Anisotropic parameters of layered media in terms of composite elastic properties

Geophysics ◽  
1995 ◽  
Vol 60 (4) ◽  
pp. 1243-1248 ◽  
Author(s):  
John Brittan ◽  
Mike Warner ◽  
Gerhard Pratt
Keyword(s):  
Elastic Properties ◽  
Seismic Wave ◽  
Anisotropic Medium ◽  
Transversely Isotropic ◽  
Individual Layer ◽  
Rigorous Testing ◽  
Earth Models ◽  
Axis Of Symmetry ◽  
The Individual ◽  
Layered Sequence

In elastic earth models, at a wide variety of scales, the subsurface is a layered sequence of different constituent media. It is therefore important to understand the elastic properties of such a sequence, in particular to determine the response of the layering to an investigating seismic wave. It can be shown that if the individual layer thicknesses are much less than the wavelength of a seismic wave passing through the stack, the wave will propagate as though it were traversing a homogenous, anisotropic medium (Postma, 1955). This property has been subjected to rigorous testing both experimentally (Melia and Carlson, 1984) and numerically (Carcione et al., 1991). The elastic properties of this “equivalent medium” can be derived algebraically from the elastic properties of the materials that compose the layers (Backus, 1962). The homogenous equivalent medium will be transversely isotropic (hereafter referred to as TI), the axis of symmetry lying perpendicular to the layering.

scholarly journals Scanning anisotropy parameters in complex media

Geophysics ◽  
2011 ◽  
Vol 76 (2) ◽  
pp. U13-U22 ◽  
Author(s):  
Tariq Alkhalifah
Keyword(s):  
Anisotropic Medium ◽  
Homogeneous Medium ◽  
Transversely Isotropic ◽  
Transient Behavior ◽  
Complex Media ◽  
Linear Partial Differential Equations ◽  
Anisotropy Parameters ◽  
Axis Of Symmetry ◽  
Ti Media ◽  
Taylor’S Series

Parameter estimation in an inhomogeneous anisotropic medium offers many challenges; chief among them is the trade-off between inhomogeneity and anisotropy. It is especially hard to estimate the anisotropy anellipticity parameter η in complex media. Using perturbation theory and Taylor’s series, I have expanded the solutions of the anisotropic eikonal equation for transversely isotropic (TI) media with a vertical symmetry axis (VTI) in terms of the independent parameter η from a generally inhomogeneous elliptically anisotropic medium background. This new VTI traveltime solution is based on a set of precomputed perturbations extracted from solving linear partial differential equations. The traveltimes obtained from these equations serve as the coefficients of a Taylor-type expansion of the total traveltime in terms of η. Shanks transform is used to predict the transient behavior of the expansion and improve its accuracy using fewer terms. A homogeneous medium simplification of the expansion provides classical nonhyperbolic moveout descriptions of the traveltime that are more accurate than other recently derived approximations. In addition, this formulation provides a tool to scan for anisotropic parameters in a generally inhomogeneous medium background. A Marmousi test demonstrates the accuracy of this approximation. For a tilted axis of symmetry, the equations are still applicable with a slightly more complicated framework because the vertical velocity and δ are not readily available from the data.

Determination of Elastic Constants for Human Femurs

1979 ◽  
Vol 101 (3) ◽  
pp. 193-197 ◽  
Author(s):  
V. G. Lappi ◽  
M. S. King ◽  
I. Le May
Keyword(s):  
Elastic Properties ◽  
Elastic Constants ◽  
Isotropic Material ◽  
Rotational Symmetry ◽  
Transversely Isotropic ◽  
Longitudinal Axis ◽  
Transversely Isotropic Material ◽  
Axis Of Symmetry ◽  
Plane Of Isotropy

The elastic properties of the bone constituting human femurs have been determined from measurements of the velocities of ultrasonic compressional and shear waves through wet, embalmed bone samples. The bone has been shown to be a transversely isotropic material with the axis of symmetry parallel to the longitudinal axis of the bone. The values of the elastic constants were determined to be: c11=6860±330MPaE3=5500MPac12=2700±570MPaE1=4990MPac13=3760±1570MPaν31=0.39c33=8480±760MPaν12=0.20c44=2240±180MPaG31=2240MPa where the 3-axis is that of rotational symmetry and the 1- and 2-axes are in the plane of isotropy.

Rayleigh and Love Waves in Cladded Anistropic Medium

1990 ◽  
Vol 57 (2) ◽  
pp. 398-403 ◽  
Author(s):  
M. Bouden ◽  
S. K. Datta
Keyword(s):  
Anisotropic Medium ◽  
Guided Waves ◽  
Transversely Isotropic ◽  
Guided Wave ◽  
Fiber Reinforced Composites ◽  
Isotropic Layer ◽  
Reinforced Composites ◽  
Guided Wave Propagation ◽  
Rayleigh And Love Waves ◽  
Axis Of Symmetry

Guided waves in coated anisotropic medium are of interest in electronics. Also, in recent years, cladded fiber-reinforced composites are being developed for use as aerospace structures. This paper deals with guided wave propagation in a cladded or coated anisotropic medium. The cladding (coating) is assumed to be a thin isotropic layer, which is bonded to a transversely isotropic substrate with the axis of symmetry parallel to the layer. It is shown that the anisotropy of the substrate affects the dispersion behavior in a manner that is substantially different than in the case of isotropic substrate.

scholarly journals Effective elastic properties of transversely isotropic materials with concave pores

2021 ◽  
Vol 153 ◽  
pp. 103665
Author(s):  
K. Du ◽  
L. Cheng ◽  
J.F. Barthélémy ◽  
I. Sevostianov ◽  
A. Giraud ◽  
...  
Keyword(s):  
Elastic Properties ◽  
Transversely Isotropic ◽  
Effective Elastic Properties ◽  
Isotropic Materials ◽  
Transversely Isotropic Materials

scholarly journals Mechanics of tubular helical assemblies: ensemble response to axial compression and extension

2021 ◽  
Author(s):  
Jacopo Quaglierini ◽  
Alessandro Lucantonio ◽  
Antonio DeSimone
Keyword(s):  
Boundary Conditions ◽  
Elastic Properties ◽  
Central Region ◽  
Mechanical Response ◽  
Different Boundary Conditions ◽  
Kirchhoff Rods ◽  
Model Versus ◽  
The Individual ◽  
Opposite Chirality

Abstract Nature and technology often adopt structures that can be described as tubular helical assemblies. However, the role and mechanisms of these structures remain elusive. In this paper, we study the mechanical response under compression and extension of a tubular assembly composed of 8 helical Kirchhoff rods, arranged in pairs with opposite chirality and connected by pin joints, both analytically and numerically. We first focus on compression and find that, whereas a single helical rod would buckle, the rods of the assembly deform coherently as stable helical shapes wound around a common axis. Moreover, we investigate the response of the assembly under different boundary conditions, highlighting the emergence of a central region where rods remain circular helices. Secondly, we study the effects of different hypotheses on the elastic properties of rods, i.e., stress-free rods when straight versus when circular helices, Kirchhoff’s rod model versus Sadowsky’s ribbon model. Summing up, our findings highlight the key role of mutual interactions in generating a stable ensemble response that preserves the helical shape of the individual rods, as well as some interesting features, and they shed some light on the reasons why helical shapes in tubular assemblies are so common and persistent in nature and technology. Graphic Abstract We study the mechanical response under compression/extension of an assembly composed of 8 helical rods, pin-jointed and arranged in pairs with opposite chirality. In compression we find that, whereas a single rod buckles (a), the rods of the assembly deform as stable helical shapes (b). We investigate the effect of different boundary conditions and elastic properties on the mechanical response, and find that the deformed geometries exhibit a common central region where rods remain circular helices. Our findings highlight the key role of mutual interactions in the ensemble response and shed some light on the reasons why tubular helical assemblies are so common and persistent.

scholarly journals Parameterization of elastic stress sensitivity in shales

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. WA147-WA155 ◽  
Author(s):  
Marina Pervukhina ◽  
Boris Gurevich ◽  
Pavel Golodoniuc ◽  
David N. Dewhurst
Keyword(s):  
Elastic Properties ◽  
Anisotropy Parameter ◽  
Transversely Isotropic ◽  
Bedding Plane ◽  
Stress Sensitivity ◽  
Crack Orientation ◽  
Fluid Identification ◽  
Orientation Anisotropy ◽  
Characteristic Pressure ◽  
Stress Dependency

Stress dependency and anisotropy of dynamic elastic properties of shales is important for a number of geophysical applications, including seismic interpretation, fluid identification, and 4D seismic monitoring. Using Sayers-Kachanov formalism, we developed a new model for transversely isotropic (TI) media that describes stress sensitivity behavior of all five elastic coefficients using four physically meaningful parameters. The model is used to parameterize elastic properties of about 20 shales obtained from laboratory measurements and the literature. The four fitting parameters, namely, specific tangential compliance of a single crack, ratio of normal to tangential compliances, characteristic pressure, and crack orientation anisotropy parameter, show moderate to good correlations with the depth from which the shale was extracted. With increasing depth, the tangential compliance exponentially decreases. The crack orientation anisotropy parameter broadly increases with depth for most of the shales, indicating that cracks are getting more aligned in the bedding plane. The ratio of normal to shear compliance and characteristic pressure decreases with depth to 2500 m and then increases below this to 3600 m. The suggested model allows us to evaluate the stress dependency of all five elastic compliances of a TI medium, even if only some of them are known. This may allow the reconstruction of the stress dependency of all five elastic compliances of a shale from log data, for example.

Reflection moveout approximations for P-waves in a moderately anisotropic homogeneous tilted transverse isotropy layer

Geophysics ◽  
2017 ◽  
Vol 82 (5) ◽  
pp. C175-C185 ◽  
Author(s):  
Ivan Pšenčík ◽  
Véronique Farra
Keyword(s):  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
P Wave ◽  
Weak Anisotropy ◽  
P Waves ◽  
3D Space ◽  
Axis Of Symmetry ◽  
Relative Errors ◽  
Symmetry Tests ◽  
Ti Media

We have developed approximate nonhyperbolic P-wave moveout formulas applicable to weakly or moderately anisotropic media of arbitrary anisotropy symmetry and orientation. Instead of the commonly used Taylor expansion of the square of the reflection traveltime in terms of the square of the offset, we expand the square of the reflection traveltime in terms of weak-anisotropy (WA) parameters. No acoustic approximation is used. We specify the formulas designed for anisotropy of arbitrary symmetry for the transversely isotropic (TI) media with the axis of symmetry oriented arbitrarily in the 3D space. Resulting formulas depend on three P-wave WA parameters specifying the TI symmetry and two angles specifying the orientation of the axis of symmetry. Tests of the accuracy of the more accurate of the approximate formulas indicate that maximum relative errors do not exceed 0.3% or 2.5% for weak or moderate P-wave anisotropy, respectively.

Control of cracks by interfaces in composites

1975 ◽  
Vol 341 (1627) ◽  
pp. 409-428 ◽  
Keyword(s):  
Composite Material ◽  
Elastic Properties ◽  
Adhesive Joint ◽  
Composite Structures ◽  
Crack Path ◽  
Brittle Materials ◽  
Novel Theory ◽  
The Individual ◽  
Model Crack

A novel theory is proposed to show how a crack may he accelerated or retarded when it meets an interface between two equally brittle materials of different elastic properties. Measurements of a model crack travelling through a brittle adhesive joint have substantially verified the theory. The results demonstrate that the toughness of a composite material, having a periodic stiffness change along the crack path, may be very much greater than the toughness of the individual components of the composite. The relevance of these ideas to the design of tough composite structures is discussed.

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