Method of correcting resistivity measurements for toll bending effects

1. A method for correcting downhole resistivity measurements to account for tool bending, the method comprising:

(a) acquiring resistivity measurements of a subterranean formation, the resistivity measurements including at least one measured coupling component and at least one measured cross-coupling component;

(b) acquiring a value of a bending angle;

(c) processing the at least one coupling component and the at least one cross-coupling component acquired in (a) in combination with the value of the bending angle acquired in (b) to obtain corrected resistivity measurements.

2. The method of claim 1 , wherein the corrected resistivity measurements comprise a corrected cross-coupling component.

3. The method of claim 1 , wherein the corrected resistivity measurements are obtained in (c) via removing the at least one measured coupling component from the at least one measured cross-coupling component.

4. The method of claim 1 , wherein the at least one measured cross-coupling component comprises a z-mode reception of an x-mode transmission and the at least one coupling component comprises a z-mode reception of a z-mode transmission.

5. The method of claim 4 , wherein the corrected resistivity measurements obtained in (c) comprise a corrected cross-coupling component obtained according to the following equation:

H uw =H xz cos 2 θ+H zz sin θ cos θ

wherein H uw represents the corrected cross-coupling component, H xz represents the z-mode reception of the x-mode transmission, H zz represents the z-mode reception of the z-mode transmission, and θ represents the value of the bending angle.

6. The method of claim 1 , wherein the at least one cross-coupling component comprises a z-mode reception of an x-mode transmission and the at least one coupling component comprises an x-mode reception of an x-mode transmission.

7. The method of claim 6 , wherein the corrected resistivity measurements obtained in (c) comprise a corrected cross-coupling component obtained according to the following equation:

H uw =H xz cos 2 θ+H xx sin θ cos θ

wherein H uw represents the corrected cross-coupling component, H xz represents the z-mode reception of the x-mode transmission, H xx represents the x-mode reception of the x-mode transmission, and θ represents the value of the bending angle.

8. The method of claim 1 , wherein the at least one cross-coupling component comprises an x-mode reception of a z-mode transmission and the at least one coupling component comprises a z-mode reception of a z-mode transmission.

9. The method of claim 8 , wherein the corrected resistivity measurements obtained in (c) comprise a corrected cross-coupling component obtained according to the following equation:

H wu =H zx cos 2 θ−H zz sin θ cos θ

wherein H wu represents the corrected cross-coupling component, H zx the x-mode reception of the z-mode transmission, H zz represents the z-mode reception of the z-mode transmission, and θ represents the value of the bending angle.

10. The method of claim 1 , wherein the at least one cross-coupling component comprises an x-mode reception of a z-mode transmission and the at least one coupling component comprises an x-mode reception of an x-mode transmission.

11. The method of claim 10 , wherein the corrected resistivity measurements obtained in (c) comprise a corrected cross-coupling component obtained according to the following equation:

H wu =H zx cos 2 θ−H xx sin θ cos θ

wherein H wu represents the corrected cross-coupling component, H zx the x-mode reception of the z-mode transmission, H xx represents the x-mode reception of the x-mode transmission, and θ represents the value of the bending angle.

12. A method for correcting resistivity measurements to account for tool bending, the method comprising:

(a) acquiring resistivity measurements of a subterranean formation, the resistivity measurements including first and second measured coupling components and first and second measured cross-coupling components;

(b) acquiring a value of a bending angle;

(c) processing the first and second coupling components and the first and second cross-coupling components acquired in (a) in combination with the value of the bending angle acquired in (b) to obtain corrected resistivity measurements.

13. The method of claim 12 , wherein the corrected resistivity measurements comprise at least one corrected cross-coupling component.

14. The method of claim 12 , wherein the corrected resistivity measurements are obtained in (c) via removing the first and second measured coupling components from at least one of the first and second measured cross-coupling components.

15. The method of claim 12 , wherein the first and second measured cross-coupling components comprise an x-mode reception of a z-mode transmission and a z-mode reception of an x-mode transmission and the first and second coupling components comprise a z-mode reception of a z-mode transmission and an x-mode reception of an x-mode transmission.

16. The method of claim 15 , wherein the corrected resistivity measurements obtained in (c) comprise at least one corrected cross-coupling component obtained according to at least one of the following equations:

H uw =H xz cos 2 θ+H xx sin θ cos θ+ H zz sin θ cos θ;

H wu =H zx cos 2 θ−H xx sin θ cos θ− H zz sin θ cos θ;

H uw =H xz sin θ cos θ+ H xz cos 2 θH zx sin 2 θ+H zz sin θ cos θ;

and

H wu =−H xx sin θ cos θ+ H xz sin 2 θH zx cos 2 θ−H zz sin θ cos θ

wherein H uw and H wu represent the corrected cross-coupling components, H xz represents the z-mode reception of the x-mode transmission, H zx the x-mode reception of the z-mode transmission, H xx represents the x-mode reception of the x-mode transmission, H zz represents the z-mode reception of the z-mode transmission, and θ represents the value of the bending angle.

17. The method of claim 12 , wherein the first and second measured coupling components and the first and second measured cross-coupling components are measured using a directional resistivity tool having (i) first and second transmitting antennae located at a first longitudinal position on the tool and (ii) first and second receiving antennae located at a second longitudinal position on the tool.