Krylov-space-based quasi-newton preconditioner for full-wavefield inversion

1. A method, comprising:

storing, in a computer memory, seismic data acquired from a seismic survey of a subsurface region;

generating, with a computer, a final subsurface physical property model of the subsurface region by processing the seismic data with an iterative full wavefield inversion method, wherein the iterative full wavefield inversion method includes a non-linear outer iteration process comprising a plurality of outer iterations, each of which updates physical property values m of the physical property model and a nested linear inner iteration process, wherein:

(1) each iteration i of the plurality of non-linear outer iterations includes a nested linear inner iteration process for determining a search direction d i to be used in updating the physical property values m i of said non-linear outer iteration; and

(2) each of the second and subsequent outer iterations of the plurality of non-linear outer iterations further includes applying a preconditioner to the nested linear inner iteration process of such respective second and subsequent non-linear outer iteration, wherein the preconditioner at such non-linear outer iteration i+1 is generated based at least in part upon the nested linear inner iteration process of the immediately previous outer iteration i and wherein the preconditioner is generated using vectors {γ l , H i γ l } solved for in the nested inner iteration process, where γ l is the search direction for the linear system and where H i γ l is the product of the vector γ l with a Hessian operator H i ; and

creating, with a process, an image of the subsurface region from the final subsurface physical property model.

2. The method of claim 1 , comprising using a Krylov-space method as a linear solver for the nested inner iteration processes.

3. The method of claim 1 , comprising using a conjugate gradient method as a linear solver for the nested inner iteration processes.

4. The method of claim 2 , wherein each preconditioner is generated based on the nested inner iteration process of the immediately previous outer iteration using a limited-memory Broyden-Fletcher-Goldfarb-Shanno (BFGS) method.

5. The method of claim 2 , wherein each preconditioner is generated based on the nested inner iteration process of the immediately previous outer iteration using a quasi-Newton method.

6. The method of claim 1 , wherein the preconditioner of each of the second and subsequent outer iterations is a variable preconditioner such that the preconditioner can change when solving a linear system, and the preconditioner is generated based on the nested iteration process of the then-current outer iteration in addition to the nested inner iteration process of the immediately previous outer iteration.

7. The method of claim 1 , further comprising managing hydrocarbons based on the final subsurface physical property model of the subsurface region.

8. The method of claim 1 , further comprising:

using the final subsurface physical property model in interpreting a subsurface region for hydrocarbon exploration or production.

9. The method of claim 1 , further comprising drilling for hydrocarbons at a location determined using the final subsurface physical property model of the subsurface region.

10. The method of claim 1 , wherein a generalized minimal residual method is used as a linear solver for the nested inner iteration processes.