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  • 1
    Electronic Resource
    Electronic Resource
    Rayleigh waves in isotropic viscoelastic media (1992)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 108 (1992), S. 0 
    Details
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: In the surface of a linear viscoelastic medium, two types of Rayleigh waves may propagate. One of them, which always occurs, has wave characteristics which are close to those of the corresponding elastic solid. The second surface wave, not present in the elastic case, is possible for certain values of the material parameters, and for a given range of frequencies. Its properties are different from those of the first surface wave, particularly the energy velocity which is closer to the compressional body wave velocity. In this work, the properties of the two wave modes are analysed by using energy considerations. The energy balance for the Rayleigh waves is computed, and the quality factors and energy velocities are calculated as a function of the frequency, of depth, and per unit surface area.The main results indicate that the anelastic properties calculated from energy considerations are close, for practical purposes, to those obtained from the Rayleigh secular equation, i.e. phase velocity and attenuation factors give a good approximation to the dispersive and dissipation characteristics of the waves. In relation to the elastic case, the energy is more evenly distributed with depth, particularly in the v.e. mode. This wave has similar anelastic properties to those of the compressional body wave.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-246X.1992.tb04628.x
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  • 2
    Electronic Resource
    Electronic Resource
    A rheological model for anelastic anisotropic media with applications to seismic wave propagation (1994)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 119 (1994), S. 0 
    Details
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: This work presents a new constitutive law for linear viscoelastic and anisotropic media, to model rock behaviour and its effects on wave propagation. In areas with high dissipation properties (e.g. hydrocarbon reservoirs), the interpretation of seismic data based on the isotropic and purely elastic assumption might lead to misinterpretations or, even worse, to overlooking useful information. Thus, a proper description of wave propagation requires a rheology which accounts for the anisotropic and anelastic behaviour of rocks. the present model is based on the following mechanical interpretation; each eigenvector (eigenstrain) of the stiffness tensor of an anisotropic solid defines a fundamental deformation state of the medium. the six eigenvalues (eigenstiffnesses) represent the genuine elastic parameters. Since they are independent of the reference system, they have an intrinsic physical content. From this fact and the correspondence principle we infer that in a real medium the rheological properties depend essentially on six relaxation functions, which are the generalization of the eigenstiffnesses to the viscoeiastic case. the existence of six or less complex moduli depends on the symmetry class of the medium. We probe the new stress-strain relation with homogeneous viscoelastic plane waves, and give expressions for the slowness, attenuation, phase velocity, energy velocity (wavefront) and quality factor of the different wave modes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-246X.1994.tb00931.x
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  • 3
    Electronic Resource
    Electronic Resource
    Full frequency-range transient solution for compressional waves in a fluid-saturated viscoacoustic porous medium (1996)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 44 (1996), S. 0 
    Details
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: An analytical transient solution is obtained for propagation of compressional waves in a homogeneous porous dissipative medium. The solution, based on a generalization of Biot's poroelastic equations, holds for the low- and high-frequency ranges, and includes viscoelastic phenomena of a very general nature, besides the Biot relaxation mechanism. The viscodynamic operator is used to model the dynamic behaviour associated with the relative motion of the fluid in the pores at all frequency ranges. Viscoelasticity is introduced through the standard linear solid which allows the modelling of a general relaxation spectrum. The solution is used to study the influence of the material properties, such as bulk moduli, porosity, viscosity, permeability and intrinsic attenuation, on the kinematic and dynamic characteristics of the two compressional waves supported by the medium. We also obtain snapshots of the static mode arising from the diffusive behaviour of the slow wave at low frequencies.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-2478.1996.tb00141.x
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  • 4
    Electronic Resource
    Electronic Resource
    ANISOTROPIC Q AND VELOCITY DISPERSION OF FINELY LAYERED MEDIA (1992)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 40 (1992), S. 0 
    Details
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: When a seismic signal propagates through a finely layered medium, there is anisotropy if the wavelengths are long enough compared to the layer thicknesses. It is well known that in this situation, the medium is equivalent to a transversely isotropic material. In addition to anisotropy, the layers may show intrinsic anelastic behaviour. Under these circumstances, the layered medium exhibits Q anisotropy and anisotropic velocity dispersion.The present work investigates the anelastic effect in the long-wavelength approximation. Backus's theory and the standard linear solid rheology are used as models to obtain the directional properties of anelasticity corresponding to the quasi-compressional mode qP, the quasi-shear mode qSV, and the pure shear mode SH, respectively. The medium is described by a complex and frequency-dependent stiffness matrix. The complex and phase velocities for homogeneous viscoelastic waves are calculated from the Christoffel equation, while the wave-fronts (energy velocities) and quality factor surfaces are obtained from energy considerations by invoking Poynting's theorem.We consider two-constituent stationary layered media, and study the wave characteristics for different material compositions and proportions. Analyses on sequences of sandstone-limestone and shale-limestone with different degrees of anisotropy indicate that the quality factors of the shear modes are more anisotropic than the corresponding phase velocities, cusps of the qSV mode are more pronounced for low frequencies and midrange proportions, and in general, attenuation is higher in the direction perpendicular to layering or close to it, provided that the material with lower velocity is the more dissipative. A numerical simulation experiment verifies the attenuation properties of finely layered media through comparison of elastic and anelastic snapshots.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-2478.1992.tb00551.x
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  • 5
    Electronic Resource
    Electronic Resource
    Seismic modelling study of a subglacial lake (2003)
    PO Box 1354, 9600 Garsington Road , Oxford OX4 2XG , UK . : Blackwell Publishing Ltd
    Geophysical prospecting 51 (2003), S. 0 
    Details
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: We characterize the seismic response of Lake Vostok, an Antarctic subglacial lake located at nearly 4 km depth below the ice sheet. This study is relevant for the determination of the location and morphology of subglacial lakes. The characterization requires the design of a methodology based on rock physics and numerical modelling of wave propagation. The methodology involves rock-physics models of the shallow layer (firn), the ice sheet and the lake sediments, numerical simulation of synthetic seismograms, ray tracing, τ–p transforms, and AVA analysis, based on the theoretical reflection coefficients. The modelled reflection seismograms show a set of straight events (refractions through the firn and top-ice layer) and the two reflection events associated with the top and bottom of the lake. Theoretical AVA analysis of these reflections indicates that, at near offsets, the PP-wave anomaly is negative for the ice/water interface and constant for the water/sediment interface. This behaviour is shown by AVA analysis of the synthetic data set. This study shows that subglacial lakes can be identified by using seismic methods. Moreover, the methodology provides a tool for designing suitable seismic surveys.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1046/j.1365-2478.2003.00388.x
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  • 6
    Electronic Resource
    Electronic Resource
    Velocity and attenuation in partially saturated rocks: poroelastic numerical experiments (2003)
    PO Box 1354, 9600 Garsington Road , Oxford OX4 2XG , UK . : Blackwell Publishing Ltd
    Geophysical prospecting 51 (2003), S. 0 
    Details
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: We use a poroelastic modelling algorithm to compute numerical experiments on wave propagation in a rock sample with partial saturation using realistic fluid distribution patterns from tomography scans. Frequencies are in the range 10 to 500 kHz. The rock is a homogeneous isotropic sandstone partially filled with gas and water, which are defined by their characteristic values of viscosity, compressibility and density. We assume no mixing and that the two different pore-fills occupy different macroscopic regions. The von Kármán self-similar correlation function is used, employing different fractal parameters to model uniform and patchy fluid distributions, respectively, where effective saturation is varied in steps from full gas to full water saturation.Without resorting to additional matrix–fluid interaction mechanisms, we are able to reproduce the main features of the variation in wave velocity and attenuation with effective saturation and frequency, as those of published laboratory experiments. Furthermore, the behaviour of the attenuation peaks versus water saturation and frequency is similar to that of White's model. The conversion of primary P-wave energy into dissipating slow waves at the heterogeneities is shown to be the main mechanism for attenuating the primary wavefield. Fluid/gas patches are shown to affect attenuation more than equivalent patches in the permeability or solid-grain properties.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1046/j.1365-2478.2003.00393.x
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  • 7
    Electronic Resource
    Electronic Resource
    The seismic response to overpressure: a modelling study based on laboratory, well and seismic data (2001)
    Oxford, UK : Blackwell Science Ltd
    Geophysical prospecting 49 (2001), S. 0 
    Details
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: We investigate the seismic detectability of an overpressured reservoir in the North Sea by computing synthetic seismograms for different pore-pressure conditions. The modelling procedure requires the construction of a geological model from seismic, well and laboratory data. Seismic inversion and AVO techniques are used to obtain the P-wave velocity with higher reliability than conventional velocity analysis. From laboratory experiments, we obtain the wave velocities of the reservoir units versus confining and pore pressures. Laboratory experiments yield an estimate of the relationship between wave velocities and effective pressure under in situ conditions. These measurements provide the basis for calibrating the pressure model. Overpressures are caused by different mechanisms. We do not consider processes such as gas generation and diagenesis, which imply changes in phase composition, but focus on the effects of pure pore-pressure variations. The results indicate that changes in pore pressure can be detected with seismic methods under circumstances such as those of moderately deep North Sea reservoirs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1046/j.1365-2478.2001.00273.x
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  • 8
    Electronic Resource
    Electronic Resource
    Non-equilibrium compaction and abnormal pore-fluid pressures: effects on rock properties1 (2000)
    Oxford, UK : Blackwell Science Ltd
    Geophysical prospecting 48 (2000), S. 0 
    Details
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: Knowledge of pore pressure using seismic data will help in planning the drilling process to control potentially dangerous abnormal pressures. Various physical processes cause anomalous pressures on an underground fluid. Non-equilibrium compaction is a significant process of overpressure generation. This occurs when the sedimentation rate is so rapid that the pore fluids do not have a chance to ‘escape’ from the pore space.The model assumes a closed system and that the pore space is filled with water and hydrocarbon in a liquid state. Balancing mass and volume fractions yields the fluid pressure versus time of deposition and depth of burial. Thermal effects are taken into account. The pore pressure, together with the confining pressure, determines the effective pressure which, in turn, determines the bulk moduli of the rock matrix.We assume a sandstone saturated with hydrocarbons and water, for which calibration of the model with experimental data is possible. The seismic velocities and attenuation factors are computed by using Biot’s theory of dynamic poroelasticity and the generalized linear solid. The example shows that the formation can be overpressured or underpressured depending on the properties of the saturating fluid. Wave velocities and quality factors decrease with decreasing differential pressure. The effect is important below approximately 20 MPa. The model is in good agreement with experimental data for Berea sandstone and provides a tool for predicting pore pressure from seismic attributes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1046/j.1365-2478.2000.00197.x
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  • 9
    Electronic Resource
    Electronic Resource
    Viscoelastic effective rheologies for modelling wave propagation in porous media[ Received ] (1998)
    Oxford BSL : Blackwell Publishing Ltd
    Geophysical prospecting 46 (1998), S. 0 
    Details
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: Biot's poroelastic differential equations are modified for including matrix–fluid interaction mechanisms. The description is phenomenological and assumes a solid–fluid relaxation function coupling coefficient. The model satisfies basic physical properties such as, for instance, that P-wave velocities at low frequencies are lower than those predicted by Biot's theory. In many cases, the results obtained with the Biot (two-phase) modelling are equal to those obtained with single-phase elastic modelling, mainly at seismic frequencies. However, a correct equivalence is obtained with a viscoelastic rheology, which requires one relaxation peak for each Biot (P and S) mechanism. The standard viscoelastic model, which generalizes compressibility and shear modulus to relaxation functions, is not appropriate for modelling the Biot complex moduli, since Biot's attenuation is of a kinetic nature (i.e. it is not related to bulk deformations). The problem is solved by associating relaxation functions with each wave modulus. The equivalence between the two modelling approaches is investigated for a homogeneous water-filled sandstone and a periodically layered poroelastic medium, alternately filled with gas and water. The simulations indicate that, in the homogeneous case, particle velocities in the solid skeleton, caused by a source applied to the matrix, are equivalent to viscoelastic particle velocities. In a finely layered medium, viscoelastic modelling is not, in principle, equivalent to porous modelling, due to substantial mode conversion from fast wave to slow static mode. However, this effect, caused by local fluid-flow motion, can be simulated by including an additional relaxation mechanism similar to the squirt-flow.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1046/j.1365-2478.1998.00087.x
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  • 10
    Electronic Resource
    Electronic Resource
    Seismic and ultrasonic velocities in permafrost (1998)
    Oxford BSL : Blackwell Publishers
    Geophysical prospecting 46 (1998), S. 0 
    Details
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: We calculate the compressional- and shear-wave velocities of permafrost as a function of unfrozen water content and temperature. Unlike previous theories based on simple slowness and/or moduli averaging or two-phase models, we use a Biot-type three-phase theory that considers the existence of two solids (solid and ice matrices) and a liquid (unfrozen water). The compressional velocity for unconsolidated sediments obtained with this theory is close to the velocity computed with Wood's model, since Biot's theory involves a Wood averaging of the moduli of the single constituents. Moreover, the model gives lower velocities than the well-known slowness averaging theory (Wyllie's equation). For consolidated Berea sandstone, the theory underestimates the value of the compressional velocity below 0°C. Computing the average bulk moduli by slowness averaging the ice and solid phases and Wood averaging the intermediate moduli with the liquid phase yields a fairly good fit of the experimental data. The proportion of unfrozen water and temperature are closely related. Fitting the wave velocity at a given temperature allows the prediction of the velocity at the whole range of temperatures, provided that the average pore radius and its standard deviation are known.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1046/j.1365-2478.1998.1000333.x
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