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.

Interaction between P, S1 and S2 waves in multilayered periodic monoclinic media at low frequencies

2019 ◽  
Vol 220 (3) ◽  
pp. 1947-1955
Author(s):  
Alexey Stovas ◽  
Yuriy Roganov ◽  
Vyacheslav Roganov
Keyword(s):  
Wave Propagation ◽  
Seismic Data ◽  
Layered Medium ◽  
Anisotropic Media ◽  
Pass Band ◽  
Low Frequencies ◽  
Propagator Method ◽  
The Matrix ◽  
Floquet Theorem ◽  
Insight Into

SUMMARY Application of the Floquet theorem and the matrix propagator method reduces the problem of the plane wave propagation in a periodically layered anisotropic media, to analysis of the properties of stationary envelopes of different wave modes propagating up- and downwards. We analyse the interchanging of stop- and pass-bands and their structure at low frequencies for a periodically layered medium with monoclinic symmetry. The analysis shows the effect of interaction between P,S1 and S2 wave multipliers for stop- and pass-band structure and gives insight into the wave propagation in vertically heterogeneous anisotropic media which is important in modelling and interpretation of seismic data.

scholarly journals Modelling of the wave fields by the modification of the matrix method in anisotropic media

2014 ◽  
Vol 6 (1) ◽  
pp. 467-485
Author(s):  
A. Pavlova
Keyword(s):  
Free Surface ◽  
Anisotropic Medium ◽  
Matrix Method ◽  
Layered Medium ◽  
Displacement Vector ◽  
Moment Tensor ◽  
Anisotropic Media ◽  
Seismic Moment Tensor ◽  
Arbitrary Boundary ◽  
The Matrix

Abstract. The modification of the matrix method of construction of wave field on the free surface of an anisotropic medium is presented. The earthquake source represented by a randomly oriented force or a seismic moment tensor is placed on an arbitrary boundary of a layered anisotropic medium. The theory of the matrix propagator in a homogeneous anisotropic medium by introducing a "wave propagator" is presented. It is shown that, for an anisotropic layered medium, the matrix propagator can be represented by a "wave propagator" in each layer. The matrix propagator P (z, z0 = 0) acts on the free surface of the layered medium and generates stress-displacement vector at depth z. The displacement field on the free surface of an anisotropic medium is obtained from the received system of equations considering the radiation condition and that the free surface is stressless. The approbation of the modification of the matrix method for isotropic and anisotropic media with TI symmetry is done. A comparative analysis of our results with the synthetic seismic records obtained by other methods and published in foreign papers is executed.

Estimating SV‐wave stacking velocities for transversely isotropic solids

Geophysics ◽  
1991 ◽  
Vol 56 (10) ◽  
pp. 1596-1602 ◽  
Author(s):  
Patricia A. Berge
Keyword(s):  
Shear Wave ◽  
Isotropic Medium ◽  
Transversely Isotropic ◽  
Anisotropic Media ◽  
Vertical Axis ◽  
Transversely Isotropic Medium ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Snell’S Law ◽  
Snell's Law

Conventional seismic experiments can record converted shear waves in anisotropic media, but the shear‐wave stacking velocities pose a problem when processing and interpreting the data. Methods used to find shear‐wave stacking velocities in isotropic media will not always provide good estimates in anisotropic media. Although isotropic methods often can be used to estimate shear‐wave stacking velocities in transversely isotropic media with vertical symmetry axes, the estimations fail for some transversely isotropic media even though the anisotropy is weak. For a given anisotropic medium, the shear‐wave stacking velocity can be estimated using isotropic methods if the isotropic Snell’s law approximates the anisotropic Snell’s law and if the shear wavefront is smooth enough near the vertical axis to be fit with an ellipse. Most of the 15 transversely isotropic media examined in this paper met these conditions for short reflection spreads and small ray angles. Any transversely isotropic medium will meet these conditions if the transverse isotropy is weak and caused by thin subhorizontal layering. For three of the media examined, the anisotropy was weak but the shear wave-fronts were not even approximately elliptical near the vertical axis. Thus, isotropic methods provided poor estimates of the shear‐wave stacking velocities. These results confirm that for any given transversely isotropic medium, it is possible to determine whether or not shear‐wave stacking velocities can be estimated using isotropic velocity analysis.

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.

scholarly journals Shear‐wave reflection moveout for azimuthally anisotropic media

1999 ◽  
Author(s):  
AbdulFattah Al‐Dajani ◽  
Nafi Toksöz
Keyword(s):  
Shear Wave ◽  
Wave Reflection ◽  
Anisotropic Media

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.

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