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Comparison of ν(θ) Equations in TI Medium

By
Alexandre Stopin
Alexandre Stopin
Institut Français du Pétrole, 1 & 4 avenue de Bois-Préau, 92852 Rueil-Malmaison, France
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Published:
January 01, 2001

Abstract

In TI media, exact phase-velocity equations ν(θ) are complex and difficult to exploit, in particular when derivatives with respect to some parameters have to be calculated. Moreover, traveltimes are not equally sensitive to the different parameters in the phase equations. Thus, to find simpler but still accurate equations for ν(θ), with relevant (sensitive) parameters, we examine different formulations found in the literature, and we also derive new original approximations of the phase-velocity equations. Thomsen's weak-anisotropy approximation yields simple formulas but breaks down for moderate but realistic anisotropy. We derive an approximation we call weak-anisotropy-squared approximation, which is more accurate than the former one (it respects horizontal velocities) but is still valid only for weak-anisotropy. Muir's double elliptical approximation is quite accurate, but very difficult to exploit. We derive a new empirical approximation based on Alkhalifah's ideas. This approximation is as accurate as Muir's approximation but requires fewer parameters, and it has a form allowing “easy” computation, in particular, the calculation of derivatives. Moreover, this approximation is valid for a much wider range of anisotropy parameters than the weak-anisotropy approximation. Thus we suggest using this approximation for ray-tracing and reflection tomography purposes.

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Contents

Society of Exploration Geophysicists Open File

Anisotropy 2000: Fractures, Converted Waves, and Case Studies

L. Ikelle
L. Ikelle
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A. Gangi
A. Gangi
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Society of Exploration Geophysicists
Volume
6
ISBN electronic:
9781560801771
Publication date:
January 01, 2001

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