TY - JOUR
T1 - Traveltime approximations and parameter estimation for orthorhombic media
AU - Masmoudi, Nabil
AU - Alkhalifah, Tariq Ali
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: We thank KAUST for financial support. We thank A. Stovas for many useful discussions. We also thank U. bin Waheed for his help in accessing his orthorhombic traveltime calculation. We are also grateful to I. Ravve, N. Belayouni, I. Pšenčík, and Y. Luo for their critical and helpful reviews of the paper.
PY - 2016/6/2
Y1 - 2016/6/2
N2 - 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 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 η1,
η2, and Δχ in inhomogeneous background media. The parameter
Δχ 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 η1, η2,
and Δχ. We have derived Dix-type formulas for orthorhombic
medium to convert the effective parameters to their interval
values.
AB - 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 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 η1,
η2, and Δχ in inhomogeneous background media. The parameter
Δχ 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 η1, η2,
and Δχ. We have derived Dix-type formulas for orthorhombic
medium to convert the effective parameters to their interval
values.
UR - http://hdl.handle.net/10754/614407
UR - http://library.seg.org/doi/10.1190/geo2015-0367.1
UR - http://www.scopus.com/inward/record.url?scp=84973617074&partnerID=8YFLogxK
U2 - 10.1190/geo2015-0367.1
DO - 10.1190/geo2015-0367.1
M3 - Article
SN - 0016-8033
VL - 81
SP - C127-C137
JO - GEOPHYSICS
JF - GEOPHYSICS
IS - 4
ER -