FULL-WAVEFORM INVERSION IN THE TRAVELTIME DOMAIN

• US 20110090760A1
• Filed: 10/19/2009
• Published: 04/21/2011
• Est. Priority Date: 10/19/2009
• Status: Active Grant

• Current Assignee: WesternGeco LLC
• Original Assignee: WesternGeco LLC
• Inventors: Rickett, James, Childs, Paul
• Granted Patent: US 9,244,181 B2
• Time in Patent Office: Days
• US Class Current: 367/73
• CPC Class Codes: G01V 1/282 Application of seismic models, synthetic seismograms
• CPC Class Codes: G01V 2210/679 Reverse-time modeling or coalescence modelling, i.e. starting from receivers

Abstract

A method for processing seismic data. The method includes predicting seismic data according to an earth model representing seismic properties of subterranean formations in the earth, determining a difference between seismic data acquired from one or more seismic receivers and the predicted seismic data, projecting the difference into a model space in traveltime, and updating the earth model according to the projected difference. As a result, the updated earth model more accurately represents the seismic properties of subterranean formations in the earth.

Claims

1. A method for processing seismic data, comprising:

a) predicting seismic data according to an earth model representing seismic properties of subterranean formations in the earth;

b) determining a difference between seismic data acquired from one or more seismic receivers and the predicted seismic data;

c) projecting the difference into a model space in traveltime; and

d) updating the earth model according to the projected difference, wherein the updated earth model more accurately represents the seismic properties of subterranean formations in the earth.

2. The method of claim 1, wherein predicting the seismic data comprises:

determining that the earth model is an earth model in depth;

simulating seismic data according to the earth model in depth; and

converting the earth model in depth into an earth model in traveltime.

3. The method of claim 2, wherein projecting the difference into the model space comprises:

injecting a model of one or more seismic sources into the earth model in depth forward in time to produce a forward-propagating source wavefield;

producing an earth model descent direction in depth by cross-correlating a back-propagated wavefield of the difference with the forward-propagated source wavefield; and

translating the earth model descent direction in depth to an earth model descent direction in traveltime.

4. The method of claim 3, wherein translating the earth model descent direction in depth comprises applying an adjoint of a Jacobian of a time-to-depth function to the earth model descent direction in depth, wherein the time-to-depth function converts earth models parameterized by traveltime into earth models parameterized by depth.

5. The method of claim 4, wherein the time-to-depth function is derived from a vertical integration of a vertical seismic traveltime or a zero-offset ray propagation.

6. The method of claim 4, further comprising applying spatial smoothing to the time-to-depth function to stabilize the time-to-depth function in one or more structurally complex areas.

7. The method of claim 3, wherein updating the earth model comprises:

determining a distance in a direction to update the earth model in traveltime;

calculating a product of the distance and the earth model descent direction in traveltime; and

adding the product to the earth model in traveltime.

8. The method of claim 7, wherein the distance is a step length.

9. The method of claim 7, wherein the direction corresponds to the earth model descent direction in depth.

10. The method of claim 7, wherein determining the distance comprises:

generating a trial distance;

calculating a product of the trial distance and the earth model descent direction in traveltime;

adding the product of the trial distance and the earth model descent direction in traveltime to the earth model to create a trial updated earth model;

predicting trial seismic data according to the trial updated earth model;

determining a trial difference between the acquired seismic data and the predicted trial seismic data; and

setting the trial distance to be the distance when the trial difference falls below a predetermined value.

11. The method of claim 1, further comprising repeating steps (a)-(d) using the updated earth model as the earth model until one or more predetermined conditions are met.

12. The method of claim 11, wherein the predetermined conditions comprises:

reaching a predetermined maximum number of iterations;

determining that the difference falls below a predetermined value;

determining that the updated earth model is within a specified tolerance of the earth model;

or

combinations thereof.

13. The method of claim 1, wherein determining the difference further comprises applying a filter or a window to the acquired seismic data and the predicted seismic data.

14. The method of claim 1, wherein the difference is determined using a least-square method.

15. The method of claim 1, wherein the difference is residual seismic data.

16. The method of claim 1, wherein the seismic data are seismic reflection traveltimes.

17. The method of claim 1, wherein the seismic data are in a time domain or a frequency domain.

18. The method of claim 1, wherein the earth model comprises:

one or more acoustic properties having velocities, densities, or combinations thereof;

one or more elastic properties having a parameter that is a function of a shear modulus;

one or more anisotropic properties;

one or more anelastic properties;

or

combinations thereof.

19. The method of claim 1, further comprising:

projecting the difference into a model space in depth;

projecting the difference in depth into a model space in traveltime; and

updating the earth model in traveltime according to the projected difference in traveltime.

20. The method of claim 1, wherein the predicted seismic data comprises multiple reflections, reverberations, or combinations thereof.

21. The method of claim 1, wherein the earth model comprises one or more parameters describing one or more velocities of seismic wave propagation.

22. The method of claim 21, further comprising updating the parameters at every physical scale represented in the earth model.

23. A computer-readable storage medium having stored thereon computer-executable instructions which, when executed by a computer, cause the computer to:

predict seismic data according to an earth model representing seismic properties of subterranean formations in the earth;

determine a difference between seismic data acquired from one or more seismic receivers and the predicted seismic data;

project the difference into a model space in depth

project the difference in depth into a model space in traveltime; and

update the earth model according to the projected difference in traveltime, wherein the updated earth model more accurately represents the seismic properties of subterranean formations in the earth.

24. The computer-readable storage medium of claim 23, wherein the computer-executable instructions which, when executed by the computer, cause the computer to predict the seismic data comprises computer-executable instructions which, when executed by a computer, cause the computer to:

determine that the earth model is an earth model in traveltime;

convert the earth model into an earth model in depth; and

simulate seismic data according to the earth model in depth.

25. The computer-readable storage medium of claim 24, wherein the computer-executable instructions which, when executed by the computer, cause the computer to project the difference in depth into the model space in traveltime comprises computer-executable instructions which, when executed by a computer, cause the computer to:

inject a model of one or more seismic sources into the earth model in depth forward in time to produce a forward-propagating source wavefield;

produce an earth model descent direction in depth by cross-correlating a back-propagated wavefield of the difference with the forward-propagated source wavefield; and

translate the earth model descent direction in depth to an earth model descent direction in traveltime.

26. The computer-readable storage medium of claim 25, wherein the computer-executable instructions which, when executed by the computer, cause the computer to update the earth model comprises computer-executable instructions which, when executed by a computer, cause the computer to:

determine a distance in a direction to update the earth model in traveltime;

calculate a product of the distance and the earth model descent direction in traveltime; and

add the product to the earth model in traveltime.

27. A computer system, comprising:

a processor; and

a memory comprising program instructions executable by the processor to;

predict seismic data according to an earth model in depth representing seismic properties of subterranean formations in the earth;

determine a difference between seismic data acquired from one or more seismic receivers and the predicted seismic data;

transform the earth model in depth to an earth model in traveltime; and

update the earth model in traveltime according to the difference, wherein the updated earth model more accurately represents the seismic properties of subterranean formations in the earth.

28. The computer system of claim 27, wherein the program instructions executable by the processor further comprises program instructions executable by the processor to translate the updated earth model in traveltime to an updated earth model in depth.

29. The computer system of claim 27, wherein the updated earth model in depth is transformed via an inverse of a time-to-depth function.