Coding and Decoding: Seismic Data Modeling, Acquisition and Processing

• US 20070274155A1
• Filed: 05/14/2007
• Published: 11/29/2007
• Est. Priority Date: 05/25/2006
• Status: Abandoned Application

• Current Assignee: Luc T. Ikelle
• Original Assignee: Luc T. Ikelle
• Inventors: Ikelle, Luc T.
• Application Number:
  US11/748,473
• Publication Number:
  US 20070274155A1
• Time in Patent Office: Days
• US Class Current: 367/38
• CPC Class Codes: G01V 1/005 with exploration systems emitting special signals, e.g. frequency swept signals, pulse sequences or slip sweep arrangements
• CPC Class Codes: G01V 1/36 Effecting static or dynamic corrections on records, e.g. correcting spread; Correlating seismic signals; Eliminating effects of unwanted energy

Abstract

A method for coding and decoding seismic data acquired, based on the concept of multishooting, is disclosed. In this concept, waves generated simultaneously from several locations at the surface of the earth, near the sea surface, at the sea floor, or inside a borehole propagate in the subsurface before being recorded at sensor locations as mixtures of various signals. The coding and decoding method for seismic data described here works with both instantaneous mixtures and convolutive mixtures. Furthermore, the mixtures can be underdetemined [i.e., the number of mixtures (K) is smaller than the number of seismic sources (I) associated with a multishot] or determined [i.e., the number of mixtures is equal to or greater than the number of sources). When mixtures are determined, we can reorganize our seismic data as zero-mean random variables and use the independent component analysis (ICA) or, alternatively, the principal component analysis (PCA) to decode. We can also alternatively take advantage of the sparsity of seismic data in our decoding process. When mixtures are underdetermined and the number of mixtures is at least two, we utilize higher-order statistics to overcome the underdeterminacy. Alternatively, we can use the constraint that seismic data are sparse to overcome the underdeterminacy. When mixtures are underdetermined and limited to single mixtures, we use a priori knowledge about seismic acquisition to computationally generate additional mixtures from the actual recorded mixtures. Then we organize our data as zero-mean random variables and use ICA or PCA to decode the data. The a priori knowledge includes source encoding, seismic acquisition geometries, and reference data collected for the purpose of aiding the decoding processing.

The coding and decoding processes described can be used to acquire and process real seismic data in the field or in laboratories, and to model and process synthetic data.

Claims

1. A method of analysis of seismic data, the method comprising the steps of:

collecting a single mixture of multicomponent data P(x_r,t) with a multishooting array made of I/2 monopole sources and I/2 dipole sources;

forming a linear system of equations between the components of multishot data and the desired single-shot data; and

solving the system of equations to recover single-shot gathers.

2. A method of analysis of seismic data, the method comprising the steps of:

collecting a single mixture of multicomponent data P(x_r,t) with a multishooting array made of I sources;

performing an up/down separation to produce evenly determined equations of convolutive mixtures; and

applying an ICA algorithm by treating the upgoing and downgoing wavefields as different convolution mixtures.

3. A method of analysis of seismic data, the method comprising the steps of:

collecting multisweep-multishot data in at least two mixtures using two shooting boats, or any other acquisition devices;

arranging the entire multishot gather (or any other gather type) in random variables Y_i, with i varying from 1 to I;

whitening the data Y to produce Z;

computing cumulant matrices Q^(p,q) of the whitened data vector Z;

initializing the auxiliary variables W′

=I;

choosing a pair of components i and j;

computing θ

₄^(ij) using Q^(p,q) and deducing

${\mathrm{\theta <br><br>}}_{\max }^{\left(\mathrm{ij}\right)};<br><br>$

if

${\mathrm{\theta <br><br>}}_{\max }^{\left(\mathrm{ij}\right)}><br><br>\mathrm{\varepsilon <br><br>},$

constructing W^(ij) and updating W′

←

W^(ij)W′

;

diagonalizing cumulant matrices;

Q^(p,q)←

W^(ij)Qz^(p,q)[W^(ij)]^T;

returning to the initializing step unless all possible

${\mathrm{\theta <br><br>}}_{\max }^{\left(\mathrm{ij}\right)}\le <br><br>\mathrm{\varepsilon <br><br>},$

with ε

<

<

1; and

reorganizing and resealing properly after the decoding process by using first arrivals or direct-wave arrivals.

4. The method of claim 3 wherein the step of choosing a pair of components i and j is carried out randomly.

5. The method of claim 3 wherein the step of choosing a pair of components i and j is carried out in any given order.

6. A method of analysis of seismic data, the method comprising the steps of:

collecting multisweep-multishot data in at least two mixtures using two shooting boats, or any other acquisition devices;

arranging a gather type in random variables Y_i, with i varying from 1 to I;

whitening the data Y to produce Z;

choosing I, the number of independent components, to estimate and set p=1;

initializing w_p;

doing an iteration of a one-unit algorithm on w_p;

doing an orthogonalization;

$w_p=w_p-\underset{j=1}{\overset{p-1}{\sum <br><br>}}<br><br>\left(w_p^T<br><br>w_j\right)<br><br>w_j;<br><br>$

normalizing w_p by dividing it by its norm (e.g. w_p←

w/∥

w∥

);

if w_p has not converged, returning to the step of doing an iteration;

setting p=p+1; and

if p is not greater than I, returning to the initializing step.

7. The method of claim 6 wherein the step of arranging the gather type comprises arranging the entire multishot gather.

8. A method of analysis of seismic data, the method comprising the steps of:

collecting multisweep-multishot data in at least two mixtures using two shooting boats or any other acquisition devices;

arranging a gather type in random variables Y_i, with i varying from 1 to I;

setting the counter to k=1;

select a region of the data in which only single-shot X_i contribute to the data;

computing the kth column of the mixing matrix using the ratios of mixtures;

setting k=k+1, and if k is not greater than I, then returning to the step of selecting a region;

invert the mixing matrix; and

estimating the single-shot gathers as the product of the inverse matrix with the mixtures.

9. The method of claim 8 wherein the step of arranging the gather type comprises arranging the entire multishot gather.

10. A method of analysis of seismic data, the method comprising the steps of:

collecting multisweep-multishot data in at least two mixtures using two shooting boats, or any other acquisition devices;

taking a Fourier transform of the data with respect to time;

choosing a frequency slice of data, Y_ν

;

whitening the frequency slice to produce Z_ν

and V_ν

;

applying a complex ICA to Z_ν

and producing W_ν

;

computing B_ν

=W_ν

V_ν

and deducing {circumflex over (B)}_ν

=Diag(B_ν

<sup>−

1</sup>)B_ν

;

getting the independent components for this frequency slice;

{circumflex over (X)}_ν

={circumflex over (B)}_ν

Y_ν

;

returning to the step of taking a Fourier transform unless all frequency slices have been processed;

using the fact that seismic data are continuous in frequency to produce permutations of the random variables of {circumflex over (X)}_ν

which are consistent for all frequency slices; and

taking the inverse Fourier-transform of the permuted frequency slices with respect to frequency.

11. A method of analysis of seismic data, the method comprising the steps of:

collecting at least two mixtures using either two boats or two source arrays;

estimating the mixing using orientation lines of single-shot gathers in a scatterplot with respect to an independence criterion, the decoded gathers having a covariance matrix and a fourth-order cumulant tensor and having PDFs, the independence criterion based on the fact that the covariance matrix and fourth-order cumulant tensor of the decoded gathers must be diagonal or that a joint PDF of the decoded gathers is a product of the PDFs of the decoded gathers.

decoding the multishot data using a geometrical definition of mixtures in the scatterplot, or using p-norm criterion (with p smaller than or equal to

     1) to perform the decoding point by point in the multisweep-multishot data.

12. A method of analysis of seismic data, the method comprising the steps of:

collecting single-mixture data P(x_r,t) with a multishooting array made of I shot points, which are fired with Δ

τ

between two consecutive shots;

constructing the data for the first window corresponding to the interval [0, t₁(x_r)] of the data P(x_r,t) with t₁(x_r)=t₀(x_r)+Δ

τ

, where t₀(x_r) is the first break. We denote these data Q₁(x_r,t)=K_1,1(x_r,t);

setting the counter to i=2, where the index indicates the i-th window, the interval of this window being [t₂(x_r), t₃(x_r)], with t₃(x_r)=t₂(x_r)+Δ

τ

;

constructing the data corresponding to the i-th window, denoting these data by

$Q_i<br><br>\left(x_r,t\right)=\underset{k=1}{\overset{I}{\sum <br><br>}}<br><br>K_{i,r}<br><br>\left(x_r,t\right),$

where K_i,k(x_r,t) is the contribution of the k-th single shot gathers to the multishot data in this window;

shifting and adapting K<sub>i−

1,k−

1</sub> to K_i,k;

using the adapted K<sub>i−

1,k−

1</sub> as mixtures in addition to Q_i(x_r,t), to decode Q_i(x_r,t) using an ICA technique; and

resetting the counter, i←

i+1 and returning to the step of constructing the data corresponding to the i-th window, unless the last window of the data has just been processed.

13. A method of analysis of seismic data, the method comprising the steps of:

collecting a single mixture data with a multishooting array made of I identical stationary source signatures, which are fired at different times τ

_i(x_i) and collecting a reference single-shot gather;

adapting this single-shot gather to a nearest single-shot gather in the multishot gather;

using the adapted single-shot gathers as new mixtures in addition to the recorded mixture;

applying the ICA algorithms to decode one single-shot gather and to obtain new mixtures with one single-shot gather; and

unless the output of the applying step is two single-shot gathers, returning to the applying step using the new mixture and the new single-shot gather as reference shot or with the original reference shot.

14. A method of analysis of seismic data, the method comprising the steps of:

collecting single-mixture data with a multishooting array made of I identical stationary source signatures which are fired at different times τ

_i(x_s), the firing times chosen so that the apparent velocity spectra of single-shot gathers can be significantly different;

sorting the data into receiver or CMP gathers;

transforming the receiver or CMP gathers in the F-K domain;

applying F-K dip filtering to produce an approximate separation of the data into single-shot gathers;

inverse Fourier-transforming the separated single-shot gathers;

using these single-shot receivers gathers as new mixtures in addition to p(x_s,t); and

producing the final decoded data by using ICA techniques.

15. A method of analysis of seismic data, the method comprising the steps of:

collecting single-mixture data P(x_r,t) with a multishooting array made of I different nonstationary source signatures, a₁(t), . . . , a_I(t);

setting the counter to i=b(t)=a₁(t) and U(x_r,t)=P(x_r,t);

crosscorrelating a₁(t) and U(x_r,t) to produce Q(x_r,t), whereby the data Q(x_r,t) are a mixture of stationary and nonstationary signal;

separating the nonstationary signal from the stationary signals, denoting the nonstationary signal by Q_ns(x_r,t) and the stationary signal by Q_st(x_r,t);

constructing a two-dimensional ICA using Q(x_r,t) and Q_st(x_r,t) as the mixtures;

applying ICA to obtain the single-shot gather P_i(x_r,t) and a new mixture made of the remaining single-shot gathers that denoted as U(x_r,t);

resetting the counter, i←

i+1, and returning to the cross-correlating step unless i=I.

16. A method of analysis of seismic data, the method comprising the steps of:

collecting single-mixture data with a multishooting array made of I identical stationary source signatures, which are fired at different times τ

_i(x_s), these firing times chosen so that the event of one single-shot gather of multishot gather can be stationary, whereas those of other single-shot gathers of a multishot gather are nonstationary;

sorting the data into receiver or CMP gathers;

transforming the receiver or CMP gathers to the F-K or K-T (wavenumber-time) domain;

separating the nonstationary signals from the stationary signals, denoting the nonstationary signal by Q_ns and the stationary signal by Q_s;

constructing a two-dimensional ICA using Q(x_r,t) and Q_st(x_r,t) as the mixtures;

applying ICA to obtain the single gather P_i and a new mixture made of remaining single-shot gathers denoted as U(x_r,t);

readjusting the time delay so that events associated with one shot become stationary, whereas the events associated with the other shots remain nonstationary;

returning to the separating step unless the output of the applying step is two single-shot gathers.

17. A method of analysis of seismic data, the method comprising the steps of:

collecting multisweep-multishot data in at least two mixtures using two shooting boats or any other acquisition devices;

arranging a gather type in random variables Y_i, with i varying from 1 to I;

whitening the data Y to produce Z;

initializing auxiliary variables W′

=I and Z′

=Z;

choosing a pair of components i and j;

computing θ

₄^(ij) using the cumulants of Z′ and

deducing θ

_max^(ij) thereby;

if θ

_max^(ij)>

, ε

, constructing W^(ij) and updating W′

←

W^(ij)W′

.

rotating the vector Z′

;

Z′

←

W^(ij)Z′

;

returning to the choosing step unless all possible θ

_max^(ij)≦

ε

, with ε

<

<

1; and

reorganizing and resealing properly after the decoding process by using first arrivals or direct-wave arrivals.

18. The method of claim 17 wherein the step of arranging the gather type comprises arranging the entire multishot gather.

19. The method of claim 17 wherein the step of choosing a pair of components i and j is carried out randomly.

20. The method of claim 17 wherein the step of choosing a pair of components i and j is carried out in any given order.

21. A method of subsurface exploration, the method carried out with respect to imaging software for analyzing single-shot data and developing imaging results therefrom, the method comprising the steps of:

performing a multi-shot, and collecting multi-shot data;

decoding the multi-shot data, yielding proxy single-shot data;

carrying out analysis of the proxy single-shot data by means of the imaging software, thereby yielding imaging results from the proxy single-shot data.

22. The method of claim 21 wherein the step of performing a multi-shot comprises only a single sweep, the method comprising the additional step, performed between the performing step and the decoding step, of numerically generating an additional sweep from the multi-shot data, the decoding step carried out with respect to the single sweep and the additional numerically generated sweep.

23. A method of subsurface exploration, the method carried out with respect to imaging software for analyzing single-shot data and developing imaging results therefrom, the method comprising the steps of:

acquiring multisweep-multishot data generated from several points nearly simultaneously, carried out onshore or offshore, denoting by K a number of sweeps and by I a number of shot points for each multishot location;

if K=1, numerically generating at least one additional sweep, using time delay reference shot data, multicomponent data;

if K=I, and a mixing matrix is known, performing the inversion of the mixing matrix to recover the single-shot data;

if K=I, and a mixing matrix is not known, using PCA or ICA to recover single-shot data;

if K<

I (with K equaling at least

     2), then

(i) estimate the mixing using the orientation lines of single-shot gathers in the scatterplot, the independence criterion based on the fact that the covariance matrix and fourth-order cumulant tensor of the decoded gathers must be diagonal or that the joint PDF of the decoded gathers is the product of the PDFs of the decoded gathers; and

(ii) decode the multishot data using the geometrical definition of mixtures in the scatterplot, or using p-norm criterion (with p smaller or equals to

     1) to perform the decoding point by point in the multisweep-multishot data.