Missing 'biblatex' package
The bibliography requires the 'biblatex' package.

Wiley Online Library

journaltitleGeophysical Prospecting
titleMeasured anisotropy in Pierre shale

titleA course of lectures on natural philosophy and the mechanical arts: in two volumes

booktitleAnnales de Chimie et de Physique
titleNote sur l’extension des fils et des plaques élastiques

Norwegian University of Science
Technology (NTNU)

titleFrequency-dependent wave velocities in sediments and sedimentary rocks

NTNU ROSE Consortium

titleHow can we approach the kHz range in laboratory rock physics?

booktitleAGU Fall Meeting 2019
titleHow to avoid pitfalls in laboratory measured seismic attenuation

journaltitleGeophysical Prospecting
titleAn overview of laboratory apparatuses to measure seismic attenuation in reservoir rocks
Attenuation,Fluid-saturated rock,Forced oscillation

journaltitleJournal of Geophysical Research: Solid Earth
titleHydraulic and acoustic properties as a function of porosity in Fontainebleau Sandstone
Permeability and porosity,Wave attenuation

The Royal Society London

journaltitlePhilosophical Transactions of the Royal Society of London
titleElements of a mathematical theory of elasticity

titleMémoire sur l'équilibre intérieur des corps solides homogènes

John Martyn, London

titleDe Potentia Restitutiva

journaltitlePhil. Trans
titleA Description of Helioscopes, and Some Other Instruments

journaltitleAnnalen der Physik
titleDie Grundlage der allgemeinen Relativitätstheorie

B.G. Teubner

seriesB.G. Teubners Sammlung von Lehrbüchern auf dem Gebiete der mathematischen Wissenschaften ; Bd. XXXIV
titleLehrbuch der kristallphysik: (mit ausschluss der kristalloptik)

Cambridge, United Kingdom

Cambridge university press

titleThe rock physics handbook

Wiley Online Library

journaltitleJournal of Geophysical Research
titleThe velocity of compressional waves in rocks to 10 kilobars: 2.

journaltitleGesellschaft Zürich
titleÜber die elastizität poröser medien: Vier. der Natur

Bulletin of the Seismological Society of America

journaltitleBulletin of the Seismological Society of America
titleElasticity and internal friction in a long column of granite

journaltitleReviews of Geophysics

journaltitleGeophysical Research Letters
titleMeasures of dissipation in viscoelastic media

journaltitleJournal of Geophysical Research: Solid Earth
titleStress relaxations at low frequencies in fluid-saturated rocks: Attenuation and modulus dispersion
Physical Properties of Rocks: Elasticity,fracture,and flow

Canadian Society of Exploration Geophysicists

titleMechanics of seismic $Q$

journaltitleGeophysical Research Letters
titlePore fluids and seismic attenuation in rocks
Physical Properties of Rocks: Elasticity,fracture,and flow,General or miscellaneous

titleAttenuation of seismic waves in dry and saturated rocks: II. Mechanisms

journaltitleThe Journal of the Acoustical Society of America
titleTheory of Propagation of Elastic Waves in a Fluid‐Saturated Porous Solid. I. Low‐Frequency Range

Society of Exploration Geophysicists

titleComputed seismic speeds and attenuation in rocks with partial gas saturation

American Institute of Physics

journaltitleJournal of applied physics
titleMechanics of deformation and acoustic propagation in porous media

titleSeismic wave attenuation and dispersion resulting from wave-induced flow in porous rocks - A review

journaltitleGeophysical Research Letters
titleBubbles attenuate elastic waves at seismic frequencies: First experimental evidence
seismic waves,attenuation,gas bubbles,exsolution-dissolution

journaltitleThe Journal of the Acoustical Society of America
titleTheory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range

Wiley Online Library

journaltitleReviews of Geophysics
titleSome basic stress diffusion solutions for fluid-saturated elastic porous media with compressible constituents

journaltitleGeophysical Journal International
titleFrequency-dependent seismic attenuation in shales: experimental results and theoretical analysis

journaltitleThe Leading Edge
titleFluid and rock bulk viscosity and modulus

Society of Exploration Geophysicists

titleAttenuation mechanisms in sands: Laboratory versus theoretical (Biot) data

Taylor & Francis

journaltitleJournal of the American Statistical Association
titleScience and statistics

titleFluid mobility and frequency-dependent seismic velocity - Direct measurements

journaltitleThe Journal of Chemical Physics
titleDispersion and Absorption in Dielectrics I. Alternating Current Characteristics

University of Chicago press

titleElasticity and anelasticity of metals

Optical Society of America

titleOn the theory of dispersion of x-rays

booktitleAtti Cong. Intern. Fisica (Transactions of Volta Centenary Congress) Como
titleLa diffusion de la lumiere par les atomes

Dover publications

titlePolar molecules

The Royal Society London

journaltitlePhilosophical transactions of the Royal Society of London
titleOn the dynamical theory of gases

journaltitleProc. Roy. Soc. London A
titleOn the elasticity and viscosity of metals

Wiley Online Library

journaltitleAnnalen der Physik
titleUeber innere Reibung fester Körper, insbesondere der Metalle

journaltitleNordemann Pub., New York
titleFirst report on viscosity and plasticity

Wiley Online Library

journaltitleGeophysical Research Letters
titleValidation of the laboratory measurements at seismic frequencies using the Kramers-Kronig relationship

journaltitleReview of Scientific Instruments
titleSome Dynamic Methods for Determination of Young's Modulus

journaltitleProceedings of the Institute of Radio Engineers
titleThe Piezo-Electric Resonator

American Physical Society

journaltitlePhys. Rev.
titleOn the Experimental Determination of the Viscosity of Vibrating Solids

journaltitleCanadian Journal of Research
titleVELOCITY OF LONGITUDINAL VIBRATION IN SOLID RODS (ULTRASONIC METHOD) WITH SPECIAL REFERENCE TO THE ELASTICITY OF ICE

titleThe Attenuation Constant of Earth Materials

booktitleCarbonate Seismology
title3. Seismic Properties of Carbonate Rocks

journaltitleGeophysical Research Letters
titleVelocity and attenuation in sandstone at elevated temperatures and pressures

titleSeismic attenuation: Effects of pore fluids and frictional-sliding

journaltitleThe Earth's Crust
titleInternal Friction Measurements and their Implications in Seismic Q Structure Models of the Crust

journaltitleReview of Scientific Instruments
titleSplit Hopkinson resonant bar test for sonic-frequency acoustic velocity and attenuation measurements of small, isotropic geological samples

The Royal Society

journaltitlePhilosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences
titleA Method of Measuring the Pressure Produced in the Detonation of High Explosives or by the Impact of Bullets

journaltitleProceedings of the Physical Society. Section B
titleAn Investigation of the Mechanical Properties of Materials at very High Rates of Loading

American Physical Society

journaltitlePhys. Rev.
titleTransmission of Elastic Pulses in Metal Rods

Geological Society of America

journaltitleGeological Society of America Bulletin
titleVariation of elastic moduli of igneous rocks with pressure and temperature

Wiley Online Library

journaltitleEos, Transactions American Geophysical Union
titleElastic wave velocities in sedimentary rocks

Society of Exploration Geophysicists

titleElastic wave velocities in heterogeneous and porous media

journaltitleJournal of Geophysical Research (1896-1977)
titleThe velocity of compressional waves in rocks to 10 kilobars: 1.

titleAttenuation of seismic waves in dry and saturated rocks: I. Laboratory measurements

journaltitleJournal of Geophysical Research: Solid Earth
titleFrequency dependent ultrasonic properties of high-porosity sandstones
Physical Properties of Rocks: Elasticity,fracture,and flow

Blackwell Publishing Ltd

journaltitleGeophysical Prospecting
titleTHE VARIATION OF THE ELASTIC CONSTANTS OF ROCKS WITH FREQUENCY*

journaltitleJournal of Geophysical Research (1896-1977)
titleInternal friction in shear and shear modulus of Solenhofen limestone over a frequency range of $10^7$ cycles per second

Blackwell Publishing Ltd

journaltitleGeophysical Prospecting
titleELASTIC BEHAVIOUR OF ROCKS AT LOW FREQUENCIES

American Institute of Physics

journaltitleReview of Scientific Instruments
titleA torsion pendulum instrument for measuring internal friction

American Institute of Physics

journaltitleReview of Scientific Instruments
titleAn Apparatus for Measurement of Extremely High Internal Friction

The Physical Society of Japan

journaltitleJournal of the Physical Society of Japan
titleOn the relation between creep and vibrational loss of polymethylmetacrylate

The Physical Society of Japan

journaltitleJournal of the Physical Society of Japan
titleThe relation between dynamic elastic modulus, internal friction, creep and stress relaxation in polymethylmethacrylate

journaltitleRheologica Acta
titleÜber die bestimmung des dynamischen elastizitätsmoduls und des dynamischen schubmoduls im frequenzbereich von $10^{-5}$ bis $10^{-1}$ Hz

Wiley Online Library

journaltitleRock physics and phase relations. A Handbook of physical constants
titleAcoustic velocity and attenuation in porous rocks

journaltitleGeophysical Research Letters
titleFrequency and fluid effects on elastic properties of basalt: Experimental investigations
elastic properties,basalt,frequency effect

American Institute of Physics

journaltitleReview of Scientific Instruments
titleA versatile facility for laboratory studies of viscoelastic and poroelastic behaviour of rocks

Société Française de Physique

journaltitleRevue de Physique Appliquée
titleAppareil de mesure du module d'élasticité et du frottement intérieur en flexion, à basse fréquence, sous vide entre 20 et 800° C

journaltitlePhysics of the Earth and Planetary Interiors
titleElastic modulus and internal friction in enstatite, forsterite and peridotite at seismic frequencies and high temperatures

journaltitleReview of Scientific Instruments
titleVelocity dispersion in rocks: A laboratory technique for direct measurement of P-wave modulus at seismic frequencies

titleFrequency scaling for evaluation of shale and mudstone properties from accoustic velocities

Blackwell Publishing Ltd Oxford, UK

journaltitleGeophysical Journal International
titleDriving-stress waveform and the determination of rock internal friction by the stress—strain curve method

journaltitleJournal of Geophysical Research: Solid Earth
titleInvestigation of internal friction in fused quartz, steel, plexiglass, and westerly granite from $0.01$ to $1.00$ Hertz at $10^{-8}$ to $10^{-7}$ strain amplitude
Physical Properties of Rocks: Elasticity,fracture,and flow

booktitleMethods in Experimental Physics
title2. Laboratory measurement of internal friction in rocks and minerals at seismic frequencies

journaltitleJournal of Geophysical Research: Solid Earth
titleAbsorption and modulus measurements in the seismic frequency and strain range on partially saturated sedimentary rocks

journaltitleJournal of Geophysical Research: Solid Earth
titleExperimental study of attenuation and dispersion over a broad frequency range: 1. The apparatus
Elasticity and anelasticity,Instruments and techniques,anelasticity,attenuation,dispersion,instrumentation,low frequency,rock analogue

Society of Exploration Geophysicists

booktitleSEG Technical Program Expanded Abstracts 2020
titleA new apparatus for measuring low-frequency attenuation: Low-Frequency Module

Society of Exploration Geophysicists

journaltitleThe Leading Edge
titleExperimental results on the combined effects of frequency and pressure on the dispersion of elastic waves in porous rocks

Society of Exploration Geophysicists

journaltitleThe Leading Edge
titleDispersions and attenuations in a fully saturated sandstone: Experimental evidence for fluid flows at different scales

PSL Research University

titleDispersion des modules élastiques de carbonates saturés: étude expérimentale et modélisation

titleNumerical analysis of local strain measurements in fluid-saturated rock samples submitted to forced oscillations

Colorado School of Mines

titleElastic and visco-elastic laboratory properties in carbonates

ETH Zurich

titleExperimental characterization of reservoir rocks and geotechnical materials: Low frequency attenuation, ultrasonic velocities and local pore pressure effects

journaltitleAmerican Journal of Mathematics
titleOn a new action of the magnet on electric currents

European Association of Geoscientists & Engineers

booktitleEAGE GeoTech 2021 Second EAGE Workshop on Distributed Fibre Optic Sensing
titleLaboratory measurements of elastic properties at seismic frequencies using DAS sensors

journaltitleThe Leading Edge
titleLaboratory measurements with DAS: A fast and sensitive tool to obtain elastic properties at seismic frequencies

International Association of Rock Physicists

booktitle$6^{th}$ International Workshop on Rock Physics
titleLaboratory measurements with DAS: Fast and sensitive tool to obtain rock properties at seismic frequencies

journaltitleThe Leading Edge
titleElastic properties of carbonates from laboratory measurements at seismic and ultrasonic frequencies

Wiley Online Library

journaltitleJournal of Geophysical Research: Solid Earth
titleDispersion and attenuation of elastic wave velocities: impact of microstructure heterogeneity and local measurements

Colorado School of Mines

titleFrequency dependent elastic and anelastic properties of clastic rocks

booktitleSEG Technical Program Expanded Abstracts 2010
titleA new laboratory system for the measurement of low frequency seismic attenuation

journaltitleJournal of Applied Geophysics
titleAttenuation at low seismic frequencies in partially saturated rocks: Measurements and description of a new apparatus

Imperial College London

titleThe effect of stress, pore fluid and pore structure on elastic wave velocities in sandstones

Blackwell Publishing Ltd

journaltitleGeophysical Prospecting
titleA new Seismic Wave Attenuation Module to experimentally measure low-frequency attenuation in extensional mode

American Rock Mechanics Association

booktitle$47^{th}$ US Rock Mechanics/Geomechanics Symposium
titleLow-frequency ($< 100$ Hz) dynamic fracture compliance measurement in the laboratory

journaltitleGeophysical Journal International
titleMeasurements of seismic attenuation and transient fluid pressure in partially saturated Berea sandstone: evidence of fluid flow on the mesoscopic scale

titleViscoelasticity of Ells River bitumen sand and 4D monitoring of thermal enhanced oil recovery processes

booktitleSEG Technical Program Expanded Abstracts 2013
titleProgresses on velocity dispersion and wave attenuation measurements at seismic frequency

Society of Exploration Geophysicists

journaltitleThe Leading Edge
titleSeismic-frequency loss mechanisms: Direct observation

journaltitleGeophysical Prospecting
titleMeasurements of the elastic and anelastic properties of sandstone flooded with supercritical CO$_2$

titleSeismic wave attenuation and modulus dispersion in sandstones

Wiley Online Library

journaltitleGeophysical Research Letters
titleFrequency, pressure, and strain dependence of nonlinear elasticity in Berea Sandstone

Wiley Online Library

journaltitleJournal of Geophysical Research: Solid Earth
titleSeismic attenuation in partially saturated Berea sandstone submitted to a range of confining pressures

European Association of Geoscientists & Engineers

booktitle$78^{th}$ EAGE Conference and Exhibition 2016
titleMultiscale Measurement for Wave Dispersion in Consolidated Sandstones

titleThe Effect of Partial CO2 Saturation on the Elastic Properties of Castlegate Sandstone Measured at Seismic and Ultrasonic Frequencies

booktitleSEG Technical Program Expanded Abstracts 2016
titleExperimental rock physics under micro-CT

Wiley Online Library

journaltitleJournal of Geophysical Research: Solid Earth
titleElastic dispersion and attenuation in fully saturated sandstones: Role of mineral content, porosity, and pressures

journaltitleGeophysical Research Letters
titleThe relationship between $Q^{-1}_E$ and dispersion in extensional modulus, E

European Association of Geoscientists & Engineers

booktitle$79^{th}$ EAGE Conference and Exhibition 2017
titleFluid saturation effect on the characteristic frequency and attenuation of tight sandstone

journaltitleReview of Scientific Instruments
titleAn enhanced broad-frequency-band apparatus for dynamic measurement of elastic moduli and Poisson’s ratio of rock samples

journaltitleInternational Journal of Greenhouse Gas Control
titleEffect of CO2 on P- and S-wave velocities at seismic and ultrasonic frequencies

Wiley Online Library

journaltitleGeophysical Prospecting
titleForced oscillation measurements of seismic wave attenuation and stiffness moduli dispersion in glycerine-saturated Berea sandstone

Wiley Online Library

journaltitleJournal of Geophysical Research: Solid Earth
titleFluid Substitution and Shear Weakening in Clay-Bearing Sandstone at Seismic Frequencies

booktitle$81^{st}$ EAGE Conference and Exhibition 2019
titleInfluence of the Creep Effect on the Low-Frequency Measurements of the Elastic Moduli of Sedimentary Rocks

journaltitleJournal of Geophysical Research: Solid Earth
titleRole of Saturation on Elastic Dispersion and Attenuation of Tight Rocks: An Experimental Study

AIP Publishing LLC

journaltitleReview of Scientific Instruments
titleAn apparatus to measure elastic dispersion and attenuation using hydrostatic-and axial-stress oscillations under undrained conditions

booktitleEGU General Assembly Conference Abstracts
titleComparison of the elastic properties of reservoir rocks in the field and the laboratory: link between seismic, sonic and ultrasonic measurements

journaltitleRock Mechanics and Rock Engineering
titleEffect of Pore Collapse and Grain Crushing on the Frequency Dependence of Elastic Wave Velocities in a Porous Sandstone

journaltitleGeophysical Research Letters
titleEffects of partial liquid/gas saturation on extensional wave attenuation in Berea sandstone

Wiley Online Library

journaltitleGeophysical Prospecting
titleExperimental study on frequency-dependent elastic properties of weakly consolidated marine sandstone: effects of partial saturation

Wiley Online Library

journaltitleGeophysical Prospecting
titleElastic properties of a reservoir sandstone: a broadband inter-laboratory benchmarking exercise

Oxford University Press

journaltitleGeophysical Journal International
titleDual attenuation peaks revealing mesoscopic and microscopic fluid flow in partially oil-saturated Fontainebleau sandstones

Wiley Online Library

journaltitleJournal of Geophysical Research: Solid Earth
titleSeismic Wave Attenuation and Dispersion Due to Partial Fluid Saturation: Direct Measurements and Numerical Simulations Based on X-Ray CT

journaltitleFrontiers in Earth Science
titleAttenuation of seismic waves in partially saturated Berea sandstone as a function of frequency and confining pressure

journaltitleGeophysical Journal International
titleCoupled effects of pressure and frequency on velocities of tight sandstones saturated with fluids: measurements and rock physics modeling

European Association of Geoscientists & Engineers

journaltitleGeophysical Prospecting
titleAnalysis of the frequency dependence characteristics of wave attenuation and velocity dispersion using a poroelastic model with mesoscopic and microscopic heterogeneities

European Association of Geoscientists & Engineers

booktitle$82^{nd}$ EAGE Annual Conference & Exhibition
titleVelocity Dispersion in Sandstone Under Partially Saturated Conditions

American Institute of Physics

journaltitleReview of scientific instruments
titleA new wideband (1 mHz to 100 Hz) seismic spectrometer

European Association of Geoscientists & Engineers

booktitle82nd EAGE Annual Conference & Exhibition
titleFluid Substitution in Clay-Rich Sandstone at Seismic Frequencies

journaltitleActa Mechanica Solida Sinica
titleNonlinear Young’s Modulus of New Red Sandstone: Experimental Studies

University of Alberta

titleExperimental Investigation of Rock Dynamic Geomechanical Properties at Seismic Frequencies

Oxford University Press

journaltitleGeophysical Journal International
titleMass transfer between fluids as a mechanism for seismic wave attenuation: experimental evidence from water–CO2 saturated sandstones

booktitle$16^{th}$ Greenhouse Gas Control Technologies Conference
titleExperimental study of seismic wave attenuation by mass transfer between fluids in CO2-water saturated sandstone samples

journaltitleGeophysical Journal International
titleRole of pressure and pore microstructure on seismic attenuation and dispersion of fluid-saturated rocks: laboratory experiments and theoretical modelling

booktitle$56^{th}$ Rock Mechanics/Geomechanics Symposium
titleThe Impact of Strain Amplitude on Young's Modulus in Water-Saturated Sandstone

Taylor & Francis

journaltitleExploration Geophysics
titleEffects of different pore shapes on the pressure and frequency dependence of velocities of oil-saturated tight sandstone

journaltitlepure and applied geophysics
titleAbsorption of strain waves in porous media at seismic frequencies

Society of Exploration Geophysicists

journaltitleThe Leading Edge
titleFluids and frequency dependent seismic velocity of rocks

Colorado School of Mines

titleFluid effects on attenuation and dispersion of elastic waves

Society of Exploration Geophysicists

booktitle2003 SEG Annual Meeting
titleMacro-flow and velocity dispersion

journaltitleJournal of Geophysical Research: Solid Earth
titleSeismic wave attenuation in carbonates

European Association of Geoscientists & Engineers

booktitle$76^{th}$ EAGE Conference and Exhibition 2014
titleStudies on dispersion of reservoir rocks using multi-band direct laboratory measurement methodology with $\mu$-CT scanning

booktitleWorkshop on Rock Physics
titleMulti-band direct laboratory measurement-based dispersion analysis on reservoir rocks, $3^{rd}$ Int

journaltitleGeophysical Prospecting
titleLaboratory measurements of the effect of fluid saturation on elastic properties of carbonates at seismic frequencies

journaltitleJournal of Geophysical Research: Solid Earth
titleDispersion and attenuation measurements of the elastic moduli of a dual-porosity limestone

booktitleProceedings of the $5^{rd}$ International Workshop on Rock Physics
titleThe effect of the boundary conditions on the elastic moduli measurements at low frequencies: Experimental study

European Association of Geoscientists & Engineers

booktitle$81^{st}$ EAGE Conference and Exhibition 2019
titleA Laboratory Study of the Effect of Boundary Conditions on the Elastic Moduli Measurements

Wiley Online Library

journaltitleJournal of Geophysical Research: Solid Earth
titleSeismic dispersion and attenuation in fluid-saturated carbonate rocks: effect of microstructure and pressure

Multidisciplinary Digital Publishing Institute

titleStudy of the Influence of Nonlinear Dynamic Loads on Elastic Modulus of Carbonate Reservoir Rocks

journaltitleGeophysical Prospecting
titleThe dead volume effect on the elastic moduli measurements using the forced-oscillation method

Wiley Online Library

journaltitleJournal of Geophysical Research: Solid Earth
titleInfluence of fluid distribution on seismic dispersion and attenuation in partially saturated limestone

journaltitleRock Mechanics and Rock Engineering
titleSeismic Dispersion and Attenuation in Fractured Fluid-Saturated Porous Rocks: An Experimental Study with an Analytic and Computational Comparison

titleGassmann's fluid substitution and shear modulus variability in carbonates at laboratory seismic and ultrasonic frequencies

titleHeavy oils: Their shear story

booktitleSEG Technical Program Expanded Abstracts 2015
titleLaboratory measurement of dispersion and attenuation in the seismic frequency

journaltitleGeophysical Journal International
titleStress-dependent elastic properties of shales - laboratory experiments at seismic and ultrasonic frequencies

Curtin University

titleInvestigations of Elastic Properties of Isotropic and Anisotropic Rocks at Seismic Frequencies Using Forced-Oscillation Experiments

booktitleSEG Technical Program Expanded Abstracts 2017
titleMeasurement preciseness analysis of stress-strain system at seismic frequencies

Norwegian University of Science
Technology (NTNU)

titleSeismic Dispersion and the Relation between Static and Dynamic Stiffness of Shales

journaltitleFrontiers in Earth Science
titleA Laboratory Forced-Oscillation Apparatus for Measurements of Elastic and Anelastic Properties of Rocks at Seismic Frequencies

booktitleAGU Fall Meeting 2021
titleSeismic Dispersion and Attenuation in Shale Oil Reservoir: Laboratory Experiments and Theoretical Modeling

journaltitleGeophysical Journal International
titleThe seismic dispersion and attenuation characteristics of organic shales

booktitleAGU Fall Meeting 2022
titleExperimental Study of Clay-bound Water on Wave Dispersion and Attenuation Signatures of Shale

Society of Exploration Geophysicists

booktitleSEG Technical Program Expanded Abstracts 2005
titleSeismic attenuation: Observations and mechanisms

booktitleSEG Technical Program Expanded Abstracts 2005
titleDispersive and attenuative nature of shales: multiscale and multifrequency observations

booktitleSEG Technical Program Expanded Abstracts 2010
titleAnisotropic elastic moduli of the Mancos B Shale‐ An experimental study

International Association of Rock Physicists

booktitle$1^{st}$ International Workshop on Rock Physics
titleAttenuation and physical properties of shales from the Canning Basin, Western Australia

European Association of Geoscientists & Engineers

booktitle$77^{th}$ EAGE Conference and Exhibition 2015
titleA Laboratory Study of the Elastic and Anelastic Properties of the Eagle Ford Shale

Society of Exploration Geophysicists

titleExperimental development of low-frequency shear modulus and attenuation measurements in mated rock fractures: Shear mechanics due to asperity contact area changes with normal stress

booktitleAGU Fall Meeting 2019
titleAnelasticity of the Orocopia schist under different effective pressures and temperatures.

AIP Publishing LLC

journaltitleReview of Scientific Instruments
titleAn apparatus for measuring nonlinear viscoelasticity of minerals at high temperature

booktitleAGU Fall Meeting 2021
titlePore fluid controls on seismic attenuation in a greenschist facies metapelite

booktitleAGU Fall Meeting 2022
titleThe Implication of Seismic Attenuation in the Spectra of Slow Earthquakes

journaltitleGeophysical Research Letters
titleObservations of details of hysteresis loops in westerly granite

journaltitleGeophysical Research Letters
titleRock anelasticity measurements at high pressure, low strain amplitude and seismic frequency

journaltitlePhysics of the earth and planetary interiors
title$Q^{-1}$ of forsterite single crystals

American Institute of Physics

journaltitleReview of scientific instruments
titleA high-temperature torsion apparatus for the high-resolution characterization of internal friction and creep in refractory metals and ceramics: Application to the seismic-frequency, dynamic response of Earth’s upper mantle

Wiley Online Library

journaltitleJournal of Geophysical Research: Solid Earth
titleLow-frequency shear attenuation in polycrystalline olivine: Grain boundary diffusion and the physical significance of the Andrade model for viscoelastic rheology

Society of Exploration Geophysicists

booktitleSEG Technical Program Expanded Abstracts 2019
titleLow-frequency attenuation measurements of fluids

titleLaboratory measurements of seismic attenuation in sandstone: Strain versus fluid saturation effects

titleNumerical modeling and laboratory measurements of seismic attenuation in partially saturated rock

Wiley Online Library

journaltitleJournal of Geophysical Research: Solid Earth
titleLaboratory-based seismic attenuation in Fontainebleau sandstone: Evidence of squirt flow

titleBulk modulus dispersion and attenuation in sandstones

Society of Exploration Geophysicists

titleExperimental study of Young’s modulus dispersion and attenuation in fully saturated sandstones

booktitleGeoscience new horizons, Geoconvention 2015, Telus Convention Center, 4-8 May 2015, Calgary, AB Canada
titleExperimental Rock Deformation under $\mu$CT: two new apparatuses

Oxford University Press

journaltitleGeophysical Journal International
titleFrequency scaling of seismic attenuation in rocks saturated with two fluid phases

journaltitleAdvances in Geo-Energy Research
titleCombined effects of permeability and fluid saturation on seismic wave dispersion and attenuation in partially-saturated sandstone

European Association of Geoscientists & Engineers

journaltitleGeophysical Prospecting
titleRelations between static and dynamic moduli of sedimentary rocks

Wiley Online Library

journaltitleGeophysical Prospecting
titleDrained-to-undrained transition of bulk modulus in fluid-saturated porous rock induced by dead volume variation

European Association of Geoscientists & Engineers

journaltitleGeophysical Prospecting
numberAdvances in Rock Physics
titleGeneralized poroelasticity framework for micro-
inhomogeneous rocks

Oxford University Press

journaltitleGeophysical Journal International
titleThree-dimensional numerical modelling of the drained/undrained transition for frequency-dependent elastic moduli and attenuation

journaltitleFrontiers in Earth Science
titleLow-Frequency Elastic Properties of a Polymineralic Carbonate: Laboratory Measurement and Digital Rock Physics

Society of Exploration Geophysicists

booktitleSEG Technical Program Expanded Abstracts 2016
titleElastic anisotropy of the Wellington shale at seismic frequencies: Laboratory measurements

European Association of Geoscientists & Engineers

booktitle$80^{th}$ EAGE Conference and Exhibition 2018
titleThe Effect of Water Saturation on the Elastic Properties of the Wellington Shale at Seismic Frequencies

journaltitleGeophysical Prospecting
titleSeismic dispersion and attenuation in Mancos shale - laboratory measurements

Society of Exploration Geophysicists

booktitleSEG Technical Program Expanded Abstracts 2016
titleA laboratory study of the elastic anisotropy in the Mancos shale at seismic frequencies

European Association of Geoscientists & Engineers

booktitle$79^{th}$ EAGE Conference and Exhibition 2017
titleEffects of water saturation on P-wave anisotropy in the Mancos shale at seismic frequencies

journaltitleGeophysical Prospecting
titleA new laboratory apparatus for the measurement of seismic dispersion under deviatoric stress conditions
Rock physics,Anisotropy,Elasticity,Attenuation

titleThe impact of saturation on seismic dispersion in shales — Laboratory measurements

Norwegian University of Science
Technology (NTNU)

titleFrequency dependent elastic properties of shales - Impact of partial saturation and stress changes

American Association of Rock Mechanics

booktitle$52^{nd}$ US Rock Mechanics/Geomechanics Symposium
titleStatic vs. dynamic stiffness of shales: frequency and stress effects

European Association of Geoscientists & Engineers

journaltitleGeophysical Prospecting
number4-Rock Physics: from microstructure to seismic signatures
titleStatic and dynamic stiffness measurements with Opalinus Clay

journaltitleRock Mechanics and Rock Engineering
titleFrom static to dynamic stiffness of shales: frequency and stress dependence

Multidisciplinary Digital Publishing Institute

titleOn the Effect of CO2 on Seismic and Ultrasonic Properties: A Novel Shale Experiment

Oxford Academic

journaltitleGeophysical Journal International
titleOn the low-frequency elastic response of Pierre Shale during temperature cycles

Wiley Online Library

journaltitleJournal of Geophysical Research: Solid Earth
titleQuasi-static finite element modeling of seismic attenuation and dispersion due to wave-induced fluid flow in poroelastic media

Society of Exploration Geophysicists

journaltitleThe Leading Edge
titleIntegrated numerical and laboratory rock physics applied to seismic characterization of reservoir rocks

Society of Exploration Geophysicists

booktitleSEG Technical Program Expanded Abstracts 2020
titleEffects of crack roughness on attenuation caused by squirt flow in Carrara marble

Copernicus Meetings

titleSeismic moduli dispersion and attenuation obtained using Digital Rock Physics

Society of Exploration Geophysicists

titleDigital rock physics applied to squirt flow

Society of Exploration Geophysicists

titleAn accurate analytical model for squirt flow in anisotropic porous rocks-Part 1: Classical geometry

International Association of Rock Physicists

booktitle$6^{th}$ International Workshop on Rock Physics
titleThe characteristic frequency of squirt flow in porous rocks

booktitlePoromechanics VI
titleNumerical Analysis of Laboratory Attenuation Measurements

Wiley Online Library

journaltitleJournal of Geophysical Research: Solid Earth
titleSeismic attenuation and stiffness modulus dispersion in porous rocks containing stochastic fracture networks

Wiley Online Library

journaltitleGeophysical Prospecting
titleNumerically quantifying energy loss caused by squirt flow

titleFrequency-dependent attenuation and dispersion caused by squirt flow: Three-dimensional numerical study

Wiley Online Library

journaltitleJournal of Geophysical Research: Solid Earth
titleSquirt flow in cracks with rough walls

Acoustical Society of America

journaltitleThe Journal of the Acoustical Society of America
titleComputation of dynamic seismic responses to viscous fluid of digitized three-dimensional Berea sandstones with a coupled finite-difference method

Society of Exploration Geophysicists

titleNumerical simulation of coupled fluid-solid interaction at the pore scale: A digital rock-physics technology

Society of Exploration Geophysicists
American Association of Petroleum …

titleViscoelastic substitute models for seismic attenuation caused by squirt flow and fracture leak off

journaltitleFrontiers in Earth Science
titleDigital rock physics: A geological driven workflow for the segmentation of anisotropic Ruhr sandstone

booktitle$81^{st}$ EAGE Conference and Exhibition 2019
titleNumerical Modeling of Stress-Strain Oscillation Experiments Using the Finite Element Method

journaltitleJournal of Geophysics and Engineering
titlePrecision analysis of forced-oscillation device: numerical modelling and experimental investigations

American Institute of Physics

journaltitleReview of scientific instruments
titleDevice for the independent verification of subresonant mechanical damping measurements

The Physical Society of Japan

journaltitleJournal of the Physical Society of Japan
titleInternal friction peaks of cold worked pure aluminum and its dilute alloys

Wiley Online Library

journaltitlephysica status solidi (a)
titleHigh-temperature internal friction peaks of pure aluminum single-, bi-, and polycrystals measured with an inverted flexure pendulum

journaltitleJournal de Physique Colloques
titleMedium temperature internal friction in high purity fcc and hcp metals

journaltitleMaterials Science and Engineering: A
titleEffects of macroscopic graphite particulates on the damping behavior of commercially pure aluminum

journaltitleJournal of alloys and compounds
titleMeasurement of high damping: techniques and analysis

Lawrence Berkeley National Laboratory

Berkeley, CA, USA

howpublishedPrivate Communication

Wiley Online Library

titleCharacterizing Materials in the Frequency Domain: Validation Experiments

Cambridge University Press

titleViscoelastic Materials

booktitle$73^{rd}$ EAGE Conference and Exhibition incorporating SPE EUROPEC 2011
titleLaboratory Measurements of Seismic Attenuation from $0.01$ to $100$ Hz

University of Texas at Austin

titleLow-frequency attenuation measurements of fluids

University of Houston

titleVelocity dispersion and wave attenuation in reservoir rocks

Wiley Online Library

journaltitleJournal of Polymer Science: Polymer Physics Edition
titleDynamic bulk and shear relaxation in glassy polymers. I. Experimental techniques and results on PMMA

journaltitleJournal of Geophysical Research: Solid Earth
titlePressure and Fluid Effect on Frequency-Dependent Elastic Moduli in Fully Saturated Tight Sandstone
low-frequency experiments,seismic dispersion and attenuation,tight sandstone

journaltitleJournal of Geophysical Research: Solid Earth
titleInfluence of frequency and fluid distribution on elastic wave velocities in partially saturated limestones
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# Revisit of magnetic orders in 1/1 approximant crystals of Tsai-type
quasicrystal from theoretical points of view

Takanori Sugimoto1<EMAIL_ADDRESS>Shintaro Suzuki2 Ryuji
Tamura3 Takami Tohyama4 1Center for Quantum Information and Quantum
Biology1Center for Quantum Information and Quantum Biology Osaka University
Osaka University Toyonaka Toyonaka Osaka 560-0043 Osaka 560-0043 Japan
2Department of Physical Science Japan
2Department of Physical Science Aoyama Gakuin University Aoyama Gakuin
University Sagamihara Sagamihara Kanagawa 252-5258 Kanagawa 252-5258 Japan
3Department of Materials Science and Technology Japan
3Department of Materials Science and Technology Tokyo University of Science
Tokyo University of Science Katsushika Katsushika Tokyo 125-8585 Tokyo
125-8585 Japan
4Department of Applied Physics Japan
4Department of Applied Physics Tokyo University of Science Tokyo University of
Science Katsushika Katsushika Tokyo 125-8585 Tokyo 125-8585 Japan Japan

###### Abstract

The various magnetic orders observed in approximant crystals of Tsai-type
quasicrystal are important for deepening our understanding of mysterious
magnetism in quasicrystals. Using an icosahedral cluster model with inter-
cluster interactions, we give an intuitive explanation of the mechanism of
magnetic orders previously reported by classical Monte-Carlo simulations for
an approximant-crystal model describing a Gd-based Tsai-type 1/1 approximant
crystal.

Recent experimental discovery of ferromagnetism in quasicrystals (QCs) has
stimulated both experimental and theoretical investigations of peculiar
magnetism inherent in QCs [1, 2]. However, microscopic magnetic structure and
mechanism of the ferromagnetic order have not been clarified so far. For
solving this problem, approximant crystals (ACs) of the QCs can provide
crucial information as emphasized before [3, 4, 5]. In fact, recent
comprehensive experimental studies on the magnetism of ACs [4, 6, 7, 8, 9, 10,
11, 12, 13] are helpful for understanding the mechanism of ferromagnetism in
QCs.

Contrary to QCs, ACs retain translational symmetry, while a large unit cell in
ACs has the same local structure as QCs. Hence, the ACs are suitable for
theoretical studies of magnetic properties in QCs. For this sake, two of the
present authors together with others have conducted classical Monte-Carlo
(CMC) simulations for an AC model of a Gd-based Tsai-type 1/1 AC [14], where
magnetic moments of Gd ions at the vertices of icosahedrons composed of the
bcc structure [see Fig. 1(a)] are coupled each other via the so-called
Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction [15]. Since a Gd ion has zero
orbital angular momentum for localized $f$ electrons, single-ion anisotropy
can be ignored in the Gd system. Therefore, the AC model for the Gd system
contains magnetic interactions among localized magnetic moments
$\bm{S}_{\bm{r}}$ defined as
$\mathcal{H}=-\sum_{|\bm{r}-\bm{r}^{\prime}|<R_{c}}J_{|\bm{r}-\bm{r}^{\prime}|}\,\bm{S}_{\bm{r}}\cdot\bm{S}_{\bm{r}^{\prime}}$
with the RKKY interaction $J_{R}=Jf(2k_{F}R)$, the Friedel oscillation
$f(x)=(-x\cos x+\sin x)/x^{4}$, the Fermi wavenumber $k_{F}$, and the cutoff
length $R_{c}$. The CMC calculations for a sufficiently large system have
yielded a phase diagram and magnetic orders shown in Fig. 1(b) and Fig. 1(c),
respectively [14], where antiferromagnetic (A), incommensurate (IC),
ferromagnetic (F), and cuboc (Cb) phases appear. The resulting phase diagram
qualitatively explained an experimentally reported behavior [4].

Figure 1: (a) Crystal structure of Tsai-type 1/1 AC. Icosahedral clusters
consist of bcc structure, where magnetic moments are located at the vertices
of icosahedra. Red and green arrows denote the 1st and 2nd neighbor clusters
based on the cluster at the origin. (b) Magnetic phase diagram with the Curie-
Weiss temperature $\theta_{\mathrm{CW}}$ and the ground-state energy $E/J$,
determined by the CMC simulation in the AC model [14]. (c) Magnetic structures
in the F, A, and Cb phases. Different colors of arrows correspond to different
directions.

Even though a qualitative explanation of the experimental behavior was given
by the AC model, full understanding of the mechanism of magnetic orders was
not completed. To deepen our understanding, three of the present authors have
also examined a cluster model, where only 12 localized spins located at the
vertices of an icosahedral cluster are considered and they are mutually
coupled each other via the first (1st), second (2nd), and third (3rd) neighbor
exchange interactions, $J_{1}$, $J_{2}$, and $J_{3}$, respectively,
parametrized by two angles $\phi_{J}$ and $\theta_{J}$ [16] (see the caption
of Fig. 2). In this model, only four phases of the cluster have been found:
ferromagnetic (Fc), hedgehog antiferromagnetic (HAc), dual-hedgehog
antiferromagnetic (DHAc), and parallel-pairs’ antiferromagnetic (PPAc) orders
[see Fig. 2(a) and Fig. 2(b)]. Note that definition of the signs of $J_{1}$,
$J_{2}$, and $J_{3}$ in Fig. 2 differs from that in the previous study [16].

As mentioned above, the present authors investigated the magnetic orders in
Gd-based ACs by using two models separately: the AC model and the cluster
model. However, relations between the two models have not been yet clarified.
In this short note, we show an intuitive understanding of emerging magnetic
orders in the AC model by using the cluster model but with effective inter-
cluster interactions.

Figure 2: (a) Phase diagram of magnetic orders in the cluster model.
$(J_{1},J_{2},J_{3})=(\sin\theta_{J}\cos\phi_{J},\sin\theta_{J}\sin\phi_{J},\cos\theta_{J})$
are used [16]. Red, yellow, green, and purple regions represent Fc, HAc, DHAc,
and PPAc orders, respectively. Colored line denotes approximate parameter
values for the Fermi wavenumber $k_{F}\in[1.2,1.7]\,\mathrm{\AA}^{-1}$
according to the RKKY interaction. Colors on the line correspond to colors of
phases in the AC model: blue (A), gray (IC), green (F), and yellow (Cb),
respectively. (b) Magnetic structures in the cluster model. (c) Effective
inter-cluster interactions, $J_{1}^{\prime}$ and $J_{2}^{\prime}$, for the 1st
(orange solid line) and 2nd (purple dashed line) neighbor clusters,
respectively [see Fig. 1(a)]. Colored regions correspond to phases in the AC
model.

In Fig. 2(a), possible phases in the cluster model are shown by changing the
two angles $\phi_{J}$ and $\theta_{J}$ [16], where the values of $J_{1}$,
$J_{2}$, and $J_{3}$ are determined from the angles. In Gd-based ACs, $J_{1}$,
$J_{2}$, and $J_{3}$ are determined by corresponding bond lengths in an
icosahedron according to the RKKY interactions mentioned above. We plot
approximate values of $\phi_{J}$ and $\theta_{J}$ evaluated from $J_{1}$,
$J_{2}$, and $J_{3}$ for Gd-based ACs with
$k_{F}\in[1.2,1.7]\,\mathrm{\AA}^{-1}$ on Fig. 2(a) as a colored line (note
2$\pi$ periodicity of $\phi_{J}$). The color on the line corresponds to the
color of each phase obtained using the AC model as shown in Fig. 1(b). We find
that a segment of the line for $k_{F}\in[1.25,1.55]\,\mathrm{\AA}^{-1}$, which
corresponds to all phases except for the Cb phase in Fig. 1(b), is located at
the ferromagnetic Fc phase in the cluster model as shown in Fig. 2(a).
Therefore, the emergence of the A and IC phases in the AC model is attributed
to the presence of inter-cluster interactions. An effective inter-cluster
interaction $J_{1}^{\prime}$ ($J_{2}^{\prime}$) for the Fc phase can be
evaluated by summing over all possible RKKY interactions between the cluster
at the origin and its 1st (2nd) neighbor cluster as shown by red (green) arrow
in Fig. 1(a). The resulting $J_{1}^{\prime}$ and $J_{2}^{\prime}$, denoted by
solid and broken lines, respectively, in Fig. 2(c), show opposite signs in the
IC phase and A phases in the AC model [see colored regions in Fig. 2(c)].

Combining the results in the AC and cluster models, we give below an intuitive
explanation on the magnetic orders of the Gd-based Tsai-type 1/1 AC obtained
by the AC model.
The F phase. The intra-cluster interactions favor the Fc order in a cluster.
Moreover, both $J_{1}^{\prime}$ and $J_{2}^{\prime}$ are ferromagnetic
($J_{1}^{\prime}>0$ and $J_{2}^{\prime}>0$) as shown in Fig. 2(c), resulting
in trivial ferromagnetism in the AC.
The A phases. The Fc order is favored in a cluster, while the inter-cluster
interactions are different from the F phase: $J_{1}^{\prime}<0$ and
$J_{2}^{\prime}>0$. Hence, there appears a two-sublattice antiferromagnetic
structure consisting of the body-centered and cube-cornered clusters like the
Néel structure in the bcc lattice. Thus, we can call this cluster Néel order.
The IC phases. The intra-cluster interactions prefer the Fc order, whereas
magnetic frustration exists. In the IC phase for
$k_{F}\in[1.41,1.54]\,\mathrm{\AA}^{-1}$ in Fig. 2(c), $J_{1}^{\prime}>0$ and
$J_{2}^{\prime}<0$. Hence, magnetic frustration occurs in a triangle formed by
the 1st-1st-2nd neighbor inter-cluster bonds. On the contrary, in the IC phase
for $k_{F}\in[1.28,1.32]\,\mathrm{\AA}^{-1}$, there is magnetic frustration in
a plaquette formed by the 1st neighbor inter-cluster bonds and the intra-
cluster bonds. In this IC phase, all the intra-cluster interactions are
ferromagnetic, while there are comparable ferromagnetic and antiferromagnetic
interactions in the 1st neighbor inter-cluster interactions as evidenced from
zero crossing of $J_{1}^{\prime}$. Thus, there is a plaquette consisting of
two ferromagnetic intra-cluster bonds and comparable ferromagnetic and
antiferromagnetic inter-cluster bonds in the 1st neighboring cluster, inducing
magnetic frustration.
The Cb phase. This phase corresponds to the DHAc phase in the cluster model.
Since the net moment of the DHAc order is zero, effective inter-cluster
interactions are not a good quantity to be discussed. Rather inter-cluster
RKKY interactions but only for short distance (without summation) seem to be
crucial. These interactions are antiferromagnetic for both the 1st and 2nd
neighbor clusters. In the DHAc order, magnetic moments on opposite side of
cluster are anti-parallel. Hence, the magnetic moments facing neighboring
clusters can mediate the ferroic order between the two DHAc clusters.
Consequently, the Cb order obtained in the AC model is a consequence of the
DHAc order in the cluster model, although high symmetry in the DHAc order is
reduced to the lower one in the Cb order in the 1/1 AC.

In summary, we give an intuitive explanation of magnetic orders in the 1/1 ACs
based on the cluster model including inter-cluster interactions. We have found
that the F, A, and IC phases in the AC model correspond to the Fc phase in the
cluster model without inter-cluster interactions. Therefore, the presence of
the A and IC phases are due to the presence of effective inter-cluster
interactions. Introducing only the 1st and 2nd neighbor effective inter-
cluster interactions gives us a consistent understanding of magnetic phases in
the 1/1 ACs. In contrast, the Cb phase in the AC model corresponds to the DHAc
phase in the cluster model.

This work was supported by Challenging Research (Exploratory) (Grant No.
JP17K18764), Grant-in-Aid for Scientific Research on Innovative Areas (Grant
No. JP19H05821), and Grant-in-Aid for Scientific Research (B) (Grant No.
JP21H01044).

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