figure 2 and 3, compare to 2.2.1). The Jura is divided into an external and an internal part, based on different tectonic styles (Figure 1). The external Jura consists of flat areas, plateaux, separated from Figure 2: Stratigraphy of the Jura and adjacent Molasse Basin (modified after SOMMARUGA, 1998). Figure 3: Cross section through the Jura Mountains (SOMMARUGA, 1998). Fig[ 2[ "a# Large!scale balanced cross!section across the Molasse Basin from the external Jura to the Alps "external crystalline massifs#[ For location\ see Fig[ 1[ Modi_ed from Burkhard and Sommaruga "0887#^ "b# Enlargement of the Jura Haute Cha(ne*Molasse Basin region from the above large scale cross!section[ 6 The Geometry and Evolution of the Jura Mountains: Fernschub mechanics Tabea Kleineberg 319001 A[ Sommaru`a:Marine and Petroleum Geolo`y 05 "0888# 000 023 002 7 The Geometry and Evolution of the Jura Mountains: Fernschub mechanics Tabea Kleineberg 319001 each other by Faisceaux, narrow stripes comprising numerous small-‐scale imbrications and tear faults. The internal Jura consists of a well-‐developed fold train. At a large scale, deformation is characterized by major folds, the trend of which swings through 90° from east to south. Major tear faults, oriented at a high angle to fold axes, cut the internal Jura at regular intervals (SOMMARUGA , 1998). The crucial rock types of the sediment cover are Triassic evaporites (compare 2.2.1) and shales, Jurassic and Cretaceous limestones (compare 2.3) and molasse sediments from Oligoene and Miocene times (BECKER , 2000). 2.2.1 The basal décollement within the Triassic evaporites In order to shear off the sediment cover and to accomplish folding of the Jura Mountains, a basal décollement with a low basal friction is required. These properties are given by the Triassic evaporitic sequences of the Muschelkalk and the Keuper formations. The most important lithologies for generating décollement horizons are halite, anhydrite and, at depths of less than approximately 500m, gypsum (BECKER, 2000). The distribution of halite in the Triassic (Figure 4) correlates with the location of the Jura Mountains, most obviously at their southern and eastern end. Southwards, the halite Figure 4: Distribution of Halite of the Keuper and Muschelkalk in the Jura Mountains (BECKER, 2000). disappears before reaching the Alpine front, and anhydrite is replaced increasingly by dolomite and marl. The thickness of the Triassic decreases from more than 1000m in the southern and central Jura Mountains to less than 50m in the North Helvetic domain, 60 km to the south (SOMMARUGA, 1998). 2.3 Evolution of the Jura Mountains After the end of the Hercynian Orogeny, the Alpine cycle started with peneplanation and a subsequent transgression in the Early Triassic. After the Jurassic, the Jura and Molasse Basin realm became part of the Alpine Tethys passive margin. During the Triassic, up to 1 km of evaporites and shales accumulated in an elliptical depocenter in the area of the future Jura arc (Figure 2 and 3). Limestones were sedimented in Dogger and Malm, as well as in the Carboniferous. During the Oligocene and Miocene, fluvial, lacustrine and marine clastic molasse sediments were deposited in the Alpine foredeep as a sedimentary wedge, the Molasse Basin. Its thickness decreases from up to 3 km in the south to a few hundred meters in the north (SOMMARUGA, 1998). In upper Miocene and lower Pliocene times, the latest stage of the Alpine orogeny, the Jura belt formed, at the front of the Alpine foredeep. Originally, the Molasse Basin extended further north-‐ 8 The Geometry and Evolution of the Jura Mountains: Fernschub mechanics Tabea Kleineberg 319001 and westwards into the region of the present Jura Mountains and is preserved in the Jura Mountains as relicts. In the Oligocene, this region experienced normal faulting synchronous with formation of the Bresse Graben. Later, the upper Miocene to early lower Pliocene the Jura deformation reactivated these extensional structures which probably played a role in the distribution of thrusts. At that time, the frontal Jura was thrust above the eastern border of the Bresse Graben (AFFOLTER ET AL., 2004). 2.4 Palinspastic reconstruction Palinspastic reconstructions are used for a clearer understanding of the pattern of strain of a heterogeneous deformation. They are achieved by dividing the area into homogeneous domains with a subsequent restoring and best-‐fitting of the individual domains to realize the initial undeformed state. The structure of the Weissenstein Anticline (upper section of Figure 5) exhibits two geometrically distinguishable tectonic generations. The shortening of the wedge system decreases, which is apparent from the decreasing height of the Weissenstein anticline. In contrast, the Ausserberg-‐thrust shows no Figure 5: Restored cross-‐section of the change (BITTERLI, 1990). region "Volgelsberg" (BITTERLI, 1990). 9 The Geometry and Evolution of the Jura Mountains: Fernschub mechanics Tabea Kleineberg 319001 3. Structures Two different types of folds appear in the Jura Mountains: evaporite-‐related and thrust-‐ related folds. The Molasse Basin and the external Plateaux Jura feature folds of the first mentioned type. The second type is present in the internal Jura (SOMMARUGA, 1998). Strike-‐slip faults disrupt the lateral continuity of the folds, but no clear crosscutting relationships exist between both on geological maps (AFFOLTER ET AL., 2004) 3.1 Evaporite-‐related folds Evaporite-‐related folds are broad, long-‐wavelength, low-‐ amplitude folds that are cored by Triassic evaporites (Figure 6). They are difficult to recognize in the field or on geological maps, therefore an interpretation by seismic lines is required. Seismic sections prove that the folds are controlled by evaporite, salt and clay stacks within a ductile unit of the Triassic layer. Within the Plateaux Jura the folds have two long asymmetric limbs dipping with a very low angle towards the north and the south, respectively. The geometry of the folds is highlighted by a well-‐layered series of reflectors representing Cretaceous, Jurassic and Upper Triassic strata (Figure 6). Due to the scarcity and thinness of pure rock salt layers in the Triassic series and the lack of early extension or Figure 6: Seismic section of an Evaporite-‐ related anticline in the Plateau Jura (SOMMARUGA, 1998). differential sedimentary loading, no salt diapir occurs in the Jura belt and the Molasse Basin (SOMMARUGA, 1998). 3.2 Thrust-‐related folds Thrust-‐related folds are characterized by high-‐amplitude folds. These folds formed above thrust faults stepping up from the basal Triassic décollement zone. These anticlines duplicate the entire Jurassic sequence (Figure 7) (SOMMARUGA, 1998). The short wavelength of these folds is thought to be due to the reduced Figure 7: Geological profile through the thrust-‐related folds around thickness of sediments involved in Grenchenberg (PFIFFNER, 2010). deformation in this external area. This reduced thickness is due to a period of peneplanation 10 The Geometry and Evolution of the Jura Mountains: Fernschub mechanics Tabea Kleineberg 319001 (compare to 2.3), thought to have lasted from Late Cretaceous times to the onset of Jura deformation in upper Miocene (AFFOLTER ET AL., 2004). Thrust-‐related anticlines are separated by broad or tight synclines. Many thrust faults are NW (NNW)-‐verging, for example the main thrust system (foreland-‐vergent thrust), and have at least kilometric dip slip. SE (SSE)-‐vergent thrust faults are considered as backthrusts (hinterland-‐vergent thrusts), and have few tens or hundreds of meters of displacements. Thrust faults include both flats and ramps. All mapped foreland-‐vergent thrust faults reach the surface, breaking through the structures in the steep frontal limbs (SOMMARUGA, 1998). 3.3 Tear faults Tear faults are small strike-‐slip faults which affect the whole Mesozoic and Cenozoic cover but do not show any offset of the basement top within the seismic resolution. (TWISS ET AL., 2007 and SOMMARUGA, 1998). These faults are defined here as belonging to an allochthonous cover with a transcurrent movement, and terminating into a décollement zone that can be well recognized on geological maps (Figure 8 right). They are sinistral and occur mainly in the Internal Jura; oriented NW-‐SE in the southern Jura, NNW-‐SSE to N-‐S in the central Jura and NNE-‐SSW in the eastern Jura (Figure 8 right). In Figure 8 the left part shows different types of tear faults. A mixture of A and B would represent the most common type in the Jura Mountains, where shortening is accommodated by trust-‐ related folds on both sides of Figure 8: Left: thrust sheets segmented by tear faults (Twiss et al., 2007). Right: location of tear faults on the Jura anticline map after Heim 1916 (SOMMARUGA, 1998). the tear fault. 11 The Geometry and Evolution of the Jura Mountains: Fernschub mechanics Tabea Kleineberg 319001 4. Fernschub hypothesis The Fernschub hypothesis was conceived by Buxtorf in 1907. It states that the process begins with the subduction of the European plate accompanied by the rise of the Aar massif (Figure 3). The resulting push affected the sedimentary wedge of the Molasse Basin and the linked Jura Mountains, resulting in deformation of the sediment cover and shear of décollement nappe. The shear was enhanced by the basal detachment, consisting of a Triassic salt layer with low friction. Beneath this detachment, the rocks remain mostly undeformed (Figure 3) (DAHLEN, 1990). 4.1 Mechanics Mechanically, a fold-‐and-‐thrust belt is similar to a wedge of snow in front of a moving snow plough (DAHLEN, 1990). The snow deforms until it develops a constant critical taper, after which it slides stea-‐ dily, continuing to grow at constant taper as additional material is accreted at the toe (DAVIS, 1983). The mechanical possibilities of thrusting an extensive thin sheet of sediments are controlled by the amount of friction at its base (LAUBSCHER, 1961), therefore an increase in the sliding resistance increases the critical taper. In contrast, an increase in the wedge strength decreases the critical taper, since a stronger wedge can be thinner, not deforming while sliding constantly over a rough base (DAHLEN, 1990). A computed specific friction value is 30 kg/cm2 for the base of the Plateaux Jura, and three times this value for the Molasse Basin. Those low values are due to plastic yielding of salt within the Triassic evaporite series (LAUBSCHER, 1961). DAVIS (1983) emphasized that fold-‐and-‐thrust belts features two further characteristics besides the above-‐mentioned basal décollement. First, large horizontal compression in the strata that overlie the décollement (see chapter 2.2 and 3) and second, a distinctive wedge shape of the deformed strata tapering toward the margin of the mountain belt (compare to Figure 3). The Jura Mountains exhibit all three characteristics. Annu. Rev. Earth Planet. Sci. 1990.18:55-99. Downloaded from www.annualreviews.org by WIB6264 - Technische Hochschule Aachen on 09/24/13. For personal use only. :K EK BȒ BK?:KKGK ?K E0J?-F5<CG(K ?:K To illustrate the kinematics behind the Fernschub-‐Hypothesis, the example of a bulldozer wedge will ο _±£Ћ ;ř GKK be used again. With a given rigid hillside of slope β with an evenly sedimented layer of thickness h {ÔЋ 1Ī SЋ AЋ {Ћ {SAɧЋ SЋ ͟ο HSЋ_ êFЋЋAЋ Ћ AЋ Ћ {SAЋ SèЋ (Figure 9), the bulldozer starts moving upwards at time=0 at an uniform velocity V, resulting in formation of a critically tapered sediment wedge in front of it (DAHLEN, 1990). The surface slope of the deformed wedge is labelled α and α+β denotes the critical '!'+ C'J'0\ E=C\ 6:0\ #Ìř ( ( ( mass "'( $( taper at the toe. The flux ±;=Óû6Ĕ;ËčĪ per unit length is characterised by GK ~Ћ $SЋ {SAЋ Ћ S2ISŭЋ SSЋ MЋ Ћ SЋ MЋ Ћ $IIĨЋ ("(+ ρhV, where ρ is the density of the {mЋ22ЋЋÔuuЋuIIuЋMЋ I2Ћ u ЋõÔЋ{uЋЋuMÔЋIÔЋ MЋ ЋЋMЋand SwЋ \ ŠMЋ ЋSЋ ο Ћ $IIĨЋ $SЋ sediment is _ĐSЋ constant SЋ2SIIЋЋЋSMЋISAЋ ;ř2SЋ2ЋBЋЋSASIIЋ2Ћ (compaction will be ignored). The {ЋMЋMЋЋ{SIIЋMЋSЋMЋMЋ ЋSЋ$IIϽmЋēAЋŢƨ Ћ AЋ MЋ I2Ћ MЋ ASЋ MЋ {ƴЋ AЋÔSASIЋ 2ЋSЋ AЋ $ÿHġillustrating ο ¢!!$ǿ iƔ$ǿ Üǿ )ª\ƕ)ǿ!@ƃǿ!ªǿ the self-‐similar growth ǿC))i!ǿ@iǿ of a bulldozer wedge mass conservation law describes Figure 9: Sketch IЋЋAЋ ʼnЋ 9ЋЋ̸qЋ2ЋSЋ Ћ ЋSwЋSЋ Ћ (DAHLEN, 1990). ЋM Ћ{ЋSЋ ř{Ћ Aο SЋAЋЋSmЋ~ЋSЋ2SЋ the growth of the wedge with Ћ Ћ Ћ SЋ Ћ AmЋ 9Ћ {Ћ MЋ Ћ {Ћ {SЋ SЋSЋ time S$ūЋ$ЋAЋЋSЋI{Ћ :K EK BȒ BK?:KKGK ?K E0J?-F5<CG(K ?:K;ř (1) ο _±£Ћ GKK {ÔЋ where WSЋ is AЋ the {Ћ wedge {SAɧЋ width. SЋ The surface slope doesn’t change ith time so the equation reduces to 1Ī ͟ο Ћ AЋ Ћ {SAЋ w SèЋ 1-;>4A HSЋ_ êFЋЋAЋ 1-;>4A =2 2 =2 =t u4d( 2 =t u4d( (2) /TXqT4quT?qf^|sXfd with the solution /TXqT4quT?qf^|sXfd ;C s4d(i (+ s4d(i (+ 0T? EWd4^4ggjfVb4uXfdVq}4^X=Cfj4 ~?=P?fC ) (3) (DAHLENd4kkf~u4g?k , 1990). 0T? EWd 4^4ggjfVb4uXfdVq}4^X=Cfj4 ~?=P?fC d4kkf~u4g?k ) ~T@n@ 4d= , 4j@ b@4q|j@= Xd j4=X4dq "?:4|q@ uT@ :jVuX:4^ s4g@j Xq Equation (3) gives a final approximation for a narrow tapered wedge, α+β << 1, if α and β are ~T@n@ 4d= , 4j@ b@4q|j@= '!'+ Xd j4=X4dq "?:4|q@ uT@ :jVuX:4^ s4g@j Xq Pf}@kd?=fd^6sT?|d}4kVdPqsk@dPsTfCsT?q4d=4d=sT?64q4^CkX9sXfd Pf}@kd?=fd^6sT?|d}4kVdPqsk@dPsTfCsT?q4d=4d=sT?64q4^CkX9sXfd 6fsT uT? ~X=uT 4d= sT?DT@XPTu 6|^^=f ?j ~?=P? ^X]? ! /T? measured in radians. ue to ifC ts 4 critical taper, the wPjf~ edges’ width and the height grow at a rate of t1/2. 6fsT uT? 4d= sT? fC 4uT4s 6|^^=f ?j ~?=P?4s Pjf~ ^X]? /T? Pkf~sT Vq~X=uT q?^DqYbV^4k VdT@XPTu sT? q?dq? sU? ~?=P? sVb? t ! Xq Vd=Xr Pkf~sT Vq q?^DqYbV^4k sU?proportionally ~?=P? s4s sVb?identical, t Xq Vd=Xr The wedges at time Vd t sT? and q?dq? time uT4s 2t b4PdVL?= are with time 2t magnified 21/2 times uVdP|XqT46^?CkfbuU?~?=P?4usXb?t Vb?q uVdP|XqT46^?CkfbuU?~?=P?4usXb?t b4PdVL?= sVb?q !d @jf=VdP~@=P@ ~X^^ 4ss5Xd 4 =d4bV9 qs@4= qs4s@ ~T@d sT@ 4;;j@ (Figure 9). The growth denoted as self-‐similar (DAHLEN , 1990). !d @jf=VdP~@=P@ ~X^^is 4ss5Xd 4 =d4bV9 qs@4= qs4s@ ~T@d sT@ 4;;j@ uVfd4kVdM|k4u?fDDk?qTb4u?kV4^VdvfuT?wf?Vq64^4d9?=6sT??kfqV}? uVfd4kVdM|k4u?fDDk?qTb4u?kV4^VdvfuT?wf?Vq64^4d9?=6sT??kfqV}? ?J|%XP|j? /T?qu?4=qs4u?~V=uT fC4|dVCfjb^?jf=XdP~?=P?Xq ("(+ ?J|%XP|j? /T?qu?4=qs4u?~V=uT fC4|dVCfjb^?jf=XdP~?=P?Xq PX}?d6uT@G`|64^4d:?:fd=VsXfd PX}?d6uT@G`|64^4d:?:fd=VsXfd A2q?:a i A2 S A2q?:a i A2 S ~T?o? ^ Vq sT? k4s? fC ?kfqVfd ! qs@4=qs4s@ ~@=P@ b|qs 9fdsVd|4^^ ~T?o? ^ Vq sT? k4s? fC ?kfqVfd ! qs@4=qs4s@ ~@=P@ b|qs 9fdsVd|4^^ =@Cfjb7fxTuf4::fbbf=4x?xT?ZdN|fFCj?qTb4x?jZ4^ZdufZyqyf?4d= =@Cfjb7fxTuf4::fbbf=4x?xT?ZdN|fFCj?qTb4x?jZ4^ZdufZyqyf?4d= sfb4Xds4XdXuq:jXsX94^s4g?j4P4Xdqs?jfqXfd sfb4Xds4XdXuq:jXsX94^s4g?j4P4Xdqs?jfqXfd 2 2 ;C v. Earth Planet. 1990.18:55-99. Downloaded from www.annualreviews.org Earth Planet. Sci.Sci. 1990.18:55-99. Downloaded from www.annualreviews.org B6264 - Technische Hochschule Aachen on 09/24/13. personal only. 264 - Technische Hochschule Aachen on 09/24/13. ForFor personal use use only. by WIB6264 - Technische Hochschule Aachen on 09/24/13. For personal use only. 12 GK ~Ћ $SЋ {SAЋ Ћ S2ISŭЋ SSЋ MЋ Ћ SЋ MЋ Ћ $IIĨЋ {mЋ22ЋЋÔuuЋuIIuЋMЋ I2Ћ u ЋõÔЋ{uЋЋuMÔЋIÔЋ MЋ ЋЋ MЋ SwЋ _ĐSЋ \ ŠMЋ ЋSЋ ο Ћ $IIĨЋ $SЋ SЋ2SIIЋЋЋSMЋISAЋ ;ř2SЋ2ЋBЋЋSASIIЋ2Ћ The Geometry and Evolution of the Jura M{ЋMЋMЋЋ{SIIЋMЋSЋMЋMЋ ountains: Fernschub mechanics ЋSЋ$IIϽmЋēAЋ Tabea Kleineberg 319001 Ţƨ Ћ AЋ MЋ I2Ћ MЋ ASЋ MЋ {ƴЋ AЋÔSASIЋ 2ЋSЋ AЋ IЋЋAЋ ʼnЋ 9ЋЋ̸qЋ2ЋSЋ Ћ ЋSwЋSЋ Ћ ЋM Ћ{ЋSЋ ř{ЋAο SЋAЋЋSmЋ~ЋSЋ2SЋ Ћ Ћ Ћ SЋ Ћ AmЋ 9Ћ {Ћ MЋ Ћ {Ћ {SЋ SЋSЋ S$ūЋ$ЋAЋЋSЋI{Ћ 4.1.1 Kinematics 9C 9C $ÿHġ ο ¢!!$ǿ iƔ$ǿÜǿ )ª\ƕ)ǿ!@ƃǿ!ªǿ ǿC))i!ǿ@iǿ *?s 6? 4 qqu?bfC #4ku?qV4d 9ffk=Vd4u?q ~VsT 4^VPd?=4^fdP uT? *?s 6? 4 qqu?bfC #4ku?qV4d 9ffk=Vd4u?q ~VsT 4^VPd?=4^fdP uT? ufgfDsT@~@=P@4d= gfVdsVdP=f~d%VP|k@0f=@u@kbVd@uT@9kVuV94_ ufgfDsT@~@=P@4d= gfVdsVdP=f~d%VP|k@0f=@u@kbVd@uT@9kVuV94_ 13 The Geometry and Evolution of the Jura Mountains: Fernschub mechanics Tabea Kleineberg 319001 4.1.2 Critical taper 1158 DAVIS ET AL.' MECHANICSOF FOLD-AND-THRUST BELTS The critical taper for the compressive wedge in Figure A 9 is governed by the balance of four forces in moving direction. First, a gravitational body force; second (in a submarine regime), the pressure of water overburden; third the frictional resistance of sliding over a basal décollement; and fourth, the compressive push of the normal tractions acting on the two side walls of the wedge (DAVIS, 1983). =7¬ !% S $ !S S (4) . =¬ =7¬ !% S $ !S S N{j{¬ Equation (4) shows that the increase of the critical dMȒ Ȓ ȒȒ%Ȓ ȒäřȒȒ Ȓ ȒĹȒȒȒ Ȓ @Ȓ@ȒȒȒȒ taper correlates with the increase of the coefficient of Ȓ Ȓ ƤȒ %Ȓ Ȓ ȒȒ ȒȒ> Ȓ >Ȓ4 Ȓب Ȓ ţ>ȒØȒ Ȓ@ Ȓ ' Ȓ>Ȓ >@Ȓ T the basal friction μ , as it was already mentioned in Ȓ dMȒ Ȓ Ȓ Ȓby Ȓ Ȓ%Ȓ Ȓ©uåùřof ȒĹȒ Ȓthe ȒȒ Ȓ @Ȓ@ȒÅȒ ȒȒȒ ȒȒ ȒȒ4'Ȓ2@Ȓ ~ ȒýȒ 4Ȓ 4.1, while it decreases an internal Ȓ Ȓ ƤȒ %Ȓ Ȓ %Ȓ äincrease řȒ Ȓ Ȓ 'Ȓ Ȓ Ȓ Ȓ Ȓ Ȓ 4Ȓ ȒȒ %ȒȒ ȒȒ> Ȓ >Ȓ4 Ȓب Ȓ ţ>ȒØȒ Ȓ@ Ȓ ' Ȓ>Ȓ >@Ȓ T Ȓ Ȓ 4 Ȓ %Ȓ Ȓ ŁȒ Ȓ Ȓ % Ȓ Ȓ Ȓ %Ȓ Ȓ Ȓ %Ȓ friction angle ϕ. For the typical value for dry sand of Ȓ Ȓ ȒȒ Ȓ @Ȓ õȒ < Ȓ%Ȓ ȒȒ ȒȒ4'Ȓ2@Ȓ ©uåùř ~ ȒýȒ 4Ȓ 'Ȓ Ȓ Ȓ Ȓ Ȓ Ȓ 4Ȓ Ȓ dMȒ ȒȒMOƺȒ2 Ȓ%Ȓ%ȒȒ@ȒČ %ȒȒ ÅȒ ϕ=30°, the critical surface slope is given by α≈⅓(μ -‐2β) Ȓ Ȓ 4 Ȓ %Ȓ Ȓ ŁȒ Ȓ Ȓ % Ȓ Ȓ Ȓ %Ȓ Ȓ Ȓ %Ȓ X Ȓ³4Ȓ4Ȓ ȒȒȒ% Ȓ < Ȓ 8Ȓ XȒȒ%ȒȒ (D :ȒȒ , 1990). Ȓ Ȓ ``²Ȓ Ȓ Ȓ ȒȒ%Ȓ%ȒȒ@ȒČ ȒȒȒ @Ȓ Ȓ@Ȓ õ< ȒȒÅ 'ȒȒ Ȓ `>Ȓ Ȓ̀ Ȓ̀ Ȓ `Ȓ ǻ>2> : æȒ Ȓ ² >`²@Ȓ̀ > Ȓ dMȒ ȒȒMOƺȒ2 In a Ȓ critically tapered wedge, the Ȓ horizontal 4T Ȓ Ȓ Ȓ @Ȓ Ȓk 2Ȓ% ŐȒ XȒȒ%ȒȒ X Ȓ³4Ȓ4Ȓ ȒȒȒ% Ȓ < Ȓ8Ȓ Ȓ : Ȓ ȒȒ @Ȓ Ȓ ȒȒÅ Ȓ 'ȒȒ Ȓstress σ ≈ -‐ρgz by the Coulomb compressive &K stress σȒ is related with the lithostatic overburden Ń 8 řȒ `>Ȓ Ȓ̀ Ȓ̀ Ȓ `Ȓ ``²Ȓ ǻ>2> : Ȓ æȒ Ȓ ² >`²@Ȓ̀ > Ȓ 11ř failure 4T Ȓ law ȒłȒ ȒȒ @ȒȒk2Ȓ%ȒŐȒ Ȓ- &K}ŕ`ě8řYȒ ŃȒqȒ 4Ȓ4Ȓ ȒȒȒ ȒȒȒř ĬąÐř ȒȒ 4ȒȒ ȒȒȒȒȒȒ 11ř 4ȒȒ łȒ O . Ȓ y Ȓ cȒXȒ- q Ȓ 4ȒȒ ȒȒ Ŗŗ ĺīôř ǭȒ t Ȓ ÃȒȒ2Ȓ }ŕ`ěa ȒȒ Ã(subcritical) Ȓt tȒtćÃȒ % ȒȒȒ %Ȓ ćt Ȓ- qȒ 4Ȓ4Ȓ ȒȒȒ Ȓ řσ Ȓ would fail, and increase its Therefore, thinner wedge with t4Ȓt%Ȓ a greater σȒȒ than YĬąÐř 4ȒȒ ȒȒ 4Ȓ Ȓ ȒȒȒȒ ȒȒ Ȓ Ȓ < Ȓ ~Ȓ 4Ȓ Ȓ Ȓ : 'Ȓ 'Ȓ Ȓ Ȓ Oĺīôř with a lower σ than σ taper until it gets critical. In contrast, a Ȓ thicker (supercritical) Ȓ y Ȓ cȒXȒ- q Ȓ 4ȒȒ ȒȒ Ŗŗwedge Ȓ @Ȓ Ĝ Ȓ Ȓ Ȓ Ȓ 4Ȓ R Ȓ Ȓ Ȓ 4Ȓ 2: ȒȒ ȒȒ Ȓ ȒtȒtćÃȒ % Ȓ4Ȓ ȒȒ%ȒȒ Ȓ< Ȓc@Ȓ 4Ȓ ȒȒ %ćt ' Ȓ Ȓ ȒȒ ǭȒ t Ȓ ÃȒȒ2Ȓ ÃȒt t4Ȓt%Ȓ ȒȒȒȒ %Ȓ would not deform if no fresh material would be encountered at the toe (D , 1990). @Ȓ4Ȓ Ȓ Ȓ 4'Ȓ% Ȓ Ȓ < Ȓ ~Ȓ Ȓ : Ȓ 'Ȓ Ȓ O `aY Ĝ ȑ Ȓ >depicting Ȓ Ȓ Ȓin ȒyȒsuch a wedge, where (A) 'Ȓ Ȓ 4Ȓ @Ȓ ƮȒ Ȓdiagram ȒȒ ȒȒȒ 4Ȓ <ȒȒ%Ȓ Ȓ RȒ Ȓ ȒȒ Ȓ |ł ř 0, In Figure 1 MȒ ohr is shown the state of stress 1ÒÓ 2 : Ȓ Ȓ Ȓ Ȓ Ȓ c@Ȓ 4Ȓ % illustrates the stress at an arbitrary pȒ%ȒȒ oint and (B) at the base of the wȒedge. ψ and ψ are the angles @Ȓ4Ȓ Ȓ Ȓ 4'Ȓ% Ȓ ȒȒ OY ` ȒȒȒ> Ȓ%ȒȒȒȒ y@ȒȒ 'Ȓ |ł1ÒÓřσȑ and tƮȒ between he x axis within the wedge and base of the wedge, while ϕ and ϕ represent the 8Ȓ Ȓƚ Ȓ 4Ȓ%ȒXȒȒȒȒȒȒ4¶¹ Ȓ2@ȒȒ>Ȓ%Ȓ>Ȓ Ȓ`>Ȓ> Ȓ>Ȓ ¨4ȒȒ Ȓ8Ȓ failure law |τ| = μ σ * with angles of the internal and basal friction. The intersection of the frictional 8Ȓ >Ȓ> Ȓ @ Ȓ2@Ȓ>O Ȓ>>ȒȒǼ>>`Ȓ% the Mohr stress circle corresponding to the basal depth H gives @Ȓ the @bȒasal shear traction τ . σ * and öȒƻ³ȒȒȒȒ Ȓ Ȓ ȒȒ%ȒªȒ Ȓƚ Ȓ4Ȓ%ȒXȒȒȒȒȒȒ4¶¹ 8Ȓ Ȓ Ȓ C @ Ȓ Ȓ Ȓ Ȓ Ȓ 4Ȓ 'Ȓ Ȓ2@ȒȒ>Ȓ%Ȓ>Ȓ Ȓ`>Ȓ> Ȓ >Ȓ ¨ Ȓ 8ȒȒ respectively (D , 1983). σ>Ȓ> * denote the m aximum a Ȓ nd m inimum effective % compressive s4 tresses, @Ȓ < Ȓ ¬Ȓ Ȓ Ȓ Ȓ Ȓ '@Ȓ 4Ȓ Ȓ öȒƻ³ȒȒȒȒ Ȓ @ Ȓ2@Ȓ>O Ȓ>>ȒȒǼ>>`Ȓ% 4ȒȒ ȒȒ>Ȓ ȒȒ Ȓ C Ȓ%ȒȒ%ȒĊ> Ȓ@ȒȒȒƩ ȒȒȒ ȒȒ%ȒªȒ @Ȓ >Ȓ Ȓ é2>Ȓ s>Ȓ Ť 22>Ȓ 2@Ȓ 8Ȓ Ȓ @ Ȓ Ȓ Ȓ Ȓ Ȓ 4Ȓ 'Ȓ 8ȒȒȒ2 ȒȒȒȒ2Ȓ' X ȒȒ'Ȓ ȒȒȒ @Ȓ < Ȓ ¬Ȓ Ȓ Ȓ Ȓ Ȓ Ȓ '@Ȓ % 4Ȓ Ȓ 4 @ : Ȓ ȒȒ ȒȒȒ Ȓ Ȓ < Ȓ ȒȒ>Ȓ Ȓ%ȒȒ%ȒĊ> Ȓ@ȒȒȒƩ ȒȒȒ >Ȓ Ȓ-é2>Ȓ s>Ȓ X ȒȒ'Ȓ Ť22>Ȓ 2@Ȓ ȒȒ 8ȒȒȒ2 ȒȒȒȒ2Ȓ' @:Ȓ ȒȒ ȒȒȒȒ Ȓ<Ȓ /=¬ ;] N{j{¬ 'ο 8$ª¬ b /=¬ Annu. Rev.Annu. Earth Rev. Planet. Sci.Planet. 1990.18:55-99. Downloaded from www.annualreviews.org Earth Sci. 1990.18:55-99. Downloaded from www.annualreviews.org by WIB6264 Technische HochschuleHochschule Aachen on Aachen 09/24/13. personal usepersonal only. use only. by-WIB6264 - Technische onFor 09/24/13. For •b . =¬ 7$«¬ (2¬ ²ƨ AHLEN ĚõīĵźŜĕƨ ŘЋ ĚõīĵźŜĕƨ (2¬ •* E¨¨ο # $ E¨¨ο h GƘƙƨ Ƨƨ g AʽήĿο GƘƙƨ Ƨƨ g AʽήĿο gg} be written h as •'0 = /XbO'z *= ,U,b(1- Ko)pgH (8) where/x0= tan (b0is thebasalcoefficient offrictionand)tois the generalizedHubbert-Rubeyratio (6) on the base. In gg} introducing thebasalvaluesgoand)towe allowexplicitly zzfor ÊЋ weakness,either becauseof a lower intrinsic strengthor because of elevated fluid pressures.For a wedge with uniforminternalproperties/x and X, we must necessarily have(1 - •.b)ld, b • (1 - X)/xfor the baseof the wedgeto be a throughgoingdecollement. To determinethe remainingunknown quantity tr; in the /?¬ hh} /?¬ # $ |} |} Fig. 6. Mohrdiagram illustrating thestateof stress (a) at somepointwithinthewedge and(b)at thebaseof the wedge. Thequantities 4•and4•,aretheangles ofinternal andbasal friction, and½and%,aretheangles between o-•and thex axiswithinthewedge andat thebaseof thewedge. Thebasalsheartraction r/,isgivenbytheintersection of the frictional failurelaw Irl = •,rr,* withtheMohrstress circlecorresponding to thebasaldepthH. Figure 10: Mohr diagram depicting the state of stress (A) at some point within the wedge and ÊaЋt frictional the bsliding ase o the edge (Dthat AVIS , basal 1983). the fact the decollementwill usually be a zone of The traction•'0(B) resisting onf the basew will b 7$«¬ xx |} |} E¦¦ο ;]f QʀF\Ћ ;] 'ο 8$ª¬ ôƨ ¬ƨ f QʀF\Ћ ;] C ôƨ ¬ƨ ²ƨ E¦¦ο 0 ÊЋƍƎƨ ŘЋ xx xx failure hh} xx ÊЋƍƎƨ xx AHLEN F śĔä ( ( ( ( ( "( "( F 1 b śĔä b ( ( ( ( ( "( "( Ī /C:C¬ 3 /C:C¬ . D>&¬ . D>&¬ . D> . ¬ . D> . ¬ ο ο b n b 7$¬ Ī . D>& . D>7$¬ . !¬ . D>& . D> . !¬ AVIS 1 failure between wedge taper (α, β), thickness H, and strength parameters is the elegant general weak-base theory of Dahlen (1990), which we take as our starting point, using the special case of a mechanically homogeneous wedge 1990, equation 99): of the Jura Mountains: Fernschub mechanics Tabea Kleineberg 319001 The (Dahlen, Geometry and Evolution xceedingly weak questions. thrust belt, Niger 14 α+β = ) ( β 1 − ρf ρ + µ b (1 − λ b ) + Sb ρgH , sin φ 1 − ρ f ρ + 2 (1 − λ ) + C ρgH 1 − sin φ (1a) aults within it has eorge Airy recog- 4.2 Laboratory experiments an the strength of The theory mentioned in 4.1 states that the covariation of surface slope α with décollement dip β is remain difficult to where Sb and C are the non-pressure-dependent parts of the fault and wedge and theories con- used strength. equations contain a number of fault to Such determine the strengths of average active regional-scale thrust-‐belt wedges and their basal décollement. It was observe. Available and crustal strength parameters about which we would like to know much significant fraction tested more, butwith unfortunately have little direct constraint in actively deforming a sandbox deformational model in the laboratory by SUPPE (2007), among others. The 1978), suggesting regions. Therefore we simplify Equation 1a to something more manageable conducted mechanics into a very simple form, to 997; Townend and experiments by collecting the were fault-strength terms asto F =recast µb (1 − critical-‐taper λ b) + Sb /ρgH andwedge the st sheets, some of wedge-strength terms as W = 2(1 − λ)[sinφ/(1 − sinφ)] + C/ρgH, obtaining determine absolute regional strength achments relative sion and probably fluid pressure. Mechanically heterogeneous wedges 1 − ρ f ρ + F β lem addressedαby (1b) require more observational constraints +β = . are beyond the geometries scope of this from andobserved in 1 − ρ f ρ + W ges and fold-andsion and fluid pressure. Mechanically Dry-sand wedge short paper (seeprobably Fletcher, 1989; Dahlen, 1990, equations heterogeneous 98 and 103). wedges β 1 − ρ f ρ + F al strength within α + β = (1b) Carena . α require et more observational constraints aremeasurements beyondconditions. the scope al. (2002) presented a set of and taper acrossof this appropriate geologic The Mylar − ρf ρ + W tence, cause, and short paper Fletcher, 1989; Dahlen, 1990, equations 98 andslope, 103). (Fig. simplified equation 8° raises a1hope that we might constrain the Taiwan 2A)(see that shows a quasi-linear relationship of negative base β oversial. Much of mechanical in Shaw the (2005) laboratory Carena et al. (2002)wedges. presented a setmodel ofBilotti taperand measurements across wedge strengths (F, W ) from appropriate observations of wedge as predicted for homogeneous Similarly, faults such as the Taiwan (Fig. 2A) This simplifi equationbecause raises athehope we might thatkm) shows a quasi-linear negative slope, β). This seemsedplausible onlythat remaining termconstrain in the the presented regional (~100 measurements of relationship taper in theofdeep-water Take-up spool enbruch and Sass, consists of a bottomless box containing t[1and wedge strengthsthe (F,ratio W ) of from observations predicted for of homogeneous wedges. Similarly, Bilotti andrelationShaw (2005) − (ρ thrustasbelt of the toe the Niger delta that show a quasi-linear the appropriate density of the overlying flof uidwedge f /ρ)], contains Scholz and Hanks, ship with a negative slope(~100 (Fig. km) 2B).measurements We compute the air)β).toThis the seems mean density rock and thusremaining 1 for subaerial peor(α, plausibleofbecause theisonly term in the presented regional of normalized taper in thewedge deep-water sand with transparent side walls, which xen, 2004). – s strength W = (σ nd ~0.6 wedges. Furthermore, it can be shown that − σ )/ρgH based on the regression slopes and obtain ation, [1for − (ρsubmarine thrust belt of the toe of the Niger delta that show a quasi-linear relation/ρ)], contains the ratio of the density of the overlying fl uid f 1 3 cast critical-taper 4° shear egional traction F =and στ /ρgH, similar results both wedges. Taiwan gives W = 0.6 and the Niger delta ship withfor a negative slopesits (Fig.upon 2B). We compute the normalized wedge water ornormalized air) to the basal mean density of rock is thusdetermined 1 for subaerial a sheet of Mylar. The base very simple form gives strength ure on detachment, and W is the normalized differential W = 0.7,Wwhich moderately wedges, as discussed = (σ1indicate ges andthe ~0.6 for submarine wedges. Furthermore, it can be stress shown that − σ3)/ρgH based onstrong the regression slopes and obtain absolute regionalsection. The normalized basal shear F =flat στ /ρgH, σ )/ρgH at failure (see Dahlen, 1990, traction equations 91, 97). In in thesimilar the normalized basal shear F 88, = σ90, results for both wedges. gives Wlies = 0.6is and the Niger upon Taiwan which it traction and delta rigid τ /ρgH, determined βnext 2 regional ctive critical-taper α=be 0° considered an effective coefficient of friction, is F = 0.08 wefailure show on twothe ways to apply this simplifi ednormalized Equation 1b. whichgives can he detachment, and W is the differential stress W = 0.7, which indicate moderately strong wedges, as discussed apply this theory, (Figure 11, basal top right) (D AVIS 1983). critical α (see of a Dahlen, mechanically homogeneous wedge = 0.04 for Niger delta. The shear observed ratio (σ1 −wedges. in the and nextF section. Thethe normalized traction Fof, =fault στ /ρgH,By σ2surface )/ρgH atslope failure 1990, equations 88, 90, 91, 97). for In Taiwan rong related the dip the detachment as shown by rearranging strength to wedge F/Wan=effective στ /(σ1 −coeffi σ3) is 0.13offor Taiwan paper wetoshow twoofways to apply thisβ,simplifi ed Equation 1b. which can be strength considered cient friction, is and F = 0.08 0° the Mylar sheet, the will 1b: Nigerand delta. results that the The basal detachments are forthe Taiwan F =These 0.04 pulling for theshow Niger delta. observed ratiosand of fault 0°of a mechanically 4°homogeneous wedge 8° 0.06 for SThe critical surface slope α β exceedingly weak absolutely and relative to the wedge strengths. nearly related to the dip of the detachment β, as shown by rearranging strength to wedge strength F/W = στ /(σ1 − σ3) is 0.13 for Taiwan and cs is that actively F W get pressed against the back wall, Dry-sand (2a) = βtapers , − ation 1b: 0.06 for the Niger delta. These results show that the basal detachments are es areα simultane1 − ρ f ρ + W 1 − ρ f ρ + W COMPARISON DEEP BOREHOLE DATA exceedingly WITH weak absolutely and relative to the wedge which is plausible miming tfrom he pTaiwan rocess of the pstrengths. late subduction. Figure Schematic W model of critical taper laboratory measurements. F 11.1: Critical-taper We compare the wedge strengths W and Niger delta Figure measurements of dry-sand wedges on Mylar (2a) α = β , − e by deformation Linear regression gives a slope to compute the fault and wedge detachment (Davis 1983). Linear regression gives a slope 1 − ρ fetρ al., +W with stress measurements from two scientifi c boreholes (Fig. 3). In the Gerhe equation of a1line off negative ρ ρ + W slope COMPARISON WITH DEEP BOREHOLE DATA To minimize inhomogeneities, the sand − strengths , and UPPE 2007). s = 0.66 ±(S0.14 an intercept βα= 0° = 5.6°man ± 0.2°, which we σ use to KTB borehole is vertical (Brudy et al., 1997), whereas in compresWe compare 2 the wedge strengths W from Taiwan and the Niger delta Taiwan University, compute the fault and wedge strengths (F, W ) using Equations 3 σ3is ismeasurements vertical; therefore we scientifi represent the KTB stress data as Ger= α4βof ,e packed t−negative o sβbtext). side wsive all wedges fwith riction reduced by from a graphite coating (DAVIS , 13). 983). =0 stress two c boreholes (Fig. In the ch is the equation of αneeds a line slope evenly and (2b) and (see W* =man (σ1 −KTB σ3)/σborehole , which σ is directly comparable to W.1997), W* iswhereas relatively con3 is vertical (Brudy et al., in compres2 compute the regression fault and (2b) wedge equations are necessary to draw a linear stant as astrengths, function indicating that the regionthe is KTB dominated andorder intercept obtained by linear = 0 and s are the slopeIn sive wedges of σ3depth, istwo vertical; therefore weKTB represent stressby data as α = α βto =0 − sβ, strength, with W* = 1.0 ± 0.2 to a depth of 8 km. data contact (α, β) from an active mechanically wedge pressure-dependent oe copy, Copyright Permissions, GSA, orhomogeneous editing@geosociety.org. W* = (σ1 − σ3)/σ3, which is directly comparable to W. W* is relatively conregression left). Both Inresult from the rearranging of equation (99) from 0.1130/G24053A.1; 5 fifi gures. contrast, W in1127 thedepth, California SAFOD pilot hole (Hickman andDAHLEN From 2 we nd that wedge(Figure strength 11 W isbottom a very simple re αβ Equation stant as a function of indicating that the KTB region is dominated by = 0 and s are the slope and intercept obtained by linear regression Zoback, 2004) shows a strong decrease 3),a suggesting that of the slope pressure-dependent strength, with with W* =depth 1.0 ±(Fig. 0.2 to depth of 8 km. uitable data of (α,the β)regression from an active mechanically homogeneous wedge (1990). The wedge strength W is a simple function of the slope of the regression (equation (4)) and the measurements, which a depth of 1–2SAFOD km in granite, are still within and In contrast, Ware in atthe California pilot hole (Hickman . 1). From Equation 2 swe find that wedge strength W is a very simple 1 − ρ f ρ , the near-surface boundary in which cohesion dominates (cf.suggesting (3)strength Zoback, 2004) showslayer a strong decrease withtimes depth (Fig. 3), that ction of the slopeWof=the equation (5) shows that the fault F is the regression intercept βα=0 wedge sDahlen trength. 1 −regression s et al., the 1984). The cohesive strength C = ~46 MPa given by linear regression measurements, which are at a depth of 1–2 km in granite, are still within s strength F is simply the regression β (Fig. 1) times of the data is a factor of four less than the borehole-scale cohesion estimated 1 − intercept (3) the near-surface boundary layer in which cohesion dominates (cf. Dahlen W= ρ f ρ , α=0 for the SAFOD pilot hole at 197–212 MPa (Hickman and Zoback, 2004). ength 1− s (4) et al., 1984). The cohesive strength C = ~46 MPa given by linear regression Knowing C, we obtain the pressure-dependent component of the stress of fault strength F is simply the regression intercept βα=0 (Fig. 1) times of the data is a factor of four less than the borehole-scale cohesion estimated (4) F = β α = 0W . for the SAFOD pilot hole at 197–212 MPa (Hickman and Zoback, 2004). ge strength (5) Knowing C, we obtain the pressure-dependent component of the stress of s is the , we should be ablewhere to determine theslope. wedge and detachment (4)4° A) F = β α = 0W . (W, F) simply from the linear covariation of surface slope α Taiwan tapers Based on this linear wedges, regression, t is possible to determine the wedge and décollement strength. chment dip β in mechanically homogeneous based ion refore, we should be able to determine the wedge and detachment ression. 4° A) ngths (W, F) simply from the linear covariation of surface slope α2° Taiwan tapers β = 7.7° h detachment dip β in mechanically homogeneous wedges, based on α α = 0° ATION TO ACTIVE WEDGES β 0° 2° fiarrstregression. consider laboratory experiments with dry-sand wedges on a 5° 10° 15° 20° β = 7.7° se, looking at the response of critical surface slope α to changes α α = 0° PLICATION TO1). ACTIVE WEDGESof the data of Davis et al. ment dip β (Fig. Linear regression –s = –0.37 β Weafibasal rst consider laboratory experiments dry-sand wedges on a-2° 0° elds coefficient of friction of F = µwith 5° 10° 15° 20° b = 0.27 and a wedge ar base, looking at the response of critical surface slope α to changes W = 1.9, which corresponds to a cohesionless internal friction of etachment dip βvalues (Fig. are 1). Linear of the of Davis –s = –0.37 = 0.57. These similarregression to the basal anddata internal fric- et al. -4° -2° 83) yields a basal coeffi cient of friction of F = µ = 0.27 and a wedge b et al. (1983), = 0.3, µ = 0.58) measured independently by Davis ngth = 1.9, which corresponds to and a cohesionless internal g theWviability of estimating wedge fault strengths fromfriction the of2° B) tanφ = 0.57. These values arefisimilar to the basal and internal fricNiger delta tapers variation of α and β, if we can nd suitable geological examples -4° –s = –0.55 s (µbdetachment = 0.3, µ = 0.58) independently Davis et al. (1983), α able dip β measured and plausible mechanicalby homogeneity. gesting the of estimating wedge andand fault from the 2° B) consider twoviability active geologic wedges, Taiwan thestrengths Niger delta, 1° Niger delta tapers ar covariation of α and β, if we can fi nd suitable geological examples approximate the assumption of large-scale homogeneity because –s = –0.55 α h variable detachment dip β and plausible mechanical homogeneity. β w approximate linear covariation of α and β, and because they are α = 0° = 3.35° geologic andlikely the Niger ckWe (Hconsider = 5–12 two km);active therefore theirwedges, strengthsTaiwan are less to be delta, may approximate assumption of large-scale homogeneity because0° 1° hanging laterally. Inthe contrast, the thin toes (H < ~1 km) of active β βα = 0° = 3.35° show approximate linear covariation of αBarbados and β, and because they are 0° 1° 2° 3° 4° ary wedges such as the Nankai trough and show surface +α ( ( ) )( ) ( ) ( ) −α ( ) ( ) ( ) ) ( ( ) ( ) 15 The Geometry and Evolution of the Jura Mountains: Fernschub mechanics Tabea Kleineberg 319001 5. Conclusion The Jura Mountains and the Molasse Basin are closely linked and share a mutual evolution. Figure 12 depicts a simplified sketch of their evolution and the accompanied formation into an foreland fold-‐ and thrust belt. In the buckling stage, folds evolve to low-‐amplitude buckle folds in response to compression induced by the rise of the Aar-‐massif. The weak Triassic evaporites infill the space generated by rising anticlines at the space of the sedimentary cover. After thickening of the basal zone, fault ramps nucleate and prograde upwards, doubling the sediment cover (SOMMARUGA, 1998). This evolutionary stage resulted in the present day structural units of the Jura Mountains. Evaporite-‐ and thrust-‐related folds, as well as tear faults are its major tectonic features. In contrast, the Molasse Basin stayed relatively undeformed. The paper by Eva Görke elaborates in more detail on the sedimentary wedge, as well as further features of the Molasse Basin and the paper by Simon Freitag concentrates on the Hydrocarbon-‐ system within the Jura-‐arc-‐Molasse-‐Basin-‐system. The underlying mechanics of fold-‐and-‐thrust belts can be described by the wedge forming in front of a snow plough/bulldozer. Various papers (both older and more recent) give accurate descriptions of these processes, so that fold-‐and-‐thrust belts and accretionary wedges are one of the best understood deformational features of the Earth’s upper crust (DAHLEN, 1990). Figure 12: Conceptual evolutionary stages of the Jura foreland between 20-‐15 Ma. This sketch is without scale (SOMMARUGA, 1998). 16 The Geometry and Evolution of the Jura Mountains: Fernschub mechanics Tabea Kleineberg 319001 6. Literature LAUBSCHER, H. (1961): Die Ferschubhypothese der Jurafaltung. Eclog. Geol. Helvet., 54, 221-‐281. AFFOLTER, T., GRATIER, J.-‐P. (2004): Map view retrodeformation of an arcuate fold-‐and-‐thrust belt: The Jura case; J. Geophys. Res. 109, B03404 BECKER, A. (2000): The Jura Mountains -‐ an active foreland fold-‐and-‐thrust belt; Tectonophysics 321, 381-‐406 SOMMARUGA, A. (1999): Décollement tectonics in the Jura foreland fold-‐and-‐thrust belt; Marine and Petroleum Geochemistry 16, 111-‐134 BITTERLI, T (1990): The kinematic evolution of a classical Jura fold : a reinterpretation based on 3-‐ dimensional balancing techniques (Weissenstein Anticline, Jura Mountains, Switzerland) ; Eclog. Geol. Helvet., 83, 493-‐511 PFIFFNER, O.A. (2010): Geologie der Alpen; Haupt: Bern, Stuttgart, Wien. TWISS, R. J., MOORES, E. M. (2007): Structural Geology; Freeman and Company: New York. BURKHARD (1990): Aspects of the large-‐scale Miocene deformation in the most external part of the Swiss Alps (Subalpine Molasse to Jura fold belt). Eclog. Geol. Helvet., 83, 559-‐583. DAHLEN, F.A. (1990): Critical taper model of fold-‐and-‐thrust belts and accretionary wedges: Annual Review of Earth and Planetary Sciences, v. 18, p. 55–99. DAVIS, D., SUPPE, J., AND DAHLEN, F.A., 1983, Mechanics of fold-‐and-‐thrust belts and accretionary wedges: Journal of Geophysical Research, v. 88, p. 1153–1172. SUPPE, J. (2007): Absolute fault and crustal strength from wedge tapers. The Geological Society of America, v. 35, no. 12, p. 1127-‐1130.