Hydrogeology of the Oceanic Lithosphere Edited by Earl E

Cambridge University Press 0521819296 - Hydrogeology of the Oceanic Lithosphere Edited by Earl E. Davis and Harry Elderfield Frontmatter More information

HYDROGEOLOGY OF THE OCEANIC LITHOSPHERE

A comprehensive and up-to-date review of the subject of the nature, causes, and consequences of fluid flow in oceanic crust, this edited volume sets in context much recent research for the first time. The book begins with a concise review of the relatively brief history of its subject which began shortly after the dawning of plate-tectonic theory little more than 30 years ago. It then describes the nature and important consequences of fluid flow in the sub-seafloor, ending with a summary of how the oceans are affected by the surprisingly rapid exchange of water between the crust and the water column overhead. The accompanying CD-ROM includes a full and easily navigated set of diagrams and captions, references, and photos of research vessels, submersibles, and tools used in marine hydrologic studies. A valuable resource for graduate students and researchers of Earth Sciences and Oceanography.

Earl E. Davis is a senior research scientist at the Paciﬁc Geoscience Centre, Geological Survey of Canada.

Harry Elderfield is Professor of Ocean Geochemistry and Palaeochemistry in the Department of Earth Sciences, University of Cambridge.

HYDROGEOLOGY OF THE OCEANIC LITHOSPHERE

Edited by EARL E. DAVIS AND HARRY ELDERFIELD

published by the press syndicate of the university of cambridge The Pitt Building, Trumpington Street, Cambridge, United Kingdom cambridge university press The Edinburgh Building, Cambridge, CB2 2RU, UK 40 West 20th Street, New York, NY 10011–4211, USA 477 Williamstown Road, Port Melbourne, VIC 3207, Australia Ruiz de Alarc´on13, 28014 Madrid, Spain Dock House, The Waterfront, Cape Town 8001, South Africa http://www.cambridge.org

C Cambridge University Press 2004

This book is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press.

Firstpublished 2004

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A catalog record for this book is available from the British Library

Library of Congress Cataloging in Publication data Hydrogeology of the ocean lithosphere / edited by Earl E. Davis and Harry Elderﬁeld. p. cm. Includes bibliographical references and index. ISBN 0 521 81929 6 (HB) 1. Hydrogeology. 2. Ocean bottom. 3. Earth – Crust. I. Davis, Earl E., 1947– II. Elderﬁeld, Harry, 1943– GB1005 H93 2004 551.468 – dc22 2004040410

ISBN 0 521 81929 6 hardback

The publisher has used its best endeavors to ensure that the URLs for external websites referred to in this book are correct and active at the time of going to press. However, the publisher has no responsibility for the websites and can make no guarantee that a site will remain live or that the content is or will remain appropriate.

Contents

List of contributors page vii Preface xi Acknowledgments xvii List of symbols and terms xix

Part I Background 1 Variability of heat flux through the seafloor: discovery of hydrothermal circulation in the oceanic crust 3 John G. Sclater 2 Foundations of research into heat, fluid, and chemical fluxes in oceanic crust 28 Harry Elderfield, Keir Becker, and Earl E. Davis

Part II Hydrologic structure, properties, and state of the oceanic crust 3 Variability of ocean crustal structure created along the global mid-ocean ridge 59 Suzanne M. Carbotte and Daniel S. Scheirer 4 Fracturing and fluid flow in the oceanic crust: insights from borehole imaging and other downhole measurements 108 David Goldberg, Gerardo J. Iturrino, and Keir Becker 5 Hydrothermal aging of oceanic crust: inferences from seismic refraction and borehole studies 128 Ingo Grevemeyer and Anne Bartetzko 6 Sediment permeability, distribution, and influence on fluxes in oceanic basement151 Glenn A. Spinelli, Emily R. Giambalvo, and Andrew T. Fisher 7 In situ determinations of the permeability of the igneous oceanic crust 189 Keir Becker and Earl E. Davis 8 Observations of temperature and pressure: constraints on ocean crustal hydrologic state, properties, and flow 225 Earl E. Davis and Keir Becker

vi Contents

9 Hydrothermal insights from the Troodos ophiolite, Cyprus 272 Joe Cann and Kathryn Gillis

Part III Heat and fluid fluxes 10 Deep-seated oceanic heat flow, heat deficits, and hydrothermal circulation 311 Robert N. Harris and David S. Chapman 11 Rates of flow and patterns of fluid circulation 337 Andrew T. Fisher 12 Applying fundamental principles and mathematical models to understand processes and estimate parameters 376 Kelin Wang 13 Geothermal evidence for continuing hydrothermal circulation in older (>60 M.y.) ocean crust414 Richard P. Von Herzen

Part IV Geochemical state and water–rock reactions 14 Alteration and mass transport in mid-ocean ridge hydrothermal systems: controls on the chemical and isotopic evolution of high-temperature crustal fluids 451 W. E. Seyfried, Jr. and Wayne C. Shanks, III 15 Alteration of the upper oceanic crust: mineralogy, chemistry, and processes 495 JeffreyC.Alt 16 Ridge flank sediment–fluid interactions 534 Miriam Kastner and Mark D. Rudnicki 17 Microbial reactions in marine sediments 572 Jon P. Telling, Edward R. C. Hornibrook, and R. John Parkes 18 Microbial mediation of oceanic crust alteration 606 Hubert Staudigel and Harald Furnes

Part V Geochemical fluxes 19 Geochemical fluxes through mid-ocean ridge flanks 627 C. Geoffrey Wheat and Michael J. Mottl 20 Insight into the hydrogeology and alteration of oceanic lithosphere based on subduction zones and arc volcanism 659 Simon M. Peacock 21 Hydrothermal fluxes in a global context 677 Mike Bickle and Harry Elderfield

Index 691

Contributors

Jeffrey Alt Suzanne Carbotte Department of Geological Sciences Lamont-Doherty Earth Observatory 2534 C.C. Little Building 61 Route 9W The University of Michigan Palisades, NY 10964 Ann Arbor, MI 48109-1063 USA USA Dave Chapman Anne Bartetzko Department of Geology and Geophysics Applied Geophysics University of Utah RWTH Aachen 135 S 1460 E Lochnerstr. 4-20, SaltLake City, UT 84112-0111 52056 Aachen USA Germany Earl Davis Keir Becker Paciﬁc Geoscience Centre Rosenstiel School of Marine and Geological Survey of Canada Atmospheric Science 9860 W. Saanich Rd University of Miami Sidney, BC V8L 4B2 4600 Rickenbacker Causeway Canada Miami, FL 33149-1098 USA Harry Elderﬁeld Mike Bickle Department of Earth Sciences Department of Earth Sciences University of Cambridge University of Cambridge Downing Street Downing Street Cambridge, CB2 3EQ Cambridge, CB2 3EQ UK UK Andrew Fisher Joe Cann Earth Sciences Department School of Earth Sciences Earth and Marine Sciences Building University of Leeds University of California at Santa Cruz Leeds, LS2 9JT Santa Cruz, CA 95064 UK USA

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viii List of contributors

Harald Furnes Edward Hornibrook Institutt for geovitenskap Department of Earth Sciences Realfagbygget, Allegt. 41 University of Bristol 5007 Bergen Queens Rd Norway Bristol, BS8 IRJ UK Emily Giambalvo Sandia National Laboratories, Gerardo Iturrino MS-1395 Borehole Research Group 4100 National Parks Highway Lamont-Doherty Earth Observatory of Carlsbad, NM 88220 Columbia University USA Route 9W Palisades, New York 10964-8000 Kathy Gillis USA School of Earth and Ocean Sciences University of Victoria Miriam Kastner PO Box 3055 Geological Research Division Victoria, BC V8W 3P6 Scripps Institution of Oceanography Canada University of California at San Diego 9500 Gilman Dr. David Goldberg La Jolla, CA 92093-0212 Borehole Research Group USA Lamont-Doherty Earth Observatory of Columbia University Mike Mottl Route 9W Department of Oceanography Palisades, New York 10964-8000 SOEST USA 1000 Pope Rd University of Hawaii Ingo Grevemeyer Honolulu, HI 96822 GEOMAR Research Centre USA Wischhofstraße 1–3 24148 Kiel and R. John Parkes Department of Earth Sciences School of Earth, Ocean, and Planetary University of Bremen Sciences Klagenfurter Straße University of Cardiff 28359 Bremen Park Place Germany Cardiff, CF10 3YE UK Rob Harris Department of Geology and Simon Peacock Geophysics Department of Geological Sciences University of Utah Box 871404 135 S 1460 E Arizona State University SaltLake City, UT 84112-0111 Tempe, AZ 85287-1404 USA USA

List of contributors ix

Mark Rudnicki University of Missouri Division of Earth and Ocean Sciences Columbia, MO 65211 103 Old Chemistry Building USA Duke University HubertStaudigel Box 90227 Cecil H. and Ida M. Green Durham, NC 27708-0227 Institute of Geophysics and Planetary USA Physics Dan Scheirer Scripps Institution of Oceanography Department of Geological Sciences University of California at San Diego – Box 1846 0225 Brown University La Jolla, CA 92093-0225 Providence, RI 02912 USA USA Jon Telling John Sclater Department of Earth Sciences Geological Research Division University of Bristol Scripps Institution of Oceanography Wills Memorial Building University of California at San Diego Queens Rd 9500 Gilman Dr. Bristol, BS8 IRJ La Jolla, CA 92093-0220 UK USA Richard Von Herzen William Seyfried, Jr. Woods Hole Oceanographic Institution Department of Geology and Geophysics 360 Woods Hole Rd University of Minnesota Woods Hole, MA 02543 106 Pillsubury Hall USA Pillsbury Drive, S. E. Kelin Wang Minneapolis, MN 55455 Paciﬁc Geoscience Centre USA Geological Survey of Canada W. C. PatShanks 9860 W. Saanich Rd US Geological Survey Sidney, BC V8L 4B2 973 Denver Federal Center Canada Denver, CO 80225 Geoff Wheat USA NURP/MLML Marine Operations Glenn Spinelli PO Box 475 Department of Geological Sciences Moss Landing, CA 95039 101 Geology Building USA

Preface

Troublesome noise becomes signal and the subject of a book This book is being published roughly 30 years after the recognition of hydrothermal circulation in the oceanic crust. A few of the contributors were involved in the early studies of this phenomenon, others followed closely on their heels, and some became engaged relatively recently. All have experienced the pleasure of designing and executing experiments, and of discovering mechanisms, controlling factors, and consequences of fluid flow beneath the ocean floor. We hope that this book conveys to readers a sense of that pleasure. The seed for this volume was planted at the time of a workshop sponsored by the Interna- tional Lithosphere Program and the Joint Oceanographic Institutions/US Science Support Program, when a group of scientists representing a broad range of disciplines gathered in December 1998 at the University of California at Santa Cruz to discuss the current state and future direction of ocean crustal hydrogeology. It was made clear by these discussions that a wealth of knowledge about fluid flow within the crust and exchange with the ocean overhead had been gained since the early 1970s, that many new challenges lay ahead, and that a summary, offering both a retrospective and prospective review of all disciplines – including theoretical and experimental physics, chemistry, and microbiology – would be timely and useful for those attending the meeting, for their peers, and for students and new interested researchers. The importance of fluid circulation below the seafloor and exchange of water between the crust and the oceans can be easily appreciated by considering that the oceanic crust constitutes the most extensive geological formation on Earth, and that hydrologic activity within it extends from mid-ocean ridges to beneath subduction-zone accretionary prisms (Fig. 1). Its upper part is characterized by very high permeability, and it is host to huge fluxes of water. This was highlighted in a report of the second Conference on Scientific Ocean Drilling (COSOD II, 1987) which provided a succinctsummary of ocean crustal hydrothermal circulation, as well as other types of sub-seafloor fluid flow as they were known in the late 1980s. The most spectacular and directly observable manifestations of flow occur at ridge axes, where heat from magmatic intrusions drives high-temperature

Hydrogeology of the Oceanic Lithosphere, eds. E. E. Davis and H. Elderﬁeld. Published by Cambridge University Press. C Cambridge University Press 2004.

xii Davis and Elderﬁeld

Fig. 1 Schematic cross-section depicting various types of sub-seafloor fluid flow, ranging from topographically driven flow through continental margins and consolidation-driven flow at subduction zones to thermal buoyancy driven flow at mid-ocean ridge axes and in the oceanic crust beneath broad regions of the oceans. Oceanic igneous crust and sediments are shown light gray and darker gray, respectively, and magma is shown in black; flow is depicted by white arrows. The figure was originally prepared for the Integrated Ocean Drilling Program Initial Science Plan, 2003–2013, and is reproduced courtesy of JOI, Inc.

springs at the seafloor. Although important and of fundamental interest, these hydrothermal systems are short-lived in the traveling Lagrangian reference frame of the lithospheric plate, and, when considered over the lifetime of the lithosphere, or over the full areal extent of the oceanic crust in a fixed global Eulerian reference frame, the greatest contribution to the total volumetric flow of seawater in the crust is found to occur on the flanks of mid-ocean ridges. Hydrologic systems on ridge flanks are much more subtle than at ridge crests, and produce signals that were initially not understood, particularly since early observations tended to be too widely spaced and provided a highly incomplete picture of what are now known to be the primary signals reflecting crustal fluid flow. Early heat flux investigations were directed at comparing continental and oceanic thermal structure, and isolating thermal signatures of mantle convection and seafloor spreading. The investigators were frustrated by large “scatter” commonly present in the measurements, and by inexplicably low average values relative to levels expected on the basis of plate-tectonic theory as it was then emerging. This frustration ended in the early 1970s with the publication of a seminal paper by Lister (1972) who argued that the scatter, previously considered troublesome “noise,” in fact reflected a primary “signal” from crustal fluid flow, which later work confirmed. This signal is now used frequently as a quantitative guide to the nature of local crustal fluid flow. Similarly, the shortfall in average seafloor heat flux relative to that expected from the lithosphere in a plate- tectonic environment was recognized as an indication of the amount of heat carried through the seafloor advectively, and that shortfall has become widely used as a key constraint on the rate of fluid exchange between the crust and the overlying ocean.

Preface xiii

The COSOD II report also provided a simple and useful categorization of hydrological regimes based primarily on thedominantdriving forces for flow. In simplestterms,flow at ridge crests is driven by the buoyancy generated by highly localized magmatic heat; flow in ridge flank settings is driven by the deep-seated heat from the cooling lithosphere; and flow at continental margins is driven primarily by topographically or compositionally derived “head” and by consolidation caused by gravitational or tectonic stresses. While each of these hydrologic “type settings” is interesting and important, treating them all is a greater task than could be covered in a single book. Hence we have limited ourselves in this volume to only one of these settings, the most widely distributed and volumetrically important, ridge flanks.

Structure and contents of this book The contents are organized generally by discipline. The first chapter provides a personal perspective of the early seminal studies of hydrothermal circulation, and of the early inferences drawn largely on the basis of seafloor heat flow data collected “in the dark,” i.e. with no prior knowledge of the source, meaning, or scale of signals. The second chapter discusses some of the studies that followed the initial hypothesis development and discovery phase, studies that laid the foundation for much of the quantitative aspects presented later. It also contains some personal thoughts about where future efforts should be directed. Next are chapters devoted to physical structure, state, and processes. Chapters 3–6 provide a summary of the primary hydrologic architecture of the crust as it is created at mid-ocean ridge crests, and as it ages and is physically modified by hydrothermal alteration, mineral- ization, and sedimentation. Chapters 7 and 8 summarize observations of permeability, the principal property that controls the rate and direction of flow, and of pressure and temperature, the parameters of physical state that help to define buoyancy-derived driving forces and to constrain rates of flow. Chapter 9 provides a complementary view of the hydrogeology of oceanic crust gained from observations in ophiolites, where ancient crustal sections are exposed on land. Chapters 10–13 discuss inferences that can be drawn from observations and modeling concerning the routes and rates of crustal fluid flow and ocean–crust exchange, and the duration of the interval during which thermally driven flow continues within the crust after ventilation becomes insignificant. The subsequent chapters review ocean crustal hydrologic activity and its consequences over a broad range of scales, from chemical, mineralogical, and biological perspectives. Chapters 14–16 provide reviews of current information about the hydrogeology of oceanic crust from geochemical studies of the fluid and from geochemical and mineralogical studies of the alteration products, in both the sedimentary and underlying igneous parts of the oceanic crust. Chapters 17 and 18 describe the hydrologically dependent microbial popula- tions within and beneath the sediments. Chapter 19 provides a summary of the geochemical state of crustal water and inferred rates of flow. Among the aspects of the hydrogeology of the oceanic lithosphere that are particularly difficult to quantify is the depth and degree

xiv Davis and Elderﬁeld

to which the oceanic lithosphere is altered and carries water back to subduction zones; Chapter 20 examines this, in part based on inferences that can be drawn from subduction zone characteristics, such as earthquake distributions and subduction-zone alteration and metamorphism, that imply the presence of water. Finally, Chapter 21 places the inferences drawn in many of the chapters, as well as considerations of ridge-axis hydrothermal systems, in the context of global geochemical budgets.

A few reflections During the course of assembling what we hope is a coherent set of contributions spanning many disciplines, questions of terminology have often surfaced. In each of the fields of geophysics, geochemistry, and hydrogeology, sometimes confusing and often unnecessary jargon has been “articulated to the point of assimilation.” We have tried to counter this trend. Our judgmentsaboutwhatis unnecessary or confusing and aboutwhatis more or less correct may be debatable, but we feel our intention in the editing process to maintain a certain level of consistency and simplicity is well justified. “Flux” is probably the most frequently used term in the book. Several other terms are commonly applied to this quantity, and the use of this term often “sounds” wrong relative to what we might have grown accustomed to. “Flux” (material or energy transfer per unit area and time) is not the same as “flow,” yet flux is often used in the chemical community to mean flow, and flow is commonly used in the thermal community to mean flux. “Darcy velocity” and “specific discharge” are terms used by the hydrologic community that are synonymous with volumetric fluid flux. While not wishing to be dogmatic, we have tried to limit the number of terms, and stick to fundamental physical ones as consistently as possible. There also has been a confusing use of terms that relate to processes and behavior. For example, “convection” (with buoyancy as a driving force) and “advection” (transport with no mechanism invoked) are often used interchangeably (not here, we hope), and “free” and “forced” convection are so vague that we have avoided their use entirely. “Diffusion” is a term that describes a behavior, not a specific process. It can be applied equally well to ionic (chemical), molecular (heat), and frictional (pressure-flow) processes, as long as each is viewed at a scale large enough for the actual mechanisms to be “outof focus” – molecular diffusion has no meaning atthemolecular scale, and hydrologic diffusion has no meaning at the scale of an individual water-bearing fracture. “Flow” and “permeability” denote processes and properties, but like diffusion, they must be determined or applied with proper consideration of scale. Localized flow through a fractured medium documented using chemical tracers generally will not match average flow determined from thermal perturbations, but both are correctly described as flow. In cases like these, great care must be used to discriminate the process involved, but once this is accomplished, meaning can be gained from seemingly contradictory observations. We have attempted to express relationships with fundamental parameters, and to avoid the use of derived parameters (unless they make good physical sense). Consistent symbols have been used throughout the text; these are listed on p. xix following. We apologize if

Preface xv

our editorial pen seems awkward, and more importantly if we have missed the mis-use of quantitative terms. We urge the reader to maintain a critical eye, and to cultivate a desire to reduce the propagation of loose word usage.

Reflections on the future of hydrologic studies Although we have made some specific suggestions in Chapter 2 as to the “way forward,” it is, perhaps, useful to make a few points here. The greatest challenge perhaps is to face characterizing the heterogeneity of the crust, and the distribution of flow and alteration at depth. New remote techniques are needed, and some deep drilling will be required. Regional heat deficits are defined primarily by the global heat flux data base that is far from ideally suited for this purpose. Better data are needed to improve this estimate. The next steps of improving volumetric, volume-temperature, and ultimately geochemical budgets require the combined constraints of heat flux and sediment thickness. Huge areas of the ocean are uncharacterized. New “type areas” should be selected and studied using the multi-disciplinary surveys of North Pond, Costa Rica Rift, and Juan de Fuca as guides. Major advances are needed in the treatment of chemical elements transported in fluids. Often they are described almost as passive tracers with only a sideward glance at their reactivity. This is a reflection of the state of this field. Their description in models of fluid transport is in an immature state, except for transport in sediments (although that is treated purely as a two-dimensional process). Without improvements on all of these fronts, existing uncertainties in estimating global budgets will remain. A new phase of characterization and hypothesis testing is about to begin with the aug- mented tools of the Integrated Ocean Drilling Program. As recently emphasized by the Hydrogeology Program Planning Group of the Ocean Drilling Program (Ge et al., 2003), this will provide a means of penetrating deeply into the oceanic crust in a few key loca- tions via the improved capabilities of the riser drilling vessel Chikyu, and offer a suite of tools that are better suited to carrying out specific and detailed hydrologic experiments on this and the non-riser vessel. This and improvements in monitoring technology will lead to much better spatial and temporal resolution of hydrologic processes that operate at scales ranging from fractures to formations, and at periods ranging from seismic to “steady state.” Finally, we would like to emphasize that hydrologic studies of the oceanic crust and upper mantle should be considered in the context of other environments, including many on land. Similar experimental strategies can be applied, and many of the processes involved in one “type setting” will have major implications for others. For example, thermal or chemical buoyancy forcing through continental margins and oceanic islands and platforms follow the same principles as forcing in the oceanic crust and overlying sediments. And effects of a highly permeable upper oceanic crustmay have greatconsequences in themechan- ical and seismogenic deformation of subduction zone accretionary and non-accretionary prisms.

xvi Davis and Elderﬁeld

References COSOD II, 1987. Report of the Second Conference on Scientific Ocean Drilling, Stasbourg, 6–8 July, 1987, 142 pp. Ge, S., Bekins, B., Bredehoeft, J., Brown, K., Davis, E. E., Gorelick, S. M., Henrey, P., Kooi, H., Moench, A. F., Ruppel, C., Sauter, M., Screaton, E., Swart, P. K., Tokunaga, T., Voss, C. I., and Whitaker, F. 2003. Fluid flow in sub-seafloor processes and future ocean drilling. Eos, Trans. Am. Geophys. Union 84: 145–152. Lister, C. R. B. 1972. On the thermal balance of a mid-ocean ridge. Geophys. J. Roy. Astron. Soc. 26: 515–535.

Acknowledgments

We would like to express our appreciation to the International Lithosphere Program and the Joint Oceanographic Institutions through the US Science Support Program for funding the workshop that started our book-writing effort and for covering the costs of producing the CD-ROM that accompanies this volume. We thank especially the contributors to this volume for their willingness to take time out from their research to compile up-to-date summaries of the state of their science, as well as to provide internal reviews for chapters devoted to topics related to their own. Sally Thomas at Cambridge University Press provided us and the contributors a great deal of freedom to choose the contents, approach, and style they felt was most appropriate. Considerable assistance was provided by external reviewers (listed below) who improved the accuracy of the contents and clarity of the presentations. Sandra Last in the Department of Earth Sciences at Cambridge University provided admirably efﬁcient assistance during all stages of the process. Ellen Kappel of Geoprose Inc. made the compilation and production of the CD-ROM seem effortless. We know her product will be admired, and we hope it will be well used by students and educators.

Reviewers of manuscripts Roger Anderson, Lamont-Doherty Earth Observatory, Columbia University, USA Andy Barnicoat, University of Leeds, UK Robert Detrick, Woods Hole Oceanographic Institution, USA Edward Irving, Geological Survey of Canada, Canada Claude Jaupart, University of Paris, France Joris Gieskes, Scripps Institute of Oceanography, USA Keith Louden, Dalhousie University, Canada Roger Morin, US Geological Survey, USA Martin Palmer, University of Southampton, UK Philippe Pezard, University of Montpellier, France Elizabeth Screaton, University of Florida, USA Leslie Smith, University of British Columbia, Canada Tomochika Tokunaga, University of Tokyo, Japan

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xviii Acknowledgments

Damon Teagle, University of Southampton, UK David Vanko, Towson University, USA Karen Von Damm, University of New Hampshire, USA William Wilcock, University of Washington, USA Roy Wilkens, University of Hawaii, USA

Symbols and terms

Bulk modulus 1/β Pa Circular frequency = 2πf ω radians s−1 Compressibility β Pa−1 Heatflux (heatflow density) f Wm−2 Density ρ kg m−3 Dimensionless time constant τ Earthquake magnitude, body wave mb Volumetric fluid flux, Darcy flux q ms−1 Frequency f s−1 Gravitational acceleration g ms−2 Heat generation rate H Wm−3 −1 Hydraulic conductivity Kh ms Hydraulic diffusivity η m2 s−1 Hydraulic head h m 2 −1 Kinematic viscosity µ/ρf m s Length, thickness h, L, d, b m Loading efficiency γ Nusseltnumber Nu Pechletnumber Pe Permeability k m2 Poisson’s ratio ν Porosity n Pressure p Pa Radiometric decay constant λ s−1 Rayleigh number Ra Specific heat, heat capacity by mass c Jkg−1 K−1 Storage compressibility ζ Pa−1 Strain ε Stress σ Pa Temperature T K, ◦C Thermal conductivity λ Wm−1 K−1

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xx List of symbols and terms

Thermal diffusivity κ m2 s−1 Thermal expansivity α K−1 Time t s Tortuosity τ Velocity u ms−1 Viscosity, dynamic viscosity µ Pa s Volumetric heat capacity ρc Jm−3 K−1 Volumetric strain θ Young’s modulus E Pa

Subscript conventions Fluid f Solid s Solid matrix m Undrained formation mixture no subscript

Chemical concentrations mol moles M molar m milli (10−3) µ micro (10−6) n nano (10−9)