Providing for uncertainty in non-linear inversions of geophysical data

Patent metadata

Field	Value
Publication number	US-11816401-B2
Application number	US-201917050360-A
Country	US
Kind code	B2
Filing date	Apr 11, 2019
Priority date	Apr 26, 2018
Publication date	Nov 14, 2023
Grant date	Nov 14, 2023

Abstract

A method of obtaining a model of a sub-surface region, the model comprising a three dimensional matrix of sub-surface material property values. The method comprises providing a first approximation of said model, and performing simulations using the model to generate (i) a reference upgoing energy wave data set d0, where the acquisition parameters used in the simulation are a set of known acquisition parameters, and (ii) a plurality of perturbed upgoing energy wave data sets d0 where the acquisition parameters are obtained by randomly perturbing said set of known acquisition parameters. The method further comprises forming a matrix D, the columns of which are the differences di−d0 between the ith perturbed data set and the reference data set, applying an analysis to the matrix D to describe the matrix using a set of vectors, and selecting the most important vectors from said set of vectors to obtain a subset of vectors that describe said matrix D to an approximation. An iterative procedure is performed to improve said first approximation of said model, or a further approximation model, wherein, at each step of the procedure, a model update Δm is determined, the model update being that model update that minimises a measure of the data misfit between said upgoing energy wave data set drec and a data set simulated using the updated model, said measure using said subset of vectors to account for uncertainty in the upgoing energy wave data set drec.

First claim

The invention claimed is:

1. A method of obtaining a model of a sub-surface region, the model comprising a three-dimensional matrix of sub-surface material property values, and comprising:
obtaining an upgoing energy wave data set d rec associated with a set of known acquisition parameters including a source location and a plurality of spaced apart recording locations within, at or above the surface, the upgoing energy waves depending on downgoing energy waves and the sub-surface material properties;
providing a first approximation of said model;
performing simulations using said first approximation of said model to generate (i) a reference upgoing energy wave data set d 0 , where the acquisition parameters used in the simulation are said set of known acquisition parameters, and (ii) a plurality of perturbed upgoing energy wave data sets d i , where the acquisition parameters are obtained by randomly perturbing said set of known acquisition parameters;
forming a matrix D, the columns of which are the differences d i −d 0 between the ith perturbed data set and the reference data set;
applying an analysis to the matrix D to describe the matrix using a set of vectors;
selecting the most important vectors from said set of vectors to obtain a subset of vectors that describe said matrix D to an approximation; and
performing an iterative procedure to improve said first approximation of said model, or a further approximation model, wherein, at each step of the procedure, a model update Δm is determined, the model update being that model update that minimises a measure of the data misfit between said upgoing energy wave data set d rec and a data set simulated using the updated model, said measure using said subset of vectors to account for uncertainty in the upgoing energy wave data set d rec .

2. A method according to claim 1 , wherein said sub-surface material property values are sub-surface material electromagnetic property values, e.g. electrical resistance or impedance values, and said energy wave is an electromagnetic energy wave.

3. A method according to claim 1 , wherein said sub-surface material property values are sub-surface material accoustic property values, e.g. acoustic impedance, velocity and/or denisty, and said energy wave is a seismic energy wave.

4. A method according to claim 1 , wherein said step of applying an analysis to the matrix D to describe the matrix using a set of vectors comprises a principal component analysis and said vectors are singular vectors.

5. A method according to claim 4 , wherein said step of applying an analysis to the matrix D to describe the matrix using a set of vectors comprises applying singular-value decomposition, SVD, to obtain a decomposition of the matrix D in the form D=F 0 S 0 K 0 =F 0 W 0 ,
and retaining only the first Nc columns to obtain reduced matrices
D≈FSK=FW

Where the columns of F are the set of vectors.

6. A method according to claim 5 , wherein the measure of the data misfit is determined using the formula:
ϕ d ( m )=½Δ d *( FS −2 F *+(1/λ N c +1 2 )( I−FF *))Δ d

where
Δd=Δd(m)=d(m)−d rec is a column vector of size N d representing the difference between simulated and recorded data, * represents a complex conjugation, and λ Nc+1 is a singular value of a most important one of the vectors that are not selected.

7. A method according to claim 1 , wherein said step of obtaining an upgoing energy wave data set d rec comprises operating one or more energy sources at, above, or within a surface of said sub-surface region to produce said downgoing energy waves and operating detectors at said spaced apart recording locations to detect said upgoing energy waves, and recording the detected upgoing waves.

8. A method according to claim 1 , wherein said step of obtaining an upgoing energy wave data set d rec comprises operating one or more energy sources within a body of water above a surface of said sub-surface region to produce said downgoing energy waves and operating detectors at said spaced apart locations to detect said upgoing energy waves, and recording the detected upgoing waves.

9. A method of selecting a region in which to drill in order to produce hydrocarbons and comprising applying the method of claim 1 to obtain a model of a sub-surface region, and examining the model to identify locations within the sub-surface likely to produce hydrocarbons.

10. A method of producing hydrocarbons and comprising selecting a region in which to drill using the method of claim 9 , drilling one or more wells in that region, and producing hydrocarbons from the well or wells.

11. A method according to claim 1 and comprising displaying said model on a computer display such that different sub-surface material property values are represented by different colour properties.

Assignees

• Equinor Energy As

Inventors

• Causse Emmanuel
• Nordskag Janniche Iren

Classifications

• G06F30/20 Primary

  Design optimisation, verification or simulation (optimisation, verification or simulation of circuit designs G06F30/30) · CPC title

• E21B49/00

  Testing the nature of borehole walls; Formation testing; Methods or apparatus for obtaining samples of soil or well fluids, specially adapted to earth drilling or wells · CPC title

• G01V1/30

  Analysis (G01V1/50 takes precedence) · CPC title

• G01V3/38 Primary

  Processing data, e.g. for analysis, for interpretation, for correction · CPC title

• E21B2200/20

  Computer models or simulations, e.g. for reservoirs under production, drill bits · CPC title