METHODS AND APPARATUS FOR THREE-DIMENSIONAL INVERSION OF ELECTROMAGNETIC DATA

• US 20090083006A1
• Filed: 08/23/2008
• Published: 03/26/2009
• Est. Priority Date: 09/20/2007
• Status: Abandoned Application

• Current Assignee: WesternGeco LLC
• Original Assignee: WesternGeco LLC
• Inventors: Mackie, Randall
• Application Number:
  US12/197,239
• Publication Number:
  US 20090083006A1
• Time in Patent Office: Days
• US Class Current: 703/1
• CPC Class Codes: G01V 11/00 Prospecting or detecting by methods combining techniques covered by two or more of main groups G01V1/00 - G01V9/00
• CPC Class Codes: G01V 3/083 Controlled source electromagnetic [CSEM] surveying

Abstract

Methods and systems in accordance with this invention perform three-dimensional inversion of electromagnetic data, such as magnetotelluric (“MT”) data and controlled-source electromagnetic (“CSEM”) data, and three-dimensional joint inversion of MT and CSEM data. In exemplary embodiments, nonlinear conjugate gradient (“NLCG”) methods are used in lieu of iterative, linearized inversion, and line-search and preconditioning techniques are used that accommodate and exploit the structure of the MCSEM and MT problem.

Claims

1. A method for performing three-dimensional inversion of geophysical data, the method comprising:

(a) receiving initial model parameters;

(b) calculating a forward solution based on the initial model parameters;

(c) calculating an error vector based on a difference between the forward solution and observed electromagnetic data;

(d) if the calculated error vector is greater than or equal to a predetermined threshold, performing an inversion to generate updated model parameters;

(e) repeating steps (b)-(d) using the updated model parameters until the calculated error vector is less than the predetermined threshold; and

(f) outputting the updated model parameters as final model parameters.

2. The method of claim 1, wherein the observed electromagnetic data comprise magnetotelluric data.

3. The method of claim 1, wherein the observed electromagnetic data comprise controlled-source electromagnetic data.

4. The method of claim 1, wherein the observed electromagnetic data comprise magnetotelluric data and controlled-source electromagnetic data.

5. The method of claim 1, wherein calculating the forward solution comprises numerically solving the forward solution for a region of model space at which conductivity or frequency approach zero.

6. The method of claim 5, wherein calculating the forward solution comprises:

using finite difference equations to numerically solve Maxwell'"'"'s equations; and

using a vanishing gradient of conductivity times a divergence of a magnetic field.

7. The method of claim 1, wherein performing a three-dimensional inversion comprises performing a nonlinear conjugate gradient method to minimize an objective function of model space.

8. The method of claim 7, wherein performing a nonlinear conjugate gradient method comprises calculating a preconditioner that approximates an inverse of a Hessian of the objective function.

9. The method of claim 8, wherein calculating a preconditioner comprises calculating a diagonal of an approximate data Hessian.

10. The method of claim 7, wherein performing a three-dimensional inversion comprises efficiently performing a line search to minimize the objective function.

11. Apparatus for performing three-dimensional inversion of geophysical data, the apparatus comprising:

(a) means for receiving initial model parameters;

(b) means for calculating a forward solution based on the initial model parameters;

(c) means for calculating an error vector based on a difference between the forward solution and observed electromagnetic data;

(d) means for determining if the calculated error vector is greater than or equal to a predetermined threshold;

(e) means for performing a three-dimensional inversion to generate updated model parameters;

(f) means for repeating steps (b)-(e) using the updated model parameters until the calculated error vector is less than the predetermined threshold; and

(g) means for outputting the updated model parameters as final model parameters.

12. The apparatus of claim 11, wherein the observed electromagnetic data comprise magnetotelluric data.

13. The apparatus of claim 11, wherein the observed electromagnetic data comprise controlled-source electromagnetic data.

14. The apparatus of claim 11, wherein the observed electromagnetic data comprise magnetotelluric data and controlled-source electromagnetic data.

15. The apparatus of claim 11, wherein the means for calculating the forward solution comprises means for numerically solving the forward solution for a region of model space at which conductivity or frequency approach zero.

16. The apparatus of claim 15, wherein the means for calculating the forward solution comprises:

means for using finite difference equations to numerically solve Maxwell'"'"'s equations; and

means for using a vanishing gradient of conductivity times a divergence of a magnetic field.

17. The apparatus of claim 11, wherein the means for performing a three-dimensional inversion comprises a means for performing a nonlinear conjugate gradient method to minimize an objective function of model space.

18. The apparatus of claim 17, wherein the means for performing a nonlinear conjugate gradient method comprises a means for calculating a preconditioner that approximates an inverse of a Hessian of the objective function.

19. The apparatus of claim 18, wherein the means for calculating a preconditioner comprises a means for calculating a diagonal of an approximate data Hessian.

20. The apparatus of claim 17, wherein the means for performing a three-dimensional inversion comprises a means for efficiently performing a line search to minimize the objective function.