Traveltime approximations and parameter estimation for orthorhombic media

Traveltime approximations and parameter estimation for orthorhombic media

Nabil Masmoudi and Tariq Alkhalifah, "Traveltime approximations and parameter estimation for orthorhombic media", Geophysics 81 (2016): C127-C137. doi: 10.1190/geo2015-0367.1
BibTeX​ 
Nabil Masmoudi, Tariq Alkhalifah
anisotropy, effective, estimation, multiparameter, traveltime
2016
​Building anisotropy models is necessary for seismic modeling and imaging. However, anisotropy estimation is challenging due to the trade-off between inhomogeneity and anisotropy. Luckily, we can estimate the anisotropy parameters if we relate them analytically to traveltimes. Using perturbation theory, we have developed traveltime approximations for orthorhombic media as explicit functions of the anellipticity parameters η1η1, η2η2, and ΔχΔχ in inhomogeneous background media. The parameter ΔχΔχ is related to Tsvankin-Thomsen notation and ensures easier computation of traveltimes in the background model. Specifically, our expansion assumes an inhomogeneous ellipsoidal anisotropic background model, which can be obtained from well information and stacking velocity analysis. We have used the Shanks transform to enhance the accuracy of the formulas. A homogeneous medium simplification of the traveltime expansion provided a nonhyperbolic moveout description of the traveltime that was more accurate than other derived approximations. Moreover, the formulation provides a computationally efficient tool to solve the eikonal equation of an orthorhombic medium, without any constraints on the background model complexity. Although, the expansion is based on the factorized representation of the perturbation parameters, smooth variations of these parameters (represented as effective values) provides reasonable results. Thus, this formulation provides a mechanism to estimate the three effective parameters η1η1, η2η2, and ΔχΔχ. We have derived Dix-type formulas for orthorhombic medium to convert the effective parameters to their interval values.​
(print): 0016-8033 (online): 1942-2156