# US 2024/0201407 A1 · System and method for least-squares migration of time-lapse seismic data

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- Number: US 2024/0201407 A1
- Document ID: US20240201407A1
- Status: Published application
- Kind: A1
- Application number: 18/530,452
- Filed: 2023-12-06
- Published: 2024-06-20
- Earliest claimed: 2023-07-06
- Assignees: Cgg Services SAS
- Applicants: Cgg Services SAS
- Inventors: Filipe RUDRIGUES; Danilo ALBUQUERQUE; Gabriel PACHECO; Cleberton OLIVEIRA; Karine PEREIRA; Benjamin HUARD; Luis CYPRIANO; Roberto PEREIRA; Adel KHALIL
- Web page: https://patentgrep.com/patent/US20240201407A1

## CPC

- G01V 1/325: {Transforming one representation into another}
- G01V 1/282: {Application of seismic models, synthetic seismograms}
- G01V 1/302: {in 3D data cubes}
- G01V 1/345: {Visualisation of seismic data or attributes, e.g. in 3D cubes}
- G01V 2210/48: Other transforms
- G01V 2210/51: Migration
- G01V 2210/74: Visualisation of seismic data
- G01V: GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS (means for indicating the location of accidentally buried, e.g. snow-buried, persons A63B29/02)

## Abstract

A least-square migration, LSM, based method for generating a 4D image of a subsurface, the method including receiving seismic data d related to the subsurface, the seismic data d including a baseline dataset dB and a monitor dataset dM, calculating a baseline filter B and a monitor filter M based on a same common reflectivity r of the subsurface and corresponding remigrated baseline data mB1 and remigrated monitor data mM1 so that the base filter B applied to the remigrated baseline data mB1 equals the monitor filter M applied to the remigrated monitor data mM1, applying the baseline filter B to raw migrated baseline data mB0 and applying the monitor filter M to raw migrated monitor data mM0 to generate LSM baseline data mB and LSM monitor data mM, and generating the 4D image of the subsurface based on the LSM baseline data mB and the LSM monitor data mM.

## Claims

### Claim 1

A least-square migration, LSM, based method for generating a 4D image of a subsurface, the method comprising:
receiving seismic data d related to the subsurface, wherein the seismic data d includes a baseline dataset dB and a monitor dataset dM, with the monitor dataset dMbeing taken later in time than the baseline dataset dB, for the same subsurface;
calculating a baseline filter B and a monitor filter M based on a same common reflectivity r of the subsurface and corresponding remigrated baseline data mB1 and remigrated monitor data mM1 so that the base filter B applied to the remigrated baseline data mB1 equals the monitor filter M applied to the remigrated monitor data mM1;
applying the baseline filter B to raw migrated baseline data mB0 and applying the monitor filter M to raw migrated monitor data mM0 to generate LSM baseline data m and LSM monitor data mM; and
generating the 4D image of the subsurface based on the LSM baseline data mg and the LSM monitor data mM.

### Claim 2 (depends on 1)

The method of claim 1, wherein the step of calculating comprises:
performing raw migration, with a baseline migration operator LTB on the baseline dataset dB and with a monitor migration operator LTM on the monitor dataset dM, to calculate the baseline raw migrated data mB0and the monitor raw migrated data mM0.

### Claim 3 (depends on 2)

The method of claim 2, further comprising:
calculating the remigrated baseline data mB1 by applying a baseline demigration operator LB on the reflectivity r, followed by applying the baseline migration operator LTB so that the remigrated baseline data mB1=LTBLBr; and
calculating the remigrated monitor data mM1 by applying a monitor demigration operator LM on the reflectivity r, followed by applying the monitor migration operator LTM so that the remigrated monitor data mM1=LTMLMr.

### Claim 4 (depends on 3)

The method of claim 3, further comprising:
transforming the reflectivity r with a filter transform , from an image domain to a filter domain;
transforming the remigrated baseline data mB1 with the filter transform , from the image domain to the filter domain; and
transforming the remigrated monitor data mM1 with the filter transform , from the image domain to the filter domain.

### Claim 5 (depends on 4)

The method of claim 4, further comprising:
computing a baseline filter fB in the filter domain based on a filter domain representation (r) of the reflectivity r, a filter domain representation (mB1) of the remigrated baseline data mB1, and a filter domain representation (mB1) of the remigrated monitor data mM1; and
computing a monitor filter fM in the filter domain based on the filter domain representation (r) of the reflectivity r, the filter domain representation (mB1) of the remigrated baseline data mB1, and the filter domain representation (mM1) of the remigrated monitor data mM1.

### Claim 6 (depends on 4)

The method of claim 4, wherein the filter transform is a curvelet transform and the filter domain is a curvelet domain.

### Claim 7 (depends on 5)

The method of claim 5, further comprising:
subjecting the baseline filter fB in the filter domain and the monitor filter fM in the filter domain to produce a same result when applied to the remigrated baseline data mB1 and to remigrated monitor data mM1, respectively.

### Claim 8 (depends on 7)

The method of claim 7, further comprising:
transforming (1) the raw migrated baseline data mB0 to transformed raw migrated baseline data (mB0) and (2) the raw migrated monitor data mM0 to transformed raw migrated monitor data (mM0) in the filter domain with the filter transform ,
and the step of applying comprises:
applying the baseline filter fB in the filter domain, to the transformed raw migrated baseline data (mB0), and applying the monitor filter fm in the filter domain, to the transformed raw migrated monitor data (mM0), to generate the LSM baseline data fB(mB0) in the filter domain and the LSM monitor data fM(mM0) in the filter domain; and
transforming back, with an inverse transform −1, (1) the LSM baseline data fB(mg) to obtain the LSM baseline data mB=−1(fB(m0 )) and (2) the LSM monitor data fM(mM) to obtain the LSM monitor data mM=−1(fM(mM0)).

### Claim 9 (depends on 1)

The method of claim 1, wherein the LSM is performed in a pre-stack domain.

### Claim 10 (depends on 1)

The method of claim 1, wherein the LSM method performs a single iteration.

### Claim 11

A computing device for generating a 4D image of a subsurface based on a least-square migration, LSM, based method, the computing device comprising:
an interface for receiving seismic data d related to the subsurface, wherein the seismic data d includes a baseline dataset dB and a monitor dataset dM, with the monitor dataset dMbeing taken later in time then the baseline dataset dB, for the same subsurface; and
a processor connected to the interface and configured to,
calculate a baseline filter B and a monitor filter M based on a same common reflectivity r of the subsurface and corresponding remigrated baseline data mB1 and remigrated monitor data mM1 so that the base filter B applied to the remigrated baseline data mB1 equals the monitor filter M applied to the remigrated monitor data mM1;
apply the baseline filter B to raw migrated baseline data mB0 and applying the monitor filter M to raw migrated monitor data mM0 to generate LSM baseline data mB and LSM monitor data mM; and
generate the 4D image of the subsurface based on the LSM baseline data mB and the LSM monitor data mM.

### Claim 12 (depends on 11)

The computing device of claim 11, wherein the processor is further configured to:
perform raw migration, with a baseline migration operator LTB on the baseline dataset dB and with a monitor migration operator LTM on the monitor dataset dM, to calculate the monitor raw baseline data mB0 and the monitor raw migrated data mM0.

### Claim 13 (depends on 12)

The computing device of claim 12, wherein the processor is further configured to:
calculate the remigrated baseline data mB1 by applying a baseline demigration operator LB on the reflectivity r, followed by applying the baseline migration operator LTB so that the remigrated baseline data mB1=LTBLBr; and
calculate the remigrated monitor data mM1 by applying a monitor demigration operator LM on the reflectivity r, followed by applying the monitor migration operator LTM so that the remigrated monitor data mM1=LTMLMr.

### Claim 14 (depends on 13)

The computing device of claim 13, wherein the processor is further configured to:
transform the reflectivity r with a filter transform , from an image domain to a filter domain;
transform the remigrated baseline data mB1 with the filter transform , from the image domain to the filter domain; and
transform the remigrated monitor data mM1 with the filter transform , from the image domain to the filter domain.

### Claim 15 (depends on 14)

The computing device of claim 14, wherein the processor is further configured to:
compute a baseline filter fB in the filter domain based on a filter domain representation (r) of the reflectivity r, a filter domain representation (mB1) of the remigrated baseline data mB1, and a filter domain representation (mM1) of the remigrated monitor data mM1; and
compute a monitor filter fM in the filter domain based on the filter domain representation (r) of the reflectivity r, the filter domain representation (mB1) of the remigrated baseline data mB1, and the filter domain representation (mM1) of the remigrated monitor data mM1.

### Claim 16 (depends on 14)

The computing device of claim 14, wherein the filter transform is a curvelet transform and the filter domain is a curvelet domain.

### Claim 17 (depends on 15)

The computing device of claim 15, wherein the processor is further configured to:
subject the baseline filter fB in the filter domain and the monitor filter fM in the filter domain to produce a same result when applied to the remigrated baseline data mB1 and to remigrated monitor data mM1, respectively.

### Claim 18 (depends on 17)

The computing device of claim 17, wherein the processor is further configured to:
transform (1) the raw migrated baseline data mB0 to transformed raw migrated baseline data (mB0) and (2) the raw migrated monitor data mM0 to transformed raw migrated monitor data (mM0) in the filter domain with the filter transform ;
apply the baseline filter fB in the filter domain, to the transformed raw migrated baseline data (mB0), and applying the monitor filter fM in the filter domain, to the transformed raw migrated monitor data (mM0), to generate the LSM baseline data fB(mB) in the filter domain and the LSM monitor data fM(mM) in the filter domain; and
transform back, with an inverse transform −1, (1) the LSM baseline data fB(mg) to obtain the LSM baseline data mB=−1(fB(mB0)) and (2) the LSM monitor data fM(mM) to obtain the LSM monitor data mM=−1(fM(mM0)).

### Claim 19 (depends on 11)

The computing device of claim 11, wherein the LSM is performed in a pre-stack domain.

### Claim 20

A least-square migration, LSM, based method for generating an image of a subsurface, the method comprising:
receiving seismic data d related to the subsurface, wherein the seismic data d includes a baseline dataset dB and a monitor dataset dM, with the monitor dataset dMbeing taken later in time then the baseline dataset dB, for the same subsurface;
iteratively updating a least square migration baseline data mB and a least square migration monitor data mM based on descent directions of (1) a first baseline residual between baseline migrated seismic data LTBdB of the baseline dataset dB and baseline remigrated seismic data LTBLBmB of the least square migration baseline data mB, and (2) a second monitor residual between monitor migrated seismic data LTMdM of the monitor dataset dMand monitor remigrated seismic data LTMLMmM of the least square migration monitor data mM;
migrating the seismic data d with the updated least square migration baseline data mB and the updated least square migration monitor data mM; and
generating the 4D image of the subsurface based on the migrated seismic data d with the updated least square migration baseline data mB and the updated least square migration monitor data mM,
wherein the least square migration baseline data mg and the least square migration monitor data mM are preconditioned with a baseline filter B and a monitor filter M, respectively, which are calculated based on a same common reflectivity r of the subsurface and corresponding remigrated baseline data and remigrated monitor data.