Improved geometric-spreading approximation in layered transversely isotropic media

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. D85-D95 ◽  
Author(s):  
Alexey Stovas ◽  
Bjorn Ursin
Keyword(s):  
Single Layer ◽  
Transversely Isotropic ◽  
Velocity Analysis ◽  
Transversely Isotropic Medium ◽  
Numerical Tests ◽  
Transversely Isotropic Media ◽  
Geometric Spreading ◽  
Isotropic Media ◽  
Direct Approximation ◽  
Acoustic Approximation

A new approximation (direct approximation) for the relative geometric spreading of qP-waves in a layered transversely isotropic medium uses three traveltime parameters: two-way vertical traveltime, normal-moveout velocity, and the heterogeneity coefficient. These traveltime parameters, which can be estimated in velocity analysis, enter the parameters of geometric-spreading approximation. The new approximation is based on the acoustic approximation for a single-layer vertical transversely isotropic (VTI) medium with coefficients defined from Taylor expansion and asymptotic behavior at infinite offset. The acoustic approximation is used to reduce the number of parameters and to make the expression for the direct geometric-spreading approximation similar to a well-known traveltime approximation. The same traveltime parameters also allow for an independent approximation of the radiation pattern. Two numerical tests (single-layer and multilayered VTI models) prove that the new approximation is more accurate than standard approximations based on shifted hyperbola or two rational approximations.

Reflection and transmission responses in a layered transversely isotropic medium with horizontal symmetry axis

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. C143-C157 ◽  
Author(s):  
Song Jin ◽  
Alexey Stovas
Keyword(s):  
Good Accuracy ◽  
Symmetry Axis ◽  
Local Property ◽  
Transversely Isotropic ◽  
Weak Anisotropy ◽  
Reflection And Transmission ◽  
Numerical Tests ◽  
Transversely Isotropic Media ◽  
Horizontal Symmetry ◽  
Isotropic Media

Seismic wave reflection and transmission (R/T) responses characterize the subsurface local property, and the widely spread anisotropy has considerable influences even at small incident angles. We have considered layered transversely isotropic media with horizontal symmetry axes (HTI), and the symmetry axes were not restricted to be aligned. With the assumption of weak contrast across the interface, linear approximations for R/T coefficients normalized by vertical energy flux are derived based on a simple layered HTI model. We also obtain the approximation with the isotropic background medium under an additional weak anisotropy assumption. Numerical tests illustrate the good accuracy of the approximations compared with the exact results.

Moveout approximations for P- and SV-waves in dip-constrained transversely isotropic media

Geophysics ◽  
2013 ◽  
Vol 78 (6) ◽  
pp. C53-C59 ◽  
Author(s):  
Véronique Farra ◽  
Ivan Pšenčík
Keyword(s):  
Transversely Isotropic ◽  
Arbitrary Orientation ◽  
Transversely Isotropic Medium ◽  
Weak Anisotropy ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Axis Of Symmetry ◽  
Dip Angle ◽  
P And Sv Waves ◽  
Axes Of Symmetry

We generalize the P- and SV-wave moveout formulas obtained for transversely isotropic media with vertical axes of symmetry (VTI), based on the weak-anisotropy approximation. We generalize them for 3D dip-constrained transversely isotropic (DTI) media. A DTI medium is a transversely isotropic medium whose axis of symmetry is perpendicular to a dipping reflector. The formulas are derived in the plane defined by the source-receiver line and the normal to the reflector. In this configuration, they can be easily obtained from the corresponding VTI formulas. It is only necessary to replace the expression for the normalized offset by the expression containing the apparent dip angle. The final results apply to general 3D situations, in which the plane reflector may have arbitrary orientation, and the source and the receiver may be situated arbitrarily in the DTI medium. The accuracy of the proposed formulas is tested on models with varying dip of the reflector, and for several orientations of the horizontal source-receiver line with respect to the dipping reflector.

scholarly journals Dip‐moveout error in transversely isotropic media with linear velocity variation in depth

Geophysics ◽  
1993 ◽  
Vol 58 (10) ◽  
pp. 1442-1453 ◽  
Author(s):  
Ken L. Larner
Keyword(s):  
Homogeneous Model ◽  
Transversely Isotropic ◽  
Vertical Axis ◽  
Velocity Variation ◽  
Transversely Isotropic Medium ◽  
Velocity Gradients ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Axis Of Symmetry ◽  
Homogeneous Media

Levin modeled the moveout, within common‐midpoint (CMP) gathers, of reflections from plane‐dipping reflectors beneath homogeneous, transversely isotropic media. For some media, when the axis of symmetry for the anisotropy was vertical, he found departures in stacking velocity from predictions based upon the familiar cosine‐of‐dip correction for isotropic media. Here, I do similar tests, again with transversely isotropic models with vertical axis of symmetry, but now allowing the medium velocity to vary linearly with depth. Results for the same four anisotropic media studied by Levin show behavior of dip‐corrected stacking velocity with reflector dip that, for all velocity gradients considered, differs little from that for the counterpart homogeneous media. As with isotropic media, traveltimes in an inhomogeneous, transversely isotropic medium can be modeled adequately with a homogeneous model with vertical velocity equal to the vertical rms velocity of the inhomogeneous medium. In practice, dip‐moveout (DMO) is based on the assumption that either the medium is homogeneous or its velocity varies with depth, but in both cases isotropy is assumed. It turns out that for only one of the transversely isotropic media considered here—shale‐limestone—would v(z) DMO fail to give an adequate correction within CMP gathers. For the shale‐limestone, fortuitously the constant‐velocity DMO gives a better moveout correction than does the v(z) DMO.

Traveltime computation in transversely isotropic media

Geophysics ◽  
1994 ◽  
Vol 59 (2) ◽  
pp. 272-281 ◽  
Author(s):  
Eduardo L. Faria ◽  
Paul L. Stoffa
Keyword(s):  
Heterogeneous Media ◽  
Grid Point ◽  
Transversely Isotropic ◽  
Transversely Isotropic Medium ◽  
Prestack Migration ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
First Arrival ◽  
Grid Points ◽  
Arbitrary Velocity

An approach for calculating first‐arrival traveltimes in a transversely isotropic medium is developed and has the advantage of avoiding shadow zones while still being computationally fast. Also, it works with an arbitrary velocity grid that may have discontinuities. The method is based on Fermat’s principle. The traveltime for each point in the grid is calculated several times using previously calculated traveltimes at surrounding grid points until the minimum time is found. Different ranges of propagation angle are covered in each traveltime calculation such that at the end of the process all propagation angles are covered. This guarantees that the first‐arrival traveltime for a specific grid point is correctly calculated. The resulting algorithm is fully vectorizable. The method is robust and can accurately determine first‐arrival traveltimes in heterogeneous media. Traveltimes are compared to finite‐difference modeling of transversely isotropic media and are found to be in excellent agreement. An application to prestack migration is used to illustrate the usefulness of the method.

Velocity analysis and imaging in transversely isotropic media: Methodology and a case study

1996 ◽  
Vol 15 (5) ◽  
pp. 371-378 ◽  
Author(s):  
Tariq Alkhalifah ◽  
Ilya Tsvankin ◽  
Ken Larner ◽  
John Toldi
Keyword(s):  
Transversely Isotropic ◽  
Velocity Analysis ◽  
Transversely Isotropic Media ◽  
Isotropic Media

scholarly journals Numerical Analysis of the Electrical Potential Calculation in a Transversely Isotropic Media

2014 ◽  
Vol 2 (1-2) ◽  
Author(s):  
Sri Mardiyati
Keyword(s):  
Electrical Conductivity ◽  
Finite Element ◽  
Numerical Analysis ◽  
Electrical Potential ◽  
Transversely Isotropic ◽  
Element Formulation ◽  
Transversely Isotropic Medium ◽  
Infinite Elements ◽  
Transversely Isotropic Media ◽  
Isotropic Media

The electrical potential due to a point source of current supplied at the surface of a transversely isotropic medium is calculated using a finite element formulation. The finite and infinite elements are applied to calculate the potential for arbitrary electrical conductivity profiles. The accuracy of the scheme is checked against results obtainable using Chave's algorithm.

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