EARTH MODEL ESTIMATION THROUGH AN ACOUSTIC FULL WAVEFORM INVERSION OF SEISMIC DATA

• US 20130311151A1
• Filed: 09/27/2011
• Published: 11/21/2013
• Est. Priority Date: 09/28/2010
• Status: Abandoned Application

• Current Assignee: Shell Oil Company (Shell Plc)
• Original Assignee: Rene-Edouard Andre Michel Plessix
• Inventors: Plessix, Ren-Edouard Andr Michel
• Application Number:
  US13/876,139
• Publication Number:
  US 20130311151A1
• Time in Patent Office: Days
• US Class Current: 703/2
• CPC Class Codes: G01V 1/30 Analysis G01V1/50 takes precedence
• CPC Class Codes: G06F 30/20 Design optimisation, verification or simulation optimisation, verification or simulation of circuit designs G06F30/30

Abstract

An improved method of estimating an earth model utilizes an acoustic Full Waveform Inversion (FWI) of seismic data in a pseudo-time coordinate system, in which the earth model m({tilde over (m)}) is parameterized with two lateral coordinates (x,y) and a vertical coordinate ({tilde over (z)}) which expresses vertical travel time of acoustic signals used to generate the seismic data.

Claims

1. A method of estimating an earth model through an acoustic full waveform inversion of seismic data in a pseudo-time coordinate system, in which an earth model is parameterized with two lateral coordinates and a vertical coordinate which expresses vertical travel time of acoustic signals used to generate the seismic data.

2. The method of claim 1, wherein the seismic data are surface seismic data.

3. The method of claim 1, wherein the horizontal coordinates are expressed by the abbreviations x and y and the vertical coordinate which expresses the vertical travel time is expressed by the abbreviation {tilde over (z)} and is defined at each lateral position (x,y) by

4. The method of claim 3, wherein the earth model is expressed by the abbreviation m and comprises a range of variables, such as nmo velocity, reflectivity, η

, δ

, ε

VTI parameters, density, vertical and/or velocity, which variables are calculated by an iterative calculation.

5. The method of claim 4, wherein the iterative calculation comprises:

a) generating an initial earth model {tilde over (m)} in the pseudo-time coordinate system;

b) iteratively looping over a series of scales provided by frequency bands of the seismic data;

c) looping over the iterative loops to obtain an adjusted earth model, {tilde over (m)} with modelled data;

d) computing the modelled data;

e) evaluating a misfit functional between the modelled and observed data;

f) computing a gradient of the misfit functional with respect to the earth model {tilde over (m)}; and

g) updating the earth model {tilde over (m)} with a local optimization technique.

6. The method of claim 5, wherein steps c), d) and f) of the iterative calculation further comprise:

c2) applying a change of variables between the pseudo-time coordinate system to a depth coordinate system to obtain an adjusted earth model, m({tilde over (m)}), in depth, with modelled data;

d2) computing the modelled data by solving an acoustic vertical transversely isotropic wave equation in depth;

f2) computing the gradient of the misfit functional with respect to the earth model {tilde over (m)} by solving adjoint equations of the depth wave equation and correlating incident wave fields and adjoint wave fields; and

applying a change of variables between the depth coordinate system to the pseudo-time coordinate system to obtain a gradient in the pseudo-time coordinate system; and

the method further comprises;

g) using the gradient to update the earth model m in the pseudo-time coordinate system with a local optimization technique.

7. The method of claim 6, wherein step d) comprises applying the following set of equations (A.1):

8. The method of claim 7, wherein the set of equations (A.1) is rewritten with p_n=√

{square root over (1+2δ

)} p_v, the NMO pressure,

9. The method of claim 5, wherein steps c) and f) of the iterative calculation further comprise:

c3) computing the modelled data by solving a pseudo-time wave equation; and

f3) computing the gradient of the misfit functional with respect to the earth model by solving the adjoint equation of the pseudo-time wave equation and correlating the incident and adjoint wave fields.

10. The method of claim 8, wherein step c3) further comprises solving the following pseudo-time wave equation (A.5):

11. The method of claim 1, wherein the earth model {tilde over (m)} comprises one or more of the following variables:

nmo velocity, reflectivity, η

, δ

, ε

, density, vertical velocity, horizontal velocity.

12. The method of claim 1, wherein the method is used to make an image of a subsurface earth formation.

13. The method of claim 12, wherein the image is a seismic map.

14. The method of claim 13, wherein the subsurface earth formation comprises a hydrocarbon fluid and the seismic map is used to plan, manage and/or optimize the placement of at least one hydrocarbon fluid production well traversing the formation and/or the production of hydrocarbon fluid through the at least one well.