Method for imaging of pre-stack seismic data

• US 7,286,690 B2
• Filed: 10/23/2003
• Issued: 10/23/2007
• Est. Priority Date: 10/23/2003
• Status: Expired due to Fees

• Current Assignee: PGS Americas, Inc. (PGS ASA)
• Original Assignee: PGS Americas, Inc. (PGS ASA)
• Inventors: Kelly, Steve Michael
• Primary Examiner(s): Mancuso; Joseph
• Assistant Examiner(s): WANG, CLAIRE X
• Application Number:
  US10/692,185
• Publication Number:
  US 20050111702A1
• Time in Patent Office: 1,461 Days
• Field of Search: 382/109, 382/128, 382/130, 382/131, 382/154, 702/2
• US Class Current: 382/109
• CPC Class Codes: G01V 1/28 Processing seismic data, e.g. for interpretation or for event detection G01V1/48 takes precedence
• CPC Class Codes: G01V 2210/57 Trace interpolation or extrapolation, e.g. for virtual receiver; Anti-aliasing for missing receivers

Abstract

Prestack seismic data is imaged by calculating an individual reflectivity for each frequency in the seismic data. Then, a mean reflectivity is calculating over the individual reflectivities. A variance is calculated for the set of reflectivities versus frequency. A second variance is calculated for the upgoing wavefield, using the mean reflectivity. A spatially varying pre-whitening factor is then calculated, using the variance for the reflectivities and the variance for the upgoing wavefield. A reflectivity is calculated at each location, using the spatially varying pre-whitening factor.

Claims

1. A method for imaging prestack seismic data, comprising:

calculating an individual reflectivity for each frequency in the seismic data;

calculating a mean reflectivity over the individual reflectivities;

calculating a variance for the individual reflectivities;

calculating a variance for the upgoing wavefield in the seismic data, using the mean reflectivity;

calculating a spatially varying pre-whitening factor, using the variance for the reflectivities and the variance for the upgoing wavefield; and

calculating a reflectivity using the spatially varying pre-whitening factor.

2. The method of claim 1, wherein the step of calculating a variance for the upgoing wavefield comprises applying the following equation:

${\mathrm{\sigma <br><br>}}_U^2<br><br>\left(x\right)=\frac{1}{n-1}<br><br>\underset{j=1}{\overset{n}{\sum <br><br>}}<br><br><br><br>{\left[U<br><br>\left(x,{\mathrm{\omega <br><br>}}_j\right)-\langle <br><br>R<br><br>\left(x\right)\rangle <br><br>·<br><br>D<br><br>\left(x,{\mathrm{\omega <br><br>}}_j\right)\right]}^2,$

where σ

_u²(x) is the variance for the upgoing wavefield, x is the spatial location, n is the number of frequencies ω

_j, U(x,ω

_j) is the upgoing wavefield, <

R(x)>

is the mean reflectivity, and D(x,ω

_j) is the downgoing wavefield.

3. The method of claim 1, wherein the step of calculating a spatially varying pre-whitening factor comprises applying the following equation:

$\mathrm{\varepsilon <br><br>}<br><br>\left(x\right)=\frac{{\mathrm{\sigma <br><br>}}_U^2<br><br>\left(x\right)}{{\mathrm{\sigma <br><br>}}_R^2<br><br>\left(x\right)},$

where ε

(x) is the spatially varying pre-whitening factor, σ

_U² is the variance for the upgoing wavefield, and σ

_R²(X) is the variance for the reflectivities.

4. The method of claim 1, wherein the step of calculating a reflectivity using the spatially varying pre-whitening factor comprises applying the following equation:

$R<br><br>\left(x\right)=\frac{1}{n}<br><br>\underset{j=1}{\overset{n}{\sum <br><br>}}<br><br><br><br>\frac{U<br><br>\left(x,{\mathrm{\omega <br><br>}}_j\right)<br><br>D^{*}<br><br>\left(x,{\mathrm{\omega <br><br>}}_j\right)}{{<br><br>D<br><br>\left(x,{\mathrm{\omega <br><br>}}_j\right)<br><br>}^2+\frac{{\mathrm{\sigma <br><br>}}_U^2<br><br>\left(x\right)}{{\mathrm{\sigma <br><br>}}_R^2<br><br>\left(x\right)}},$

where R(x) is the reflectivity, x is the spatial location, n is the number of frequencies ω

_j, U(x,ω

_j) is the upgoing wavefield, D(x,ω

_j) is the downgoing wavefield, σ

_U² is the variance for the upgoing wavefield, and σ

_R²(x) is the variance for the reflectivities.

5. A method for imaging prestack seismic data, comprising:

constructing a downgoing wavefield for each frequency in the seismic data;

constructing an upgoing wavefield for each frequency in the seismic data;

calculating a reflectivity at a spatial location from the downgoing and upgoing wavefields using a least squares approach with a pre-whitening factor,

wherein the least squares approach comprises applying the following equation;

$R<br><br>\left(x\right)=\frac{\frac{1}{n}<br><br>\underset{j=1}{\overset{n}{\sum <br><br>}}<br><br><br><br>D^{*}<br><br>\left(x,{\mathrm{\omega <br><br>}}_j\right)<br><br>U<br><br>\left(x,{\mathrm{\omega <br><br>}}_j\right)}{\frac{1}{n}<br><br>\underset{j=1}{\overset{n}{\sum <br><br>}}<br><br><br><br>D^{*}<br><br>\left(x,{\mathrm{\omega <br><br>}}_j\right)<br><br>D<br><br>\left(x,{\mathrm{\omega <br><br>}}_j\right)+\mathrm{\varepsilon <br><br>}},$

where R(x) is the reflectivity, x is the spatial location, n is the number of frequencies ω

_j, U(x,ω

_j) is the upgoing wavefield, D(x,ω

_j) is the downgoing wavefield, and ε

is the pre-whitening factor.