Phase‐shift depth migration on locally transverse isotropic media: Stability in relation to symmetry axis variation at each medium point

Abstract Several recent investigations suggest that portions of the Earth's upper mantle behave anisotropically to seismic wave propagation. Since several types of anisotropy can produce azimuthal variations in Pn velocities, it is of particular geophysical interest to provide a framework for the recognition of the form or forms of anisotropy most likely to be manifest in the upper mantle. In this paper upper mantle material is assumed to possess the elastic properties of transversely isotropic media. Equations are presented which relate azimuthal variations in Pn velocities to the direction and angle of tilt of the symmetry axis of a transversely isotropic upper mantle. It is shown that the velocity data of Raitt and Shor taken near the Mendocino and Molokai fracture zones can be adequately explained by the assumption of transverse isotropy with a nearly horizontal symmetry axis.

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Double parameterized regularization inversion method for migration velocity analysis in transversely isotropic media with a vertical symmetry axis

Geophysical Prospecting ◽

10.1111/1365-2478.12117 ◽

2014 ◽

Vol 62 (5) ◽

pp. 1040-1053

Author(s):

Caixia Yu ◽

Yanfei Wang ◽

Jingtao Zhao ◽

Zhenli Wang

Keyword(s):

Symmetry Axis ◽

Transversely Isotropic ◽

Migration Velocity ◽

Inversion Method ◽

Velocity Analysis ◽

Transversely Isotropic Media ◽

Migration Velocity Analysis ◽

Isotropic Media

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The offset-midpoint traveltime pyramid in 3D transversely isotropic media with a horizontal symmetry axis

Geophysics ◽

10.1190/geo2013-0322.1 ◽

2015 ◽

Vol 80 (1) ◽

pp. T51-T62 ◽

Cited By ~ 3

Author(s):

Qi Hao ◽

Alexey Stovas ◽

Tariq Alkhalifah

Keyword(s):

Symmetry Axis ◽

Transversely Isotropic ◽

P Wave ◽

Analytic Representation ◽

Velocity Inversion ◽

Transversely Isotropic Media ◽

Horizontal Symmetry ◽

Time Domains ◽

Isotropic Media ◽

Hti Media

Analytic representation of the offset-midpoint traveltime equation for anisotropy is very important for prestack Kirchhoff migration and velocity inversion in anisotropic media. For transversely isotropic media with a vertical symmetry axis, the offset-midpoint traveltime resembles the shape of a Cheops’ pyramid. This is also valid for homogeneous 3D transversely isotropic media with a horizontal symmetry axis (HTI). We extended the offset-midpoint traveltime pyramid to the case of homogeneous 3D HTI. Under the assumption of weak anellipticity of HTI media, we derived an analytic representation of the P-wave traveltime equation and used Shanks transformation to improve the accuracy of horizontal and vertical slownesses. The traveltime pyramid was derived in the depth and time domains. Numerical examples confirmed the accuracy of the proposed approximation for the traveltime function in 3D HTI media.

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Wide-angle phase-slowness approximations in VTI media

Geophysics ◽

10.1190/1.2736350 ◽

2007 ◽

Vol 72 (4) ◽

pp. S177-S185 ◽

Cited By ~ 9

Author(s):

Ørjan Pedersen ◽

Bjørn Ursin ◽

Alexey Stovas

Keyword(s):

Phase Shift ◽

Taylor Series ◽

Continued Fraction ◽

Symmetry Axis ◽

Wide Angle ◽

Converted Wave ◽

Numerical Tests ◽

Series Representations ◽

Vertical Propagation ◽

Vti Media

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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GENERAL SCALARIZATION METHOD OF DYNAMIC ELASTIC FIELDS IN TRANSVERSALLY ISOTROPIC MEDIA AND ITS NEW APPLICATIONS

Vestnik of Don State Technical University ◽

10.23947/1992-5980-2018-18-3-258-264 ◽

2018 ◽

Vol 18 (3) ◽

pp. 258-264

Author(s):

I. P. Miroshnichenko ◽

V. P. Sizov

Keyword(s):

Symmetry Axis ◽

Layered Structures ◽

Mutual Arrangement ◽

Material Symmetry ◽

Displacement Fields ◽

General Technique ◽

Elastic Fields ◽

Scalarization Method ◽

Isotropic Media ◽

Transversally Isotropic

Introduction. An efficient technique of tensor field scalarization is successfully used while investigating tensor elastic fields of displacements, stresses and deformations in the layered structures of different materials, including transversally isotropic composites. These fields can be expressed through the scalar potentials corresponding to the quasi-longitudinal, quasi-transverse, and transverse-only waves. Such scalarization is possible if the objects under consideration are tensors relating to the subgroup of general coordinate conversions, when the local affine basis has one invariant vector that coincides with the material symmetry axis of the material. At this, the known papers consider structures where this vector coincides with the normal to the boundary between layers. However, other cases of the mutual arrangement of the material symmetry axis of the material and the boundaries between layers are of interest on the practical side.Materials and Methods. The work objective is further development of the scalarization method application in the boundary value problems of the dynamic elasticity theory for the cases of an arbitrary arrangement of the material symmetry axis relative to the boundary between layers. The present research and methodological apparatus are developed through the general technique of scalarization of the dynamic elastic fields of displacements, stresses and strains in the transversally isotropic media.Research Results. New design ratios for the determination of the displacement fields, stresses and deformations in the transversally isotropic media are obtained for the cases of an arbitrary arrangement of the material symmetry axes of the layer materials with respect to the boundaries between layers. Discussion and Conclusions. The present research and methodological apparatus are successfully used in determining the stress-strain state in the layered structures of transversally isotropic materials, and in analyzing the diagnosis results of the state of the plane-layered and layered cylindrical structures under operation.

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Normal moveout from dipping reflectors in anisotropic media

Geophysics ◽

10.1190/1.1443755 ◽

1995 ◽

Vol 60 (1) ◽

pp. 268-284 ◽

Cited By ~ 50

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.

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Phase-shift anisotropic depth migration using controlled illumination: Stability in relation to addition of random noise

10.3997/2214-4609-pdb.160.sbgf325 ◽

2005 ◽

Author(s):

Marco Antonio Cetale Santos ◽

Djalma Manoel Soares Filho ◽

Paulo Léo Manassi Osório and Felipe Prado Loureiro

Keyword(s):

Phase Shift ◽

Random Noise ◽

Depth Migration ◽

Controlled Illumination

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