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Tolerance of Three Annual Forage Legumes to Selected Postemergence Herbicides
- Gerald W. Evers, W. James Grichar, Claude L. Pohler, A. Michael Schubert
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- Journal:
- Weed Technology / Volume 7 / Issue 3 / September 1993
- Published online by Cambridge University Press:
- 12 June 2017, pp. 735-739
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Field studies were conducted from 1986 through 1989 to evaluate the tolerance of three clover species to selected POST herbicides. 2,4-D at 0.8 and 1.7 kg ha−1 injured rose and berseem clovers while the high rate injured subterranean clover. Bentazon and pronamide did not injure rose or subterranean clover; however, pronamide at 3.4 kg ha−1 injured berseem clover 18% when rated 72 days after treatment.
The Role of Shear Heating in the Dynamics of Large Ice Masses*
- David A. Yuen, Gerald Schubert
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- Journal:
- Journal of Glaciology / Volume 24 / Issue 90 / 1979
- Published online by Cambridge University Press:
- 30 January 2017, pp. 195-212
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Self-consistent, steady, one-dimensional, subsolidus creep models of temperature and velocity are calculated for constant-thickness ice sheets sliding down a bed of constant slope under their own weight. Surface velocities of meters per year together with ice thicknesses of hundreds of meters can be realized by models wherein no melting occurs only if the activation energy for shear deformation E* is relatively small; a value of E* of about 60.7 kJ/mol (14.5 kcal/mol) is satisfactory, but an activation energy twice as large is not. Models which satisfy these constraints always lie close to the critical point which separates subcritical solutions (surface velocity u0 and basal temperature Tb increase with ice thickness h) from supercritical ones (u0Tb decrease with h). All steady states, whether subcritical or supercritical, are stable to perturbations of infinitesimal amplitude. However these ice layers are vulnerable to finite-amplitude frictional-heating instability which may be caused, for example, by sudden increases of glacier thickness. The superexponential growth-rates of such finite-amplitude instabilities may be responsible for the disintegration of large ice sheets in short periods of time.
On a calculé pour la température et la vitesse des modèles de fluage cohérents, stables, uni-dimensionnels, quasi-solides pour une épaisseur constante de glace glissant sur un lit de pente constante sous l’effet de son propre poids. Des vitesses de surface de quelques mètres par an liées à des épaisscurs de glace de quelques centaines de mètres ne peuvent être réalisées par des modèles sans fusion que si l’énergie d’activation pour la déformation par cisaillement E* est relativement faible. Une valeur de E* d’environ 60,7 kJ/mol (14,5 kcal/mol) est satisfaisante mais une énergie d’activation double ne l’est pas. Les modéles qui satisfont à ces contraintes demeurent trés proches du point critique qui sépare les solutions sous-critiques (la vitesse de surface u0 et la température à la base Tb croissent avec l’épaisseur de glace h) des solutions sur-critiques (u0, Tb décroissent avec h). Tous les états d’équilibre, sous-critiques ou sur-critiques sont stables pour des perturbations d’amplitude infinitésimale. Cependant, ces niveaux de glace sont vulnérables à l’instabilité par réchauffement de frottement d’amplitude finie, qui peut provoquer, par exemple, un acroissement subit de l’épaisseur des glaciers. La vitesse de croissance superexponentielle de telles instabilités d’amplitude finie peut être responsable de la désintégration de grandes calottes glaciaires en de courtes périodes de temps.
Für Eisdecken mit konstanter Dicke, die über ein Bett mit konstanter Neigung unter ihrem eigenen Gewicht herabgleiten, werden in sich abgeschlossene, stetige, eindimensionale Kriechmodelle der Temperatur und Geschwindigkeit berechnet. Oberflächengeschwindigkeiten von einigen Metern pro Jahr zusammen mit Eisdicken von mehreren hundert Metern können durch Modelle erfasst werden, in denen keine Abschmelzung auftritt, wenn nur die Aktivationsenergie für die Scherdeformation E* relativ klein ist; ein Wert E* von etwa 60,7 kJ/mol (14,5 kcal/mol) erfüllt diese Bedingung, eine doppelt so grosse Aktivationsenergie dagegen nicht. Modelle, die solchen Einschränkungen genügen, liegen immer nahe dem kritischen Punkt, der unterkritische Lösungen (Oberflächengeschwindigkeit u0 und Temperatur am Untergrund Tb wachsen mit der Eisdicke h) von überkritischen (u0, Tb nehmen mit h ab) trennt. Alle stationären Zustände, gleichgültig ob unter- oder überkritisch, sind stabil gegenüber Störungen mit infinitesimaler Amplitude. Jedoch können diese Eisschichten von Instabilitäten infolge Reibungswärme mit finiter Amplitude betroffen werden, die zum Beispiel durch eine plötzliche Zunahme der Gletscherdicke verursacht werden können. Die überexponentiellen Anstiegsraten solcher Instabilitäten mit finiten Amplituden könnten der Grund für die Auflösung grosser Eisschilde in kurzen Zeitspannen sein.
Multiple flow states for ice masses: reply to Dr Fowler’s comments
- Gerald Schubert, David A. Yuen
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- Journal:
- Journal of Glaciology / Volume 25 / Issue 92 / 1980
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- 20 January 2017, p. 355
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Explosive Growth of Shear-Heating Instabilities in the Down-Slope Creep of Ice Sheets
- David A. Yuen, Marc R. Saari, Gerald Schubert
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- Journal:
- Journal of Glaciology / Volume 32 / Issue 112 / 1986
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- 20 January 2017, pp. 314-320
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The time-scale for the onset of the explosive growth of a finite-amplitude shear-heating instability in the down-slope creep of a thick ice sheet is determined by integrating the equation for the temporal evolution of the temperature-depth profile subsequent to a sudden change in ice thickness. All instabilities eventually grow explosively after a prolonged period of simmering or relatively slow monotonic growth. Though times for explosive growth depend on initial and final ice thicknesses, surface temperature, accumulation rate, basal heat flux, and ice rheological parameters, the explosion times are extremely sensitive to the activation energy and the pre-exponential constant of the ice-creep law. Sudden increases in ice-sheet thickness of 1–2 km due to a rapid climatic deterioration can lead to explosive instability and melting of the basal shear layer in only thousands of years if ice-creep activation energies are lower than about 60 kJ mol-1.
9 - Flows in Porous Media
- Donald Turcotte, University of California, Davis, Gerald Schubert, University of California, Los Angeles
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- Geodynamics
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- 28 May 2018
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- 07 April 2014, pp 425-464
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Summary
In this Chapter
This chapter introduces the fundamental concepts of flow in porous media. We will emphasize porous rocks with connected pore space. In many applications the flow of fluid in a porous medium is governed by Darcy’s law which states that flow velocity is proportional to the pressure gradient. The constant of proportionality is the permeability. Large porosity leads to large values of permeability.
We will consider in some detail groundwater hydrology. Important concepts are the water table and aquifers. Solutions for the extraction of water to a well will be given. Our analysis of groundwater flow can also be applied to the flow of oil and gas in porous media.
A geodynamic application is to the geometrical forms of volcanic edifices. The shape of a volcano is determined by the relative resistance to flow of magma due to its viscosity versus the gravitational resistance to vertical flows. A related geodynamic problem is magma migration at depth. Magma is produced beneath a mid-ocean ridge by pressure release melting. This melt is lighter than the solid matrix from which it was produced. The ascent of the light magma is quantified as a flow in a porous medium.
We will also consider porous media flows related to geothermal energy. The basic principles of flows associated with hot springs will be derived. Commercial geothermal facilities generally utilize two-phase (steam plus water) flows. Two-phase flows in porous media will be considered.
Geodynamics
- 3rd edition
- Donald Turcotte, Gerald Schubert
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- 07 April 2014
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Essential reading for any Earth scientist, this classic textbook has been providing advanced undergraduate and graduate students with the fundamentals needed to develop a quantitative understanding of the physical processes of the solid earth for over thirty years. This third edition has two completely new chapters covering numerical modelling and geophysical MATLAB® applications, and the text is now supported by a suite of online MATLAB® codes that will enable students to grasp the practical aspects of computational modelling. The book has been brought fully up to date with the inclusion of new material on planetary geophysics and other cutting edge topics. Exercises within the text allow students to put the theory into practice as they progress through each chapter and carefully selected further reading sections guide and encourage them to delve deeper into topics of interest. Answers to problems available within the book and also online, for self-testing, complete the textbook package.
Appendix B - Physical Constants and Properties
- Donald Turcotte, University of California, Davis, Gerald Schubert, University of California, Los Angeles
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- Geodynamics
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- 28 May 2018
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- 07 April 2014, pp 572-577
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2 - Stress and Strain in Solids
- Donald Turcotte, University of California, Davis, Gerald Schubert, University of California, Los Angeles
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- Geodynamics
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- 07 April 2014, pp 92-129
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Summary
In this Chapter
The elastic deformation of cold rock plays an essential role in geodynamic processes. In this chapter we introduce the concepts of stress and strain. Body forces and surface stresses generate a distribution of pressure, normal stress, and shear stress in an elastic medium. The concept of isostasy is essential to the understanding of the geodynamics of topography. Isostasy provides a simple explanation for the formation of mountains and sedimentary basins. Under compressional forces the continental crust thickens, forming mountains and their crustal roots. Under tensional forces the continental crust thins, leading to surface subsidence and sedimentary basins.
Pressure and stresses cause elastic solids to deform. Dilatation, normal strain, and shear strain are measures of displacement in analogy to pressure, normal stress, and shear stress. Measurements of surface displacements (strain) are an important constraint on tectonic processes. An example is the surface strain caused by rupture on a fault. Global Positioning System (GPS) observations have revolutionized the accuracy of surface displacement measurements. Absolute positions can now be determined with an accuracy of a few millimeters.
Introduction
Plate tectonics is a consequence of the gravitational body forces acting on the solid mantle and crust. Gravitational forces result in an increase of pressure with depth in the Earth; rocks must support the weight of the overburden that increases with depth. A static equilibrium with pressure increasing with depth is not possible, however, because there are horizontal variations in the gravitational body forces in the Earth's interior. These are caused by horizontal variations in density associated with horizontal differences in temperature. The horizontal thermal contrasts are in turn the inevitable consequence of the heat release by radioactivity in the rocks of the mantle and crust. The horizontal variations of the gravitational body force produce the differential stresses that drive the relative motions associated with plate tectonics.
One of the main purposes of this chapter is to introduce the fundamental concepts needed for a quantitative understanding of stresses in the solid Earth. Stresses are forces per unit area that are transmitted through a material by interatomic force fields. Stresses that are transmitted perpendicular to a surface are normal stresses; those that are transmitted parallel to a surface are shear stresses. The mean value of the normal stresses is the pressure. We will describe the techniques presently used to measure the state of stress in the Earth's crust and discuss the results of those measurements.
10 - Chemical Geodynamics
- Donald Turcotte, University of California, Davis, Gerald Schubert, University of California, Los Angeles
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- Geodynamics
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- 07 April 2014, pp 465-485
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Summary
In this Chapter
The concept of geochemical reservoirs in the Earth provides a basis for understanding fundamental geodynamic processes. Important reservoirs in the solid Earth include the core, mantle, and continental crust. The emphasis in chemical geodynamics is on radiogenic elements. A typical example is the decay of radiogenic rubidium 87 to strontium 87. The reference isotope is strontium 86. The ratio of strontium isotopic compositions 87/86 in a rock can be used to determine its age. One example considered is the extraction of the enriched continental crust from the depleted mantle. Volcanic processes preferentially concentrate rubidium into the continental crust. Over time the production of strontium 87 relative to the reference strontium 86 can be used to determine the mean age of the continental crust.
Introduction
Radioactive heating of the mantle and crust plays a key role in geodynamics as discussed in Section 4.5. The heat generated by the decay of the uranium isotopes 238U and 235U, the thorium isotope 232Th, and the potassium isotope 40K is the primary source of the energy that drives mantle convection and generates earthquakes and volcanic eruptions. Radiogenic isotopes play other key roles in the Earth sciences. Isotope ratios can be used to date the “ages” of rocks.
The science of dating rocks by radioisotopic techniques is known as geochronology. In many cases a rock that solidifies from a melt becomes a closed isotopic system. Measurements of isotope ratios and parent–daughter ratios can be used to determine how long ago the rock solidified from a magma and this defines the age of the rock. These techniques provide the only basis for absolute dating of geological processes. Age dating of meteorites has provided an age of the solar system of 4.57 Ga. The oldest rocks on the Earth were found in West Greenland and have an age of 3.65 Ga. Lunar samples returned by the Apollo missions have ages of over 4 Ga.
Quantitative measurements of the concentrations of radioactive isotopes and their daughter products in rocks form the basis for chemical geodynamics. Essentially all rocks found on the surface of the Earth have been through one or more melting episodes and many have experienced high temperature metamorphism.
11 - Numerical Tools
- Donald Turcotte, University of California, Davis, Gerald Schubert, University of California, Los Angeles
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- Book:
- Geodynamics
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- 28 May 2018
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- 07 April 2014, pp 486-513
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Summary
In this Chapter
The purpose of this chapter is to introduce the student to the use of the computer programming language MATLAB in the context of geodynamic problems. We first present some fundamentals of using MATLAB and we then introduce some numerical methods for solving both linear and nonlinear differential equations. Integrations of both the steady and time-dependent heat conduction equations are used to illustrate the numerical approaches and their MATLAB implementations.
Introduction
Many problems in geodynamics cannot be solved analytically. Even those that can often involve complicated functions that must be evaluated numerically. Therefore, in Chapters 11 and 12 we provide the student with the tools to evaluate complex functions and mathematical expressions and produce direct numerical solutions to problems. The material can be read at any stage in going through this book, although it would be of most benefit to the student to study this chapter early on and use the tools discussed in it throughout the book. Students with a background in numerical techniques and basic computing might already be familiar with much of this material, but we have provided it with the beginning student in mind. It is not our goal in this chapter to provide a rigorous or complete introduction to numerical analysis nor is it our purpose to train students to write sophisticated numerical codes that enable the solving of geodynamical problems. Instead we offer the student a toolbox of codes to use in problem solving with some introductory discussion of the methods employed in the codes.
We have opted to use MATLAB, a computer programming language used so widely that most students will have access to it through their college or university. There are numerous books explaining the use of MATLAB and its applications in engineering and science. We will attempt to be mostly self-contained, explaining what one needs to know to employ MATLAB as a geodynamics problem-solving package.
6 - Fluid Mechanics
- Donald Turcotte, University of California, Davis, Gerald Schubert, University of California, Los Angeles
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- Geodynamics
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- 07 April 2014, pp 263-335
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Summary
In this Chapter
We introduce the fundamental concepts of fluid mechanics. Our focus will be on mantle convection, but we will consider a variety of other geodynamic applications. These applications utilize Newtonian fluids in which the stress is proportional to the spatial gradient of velocity. The constant of proportionality is the viscosity. Solutions for isothermal problems require an equation for conservation of mass and a force balance equation. In our applications the force balance includes the pressure forces, viscous terms, and the gravitational body force. Temperature variations require addition of a buoyancy force and an energy equation. In addition to the terms included in the heat equation in Chapter 4, terms are required to account for the advection of heat (energy). Unlike the heat equation, the equations for fluid flow are usually nonlinear, for example, the product of velocity and temperature gradient in the energy equation. This nonlinearity greatly increases the difficulty of obtaining analytical solutions.
One of the important problems we will consider in this chapter is postglacial rebound. Under the load of ice during the last ice age, the continental crust was depressed in order to achieve isostatic compensation. The surface of Greenland is currently depressed below sea level due to the load of the Greenland Ice Cap. At the end of the last ice age, about 8000 years ago, large quantities of ice melted. The removal of this ice load results in a “rebound” of the Earth’s surface in order to re-establish the isostatic balance. This rebound demonstrated beyond doubt the fluid behavior of the Earth’s mantle. The rate of rebound quantified the viscosity of the mantle.
Appendix D MATLAB Solutions to Selected Problems
- Donald Turcotte, University of California, Davis, Gerald Schubert, University of California, Los Angeles
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- Geodynamics
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- 07 April 2014, pp 584-606
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5 - Gravity
- Donald Turcotte, University of California, Davis, Gerald Schubert, University of California, Los Angeles
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- Geodynamics
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- 07 April 2014, pp 230-262
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Summary
In this Chapter
A spherical body has a surface gravitational field that is proportional to its mass and inversely proportional to its radius squared. To a first approximation this result explains the Earth’s gravitational field. However, the Earth is rotating and this rotation results in the equatorial radius being larger than the polar radius (polar flattening and an equatorial bulge). The combination of mass and rotation gives the reference gravitational field for the Earth.
Deviations from the values given by the reference field are known as gravity anomalies. These anomalies are usually due to density variations in the Earth's interior. Surface gravity anomalies are used to search for mineral deposits and oil accumulations. We will also show that gravity anomalies can be used to quantify fundamental geodynamic processes.
Introduction
The force exerted on an element of mass at the surface of the Earth has two principal components. One is due to the gravitational attraction of the mass in the Earth, and the other is due to the rotation of the Earth. Gravity refers to the combined effects of both gravitation and rotation. If the Earth were a nonrotating spherically symmetric body, the gravitational acceleration on its surface would be constant. However, because of the Earth's rotation, topography, and internal lateral density variations, the acceleration of gravity g varies with location on the surface. The Earth's rotation leads mainly to a latitude dependence of the surface acceleration of gravity. Because rotation distorts the surface by producing an equatorial bulge and a polar flattening, gravity at the equator is about 5 parts in 1000 less than gravity at the poles. The Earth takes the shape of an oblate spheroid. The gravitational field of this spheroid is the reference gravitational field of the Earth. Topography and density inhomogeneities in the Earth lead to local variations in the surface gravity, which are referred to as gravity anomalies.
3 - Elasticity and Flexure
- Donald Turcotte, University of California, Davis, Gerald Schubert, University of California, Los Angeles
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- Geodynamics
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- 07 April 2014, pp 130-159
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Summary
In this Chapter
In this chapter we introduce the fundamentals of elasticity. Elasticity is the principal deformation mechanism applicable to the lithosphere. In linear elasticity strain is proportional to stress. Elastic deformation is reversible; when the applied stress is removed, the strain goes to zero. Deformation of the lithosphere, in a number of applications, can be approximated as the bending (flexure) of a thin elastic plate. Examples include bending under volcanic loads, bending at subduction zones, and bending that creates sedimentary basins.
Introduction
In the previous chapter we introduced the concepts of stress and strain. For many solids it is appropriate to relate stress to strain through the laws of elasticity. Elastic materials deform when a force is applied and return to their original shape when the force is removed. Almost all solid materials, including essentially all rocks at relatively low temperatures and pressures, behave elastically when the applied forces are not too large. In addition, the elastic strain of many rocks is linearly proportional to the applied stress. The equations of linear elasticity are greatly simplified if the material is isotropic, that is, if its elastic properties are independent of direction. Although some metamorphic rocks with strong foliations are not strictly isotropic, the isotropic approximation is usually satisfactory for the Earth's crust and mantle.
At high stress levels, or at temperatures that are a significant fraction of the rock solidus, deviations from elastic behavior occur. At low temperatures and confining pressures, rocks are brittle solids, and large deviatoric stresses cause fracture. As rocks are buried more deeply in the Earth, they are subjected to increasingly large confining pressures due to the increasing weight of the overburden. When the confining pressure on the rock approaches its brittle failure strength, it deforms plastically. Plastic deformation is a continuous, irreversible deformation without fracture. If the applied force causing plastic deformation is removed, some fraction of the deformation remains. We consider plastic deformation in Section 7.11.
Contents
- Donald Turcotte, University of California, Davis, Gerald Schubert, University of California, Los Angeles
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- Geodynamics
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- 07 April 2014, pp v-x
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8 - Faulting
- Donald Turcotte, University of California, Davis, Gerald Schubert, University of California, Los Angeles
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- Geodynamics
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- 07 April 2014, pp 386-424
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Summary
In this Chapter
Earthquakes are associated with brittle rupture in the Earth’s crust and mantle. Irreversible deformation occurs on preexisting faults. The behavior of faults is controlled by friction, which leads to stick–slip behavior. A fault locks after an earthquake and remains locked until the stress builds up to a level that will cause slip to occur, resulting in the next earthquake. During the build-up of stress elastic energy is stored. When slip occurs a large fraction of this stored energy is converted to elastic energy in seismic waves, this is elastic rebound.
The magnitude of an earthquake is determined from the amplitudes of surface displacements as measured by seismographs. The standard measure of magnitude is the Richter scale. We will consider the behavior of the San Andreas fault in some detail. This fault is the primary boundary between the Pacific plate and the North American plate in California. The fault is well instrumented, and surface displacements can be measured directly. The 1906 earthquake on this fault largely destroyed San Francisco.
Introduction
At low temperatures and pressures rock is a brittle material that will fail by fracture if the stresses become sufficiently large. Fractures are widely observed in surface rocks of all types. When a lateral displacement takes place on a fracture, the break is referred to as a fault. Surface faults occur on all scales. On the smallest scale the offset on a clean fracture may be only millimeters. On the largest scale the surface expression of a major fault is a broad zone of broken up rock known as a fault gouge; the width may be a kilometer or more, and the lateral displacementmay be hundreds of kilometers.
Earthquakes are associated with displacements on many faults. Faults lock, and a displacement occurs when the stress across the fault builds up to a sufficient level to cause rupture of the fault. This is known as stick–slip behavior. When a fault sticks, elastic energy accumulates in the rocks around the fault because of displacements at a distance. When the stress on the fault reaches a critical value, the fault slips and an earthquake occurs. The elastic energy stored in the adjacent rock is partially dissipated as heat by friction on the fault and is partially radiated away as seismic energy. This is known as elastic rebound. Fault displacements associated with the largest earthquakes are of the order of 30 m.
Plate section
- Donald Turcotte, University of California, Davis, Gerald Schubert, University of California, Los Angeles
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- Geodynamics
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Preface to the Third Edition
- Donald Turcotte, University of California, Davis, Gerald Schubert, University of California, Los Angeles
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- Geodynamics
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- 07 April 2014, pp xi-xiv
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Summary
This textbook deals with the fundamental physical processes necessary for an understanding of plate tectonics and a variety of geological phenomena. We believe that the appropriate title for this material is geodynamics. The contents of this textbook evolved from a series of courses given at Cornell University and UCLA to students with a wide range of backgrounds in geology, geophysics, physics, mathematics, chemistry, and engineering. The level of the students ranged from advanced undergraduate to graduate.
Approach
We present most of the material with a minimum of mathematical complexity. In general, we do not introduce mathematical concepts unless they are essential to the understanding of physical principles. For example, our treatment of elasticity and fluid mechanics avoids the introduction or use of tensors. We do not believe that tensor notation is necessary for the understanding of these subjects or for most applications to geological problems. However, solving partial differential equations is an essential part of this textbook. Many geological problems involving heat conduction and solid and fluid mechanics require solutions of such classic partial differential equations as Laplace's equation, Poisson's equation, the biharmonic equation, and the diffusion equation. All these equations are derived from first principles in the geological contexts in which they are used. We provide elementary explanations for such important physical properties of matter as solid-state viscosity, thermal coefficient of expansion, specific heat, and permeability. Basic concepts involved in the studies of heat transfer, Newtonian and non-Newtonian fluid behavior, the bending of thin elastic plates, the mechanical behavior of faults, and the interpretation of gravity anomalies are emphasized. Thus it is expected that the student will develop a thorough understanding of such fundamental physical laws as Hooke’s law of elasticity, Fourier’s law of heat conduction, and Darcy’s law for fluid flow in porous media.
Index
- Donald Turcotte, University of California, Davis, Gerald Schubert, University of California, Los Angeles
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- Geodynamics
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Frontmatter
- Donald Turcotte, University of California, Davis, Gerald Schubert, University of California, Los Angeles
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- Geodynamics
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- 07 April 2014, pp i-iv
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