Mapping of two-dimensional anisotropic media onto isotropic media with consideration of metric factor

1981 ◽  
Vol 101 (2) ◽  
pp. 9-13
Author(s):  
Ryuichi Terakado ◽  
Masanori Kobayashi
Keyword(s):  
Anisotropic Media ◽  
Two Dimensional ◽  
Isotropic Media

Interactions Between Dislocations and Anisotropic Elastic Elliptical Inclusions

1994 ◽  
Vol 61 (3) ◽  
pp. 548-554 ◽  
Author(s):  
Wen J. Yen ◽  
Chyanbin Hwu
Keyword(s):  
Anisotropic Media ◽  
Analytical Continuation ◽  
Two Dimensional ◽  
Closed Form Solutions ◽  
Special Cases ◽  
General Field ◽  
Isotropic Media ◽  
In Series ◽  
Elastic Inclusions ◽  
Anisotropic Elastic

A general field solution for the stresses and displacements of the interactions between dislocations and inclusions has been derived in this paper by applying the Stroh’s formalism and the Muskhelishvili’s method of analytical continuation. The solutions are valid for general elastic anisotropic media under two-dimensional deformation. The interaction energy between dislocations and elastic inclusions is obtained explicitly. The solutions in general are expressed in series form for elastic inclusions. However, for the special cases when the elastic inclusions are replaced by a hole or rigid inclusion, simple closed-form solutions are derived. The general solutions are verified by considering the isotropic media since it is the only solution available in the literature. For the general anisotropic media, a series of contour diagrams for the glide component of the force on a dislocation are provided in this paper to study the effects of inclusion hardness, shape, and matrix anisotropy.

Quasi‐shear waves in inhomogeneous weakly anisotropic media by the quasi‐isotropic approach: A model study

Geophysics ◽  
2001 ◽  
Vol 66 (1) ◽  
pp. 308-319 ◽  
Author(s):  
Ivan Pšenčík ◽  
Joe A. Dellinger
Keyword(s):  
Order Approximation ◽  
Anisotropic Media ◽  
Ray Method ◽  
Weak Anisotropy ◽  
S Waves ◽  
Model Study ◽  
Arbitrary Strength ◽  
Isotropic Media ◽  
Synthetic Models ◽  
Ray Methods

In inhomogeneous isotropic regions, S-waves can be modeled using the ray method for isotropic media. In inhomogeneous strongly anisotropic regions, the independently propagating qS1- and qS2-waves can similarly be modeled using the ray method for anisotropic media. The latter method does not work properly in inhomogenous weakly anisotropic regions, however, where the split qS-waves couple. The zeroth‐order approximation of the quasi‐isotropic (QI) approach was designed for just such inhomogeneous weakly anisotropic media, for which neither the ray method for isotropic nor anisotropic media applies. We test the ranges of validity of these three methods using two simple synthetic models. Our results show that the QI approach more than spans the gap between the ray methods: it can be used in isotropic regions (where it reduces to the ray method for isotropic media), in regions of weak anisotropy (where the ray method for anisotropic media does not work properly), and even in regions of moderately strong anisotropy (in which the qS-waves decouple and thus could be modeled using the ray method for anisotropic media). A modeling program that switches between these three methods as necessary should be valid for arbitrary‐strength anisotropy.

Normal moveout from dipping reflectors in anisotropic media

Geophysics ◽  
1995 ◽  
Vol 60 (1) ◽  
pp. 268-284 ◽  
Author(s):  
Ilya Tsvankin
Keyword(s):  
Symmetry Axis ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Anisotropic Media ◽  
Weak Anisotropy ◽  
Anisotropic Models ◽  
Transversely Isotropic Media ◽  
Wide Range ◽  
Isotropic Media ◽  
The Difference

Description of reflection moveout from dipping interfaces is important in developing seismic processing methods for anisotropic media, as well as in the inversion of reflection data. Here, I present a concise analytic expression for normal‐moveout (NMO) velocities valid for a wide range of homogeneous anisotropic models including transverse isotropy with a tilted in‐plane symmetry axis and symmetry planes in orthorhombic media. In transversely isotropic media, NMO velocity for quasi‐P‐waves may deviate substantially from the isotropic cosine‐of‐dip dependence used in conventional constant‐velocity dip‐moveout (DMO) algorithms. However, numerical studies of NMO velocities have revealed no apparent correlation between the conventional measures of anisotropy and errors in the cosine‐of‐dip DMO correction (“DMO errors”). The analytic treatment developed here shows that for transverse isotropy with a vertical symmetry axis, the magnitude of DMO errors is dependent primarily on the difference between Thomsen parameters ε and δ. For the most common case, ε − δ > 0, the cosine‐of‐dip–corrected moveout velocity remains significantly larger than the moveout velocity for a horizontal reflector. DMO errors at a dip of 45 degrees may exceed 20–25 percent, even for weak anisotropy. By comparing analytically derived NMO velocities with moveout velocities calculated on finite spreads, I analyze anisotropy‐induced deviations from hyperbolic moveout for dipping reflectors. For transversely isotropic media with a vertical velocity gradient and typical (positive) values of the difference ε − δ, inhomogeneity tends to reduce (sometimes significantly) the influence of anisotropy on the dip dependence of moveout velocity.

scholarly journals Transformation to zero offset in transversely isotropic media

Geophysics ◽  
1996 ◽  
Vol 61 (4) ◽  
pp. 947-963 ◽  
Author(s):  
Tariq Alkhalifah
Keyword(s):  
Ray Tracing ◽  
Impulse Response ◽  
Homogeneous Medium ◽  
Anisotropy Parameter ◽  
Transversely Isotropic ◽  
Anisotropic Media ◽  
Amplitude Distribution ◽  
Isotropic Media ◽  
Zero Offset ◽  
Vertical Inhomogeneity

Nearly all dip‐moveout correction (DMO) implementations to date assume isotropic homogeneous media. Usually, this has been acceptable considering the tremendous cost savings of homogeneous isotropic DMO and considering the difficulty of obtaining the anisotropy parameters required for effective implementation. In the presence of typical anisotropy, however, ignoring the anisotropy can yield inadequate results. Since anisotropy may introduce large deviations from hyperbolic moveout, accurate transformation to zero‐offset in anisotropic media should address such nonhyperbolic moveout behavior of reflections. Artley and Hale’s v(z) ray‐tracing‐based DMO, developed for isotropic media, provides an attractive approach to treating such problems. By using a ray‐tracing procedure crafted for anisotropic media, I modify some aspects of their DMO so that it can work for v(z) anisotropic media. DMO impulse responses in typical transversely isotropic (TI) models (such as those associated with shales) deviate substantially from the familiar elliptical shape associated with responses in homogeneous isotropic media (to the extent that triplications arise even where the medium is homogeneous). Such deviations can exceed those caused by vertical inhomogeneity, thus emphasizing the importance of taking anisotropy into account in DMO processing. For isotropic or elliptically anisotropic media, the impulse response is an ellipse; but as the key anisotropy parameter η varies, the shape of the response differs substantially from elliptical. For typical η > 0, the impulse response in TI media tends to broaden compared to the response in an isotropic homogeneous medium, a behavior opposite to that encountered in typical v(z) isotropic media, where the response tends to be squeezed. Furthermore, the amplitude distribution along the DMO operator differs significantly from that for isotropic media. Application of this anisotropic DMO to data from offshore Africa resulted in a considerably better alignment of reflections from horizontal and dipping reflectors in common‐midpoint gather than that obtained using an isotropic DMO. Even the presence of vertical inhomogeneity in this medium could not eliminate the importance of considering the shale‐induced anisotropy.

Interface waves along fractures in anisotropic media

Geophysics ◽  
2013 ◽  
Vol 78 (4) ◽  
pp. T99-T112 ◽  
Author(s):  
Siyi Shao ◽  
Laura J. Pyrak-Nolte
Keyword(s):  
Shear Wave ◽  
Layered Medium ◽  
Anisotropic Media ◽  
Ultrasonic Transducers ◽  
Interface Waves ◽  
The Matrix ◽  
Isotropic Media ◽  
Oriented Parallel ◽  
Matrix Shear ◽  
Fracture Interface

The detection of fractures in an anisotropic medium is complicated by discrete modes that are guided or confined by fractures such as fracture interface waves. Fracture interface waves are generalized coupled Rayleigh waves whose existence and velocity in isotropic media depend on the stiffness of the fracture, frequency of the source, and shear-wave polarization. We derived the analytic solution for fracture interface waves in an orthorhombic medium and found that the existence and velocity of interface waves in anisotropic media are also affected by the orientation of a fracture relative to the layering. Laboratory measurements of fracture interface waves using ultrasonic transducers (central frequency [Formula: see text] MHz) on garolite specimens confirmed that the presence of fracture interface waves can mask the textural shear-wave anisotropy of waves propagating parallel to the layering. At low stresses, a layered medium appears almost isotropic when a fracture is oriented perpendicular to the layering, and conversely, a layered medium exhibits stronger anisotropy than the matrix for a fracture oriented parallel to the layering. The matrix shear-wave anisotropy is recovered when sufficient stress is applied to close a fracture. The theory and experimental results demonstrated that the interpretation of the presence of fractures in anisotropic material can be unambiguously interpreted if measurements are made as a function of stress, which eliminates many fractured-generated discrete modes such as fracture interface waves.

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