Imaging of multishot seismic data

A method of imaging multishot data without decoding, the method comprising the steps of:

• recording pressure and particle velocity in a multishot experiment;
• performing an up/down separation techinique;
• and
• deconvolving the data using either a downgoing or a upgoing wavefield to obtain the mutishot data free of free-surface multiples.

A method of imaging multishot data without decoding, the method comprising the steps of:

• inputting a multishot gather;
• predicting Φn(k,k′ω)=Φn−1(k,k′ω){circumflex over (V)}0nd)(k,k′ω) by computing {circumflex over (Φ)}1;
• taking the difference between {circumflex over (Φ)}0−α{circumflex over (Φ)}1 to obtain a field of receiver ghost of primaries, wherein {circumflex over (Φ)}1 is considered the noise;
• and
• repeating the inputting, predicting and taking the difference for the multishot gather of the multishot data.

A method of imaging multishot data without decoding, the method comprising the steps of:

• inputting a multishot gather;
• defining a BMG and constructing a portion of data located above the BMG;
• denoting the portion of the data as {circumflex over (Φ)}0α;
• performing a multidimensional convolution of the portion of a particle-velocity data located above the BMG and an actual data in full to obtain the field of predicted multiples by denoting the field as {circumflex over (Φ)}1a;
• taking the difference {circumflex over (Φ)}pa={circumflex over (Φ)}0−α{circumflex over (Φ)}1a to obtain a data without multiples, wherein {circumflex over (Φ)}1a is considered the noise;
• constructing a portion of data located below the BMG of {circumflex over (Φ)}pa by denoting the portion of data as {circumflex over (Φ)}pαb;
• performing a multidimensional convolution of the portion of the particle-velocity data of {circumflex over (Φ)}pa located below the BMG and the portion of the actual data located above the BMG to obtain the field of predicted multiples by denoting the field {circumflex over (Φ)}1b;
• taking the difference {circumflex over (Φ)}pb={circumflex over (Φ)}pα−α{circumflex over (Φ)}1b, wherein {circumflex over (Φ)}1b is considered the noise;
• if the multishot gather containing residual multiples, lowering the BMG and returning to the defining the BMG step;
• and
• repeating the method from the inputting step to the taking the difference step for the multishot gather.

A method of imaging multishot data without decoding, the method comprising the steps of:

• inputting a multishot gather;
• creating a version of said multishot gather without a direct wave;
• generating Φ1 with the data {circumflex over (Φ)}0 containing the direct wave;
• generating {circumflex over (Φ)}1′ for the case in which {circumflex over (Φ)}0 does not contain the direct wave;
• taking the difference {circumflex over (Φ)}1−α{circumflex over (Φ)}1′ to obtain the field of receiver ghosts of primaries, wherein {circumflex over (Φ)}1 is considered the noise;
• and
• repeating the method from the inputting step to the taking the difference step for the multishot gather.

A method of imaging multishot data without decoding, the method comprising the steps of:

• inputting a multishot data in the form of a multishot gather;
• predicting the field of multiples Φk(xs,ω,xr);
• filtering an artifacts contained in Φk(xs,ω,xr) which are due to the approximation of the receiver-gather sections;
• subtracting predicted multiples from the data using the subtraction solution and the adaptive noise cancellation;
• and
• if the demultiple process requires iterations, returning to the predicting the field of multiples step using the output of the subtracting step.

A method of imaging multishot data without decoding, the method comprising the steps of:

• inputting a multishot data in the form of a multishot gather;
• predicting the field of multiples Φk(xs,ω,xr) ;
• and
• using an ICA model for 2×3 mixture to separate primary field from the data.

A method of imaging multishot data without decoding, the method comprising the steps of:

• inputting a multishot data in the form of a multishot gather;
• predicting the field of multiples Φk(xs,ω,xr);
• and
• using an ICA model for 2×2 mixture to separate primary field from the data.

A method of imaging multishot data without decoding, the method comprising the steps of:

• collecting a first marine seismic dataset at a first sea level Z0;
• repeating the experiment by collecting a second dataset at second sea level Z1;
• making sure that sources and receivers are located at the same position with respect to the sea floor during the two experiments;
• and
• applying ICA decoding for undetermined mixtures for the system of equation:
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• creating an additional mixture based on the adaptive/match filtering and reciprocity theorem.

A method of imaging multishot data without decoding, the method comprising the steps of:

• collecting a first marine seismic dataset at a first sea level Z0;
• repeating the experiment by collecting a second dataset at a second sea level Z1;
• making sure that sources and receivers are located at the same position with respect to the sea floor during the two experiments;
• applying ICA decoding for undetermined mixtures for the system of equation:
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• creating an additional mixture based on the adaptive/match filtering and reciprocity theorem.

A method of imaging multishot data without decoding, the method comprising the steps of:

• collecting a first marine seismic dataset at a first sea level Z0;
• repeating the experiment by collecting a second dataset at a second sea level Z1;
• making sure that sources and receivers are located at the same position with respect to the sea floor during the two experiments;
• taking the Fourier transform of the data with respect to time;
• whitening each frequency slice;
• initializing all the decoding matrix Wv as identity matrices;
• applying ICA for each frequency;
• resealing the results, wherein By denote the demixing matrix at the frequency slice v;
• deducing Bv′=Diag(Bv−1)Bv;
• getting the independent components for this frequency slice:
• Xv′=Bv′Yv;
• and
• taking the inverse Fourier-transform of X′=[Xv′} with respect to frequency.

A method of imaging multishot data without decoding, the method comprising the steps of:

• collecting a first marine seismic dataset at a first sea level Z0;
• repeating the experiment by collecting a second dataset at a second sea level Z1;
• making sure that sources and receivers are located at the same position with respect to the sea floor during the two experiments;
• taking the Fourier transform of the data with respect to time;
• whitening each frequency slice;
• initializing all the decoding matrix Wv as identity matrices;
• applying MICA on all frequency;
• resealing the results, wherein By denote the demixing matrix at the frequency slice v;
• deducing Bv′=Diag(Bv−1)Bv;
• getting the independent components for this frequency slice:
• Xv′=Bv′Yv;
• and
• taking the inverse Fourier-transform of X′={Xv′} with respect to frequency.

A method of imaging multishot data without decoding, the method comprising the steps of:

• reformulating a migration operator in L(xs,x,xrω)=G(xs,x,ω)G(x,xr,ω) to include the feature of multishot data and of the source-signature encoding
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• including said migration operator in the inversion and migration algorithms;
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• running the migration and inversion algorithms with this new operator to recover the velocity model of the subsurface and the images of the subsurface.

A method of imaging multishot data without decoding, the method comprising the steps of:

• reformulating a constant-velocity migration operator using the operator L(xs,x,xr,ω)=G(xs,x,ω)G(xs,x,ω) to include the feature of multishot data and of the source-signature encoding
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• performing the migration for velocity between a predefined velocity interval, Vmin and Vmax at the increment ΔV;
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• using the classical focusing-defocusing criteria to estimate the velocity model.

A method of imaging multishot data without decoding, the method comprising the steps of:

• creating an initial-velocity model using time imaging;
• using a reformulating depth migration algorithm which is based on the multishooting operator
• W=[L*L]−1L*Dobs and
• M(x)=∫dxr∫dxs∫dωL*(xs,x,xr,ω), Dobs(xs,xr,ω) so that the features of multishot data of the source-signature encoding
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• applying residual moveout (RMO) analysis encoding;
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• proceeding the classical way with a layer-by-layer approach.

A method of imaging multishot data without decoding, the method comprising the steps of:

• creating an initial-velocity model using time imaging;
• using a reformulating depth migration algorithm which is based on the multishooting operator
• W=[L*L]−1L*Dobs and
• M(x)=∫dxr∫dxs∫dωL*(xs,x,xr,ω), Dobs(xs,xr,ω) so that the features of multishot data of the source-signature encoding
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• applying residual moveout (RMO) analysis encoding;
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• proceeding with a global scheme.

A method of imaging multishot data without decoding, the method comprising the steps of:

• casting the seismic imaging into an ICA, wherein seismic data are a mixing matrix;
• forming the independent components as products of the subsurface inhomogeneities and Green's function from the source points to the image points;
• forming the mixing matrix with the Green's function from the image points to the receiver points;
• using the classical ICA technique to recover the mixing matrix and the independent components;
• determining the location and the strength of the subsurface inhomogeneities by fitting the Green's function predicted by the ICA model and those predicted by standard migration techniques.