Method and apparatus for unambiguously estimating seismic anisotropy parameters
The orientation of the symmetry axis of an underground formation including an HTI layer is determined by comparing azimuthal Fourier coefficient of inversion results in distinct source-receiver azimuth ranges with values expected from the HTI assumption. A branch-stacking technique or prior knowledge may be used to select one of the anisotropy axis orientation values.
1. A method for planning hydrocarbon extraction from an underground formation including a horizontally transverse isotropic, HTI, layer, the method comprising:
performing isotropic elastic inversions on portions of seismic data acquired during a seismic survey of the underground formation to obtain values of one or more effective elastic parameters or combinations thereof, the portions of the seismic data corresponding to distinct source-receiver azimuth ranges;
calculating azimuthal Fourier coefficients, AFCs, for each of the one or more effective elastic parameters or combinations based on the values;
unambiguously estimating an anisotropy axis orientation by solving equations that correspond to a minimization of a distance between the calculated AFCs and expected AFCs corresponding to an HTI assumption; and
using the estimated anisotropy axis orientation to drill for hydrocarbon production taking into consideration orientation of stress and/or cracks as indicated by the anisotropy axis orientation thereby improving efficiency of hydrocarbon production.
2. The method of claim 1 , wherein the estimating of the anisotropy axis orientation includes applying branch-stacking to average AFCs within a 3D window yielding a seismic attribute that indicate a most likely value of the anisotropy axis orientation.
3. The method of claim 2 , wherein the seismic attribute is maximum for the most likely value of the anisotropy axis orientation.
4. The method of claim 2 , wherein the seismic attribute changes sign for the most likely value of the anisotropy axis orientation.
5. The method of claim 1 , further comprising:
inferring anisotropy parameters using the anisotropy axis orientation, wherein the inferred anisotropy parameters are also used for designing the hydrocarbon production plan.
6. The method of claim 5 , wherein the estimating of the anisotropy axis orientation and the inferring of the anisotropy parameters are iterated until a criterion related to a residual distance is met.
7. The method of claim 5 , wherein the estimated anisotropy axis orientation and the inferred anisotropy parameters are used as initial values to repeat performing the isotropic elastic inversions on the portions of the seismic data, calculating the AFCs, estimating the anisotropy axis orientation, and inferring the anisotropy parameters until a criterion related to a residual distance is met.
8. The method of claim 1 , wherein a Thomsen-type HTI assumption is employed to calculate the expected AFCs and the minimization refers to
S
=
∑
n
,
i
B
n
i
(
ϕ
)
-
H
n
i
(
ϕ
n
i
)
2
subject to b n i =D na i T a +δ n0 ln P i , where b n i are generic HTI coefficients, P i are elastic parameters, δ nm is the Kronecker delta and D na i are matrices that depend on K=( V s / V p ) 2 , averages of secondary and primary wave propagation velocities.
9. The method of claim 1 , wherein the distinct source-receiver azimuth ranges are substantially equal, and divide a range of 0 to π in at least six sectors.
10. The method of claim 1 , wherein the distinct source-receiver azimuth ranges divide a range of 0 to π in sectors of uneven size for which the data is resampled or re-binned in the azimuthal dimension to become six or more regular sectors.
11. The method of claim 1 , wherein the calculating of the AFCs includes a moving window average.
12. The method of claim 1 , wherein the estimating of the anisotropy axis orientation includes selecting a solution value based on additional information.
13. A data processing apparatus for planning hydrocarbon extraction from an underground formation including a horizontally transverse isotropic, HTI, layer, comprising:
a memory storing program instructions; and
a processor connected to the memory and configured to execute the program instructions that cause:
performing isotropic elastic inversions on portions of seismic data acquired during a seismic survey of the underground formation to obtain values of one or more effective elastic parameters or combinations thereof, the portions of the seismic data corresponding to distinct source-receiver azimuth ranges;
calculating azimuthal Fourier coefficients, AFCs, for each of the effective elastic parameters or combinations based on the values;
unambiguously estimating an anisotropy axis orientation by solving equations that correspond a minimization of distance between the calculated AFCs and expected AFCs corresponding to an HTI assumption; and
control drilling using the estimated anisotropy axis orientation to take into consideration orientation of stress and/or cracks as indicated by the anisotropy axis orientation thereby improving efficiency of hydrocarbon production.
14. The apparatus of claim 13 , wherein the estimating of the anisotropy axis orientation includes applying branch-stacking to average AFCs within a 3D window yielding a seismic attribute that indicate a most likely value of the anisotropy axis orientation.
15. The apparatus of claim 14 , wherein the seismic attribute is maximum for the most likely value of the anisotropy axis orientation.
16. The apparatus of claim 14 , wherein the seismic attribute changes sign for the most likely value of the anisotropy axis orientation.
17. The apparatus of claim 13 , wherein the processor executing the program instructions further performs:
inferring anisotropy parameters using the anisotropy axis orientation, wherein the inferred anisotropy parameters are also used for designing the hydrocarbon production plan.
18. The apparatus of claim 17 , wherein the processor executing the program instructions iterates estimating the anisotropy axis orientation and inferring the anisotropy parameters until a criterion related to residual distance is met.
19. The apparatus of claim 17 , wherein the processor executing the program instructions uses the estimated anisotropy axis orientation and the inferred the anisotropy parameters as initial values to repeat performing the isotropic elastic inversions on the portions of the seismic data, calculating the AFCs, estimating the anisotropy axis orientation, and inferring the anisotropy parameters until a criterion related to residual distance is met.
20. The apparatus of claim 13 , wherein a Thomsen-type HTI assumption is employed to calculate the estimates of the AFCs and the minimization refers to
S
=
∑
n
,
i
B
n
i
(
ϕ
)
-
H
n
i
(
ϕ
n
i
)
2
subject to b n i =D na i T a +δ n0 ln P i , where b n i are generic HTI coefficients, P i are elastic parameters, δ nm is the Kronecker delta and D na i are matrices that depend on K=( V s / V p ) 2 , averages of secondary and primary wave propagation velocities.