Anisotropy and dip angle determination using electromagnetic (EM) impulses from tilted antennas

1. A computer-implemented method, comprising:

deriving transient responses of a tri-axial resistivity tool corresponding to an electromagnetic (EM) impulse;

deriving a transient response of a directional resistivity tool (DRT) corresponding to the EM impulse based on the transient responses of the tri-axial resistivity tool;

deriving a theoretical late time transient response of the DRT based on the transient response of the DRT;

measuring the late time transient response of the DRT; and

determining an anisotropy, a horizontal conductivity, and a dip angle based on the measured late time transient response and the theoretical late time transient response, including:

determining, using a first combination of values of the anisotropy, the horizontal conductivity, and the dip angle, a first error between the measured late time transient response and the theoretical late time transient response;

determining, using a second combination of values of the anisotropy, the horizontal conductivity, and the dip angle, a second error between the measured late time transient response and the theoretical late time transient response; and

determining the anisotropy, the horizontal conductivity and the dip angle from either the first combination of values or the second combination of values responsive to a comparison of the first error and the second error.

2. The method of claim 1 , wherein the DRT includes one transmitter and one receiver, at least one of a dipole of the transmitter or a dipole of the receiver tilted from a tool axis.

3. The method of claim 2 , wherein the tri-axial resistivity tool includes three mutually orthogonal transmitters and three mutually orthogonal receivers, the transmitters and the receivers of the tri-axial resistivity tool co-located with the transmitter and the receiver of the DRT, respectively.

4. The method of claim 1 , wherein deriving the theoretical late time transient response includes having a time in the transient response approach to a large value.

5. The method of claim 1 , wherein measuring the late time transient response includes measuring the late time transient response at different azimuth angles.

6. The method of claim 1 , wherein determining the anisotropy, the horizontal conductivity, and the dip angle includes choosing the anisotropy, the horizontal conductivity, and the dip angle such that a difference between the measured late time transient response and the theoretical late time transient response is minimized.

7. The method of claim 1 , wherein the anisotropy is at least one of a resistivity anisotropy or a conductivity anisotropy.

8. A non-transitory, computer-readable medium storing one or more instructions executable by a computer system to perform operations comprising:

deriving transient responses of a tri-axial resistivity tool corresponding to an electromagnetic (EM) impulse;

deriving a transient response of a directional resistivity tool (DRT) corresponding to the EM impulse based on the transient responses of the tri-axial resistivity tool;

deriving a theoretical late time transient response of the DRT based on the transient response of the DRT;

measuring the late time transient response of the DRT; and

determining an anisotropy, a horizontal conductivity, and a dip angle based on the measured late time transient response and the theoretical late time transient response, including:

determining, using a first combination of values of the anisotropy, the horizontal conductivity, and the dip angle, a first error between the measured late time transient response and the theoretical late time transient response;

determining, using a second combination of values of the anisotropy, the horizontal conductivity, and the dip angle, a second error between the measured late time transient response and the theoretical late time transient response; and

determining the anisotropy, the horizontal conductivity and the dip angle from either the first combination of values or the second combination of values responsive to a comparison of the first error and the second error.

9. The non-transitory, computer-readable medium of claim 8 , wherein the DRT includes one transmitter and one receiver, at least one of a dipole of the transmitter or a dipole of the receiver tilted from a tool axis.

10. The non-transitory, computer-readable medium of claim 9 , wherein the tri-axial resistivity tool includes three mutually orthogonal transmitters and three mutually orthogonal receivers, the transmitters and the receivers of the tri-axial resistivity tool co-located with the transmitter and the receiver of the DRT, respectively.

11. The non-transitory, computer-readable medium of claim 8 , wherein deriving the theoretical late time transient response includes having a time in the transient response approach to a large value.

12. The non-transitory, computer-readable medium of claim 8 , wherein measuring the late time transient response includes measuring the late time transient response at different azimuth angles.

13. The non-transitory, computer-readable medium of claim 8 , wherein determining the anisotropy, the horizontal conductivity, and the dip angle includes choosing the anisotropy, the horizontal conductivity, and the dip angle such that a difference between the measured late time transient response and the theoretical late time transient response is minimized.

14. The non-transitory, computer-readable medium of claim 8 , wherein the anisotropy is at least one of a resistivity anisotropy or a conductivity anisotropy.

15. A computer system, comprising:

a computer memory; and

a hardware processor interoperably coupled with the computer memory and configured to perform operations comprising:

deriving transient responses of a tri-axial resistivity tool corresponding to an electromagnetic (EM) impulse;

deriving a transient response of a directional resistivity tool (DRT) corresponding to the EM impulse based on the transient responses of the tri-axial resistivity tool;

deriving a theoretical late time transient response of the DRT based on the transient response of the DRT;

measuring the late time transient response of the DRT; and

determining an anisotropy, a horizontal conductivity, and a dip angle based on the measured late time transient response and the theoretical late time transient response, including:

determining, using a first combination of values of the anisotropy, the horizontal conductivity, and the dip angle, a first error between the measured late time transient response and the theoretical late time transient response;

determining, using a second combination of values of the anisotropy, the horizontal conductivity, and the dip angle, a second error between the measured late time transient response and the theoretical late time transient response; and

determining the anisotropy, the horizontal conductivity and the dip angle from either the first combination of values or the second combination of values responsive to a comparison of the first error and the second error.

16. The computer system of claim 15 , wherein the DRT includes one transmitter and one receiver, at least one of a dipole of the transmitter or a dipole of the receiver tilted from a tool axis.

17. The computer system of claim 16 , wherein the tri-axial resistivity tool includes three mutually orthogonal transmitters and three mutually orthogonal receivers, the transmitters and the receivers of the tri-axial resistivity tool co-located with the transmitter and the receiver of the DRT, respectively.

18. The computer system of claim 15 , wherein deriving the theoretical late time transient response includes having a time in the transient response approach to a large value.

19. The computer system of claim 15 , wherein measuring the late time transient response includes measuring the late time transient response at different azimuth angles.

20. The computer system of claim 15 , wherein determining the anisotropy, the horizontal conductivity, and the dip angle includes choosing the anisotropy, the horizontal conductivity, and the dip angle such that a difference between the measured late time transient response and the theoretical late time transient response is minimized.