Method and system for updating a seismic velocity model

1. A method of updating a seismic velocity model of a subterranean region of interest, comprising:

receiving an observed seismic dataset for the subterranean region of interest comprising a plurality of observed seismic traces;

receiving the seismic velocity model for the subterranean region of interest;

generating, using a computer processor, a simulated seismic dataset comprising a plurality of simulated seismic traces based, at least in part, on the seismic velocity model and a geometry of the observed seismic dataset;

determining, using the computer processor, a transformed observed seismic dataset, comprising:

forming a first regularized estimate of a first instantaneous frequency of at least one member of the plurality of observed seismic traces,

wherein the first regularized estimate is based, at least in part, on a first smoothing matrix, and

determining the first instantaneous frequency based, at least in part, on the first regularized estimate;

determining, using the computer processor, a transformed simulated seismic dataset, comprising:

determining a second instantaneous frequency of at least one member of the plurality of simulated seismic traces;

forming, using the computer processor, an objective function based, at least in part, on the transformed observed seismic dataset and the transformed simulated seismic dataset; and

determining, using the computer processor, an updated seismic velocity model based, at least in part, upon finding an extremum of the objective function.

2. The method of claim 1 , further comprising:

forming, using the computer processor, an image of the subterranean region of interest based, at least in part, on the updated seismic velocity model;

identifying a portion of the subterranean region of interest with a high likelihood of containing hydrocarbons based, at least in part, on the image of the subterranean region of interest;

determining a well path through the subterranean region of interest based, at least in part, on the identified portion of the subterranean region of interest; and

performing the well path using a drilling system.

3. The method of claim 1 , wherein the objective function comprises a least-squares objective function.

4. The method of claim 1 , wherein the objective function comprises a penalized cross-correlation objective function.

5. The method of claim 1 , wherein the seismic velocity model comprises an elastic seismic velocity model.

6. The method of claim 1 , wherein the seismic velocity model comprises an anisotropic seismic velocity model.

7. The method of claim 1 , wherein determining the updated seismic velocity model comprises:

determining an adjoint source for each of a plurality of seismic receiver locations based, at least in part, on the observed seismic dataset and the simulated seismic dataset;

simulating, for each of a plurality of seismic source locations and the plurality of seismic receiver locations, propagation of a seismic wave generated by the adjoint source backward in time;

simulating, for each of the plurality of seismic source locations, propagation of a seismic wave forward in time;

determining a seismic velocity gradient using an imaging condition based, at least in part, on the simulated seismic wave propagated forward in time and the simulated seismic wave propagated backward in time;

determining a seismic velocity increment model by scaling the seismic velocity gradient based, at least in part, on the extremum of the objective function; and

updating the seismic velocity model based, at least in part, on the seismic velocity increment model.

8. A non-transitory computer readable medium storing instructions executable by a computer processor, the instructions comprising functionality for:

receiving an observed seismic dataset for a subterranean region of interest comprising a plurality of observed seismic traces;

receiving a seismic velocity model for the subterranean region of interest;

generating a simulated seismic dataset comprising a plurality of simulated seismic traces based, at least in part, on the seismic velocity model and a geometry of the observed seismic dataset;

determining a transformed observed seismic dataset comprising:

forming a first regularized estimate of a first instantaneous frequency of at least one member of the plurality of observed seismic traces,

wherein the first regularized estimate is based, at least in part, on a first smoothing matrix, and

determining the first instantaneous frequency based, at least in part, on the first regularized estimate;

determining a transformed simulated seismic dataset comprising:

determining a second instantaneous frequency of at least one member of the plurality of simulated seismic traces;

forming an objective function based, at least in part, on the transformed observed seismic dataset and the transformed simulated seismic dataset; and

determining, using the computer processor, an updated seismic velocity model based, at least in part, upon finding an extremum of the objective function.

9. The non-transitory computer readable medium of claim 8 , further comprising:

forming an image of the subterranean region of interest based, at least in part, on the updated seismic velocity model;

identifying a portion of the subterranean region of interest with a high likelihood of containing hydrocarbons based, at least in part, on the image of the subterranean region of interest; and

determining a well path through the subterranean region of interest based, at least in part, on the identified portion of the subterranean region of interest.

10. The non-transitory computer readable medium of claim 8 , wherein the objective function comprises an optimal transport objective function.

11. The non-transitory computer readable medium of claim 8 , wherein determining the second instantaneous frequency comprises:

forming a second regularized estimate of the second instantaneous frequency of at least one member of the plurality of simulated seismic traces,

wherein the second regularized estimate is based, at least in part, on a second smoothing matrix; and

determining the second instantaneous frequency based, at least in part, on the second regularized estimate.

12. The non-transitory computer readable medium of claim 8 , wherein the seismic velocity model comprises an elastic seismic velocity model.

13. The non-transitory computer readable medium of claim 8 , wherein the seismic velocity model comprises an anisotropic seismic velocity model.

14. The non-transitory computer readable medium of claim 8 , wherein determining the updated seismic velocity model comprises:

determining an adjoint source for each of a plurality of seismic receiver locations based, at least in part, on the observed seismic dataset and the simulated seismic dataset;

simulating, for each of a plurality of seismic source locations and the plurality of seismic receiver locations, propagation of a seismic wave generated by the adjoint source backward in time;

simulating, for each of the plurality of seismic source locations, propagation of a seismic wave forward in time;

determining a seismic velocity gradient using an imaging condition based, at least in part, on the seismic wave propagated forward in time and the seismic wave propagated backward in time;

determining a seismic velocity increment model by scaling the seismic velocity gradient based, at least in part, on the extremum of the objective function; and

updating the seismic velocity model based, at least in part, on the seismic velocity increment model.

15. A system for forming an image of a subterranean region of interest, comprising:

a seismic source to emit a radiated seismic wave;

a plurality of seismic receivers for detecting and recording an observed seismic dataset generated by the radiated seismic wave; and

a seismic processor configured to:

receive the observed seismic dataset for the subterranean region of interest comprising a plurality of observed seismic traces;

receive a seismic velocity model for the subterranean region of interest;

generate a simulated seismic dataset comprising a plurality of simulated seismic traces based, at least in part, on the seismic velocity model and a geometry of the observed seismic dataset;

determine a transformed observed seismic dataset comprising:

form a first regularized estimate of a first instantaneous frequency of at least one member of the plurality of observed seismic traces,

wherein the first regularized estimate is based, at least in part, on a first smoothing matrix; and

determine the first instantaneous frequency based, at least in part, on the first regularized estimate,

determine a transformed simulated seismic dataset comprising:

determining a second instantaneous frequency of at least one member of the plurality of simulated seismic traces;

form an objective function based, at least in part, on the transformed observed seismic dataset and on the transformed simulated seismic dataset; and

determine an updated seismic velocity model based, at least in part, upon finding an extremum of the objective function; and

form the image of the subterranean region of interest based, at least in part, on the updated seismic velocity model.

16. The system of claim 15 , wherein the objective function comprises a least-squares objective function.

17. The system of claim 15 , wherein the objective function comprises a penalized cross-correlation objective function.

18. The system of claim 15 , wherein the seismic velocity model comprises an elastic seismic velocity model.

19. The system of claim 15 , wherein the seismic velocity model comprises an anisotropic seismic velocity model.

20. The system of claim 15 , wherein determining the updated seismic velocity model, comprises:

determining an adjoint source for each of a plurality of seismic receiver locations based, at least in part, on the observed seismic dataset and the simulated seismic dataset;

simulating, for each of a plurality of seismic source locations and the plurality of seismic receiver locations, propagation of a seismic wave generated by the adjoint source backward in time;

simulating, for each of the plurality of seismic source locations, propagation of a seismic wave forward in time;

determining a seismic velocity gradient using an imaging condition based, at least in part, on the seismic wave propagated forward in time and the seismic wave propagated backward in time;

determining a seismic velocity increment model by scaling the seismic velocity gradient based, at least in part, on the extremum of the objective function; and

updating the seismic velocity model based, at least in part, on the seismic velocity increment model.