Dispersion and attenuation due to scattering from heterogeneities in the frame bulk and shear moduli of sand sediments

2008 ◽  
Vol 123 (5) ◽  
pp. 3441-3441
Author(s):  
Brian T. Hefner ◽  
Darrell R. Jackson ◽  
Joseph Calantoni
Keyword(s):  
Shear Moduli ◽  
Dispersion And Attenuation ◽  
Sand Sediments

Seismic wave attenuation and modulus dispersion in sandstones

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. D211-D231 ◽  
Author(s):  
James W. Spencer ◽  
Jacob Shine
Keyword(s):  
Wave Attenuation ◽  
High Viscosity ◽  
P Wave ◽  
S Wave ◽  
Local Flow ◽  
Shear Moduli ◽  
Low Viscosity ◽  
Confining Pressures ◽  
Wave Induced ◽  
Dispersion And Attenuation

We have conducted laboratory experiments over the 1–200 Hz band to examine the effects of viscosity and permeability on modulus dispersion and attenuation in sandstones and also to examine the effects of partial gas or oil saturation on velocities and attenuations. Our results have indicated that bulk modulus values with low-viscosity fluids are close to the values predicted using Gassmann’s first equation, but, with increasing frequency and viscosity, the bulk and shear moduli progressively deviate from the values predicted by Gassmann’s equations. The shear moduli increase up to 1 GPa (or approximately 10%) with high-viscosity fluids. The P- and S-wave attenuations ([Formula: see text] and [Formula: see text]) and modulus dispersion with different fluids are indicative of stress relaxations that to the first order are scaling with frequency times viscosity. By fitting Cole-Cole distributions to the scaled modulus and attenuation data, we have found that there are similar P-wave, shear and bulk relaxations, and attenuation peaks in each of the five sandstones studied. The modulus defects range from 11% to 15% in Berea sandstone to 16% to 26% in the other sandstones, but these would be reduced at higher confining pressures. The relaxations shift to lower frequencies as the viscosity increased, but they do not show the dependence on permeability predicted by mesoscopic wave-induced fluid flow (WIFF) theories. Results from other experiments having patchy saturation with liquid [Formula: see text] and high-modulus fluids are consistent with mesoscopic WIFF theories. We have concluded that the modulus dispersion and attenuations ([Formula: see text] and [Formula: see text]) in saturated sandstones are caused by a pore-scale, local-flow mechanism operating near grain contacts.

Dispersion and attenuation due to scattering from heterogeneities in the porosity of sand sediments

2006 ◽  
Vol 120 (5) ◽  
pp. 3098-3099
Author(s):  
Brian T. Hefner ◽  
Darrell R. Jackson ◽  
Joseph Calantoni ◽  
Allen H. Reed
Keyword(s):  
Dispersion And Attenuation ◽  
Sand Sediments

scholarly journals A simple model for squirt-flow dispersion and attenuation in fluid-saturated granular rocks

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. N109-N120 ◽  
Author(s):  
Boris Gurevich ◽  
Dina Makarynska ◽  
Osni Bastos de Paula ◽  
Marina Pervukhina
Keyword(s):  
Flow Model ◽  
Pore Space ◽  
Seismic Attenuation ◽  
Pore Scale ◽  
Shear Moduli ◽  
High Frequencies ◽  
Fluid Properties ◽  
Different Shapes ◽  
Attenuation And Dispersion ◽  
Dispersion And Attenuation

A major cause of seismic attenuation in fluid-saturated rocks is the flow of the pore fluid induced by the passing wave. At sonic and ultrasonic frequencies, attenuation appears to be dominated by the local (pore-scale) flow between pores of different shapes and orientations. A simple squirt flow model is developed in which all of the parameters can be independently measured or estimated from measurements. The pore space of the rock is assumed to consist of stiff porosity and compliant (or soft) pores present at grain contacts. The effect of isotropically distributed compliant pores is modeled by considering pressure relaxation in a disk-shaped gap between adjacent grains. This derivation gives the complex and frequency-dependent effective bulk and shear moduli of a rock, in which the compliant pores are liquid saturated and stiff pores are dry. The resulting squirt model is consistent with Gassmann’s and Mavko–Jizba equations at low and high frequencies, respectively. The magnitude of attenuation and dispersion given by the model is directly related to the variation of dry bulk modulus with pressure and is relatively independent of fluid properties.

scholarly journals Rigorous bounds for seismic dispersion and attenuation due to wave-induced fluid flow in porous rocks

Geophysics ◽  
2012 ◽  
Vol 77 (6) ◽  
pp. L45-L51 ◽  
Author(s):  
Boris Gurevich ◽  
Dina Makarynska
Keyword(s):  
Bulk Modulus ◽  
Inviscid Fluid ◽  
Porous Rocks ◽  
Shear Moduli ◽  
Poroelastic Media ◽  
Viscous Shear ◽  
Rigorous Bounds ◽  
Shear Relaxation ◽  
Wave Induced ◽  
Dispersion And Attenuation

The Hashin-Shtrikman (HS) bounds define the range of bulk and shear moduli of an elastic composite, given the moduli of the constituents and their volume fractions. Recently, the HS bounds have been extended to the quasi-static moduli of composite viscoelastic media. Because viscoelastic moduli are complex, the viscoelastic bounds form a closed curve on the complex plane. We analyze these general viscoelastic bounds for a particular case of a porous solid saturated with a Newtonian fluid. In our analysis, for poroelastic media, the viscoelastic bounds for the bulk modulus are represented by a semicircle and a segment of the real axis, connecting formal HS bounds that are computed for an inviscid fluid. Importantly, viscoelastic bounds for poroelastic media turn out to be independent of frequency. However, because the bounds are quasi-static, the frequency must be much lower than Biot’s characteristic frequency. Furthermore, we find that the bounds for the bulk modulus are attainable (realizable). We also find that these viscoelastic bounds account for viscous shear relaxation and squirt-flow dispersion, but do not account for Biot’s global flow dispersion, because the latter strongly depends on inertial forces.

Mathematical Model of the Effective Properties of a Fiber Reinforced Composite with a Linearly Graded Transition Zone

2010 ◽  
Vol 38 (4) ◽  
pp. 286-307
Author(s):  
Carey F. Childers
Keyword(s):  
Mathematical Model ◽  
Transition Zone ◽  
Effective Properties ◽  
Local Stress ◽  
Stress And Strain ◽  
Fiber Reinforced ◽  
Strain Fields ◽  
Shear Moduli ◽  
Fiber Reinforced Composite ◽  
Reinforced Composite

Abstract Tires are fabricated using single ply fiber reinforced composite materials, which consist of a set of aligned stiff fibers of steel material embedded in a softer matrix of rubber material. The main goal is to develop a mathematical model to determine the local stress and strain fields for this isotropic fiber and matrix separated by a linearly graded transition zone. This model will then yield expressions for the internal stress and strain fields surrounding a single fiber. The fields will be obtained when radial, axial, and shear loads are applied. The composite is then homogenized to determine its effective mechanical properties—elastic moduli, Poisson ratios, and shear moduli. The model allows for analysis of how composites interact in order to design composites which gain full advantage of their properties.

scholarly journals Seismic Dispersion and Attenuation in Fluid‐Saturated Carbonate Rocks: Effect of Microstructure and Pressure

2019 ◽  
Vol 124 (12) ◽  
pp. 12498-12522 ◽  
Author(s):  
Jan V. M. Borgomano ◽  
Lucas X. Pimienta ◽  
Jérôme Fortin ◽  
Yves Guéguen
Keyword(s):  
Carbonate Rocks ◽  
Dispersion And Attenuation ◽  
Effect Of Microstructure

Elasticity of colloidal gels: structural heterogeneity, floppy modes, and rigidity

Soft Matter ◽  
2021 ◽  
Author(s):  
D. Zeb Rocklin ◽  
Lilian C Hsiao ◽  
Megan E Szakasits ◽  
Michael J Solomon ◽  
Xiaoming Mao
Keyword(s):  
Coordination Number ◽  
Volume Fraction ◽  
Structural Parameters ◽  
Structural Heterogeneity ◽  
Colloidal Gels ◽  
Shear Moduli ◽  
Rheological Measurements

Rheological measurements of model colloidal gels reveal that large variations in the shear moduli as colloidal volume-fraction changes are not reflected by simple structural parameters such as the coordination number,...

Dispersion and attenuation of shear wave in couple stress stratum due to point source

2021 ◽  
pp. 107754632199888
Author(s):  
Richa Kumari ◽  
Abhishek K Singh
Keyword(s):  
Point Source ◽  
Shear Wave ◽  
Couple Stress ◽  
Imperfect Interface ◽  
Layered Composite ◽  
Functionally Graded ◽  
Function Technique ◽  
Dispersive Wave ◽  
Attenuation Profiles ◽  
Dispersion And Attenuation

This study discusses the propagation of a horizontally polarised shear wave in a layered composite structure consisting of couple stress stratum over a functionally graded orthotropic viscoelastic substrate due to point source existing at an imperfect interface of the stratum and substrate. Because of the CS effect in the stratum, the existence of the second kind of dispersive (shear) wave is established along with conventional first kind of a shear wave. The closed-form dispersion equations and damping equations of the first and second kind of a dispersive wave are derived by adopting non-traditional boundary conditions and Green’s function technique. The effect of characteristic length of microstructure, imperfect bonding parameter and functional gradient parameters on velocity profiles and attenuation profiles of the first and second kind of dispersive wave has been computed numerically and delineated graphically. For validation, established results are matched with the classical one.

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