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  • 1
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 101 (1990), S. 0 
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: The anisotropic linear viscoelastic rheological relation constitutes a suitable model for describing the variety of phenomena which occur in seismic wavefields. This rheology, known also as Boltzmann's superposition principle, expresses the stress as a time convolution of a fourth rank tensorial relaxation function with the strain tensor.The first problem is to establish the time dependence of the relaxation tensor in a general and consistent way. Two kernels based on the general standard linear solid are identified with the mean stress and with the deviatoric components of the stress tensor in a given coordinate system, respectively. Additional conditions are that in the elastic limit the relaxation matrix must give the elasticity matrix, and in the isotropic limit the relaxation matrix must approach the isotropic-viscoelastic matrix. The resulting rheological relation provides the framework for incorporating anelasticity in time-marching methods for computing synthetic seismograms. Through a plane wave analysis of the anisotropic-viscoelastic medium, the phase, group and energy velocities are calculated in function of the complex velocity, showing that those velocities are in general different from each other. For instance, the energy velocity which represents the wave surface, is different from the group velocity unlike in the anisotropic-elastic case. The group velocity loses its physical meaning at the cusps where singularities appear. Each frequency component of the wavefield has a different non-spherical wavefront. Moreover, the quality factors for the different propagating modes are not isotropic. Examples of these physical quantities are shown for transversely isotropic-viscoelastic clayshale and sandstone.As in the isotropic-viscoelastic case, Boltzmann's superposition principle is implemented in the equation of motion by defining memory variables which circumvent the convolutional relation between stress and strain. The numerical problem is solved by using a new time integration technique specially designed to deal with wave propagation in linear viscoelastic media. As a first application snapshots and synthetic seismograms are computed for 2-D transversely isotropic-viscoelastic clayshale and sandstone which show substantial differences in amplitude, waveform and arrival time with the results given by the isotropic and elastic rheologies.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Pure and applied geophysics 157 (2000), S. 811-827 
    ISSN: 1420-9136
    Keywords: Key Words: Wave velocities, porous medium, clay content, poroelasticity.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract —The feasibility of modeling elastic properties of a fluid-saturated sand-clay mixture rock is analyzed by assuming that the rock is composed of macroscopic regions of sand and clay. The elastic properties of such a composite rock are computed using two alternative schemes.¶The first scheme, which we call the composite Gassmann (CG) scheme, uses Gassmann equations to compute elastic moduli of the saturated sand and clay from their respective dry moduli. The effective elastic moduli of the fluid-saturated composite rock are then computed by applying one of the mixing laws commonly used to estimate elastic properties of composite materials.¶In the second scheme which we call the Berryman-Milton scheme, the elastic moduli of the dry composite rock matrix are computed from the moduli of dry sand and clay matrices using the same composite mixing law used in the first scheme. Next, the saturated composite rock moduli are computed using the equations of Brown and Korringa, which, together with the expressions for the coefficients derived by Berryman and Milton, provide an extension of Gassmann equations to rocks with a heterogeneous solid matrix.¶For both schemes, the moduli of the dry homogeneous sand and clay matrices are assumed to obey the Krief’s velocity-porosity relationship. As a mixing law we use the self-consistent coherent potential approximation proposed by Berryman.¶The calculated dependence of compressional and shear velocities on porosity and clay content for a given set of parameters using the two schemes depends on the distribution of total porosity between the sand and clay regions. If the distribution of total porosity between sand and clay is relatively uniform, the predictions of the two schemes in the porosity range up to 0.3 are very similar to each other. For higher porosities and medium-to-large clay content the elastic moduli predicted by CG scheme are significantly higher than those predicted by the BM scheme.¶This difference is explained by the fact that the BM model predicts the fully relaxed moduli, wherein the fluid can move freely between sand and clay regions. In contrast, the CG scheme predicts the no-flow or unrelaxed moduli. Our analysis reveals that due to the extremely low permeability of clays, at seismic and higher frequencies the fluid has no time to move between sand and clay regions. Thus, the CG scheme is more appropriate for clay-rich rocks.
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  • 3
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Wave Motion 18 (1993), S. 11-20 
    ISSN: 0165-2125
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Geosciences , Physics
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 22 (1998), S. 263-275 
    ISSN: 0363-9061
    Keywords: non-ideal interface ; crack scattering ; domain decomposition ; collocation methods ; Engineering ; Civil and Mechanical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: This work presents a numerical algorithm for solving crack scattering in a transversely isotropic medium whose symmetry axis is perpendicular to the crack surface. The crack is modelled as boundary discontinuities in the displacement u and the particle velocity v, of the stresses [κu+ζv], where the brackets denote discontinuities across the interface. The specific stiffness κ introduces frequency-dependence and phase changes in the interface response and the specific viscosity ζ is related to the energy loss.The numerical method is based on a domain decomposition technique that assignes a different mesh to each side of the interface, that includes the crack plane. As stated above, the effects of the crack on wave propagation are modelled through the boundary conditions, that require a special boundary treatment based on characteristic variables. The algorithm solves the particle velocity-stress wave equations and two additional first-order differential equations (two-dimensional case) in the displacement discontinuity. For each mesh, the spatial derivatives normal to the interface are solved by the Chebyshev method, and the spatial derivatives parallel to the interface are computed with the Fourier method. They allow a highly accurate implementation of the boundary conditions and computation of the spatial derivatives, and an optimal discretization of the model space. Moreover, the algorithm allows general material variability. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 9 Ill.
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  • 5
    Publication Date: 1988-05-01
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
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  • 6
    Publication Date: 2016-05-11
    Description: The present study evaluates the capacity of the Boom Clay as a host rock for disposal purposes, more precisely its seismic characterization, which may assess its long-term performance to store radioactive wastes. Although the formation is relatively uniform and homogeneous, there are embedded thin layers of septaria (carbonates) that may affect the integrity of the Boom Clay. Therefore, it is essential to locate these geobodies. The seismic data to characterize the Boom Clay has been acquired at the Kruibeke test site. The inversion, which allowed us to obtain the anisotropy parameters and seismic velocities of the clay, is complemented with further information such as log and laboratory data. The attenuation properties have been estimated from equivalent formations (having similar composition and seismic velocities). The inversion yields quite consistent results although the symmetry of the medium is unusual but physically possible, since the anisotropy parameter is negative. According to a time-domain calculation of the energy velocity at four frequency bands up to 900 Hz, velocity increases with frequency, a behaviour described by the Zener model. Then, we use this model to describe anisotropy and anelasticity that are implemented into the equation of motion to compute synthetic seismograms in the space–time domain. The technique is based on memory variables and the Fourier pseudospectral method. We have computed reflection coefficients of the septaria thin layer. At normal incidence, the P -wave coefficient vanishes at specific thicknesses of the layer and there is no conversion to the S wave. For example, calculations at 600 Hz show that for thicknesses of 1 m the septarium can be detected more easily since the amplitudes are higher (nearly 0.8). Converted PS waves have a high amplitude at large offsets (between 30° and 80°) and can be useful to identify the target on this basis. Moreover, we have investigated the effect of septaria embedded in the Boom Clay with several simulations, by considering a lateral partial continuity of the calcareous thin inclusions. The simulations with layers of calcareous material show continuity of the reflections even when the percentage of carbonate within the layer is very small (5–15 per cent), while for low content of the calcareous material, isolated septaria boulders generate diffraction events. We have also simulated the stacked seismic section obtained from processing of the field data. The matching between the field and synthetic sections is acceptable.
    Keywords: Seismology
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
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  • 7
    Publication Date: 2019
    Description: 〈div data-abstract-type="normal"〉〈p〉Global warming and the associated glacier retreat recently revealed the entrance to an ice–rock tunnel, at an altitude of ~3600 m a.s.l., in the uppermost portion of the Forni Glacier in the Central Italian Alps. The tunnel served as an entrance to an Austro-Hungarian cableway station excavated in the rocks during the Great War just behind the frontline. A comprehensive geophysical survey, based on seismic and ground-penetrating radar profiling, was then undertaken to map other possible World War I (WWI) remains still embedded in the ice. The ice–rock interface was reconstructed over the entire saddle and in the uppermost portion of the glacier. A prominent linear reflector was surprisingly similar to the common response of buried pipes. The reflector orientation, almost longitudinal to the slope, does not seem to be compatible with a glacial conduit or with other natural features. Numerical simulations of a series of possible targets constrained interpretation to a partly water-filled rounded shape cavity. The presence of a preserved WWI tunnel connecting Mount Vioz and Punta Linke could be considered a realistic hypothesis. The Forni glacier could be still considered polythermal and comprised of cold ice without basal sliding in its top portion.〈/p〉〈/div〉
    Print ISSN: 0022-1430
    Electronic ISSN: 1727-5652
    Topics: Geography , Geosciences
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  • 8
    Publication Date: 2016-02-08
    Description: Wave-induced local fluid flow is known as a key mechanism to explain the intrinsic wave dissipation in fluid-saturated rocks. Understanding the relationship between the acoustic properties of rocks and fluid patch distributions is important to interpret the observed seismic wave phenomena. A triple-layer patchy (TLP) model is proposed to describe the P -wave dissipation process in a double-porosity media saturated with two immiscible fluids. The double-porosity rock consists of a solid matrix with unique host porosity and inclusions which contain the second type of pores. Two immiscible fluids are considered in concentric spherical patches, where the inner pocket and the outer sphere are saturated with different fluids. The kinetic and dissipation energy functions of local fluid flow (LFF) in the inner pocket are formulated through oscillations in spherical coordinates. The wave propagation equations of the TLP model are based on Biot's theory and the corresponding Lagrangian equations. The P -wave dispersion and attenuation caused by the Biot friction mechanism and the local fluid flow (related to the pore structure and the fluid distribution) are obtained by a plane-wave analysis from the Christoffel equations. Numerical examples and laboratory measurements indicate that P -wave dispersion and attenuation are significantly influenced by the spatial distributions of both, the solid heterogeneity and the fluid saturation distribution. The TLP model is in reasonably good agreement with White's and Johnson's models. However, differences in phase velocity suggest that the heterogeneities associated with double-porosity and dual-fluid distribution should be taken into account when describing the P -wave dispersion and attenuation in partially saturated rocks.
    Keywords: Seismology
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
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  • 9
    Publication Date: 2011-07-08
    Description: SUMMARY A dominant P -wave attenuation mechanism in reservoir rocks at seismic frequencies is due to wave-induced fluid flow (mesoscopic loss). The P -wave induces a fluid-pressure difference at mesoscopic-scale inhomogeneities (larger than the pore size but smaller than the wavelength), generating fluid flow and slow (diffusion) Biot waves. The theory has been developed in the 1970s for the symmetry axis of the equivalent transversely isotropic (TI) medium corresponding to a finely layered medium, and has recently been generalized to all propagation angles. The new theory states that the fluid-flow direction is perpendicular to the layering plane and it is independent of the loading direction. As a consequence, the relaxation behaviour can be described by a single relaxation function, since the medium consists of plane homogeneous layers. Besides P -wave losses, the coupling between the qP and qSV waves generates shear-wave anisotropic velocity dispersion and attenuation. In this work, we introduce a set of quasi-static numerical experiments to determine the equivalent viscoelastic TI medium to a finely layered poroelastic medium, which is validated using a recently developed analytical solution. The modelling technique is the finite-element (FE) method, where the equations of motion are solved in the space-frequency domain. Numerical rock physics may, in many circumstances, offer an alternative to laboratory measurements. Numerical experiments are inexpensive and informative since the physical process of wave propagation can be inspected during the experiment. Moreover, they are repeatable, essentially free from experimental errors, and may easily be run using alternative models of the rock and fluid properties. We apply the methodology to the Utsira aquifer of the North Sea, where carbon dioxide (CO 2 ) has been injected during the last 15 years. The tests consider alternating layers of the same rock saturated with gas and brine and a sequence of gas-saturated sandstone and mudstone layers, which represent possible models of the reservoir and cap rock of the aquifer system. The numerical examples confirm the new theory and illustrate the implementation of the harmonic tests to determine the complex and frequency-dependent effective stiffnesses and the associated wave velocities and quality factors.
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
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  • 10
    Publication Date: 2014-04-16
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
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