The Experts below are selected from a list of 17115 Experts worldwide ranked by ideXlab platform
Vaclav Vavrycuk - One of the best experts on this subject based on the ideXlab platform.
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velocity attenuation and quality factor in anisotropic viscoelastic media a perturbation approach
2008Co-Authors: Vaclav VavrycukAbstract:Velocity, attenuation, and the quality (Q-) factor of waves propagating in homogeneous media of arbitrary anisotropy and attenuation strength are calculated in high-frequency asymptotics using a stationary Slowness vector, the vector evaluated at the stationary point of the Slowness surface. This vector is generally complex-valued and inhomogeneous, meaning that the real and imaginary parts of the vector have different directions. The Slowness vector can be determined by solving three coupled polynomial equations of the sixth order or by a nonlinear inversion. The procedure is simplified if perturbation theory is applied. The elastic medium is viewed as a background medium, and the attenuation effects are incorporated as perturbations. In the first-order approximation, the phase and ray velocities and their directions remain unchanged, being the same as those in the background elastic medium. The perturbation of the Slowness vector is calculated by solving a system of three linear equations. The phase att...
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asymptotic green s function in homogeneous anisotropic viscoelastic media
2007Co-Authors: Vaclav VavrycukAbstract:An asymptotic Green’s function in homogeneous anisotropic viscoelastic media is derived. The Green’s function in viscoelastic media is formally similar to that in elastic media, but its computation is more involved. The stationary Slowness vector is, in general, complex valued and inhomogeneous. Its computation involves finding two independent real-valued unit vectors which specify the directions of its real and imaginary parts and can be done either by iterations or by solving a system of coupled polynomial equations. When the stationary Slowness direction is found, all quantities standing in the Green’s function such as the Slowness vector, polarization vector, phase and energy velocities and principal curvatures of the Slowness surface can readily be calculated. The formulae for the exact and asymptotic Green’s functions are numerically checked against closed-form solutions for isotropic and simple anisotropic, elastic and viscoelastic models. The calculations confirm that the formulae and developed numerical codes are correct. The computation of the P-wave Green’s function in two realistic materials with a rather strong anisotropy and absorption indicates that the asymptotic Green’s function is accurate at distances greater than several wavelengths from the source. The error in the modulus reaches at most 4% at distances greater than 15 wavelengths from the source.
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calculation of the Slowness vector from the ray vector in anisotropic media
2006Co-Authors: Vaclav VavrycukAbstract:The wave quantities needed in constructing wave fields propagating in anisotropic elastic media are usually calculated as a function of the Slowness vector, or of its direction called the wave normal. In some applications, however, it is desirable to calculate the wave quantities as a function of the ray direction. In this paper, a method of calculating the Slowness vector for a specified ray direction is proposed. The method is applicable to general anisotropy of arbitrary strength with arbitrary complex wave surface. The Slowness vector is determined by numerically solving a system of multivariate polynomial equations of the sixth order. By solving the equations, we obtain a complete set of Slowness vectors corresponding to all wave types and to all branches of the wave surface including the Slowness vectors along the acoustic axes. The wave surface can be folded to any degree. The system of equations is further specified for rays shot in the symmetry plane of an orthorhombic medium and for a transversely isotropic medium. The system is decoupled into two polynomial equations of the fourth order for the P –SV waves, and into equations for the SH wave, which yield an explicit closed-form solution. The presented approach is particularly advantageous in constructing ray fields, ray-theoretical Green functions, wavefronts and wave fields in strong anisotropy.
Gustavo Deco - One of the best experts on this subject based on the ideXlab platform.
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the rediscovery of Slowness exploring the timing of cognition
2015Co-Authors: Morten L Kringelbach, Anthony R Mcintosh, Petra Ritter, Viktor K Jirsa, Gustavo DecoAbstract:Slowness of thought is not necessarily a handicap but could be a signature of optimal brain function. Emerging evidence shows that neuroanatomical and dynamical constraints of the human brain shape its functionality in optimal ways, characterized by Slowness during task-based cognition in the context of spontaneous resting-state activity. This activity can be described mechanistically by whole-brain computational modeling that relates directly to optimality in the context of theories arguing for metastability in the brain. We discuss the role for optimal processing of information in the context of cognitive, task-related activity, and propose that combining multi-modal neuroimaging and explicit whole-brain models focused on the timing of functional dynamics can help to uncover fundamental rules of brain function in health and disease.
Alexey Stovas - One of the best experts on this subject based on the ideXlab platform.
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p wave Slowness surface approximation for tilted orthorhombic media
2016Co-Authors: Qi Hao, Alexey StovasAbstract:ABSTRACTWe have developed an analytic and approximate formula for vertical Slowness components of down- and upgoing plane P waves in 3D tilted orthorhombic media. A perturbation method and Shanks transform were used to derive the approximation for Slowness surface of P waves in tilted orthorhombic media. We have also quantitatively described the validity range of the radial horizontal Slowness components for the proposed formula. The validity range was affected by the strength of the anellipticity of an orthorhombic medium: the stronger the anellipticity, the smaller the validity range. Numerical examples determined that the proposed formula is accurate for tilted orthorhombic media with weak to strong anellipticity. We have also evaluated in detail the application of the proposed formula on calculating the P-wave intercept time in the τ-p domain for horizontally layered, tilted orthorhombic models. Our formula is useful for ray tracing, phase-shift migration, and τ-p domain intercept time approximation f...
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a tilted transversely isotropic Slowness surface approximation
2013Co-Authors: Alexey Stovas, Tariq AlkhalifahAbstract:The relation between vertical and horizontal Slownesses, better known as the dispersion relation, for transversely isotropic media with a tilted symmetry axis (TTI) requires solving a quartic polynomial equation, which does not admit a practical explicit solution to be used, for example, in downward continuation. Using a combination of the perturbation theory with respect to the anelliptic parameter and Shanks transform to improve the accuracy of the expansion, we develop an explicit formula for the vertical Slowness that is highly accurate for all practical purposes. It also reveals some insights into the anisotropy parameter dependency of the dispersion relation including the low impact that the anelliptic parameter has on the vertical placement of reflectors for a small tilt in the symmetry angle.
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wide angle phase Slowness approximations in vti media
2007Co-Authors: Orjan Pedersen, Bjorn Ursin, Alexey StovasAbstract:An anisotropic medium with vertical symmetry axis (VTI) often presents a good model for describing real rocks. Propagation of quasi-P- and quasi-SV-waves in such media requires an expression of the vertical phase Slowness, a complicated function of the horizontal phase Slowness and the medium parameters. For converted-wave phase-shift migration methods, it is desired to have Slowness expressions that are simple and accurate at wide angles of propagation. Taylor-series representations of the squared vertical Slowness for quasi-P- and quasi-SV-waves result in new wide-angle phase-Slowness approximations based on truncated series and continued-fraction representations. Slowness approximations that are exact for both vertical propagation and at a horizontal Slowness corresponding to horizontally traveling qP-waves are derived. The approximation for quasi-SV-waves can be used in phase-shift migration in media where the quasi-SV wavefront contains triplications. These approximations are tested on several models and compared to previously published approximations. The numerical tests suggest that the new continued-fraction approximations are more accurate. They can be used in phase-shift migration algorithms, which are more efficient for large angles than the existing approximations.
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wide angle phase Slowness approximations in vti media
2006Co-Authors: Orjan Pedersen, Bjorn Ursin, Alexey StovasAbstract:Several phase-shift migration methods depend on the vertical Slowness, which in general can be represented as a nonlinear function of the horizontal Slowness. In a VTI media, the dispersion relations relating the vertical and horizontal Slowness, are complex expressions. Simple and accurate approximations of the exact Slowness for both qP and qSV waves are desired for computationally fast and accurate migration algorithms. We describe new wide-angle phase Slowness approximations for a VTI media.
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reflection and transmission responses of layered transversely isotropic viscoelastic media
2003Co-Authors: Alexey Stovas, Bjorn UrsinAbstract:We consider a layered heterogeneous viscoelastic transversely isotropic medium with a vertical symmetry axis (a viscoelastic TIV medium) and parameters that depend on depth only. This takes into account intrinsic attenuation, anisotropy and thin layering. The seismic wavefield is decomposed into up- and downgoing waves scaled by the vertical energy flux. This scaling gives important symmetry relationships for both reflection and transmission (R/T) responses. For a stack of homogeneous layers, the exact reflection response can be computed in a numerically stable way by a simple layer-recursive algorithm. We derive exact plane-wave R/T coefficients and several linear and quadratic approximations between two viscoelastic TIV media, as functions of the real-valued horizontal Slowness. The approximations are valid for pre- and post-critical values of horizontal Slowness provided that the proper complex square roots are used when computing the vertical Slowness. Numerical examples demonstrate that the quadratic approximations can be used for large differences in medium parameters, while the linear approximations can be used for small differences. For weak anisotropy it is sufficient to use an isotropic background medium, while for strong anisotropy it is necessary to use a weak TIV or TIV background medium. We also extend the O'Doherty-Anstey formula to the P- and SV-wave transmission responses of a stack of viscoelastic TIV layers, taking into account intrinsic attenuation, anisotropy and thin layering.
Jungju Lee - One of the best experts on this subject based on the ideXlab platform.
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the group velocity variation of lamb wave in fiber reinforced composite plate
2007Co-Authors: Sangho Rhee, Jeongki Lee, Jungju LeeAbstract:Experimentally measured Lamb wave group velocities in composite materials with anisotropic characteristics are not the same as the theoretical group velocities which is calculated with the Lamb wave dispersion equation. This discrepancy arises from the fact that the angle between the group velocity direction and the phase velocity direction in anisotropic materials exists. Wave propagation in a composite material with anisotropic characteristics should be considered with respect to magnitude correction in addition to direction correction. In this study, S0 mode phase velocity dispersion curves are depicted with the variation of degree with respect to the fiber direction using a Lamb wave dispersion relation in the unidirectional, bidirectional, and quasi-isotropic composite plates. Slowness surface is sketched by the reciprocal value of the phase velocity curves. The magnitude and direction of the group velocity could be calculated from the Slowness surface. The recalculated group velocities with consideration of the magnitude and direction from the Slowness surface are compared with experimentally measured group velocities. The proposed method shows good agreements with theoretical and experimental results.
G R Liu - One of the best experts on this subject based on the ideXlab platform.
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elastic waves in a functionally graded piezoelectric cylinder
2003Co-Authors: Xu Han, G R LiuAbstract:An analytical–numerical method is presented for analyzing dispersion and characteristic surface of waves in a circular cylinder composed of functionally graded piezoelectric material (FGPM). In this method, the FGPM cylinder is divided into a number of annular elements with three-nodal lines in the wall thickness. The elemental mechanical as well as electrical properties are assumed to vary linearly in the thickness direction so as to better model the spatial variation of the mechanical and electrical properties of FGPM. The associated frequency dispersion equation is developed and the phase velocity and Slowness as well as the group velocity and Slowness are established in terms of the Rayleigh quotient. Six characteristic wave surfaces are introduced to visualize the effects of anisotropy and piezoelectricity on wave propagation. The calculation examples provide a full understanding of the complex phenomena of elastic waves in FGPM cylinders.
