Stratigraphic Controls on Vertical Fracture Patterns in Silurian

Total Page:16

File Type:pdf, Size:1020Kb

Stratigraphic Controls on Vertical Fracture Patterns in Silurian Stratigraphic controls on AUTHORS Chad A. Underwood ϳ Geological vertical fracture patterns in Engineering Program, University of Wisconsin, Madison, Wisconsin, 53706-1692; current Silurian dolomite, northeastern address: Montgomery Watson Harza, One Science Court, Madison, Wisconsin, 53711; Wisconsin [email protected] Chad A. Underwood received a B.S. degree in Chad A. Underwood, Michele L. Cooke, J. A. Simo, geology from the University of Wisconsin at and Maureen A. Muldoon Eau Claire and an M.S. degree in geological engineering from the University of Wisconsin at Madison. He currently works as a geotechnical engineer for Montgomery ABSTRACT Watson Harza (MWH) in Madison, Wisconsin. Vertical opening-mode fractures are mapped on quarry walls to Michele L. Cooke ϳ Geosciences assess the stratigraphic controls on fracture patterns in the relatively Department, University of Massachusetts, undeformed Silurian dolomite of northeastern Wisconsin. Our two- Amherst, Massachusetts, 01003–5820; [email protected] stage study uses maps of vertical fractures to assess the effectiveness of various types of stratigraphic horizons (e.g., organic partings or Michele L Cooke received a B.S.E. degree in cycle-bounding mud horizons)in terminating opening-mode frac- geological engineering from Princeton tures. First, the mechanical stratigraphy of the exposures is inter- University and an M.S. degree in civil engineering and a Ph.D. in geological and preted from the observed fracture pattern. Both visual inspection environmental sciences (with mechanical and a newly developed quantitative method are employed to iden- engineering minor) from Stanford University. tify effective mechanical interfaces. The two methods show similar Currently an assistant professor of results, confirming the validity of qualitative visual inspection. The geosciences at University of Massachusetts– second stage of our study stochastically predicts mechanical stratig- Amherst, her research applies structural raphy and subsequent fracture pattern from empirical relationships geology and rock fracture mechanics to between the observed sedimentary stratigraphy and the interpreted investigate deformation of active and ancient mechanical stratigraphy. For example, 63% of cycle-bounding mud structures. horizons within the inner-middle and middle shelf facies associa- J. A. Simo ϳ Geology and Geophysics tions serve as mechanical interfaces. These empirical percentages Department, University of Wisconsin, are input to a Monte Carlo analysis of 50 stochastic realizations of Madison, Wisconsin, 53706–1692; mechanical stratigraphy. Comparisons of the stochastically pre- [email protected] dicted and interpreted mechanical stratigraphy yield errors ranging Toni Simo received both an M.S. degree from 13 to 33%. This method yields far better results than assuming (1982) and a Ph.D. (1985) from the University that all stratigraphic horizons act as mechanical interfaces. The of Barcelona. He was a Fulbright Scholar methodology presented in this article demonstrates an improved before joining the Department of Geology and prediction of fracture pattern within relatively undeformed strata Geophysics, University of Wisconsin–Madison from both complete characterization of sedimentary stratigraphy in 1989. His primary interest is in carbonate and understanding mechanical controls on fracturing. sedimentology, sequence stratigraphy of sedimentary basins, and environmental sedimentology. Recent work in these areas includes Paleozoic epeiric sea deposition and shelf margins in the United States, synsedimentary facies associated with contractional settings in Spain and Indonesia, and stratigraphic implications in rock Copyright ᭧2003. The American Association of Petroleum Geologists. All rights reserved. fracturing and arsenic contamination. Manuscript received November 16, 2000; provisional acceptance September 21, 2001; revised manu- script received June 17, 2002; final acceptance July 29, 2002. AAPG Bulletin, v. 87, no. 1 (January 2003), pp. 121–142 121 INTRODUCTION Maureen A. Muldoon ϳ Geology Department, University of Wisconsin, Oshkosh, Wisconsin, 54901–8649; Fracture patterns exposed on both horizontal surfaces (e.g., Dyer, [email protected] 1988)and vertical outcrops (e.g., Gross et al., 1995; Bahat, 1999) Maureen Muldoon received her M.S. degree have been used to infer paleostress orientations and, thus, give evi- and Ph.D. from the University of Wisconsin– dence of the tectonic history of a region. Interpreting the geologic Madison. She worked at the Wisconsin history from vertical outcrop patterns of fractures requires consid- Geological and Natural History Survey for eration of both tectonics and stratigraphy, which can both produce seven years before joining the faculty at the variations in the fracture pattern (see Dholakia et al., 1988; Gross University of Wisconsin–Oshkosh. Her et al., 1995). Furthermore, determining the stratigraphic controls research interests include the investigation of on opening-mode fracture patterns helps us better predict the sub- groundwater quality and flow in carbonate surface flow paths of fluids such as ground water (e.g., Muldoon rocks, relationship between stratigraphy and and Bradbury, 1998)and hydrocarbons (e.g., Nelson, 1982).Un- hydraulic properties, land use impacts on derstanding the development of fracture networks within aquifers groundwater quality, and delineation of and reservoirs can improve fluid-flow prediction by constraining wellhead protection zones in fractured rock. some of the uncertainty in fracture characteristics, such as fracture length, aperture, and connectivity. In relatively undeformed sedimentary rocks, the density and height of opening-mode fractures (joints)are typically controlled by stratigraphy rather than faulting or folding (e.g., Becker and Gross, 1996; Hanks et al., 1997). Under these conditions, fracture density typically depends on the material properties and bed thick- ness of stratigraphic units (e.g., Huang and Angelier, 1989), because fractures commonly terminate at specific stratigraphic horizons (e.g., Gross et al., 1995). However, the pattern of fracturing is di- rectly controlled by mechanical stratigraphy, which does not nec- essarily correspond to the sedimentary stratigraphy (e.g., Corbett et al., 1987; Gross et al., 1995; Hanks et al., 1997). A mechanical unit represents one or more stratigraphic units that fracture inde- pendently of other units (Figure 1). Fractures typically span the thickness of the mechanical unit and commonly abut the bounding stratigraphic horizons. Such stratigraphic horizons along which many fractures abut are termed “mechanical interfaces” (Figure 1) (Gross et al., 1995). Consequently, the stratigraphic features that comprise the me- chanical stratigraphy of a sequence are those that control fracture initiation and termination in rock strata (e.g., Gross, 1993). Vertical opening-mode fractures (joints)commonly initiate from flaws somewhere within a mechanical unit and terminate at mechanical interfaces (Gross, 1993). In layered formations consisting of inter- bedded brittle/ductile rocks, fractures typically initiate in the brittle layer and terminate at the contact with ductile layers (e.g., Cook and Erdogan, 1972; Erdogan and Biricikoglu, 1973; Helgeson and Aydin, 1991; Rijken and Cooke, 2001). Within relatively homo- geneous layered formations, fractures may terminate at mechanical interfaces because of interface slip (e.g., Teufel and Clark, 1984; Renshaw and Pollard, 1995)and/or local debonding along inter- faces that are weak in tension (Cooke and Underwood, 2001). Whereas interface properties control fracture termination, me- chanical unit thickness, or spacing of mechanical interfaces, controls fracture density. Predicting fracture density therefore requires 122 Vertical Fracture Patterns in Silurian Dolomite (A) Figure 1. (A) Stratigraphic controls on fracture patterns. Fractures develop within me- Mechanical Unit chanical units and abut me- (may contain one or more chanical interfaces (modified stratigraphic horizons) from Gross et al., 1995). In- creased fracture density directly Mechanical Interface correlates with increased frac- at a Stratigraphic Horizon ture porosity. Both effective po- rosity and effective permeability are highly dependent on the connectivity of the fracture net- work; therefore, increased frac- ture density does not necessar- ily lead to increased Fracture permeability. (B) Termination of vertical fractures can redirect the vertical component of flow Exposed Vertical Fractures (B) Fluid to horizontal features, such as Flow dissolutionally enlarged bedding planes. Laterally extensive hori- Mechanical zontal high-permeability fea- Unit tures are continuous up to 14 km (9 mi) based on hydrogeo- logic studies of the Silurian do- lomite (Muldoon et al., 2001). Mechanical Interface Fracture knowledge of the distribution of mechanical interfaces. tigraphy, within a relatively undeformed setting, to test Field investigations indicate that in many relatively predictions of fracture pattern from stratigraphic in- thinly bedded rock types, the product of fracture den- formation. We interpret the mechanical stratigraphy of sity and bed thickness is approximately 1.0 (Price, a section of the shallow dipping (Ͻ2Њ)Silurian dolo- 1966; Hobbs, 1967; McQuillan, 1973; Huang and An- mite of northeastern Wisconsin (Figure 2)from careful gelier, 1989; Narr and Suppe, 1991; Gross, 1993; fracture mapping along two quarry exposures. This ar- Gross
Recommended publications
  • Boxer's Fracture • Knuckle Fracture of the Pinky
    Boxer’s Fracture • Knuckle Fracture of the Pinky Introduction Treatment A Boxer’s fracture occurs when the bone at the knuckle Many Boxer’s fractures can be treated by immobi- of the little finger breaks. It can result from a forceful lizing the joint to promote healing. Immobilization can injury during fist fighting or hitting a solid object, such be achieved with a variety of splints, a cast, or taping as a wall. A Boxer’s fracture causes swelling, pain, and techniques. “Buddy-taping” involves taping the little stiffness. Treatment involves realigning the broken bone, finger to the ring finger. when necessary, and providing stabilization while it heals. Surgery Anatomy Surgery is recommended for Boxer’s fractures if large The “knuckle” of the fifth finger (small finger or “pinky”) degrees of angulation or displacement occur, or if the is comprised of the head of the metacarpal bone from joint surface is misaligned. Displacement and angulation the hand, and the base of the finger, called the proximal means that a piece or pieces of the metacarpal bone phalanx. The main function of your little finger is to that has broken have moved out of position. An open contribute to a tight strong grip. reduction and internal fixation (ORIF) surgery allows surgical hardware, such as wires and screws, to be Causes placed in the bone to align the fracture and allow it to A Boxer’s fracture occurs when the neck of the metacarpal heal in the correct position. bone in the little finger breaks. It is commonly caused by punching an immovable object, such as a wall, or Recovery someone’s jaw or head during a fist fight.
    [Show full text]
  • Activity 21: Cleavage and Fracture Maine Geological Survey
    Activity 21: Cleavage and Fracture Maine Geological Survey Objectives: Students will recognize the difference between cleavage and fracture; they will become familiar with planes of cleavage, and will use a mineral's "habit of breaking" as an aid to identifying common minerals. Time: This activity is intended to take one-half (1/2) period to discuss cleavage planes and types and one (1) class period to do the activity. Background: Cleavage is the property of a mineral that allows it to break smoothly along specific internal planes (called cleavage planes) when the mineral is struck sharply with a hammer. Fracture is the property of a mineral breaking in a more or less random pattern with no smooth planar surfaces. Since nearly all minerals have an orderly atomic structure, individual mineral grains have internal axes of length, width, and depth, related to the consistent arrangement of the atoms. These axes are reflected in the crystalline pattern in which the mineral grows and are present in the mineral regardless of whether or not the sample shows external crystal faces. The axes' arrangement, size, and the angles at which these axes intersect, all help determine, along with the strength of the molecular bonding in the given mineral, the degree of cleavage the mineral will exhibit. Many minerals, when struck sharply with a hammer, will break smoothly along one or more of these planes. The degree of smoothness of the broken surface and the number of planes along which the mineral breaks are used to describe the cleavage. The possibilities include the following. Number of Planes Degree of Smoothness One Two Three Perfect Good Poor Thus a mineral's cleavage may be described as perfect three plane cleavage, in which case the mineral breaks with almost mirror-like surfaces along the three dimensional axes; the mineral calcite exhibits such cleavage.
    [Show full text]
  • Scaling of Critical Velocity for Bubble Raft Fracture Under Tension Chin
    Scaling of critical velocity for bubble raft fracture under tension Chin-Chang Kuo, and Michael Dennin1, a) Department of Physics and Astronomy and Institute for Complex Adaptive Matter, University of California at Irvine, Irvine, CA 92697-4575 (Dated: 9 September 2011) The behavior of materials under tension is a rich area of both fluid and solid mechanics. For simple fluids, the breakup of a liquid as it is pulled apart generally exhibits an instability driven, pinch-off type behavior. In contrast, solid materials typically exhibit various forms of fracture under tension. The interaction of these two distinct failure modes is of particular interest for complex fluids, such as foams, pastes, slurries, etc.. The rheological properties of complex fluids are well-known to combine features of solid and fluid behavior, and it is unclear how this translates to their failure under tension. In this paper, we present experimental results for a model complex fluid, a bubble raft. As expected, the system exhibits both pinch-off and fracture when subjected to elongation under constant velocity. We report on the critical velocity vc below which pinch-off occurs and above which fracture occurs as a function of initial system width W , length L, bubble size R, and fluid viscosity. The fluid viscosity sets the typical time for bubble rearrangements τ. The results for the critical velocity are consistent with a simple scaling law vcτ=L ∼ R=W that is based on the assumption that fracture is nucleated by the failure of local bubble rearrangements to occur rapidly enough. a)Corresponding Author email: [email protected] 1 I.
    [Show full text]
  • Distal Radius Fracture
    Distal Radius Fracture Osteoporosis, a common condition where bones become brittle, increases the risk of a wrist fracture if you fall. How are distal radius fractures diagnosed? Your provider will take a detailed health history and perform a physical evaluation. X-rays will be taken to confirm a fracture and help determine a treatment plan. Sometimes an MRI or CT scan is needed to get better detail of the fracture or to look for associated What is a distal radius fracture? injuries to soft tissues such as ligaments or Distal radius fracture is the medical term for tendons. a “broken wrist.” To fracture a bone means it is broken. A distal radius fracture occurs What is the treatment for distal when a sudden force causes the radius bone, radius fracture? located on the thumb side of the wrist, to break. The wrist joint includes many bones Treatment depends on the severity of your and joints. The most commonly broken bone fracture. Many factors influence treatment in the wrist is the radius bone. – whether the fracture is displaced or non-displaced, stable or unstable. Other Fractures may be closed or open considerations include age, overall health, (compound). An open fracture means a bone hand dominance, work and leisure activities, fragment has broken through the skin. There prior injuries, arthritis, and any other injuries is a risk of infection with an open fracture. associated with the fracture. Your provider will help determine the best treatment plan What causes a distal radius for your specific injury. fracture? Signs and Symptoms The most common cause of distal radius fracture is a fall onto an outstretched hand, • Swelling and/or bruising at the wrist from either slipping or tripping.
    [Show full text]
  • Human Sexual Selection
    Available online at www.sciencedirect.com ScienceDirect Human sexual selection David Puts Sexual selection favors traits that aid in competition over Here, I review evidence, focusing on recent findings, mates. Widespread monogamous mating, biparental care, regarding the strength and forms of sexual selection moderate body size sexual dimorphism, and low canine tooth operating over human evolution and consider how sexual dimorphism suggest modest sexual selection operating over selection has shaped human psychology, including psy- human evolution, but other evidence indicates that sexual chological sex differences. selection has actually been comparatively strong. Ancestral men probably competed for mates mainly by excluding The strength of human sexual selection competitors by force or threat, and women probably competed Some evidence suggests that sexual selection has been primarily by attracting mates. These and other forms of sexual relatively weak in humans. Although sexual dimorphisms selection shaped human anatomy and psychology, including in anatomy and behavior may arise from other selective some psychological sex differences. forces, the presence of sexually dimorphic ornamentation, Address weaponry, courtship displays, or intrasexual competition Department of Anthropology and Center for Brain, Behavior and indicates a history of sexual selection [3]. However, men’s Cognition, Pennsylvania State University, University Park, PA 16802, 15–20% greater body mass than women’s is comparable to USA primate species with a modest degree of mating competi- tion among males, and humans lack the canine tooth Corresponding author: Puts, David ([email protected]) dimorphism characteristic of many primates with intense male competition for mates [4]. Moreover, humans exhibit Current Opinion in Psychology 2015, 7:28–32 biparental care and social monogamy, which tend to occur This review comes from a themed issue on Evolutionary psychology in species with low levels of male mating competition [5].
    [Show full text]
  • Methods Used to Identifying Minerals
    METHODS USED TO IDENTIFYING MINERALS More than 4,000 minerals are known to man, and they are identified by their physical and chemical properties. The physical properties of minerals are determined by the atomic structure and crystal chemistry of the minerals. The most common physical properties are crystal form, color, hardness, cleavage, and specific gravity. CRYSTALS One of the best ways to identify a mineral is by examining its crystal form (external shape). A crystal is defined as a homogenous solid possessing a three-dimensional internal order defined by the lattice structure. Crystals developed under favorable conditions often exhibit characteristic geometric forms (which are outward expressions of the internal arrangements of atoms), crystal class, and cleavage. Large, well- developed crystals are not common because of unfavorable growth conditions, but small crystals recognizable with a hand lens or microscope are common. Minerals that show no external crystal form but possess an internal crystalline structure are said to be massive. A few minerals, such as limonite and opal, have no orderly arrangement of atoms and are said to be amorphous. Crystals are divided into six major classes based on their geometric form: isometric, tetragonal, hexagonal, orthorhombic, monoclinic, and triclinic. The hexagonal system also has a rhombohedral subdivision, which applies mainly to carbonates. CLEAVAGE AND FRACTURE After minerals are formed, they have a tendency to split or break along definite planes of weakness. This property is called cleavage. These planes of weakness are closely related to the internal structure of the mineral, and are usually, but not always, parallel to crystal faces or possible crystal faces.
    [Show full text]
  • Does Human Sexual Dimorphism Influence Fracture Frequency, Types and Distribution?
    AnthropologicAl review • Vol. 74, 13–23 (2011) Does human sexual dimorphism influence fracture frequency, types and distribution? Jonna Nielsen ADBOU, Forensic Institute, University of Southern Denmark, Lucernemarken 20, Dk-5260 Odense, Denmark; E-mail [email protected] ABSTRACT This study explores the hypothesis that the pattern of gender inequality in a community influences the frequency, patterns and distribution of fractures. As it is not possible to read gender relations from skeletons, it is – following several research results – assumed that the level of gender inequality is reflected in sexual dimorphism. Thus the study design consists in correlating a measure of sexual dimorphism with measures of frequencies, patterns and distribution of skeletal trauma between the two sexes. Nearly two hundreds individuals from two medieval Danish cemeteries have been examined (43 females/48 males from Jutland and 46 females/49 males from Funen). Sexual dimorphism was assessed by means of measurements on the pelvis and, in accordance with conventional wisdom, the level of sexual dimorphism was found to be lower in the Funen than in the Jutland sample. The fracture frequencies, patterns and distribution were estimated for the two skeletal samples. No significant difference between the fracture frequencies or types on the two sites was found, but the distribution of fractures between the sexes in Ribe was found to be significantly different. The study indicates a level of relationship between human sexual dimorphism, gender roles, and the distribution of fractures between the sexes. Studies of larger samples will help clarify this. KEY WORDS: interpretation of injuries, gender roles, medieval Denmark Studies of old skeletal remains often in- them having been controlled by beating by dicate a relatively high fracture frequency their men and thus that these women were in ancient communities compared to more socially inferior to men.
    [Show full text]
  • Path-Independent Integral in Fracture Mechanics of Quasicrystals ⇑ J
    Engineering Fracture Mechanics 140 (2015) 61–71 Contents lists available at ScienceDirect Engineering Fracture Mechanics journal homepage: www.elsevier.com/locate/engfracmech Path-independent integral in fracture mechanics of quasicrystals ⇑ J. Sladek a, , V. Sladek a,1, S.N. Atluri b a Institute of Construction and Architecture, Slovak Academy of Sciences, 84503 Bratislava, Slovakia b Center for Aerospace Research & Education, University of California, Irvine, CA, USA article info abstract Article history: Path-independent integrals are successfully utilized for accurate evaluation of fracture Received 6 October 2014 parameters in crystalic materials, where atomic arrangement is periodic. In quasicrystals Received in revised form 16 March 2015 (QC) the atomic arrangement is quasiperiodic in one-, two- or three-directions. The 2-d Accepted 22 March 2015 elastic problem for quasicrystal is described by coupled governing equations for phonon Available online 2 April 2015 and phason displacements. Conservation laws for quasicrystals are utilized to derive path-independent integrals for cracks. The relation between the energy release and stress Keywords: intensity factor for a crack under the mode I is given for decagonal QCs. The path-indepen- Path-independent integral dent integral formulation is valid also for cracks in QCs with continuously varying material Energy balance Elastodynamics properties. Bak’s model Ó 2015 Elsevier Ltd. All rights reserved. Decagonal quasicrystals Phonon Phason Intensity factors 1. Introduction Since the pioneering work of Eshelby [1], and independent discovery of Rice [2], innumerable number of papers have appeared in literature concerning path-independent integrals (familiary so-called J-integral) and their application to mechanics of fracture. Both papers initiated important studies, on conservation laws in finite and infinitesimal elasticity, by Knowles and Sternberg [3], and the interpretation of these in the context of the mechanics of cracks and notches in 2-dimensional bodies by Budiansky and Rice [4].
    [Show full text]
  • Quartz Crystals Subjected to Shear Stress
    minerals Article Fracture Analysis of α-Quartz Crystals Subjected to Shear Stress Giovanni Martinelli 1,2,3,* , Paolo Plescia 4 , Emanuela Tempesta 4, Enrico Paris 5 and Francesco Gallucci 5 1 INGV Istituto Nazionale di Geofisica e Vulcanologia, Via Ugo La Malfa 153, 90146 Palermo, Italy 2 Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences, Lanzhou 730000, China 3 Key Laboratory of Petroleum Resources, Lanzhou 730000, China 4 CNR-IGAG, Institute of Environmental Geology and Geoengineering, Research area of Rome-1, 00015 Monterotondo, Italy; [email protected] (P.P.); [email protected] (E.T.) 5 CREA-ING, Consiglio per la Ricerca in Agricoltura e l’Analisi dell’Economia Agraria, Unità di Ricerca per l’Ingegneria Agraria, 00015 Monterotondo, Italy; [email protected] (E.P.); [email protected] (F.G.) * Correspondence: [email protected] Received: 18 July 2020; Accepted: 29 September 2020; Published: 30 September 2020 Abstract: This study assesses the correlations between the intensity of stress undergone by crystals and the morphological characteristics of particles and fracturing products. The effects of the fractures on the microstructure of quartz are also studied. Alpha quartz, subjected to shear stress, is quickly crushed according to a fracturing sequence, with a total fracture length that is correlated to the stress rate. The shear stress generates a sequence of macro and microstructural events, in particular localized melting phenomena, never highlighted before on quartz and the formation of different polymorphs, such as cristobalite and tridymite together with amorphous silica. Keywords: quartz; shear stress; tribochemistry; fracturing 1.
    [Show full text]
  • Simulating the Pervasive Fracture and Fragmentation of Materials and Structures Using Randomly Close- Packed Voronoi Tessellations
    SANDIA REPORT SAND2008-6089 Unlimited Release September 2008 Simulating the Pervasive Fracture and Fragmentation of Materials and Structures using Randomly Close- Packed Voronoi Tessellations Joseph E. Bishop Prepared by Sandia National Laboratories Albuquerque, New Mexico 87185 and Livermore, California 94550 Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under Contract DE-AC04-94AL85000. Approved for public release; further dissemination unlimited. Issued by Sandia National Laboratories, operated for the United States Department of Energy by Sandia Corporation. NOTICE: This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government, nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, or their employees, make any warranty, express or implied, or assume any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represent that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government, any agency thereof, or any of their contractors or subcontractors. The views and opinions expressed herein do not necessarily state or reflect those of the United States Government, any agency thereof, or any of their contractors. Printed in the United States of America. This report has been reproduced directly from the best available copy.
    [Show full text]
  • Allometry and Variation in the Baculum (Os Penis) of the Harp Seal, Pagophilus Groenlandicus (Carnivora: Phocidae)
    Biological Journal of the Linnean Society (2001), 72: 345–355. With 2 figures doi:10.1006/bijl.2000.0509, available online at http://www.idealibrary.com on It’s all relative: allometry and variation in the baculum (os penis) of the harp seal, Pagophilus groenlandicus (Carnivora: Phocidae) EDWARD H. MILLER∗ and LAUREN E. BURTON Department of Biology, Memorial University of Newfoundland, St. John’s NF A1B 3X9, Canada Received 3 March 2000; accepted for publication 3 November 2000 We compared allometry and variation in the baculum (os penis), mandible, and humerus of the harp seal, Pagophilus groenlandicus. This species is presumed to have a promiscuous mating system in which choice of mate by females during intromission with different males is likely. The baculum is large and grows throughout life so may be an honest indicator of males’ quality (size) or viability (age). We predicted that bacular size would exhibit stronger allometry relative to body size than mandibles or humeri. The baculum is less functionally (mechanically) constrained than mandibles or humeri so we also predicted it would be more variable, though less variable than sexually selected traits which do not function as honest indicators. Our sample (N=67 seals) represented broad ranges of size and age (0–35 yr) so we compared variation using residuals from allometric regressions of skeletal measurements on body length. Bacular size was isometric to body length until >137 cm (when some seals enter puberty) in body length then was highly positively allometric; mandibular and humeral size were negatively allometric to body length throughout growth. Bacula were more variable than mandibles or humeri.
    [Show full text]
  • Crack Propagation in Quasicrystals
    Crack propagation in quasicrystals R. Mikulla1, J. Stadler1, F. Krul1, H.-R. Trebin1 and P. Gumbsch2 1 Institut f¨ur Theoretische und Angewandte Physik der Universit¨at Stuttgart, Pfaffenwaldring 57, D-70550 Stuttgart, Germany 2 Max-Planck-Institut f¨ur Metallforschung, Seestr. 92, 70174 Stuttgart, Germany Crack propagation is studied in a two dimensional decagonal model quasicrystal. The simulations reveal the dominating role of highly coordinated atomic environments as structure intrinsic obstacles for both dislocation motion and crack propagation. For certain overloads, these obstacles and the quasiperiodic nature of the crystal result in a specific crack propagation mechanism: The crack tip emits a dislocation followed by a phason wall, along which the material opens up. Quasicrystals are characterized by an unusual struc- crucial element in the brittle fracture mechanism at low ture: They are orientationally ordered, but with noncrys- temperature. Furthermore, we identify atomic clusters, tallographic, e.g., five- or eightfold symmetry axes [1]. inherent to the quasicrystalline structure, as obstacles Their translational order is not periodic, as in conven- and scattering centers for the brittle crack. tional crystals, but quasiperiodic. In the last few years The study of a strongly nonlinear process like dynam- it has become possible to measure physical properties ical fracture in a complex material requires simplifica- of quasicrystals, such as mass and heat transport, plas- tions. First we consider a two dimensional system (2D) ticity, and fracture, since high–quality, thermodynami- to evade the analysis of a three dimensional crack front. cally stable quasicrystals could be grown in millimeter Secondly we simulate a perfectly ordered quasicystalline sizes [2].
    [Show full text]