Theory of interval traveltime parameter estimation in layered anisotropic media |

**Yanadet Sripanich and Sergey Fomel**

Bureau of Economic Geology

John A. and Katherine G. Jackson School of Geosciences

The University of Texas at Austin

University Station, Box X

Austin, TX 78713-8924

Moveout approximations for reflection traveltimes are typically based on a truncated Taylor expansion of traveltime squared around zero offset. The fourth-order Taylor expansion involves NMO velocities and quartic coefficients. We derive general expressions for layer-stripping both second- and fourth-order parameters in horizontally-layered anisotropic strata and specify them for two important cases: horizontally stacked aligned orthorhombic layers and azimuthally rotated orthorhombic layers. In the first of these cases, the formula involving the out-of-symmetry-plane quartic coefficients has a simple functional form and possesses some similarity to the previously known formulas corresponding to the 2D in-symmetry-plane counterparts in VTI media. The error of approximating effective parameters by using approximate VTI formulas can be significant in comparison with the exact formulas derived in this paper. We propose a framework for deriving Dix-type inversion formulas for interval parameter estimation from traveltime expansion coefficients both in the general case and in the specific case of aligned orthorhombic layers. The averaging formulas for calculation of effective parameters and the layer-stripping formulas for interval parameter estimation are readily applicable to 3D seismic reflection processing in layered anisotropic media.

- Introduction
- Traveltime expansion
- General formulas for traveltime derivative tensors

- Coefficients of traveltime expansion for a stack of horizontally aligned orthorhombic layers
- General formulas for coefficients
- Formulas for interval NMO velocities
- Formulas for interval quartic coefficients
- Comparison with known expressions for quartic Taylor series coefficients
- Comparison of interval parameter estimation

- Coefficients of traveltime expansion for a stack of azimuthally rotated orthorhombic layers
- Discussion
- Conclusions
- Acknowledgments
- Appendix: Traveltime and offset as functions of ray parameters
- Bibliography
- About this document ...

Theory of interval traveltime parameter estimation in layered anisotropic media |

2017-04-14