Method for reconstructing at least one trace in a seismic image
A method for reconstructing at least one trace in a seismic image of a common receiver and time domain includes a convolutional neural network trained under an unsupervised learning approach with a modified receptive field.
1. A method for reconstructing at least one trace in a seismic image, the method comprising the steps of:
a) providing a seismic image having seismic traces extracted from a data set acquired via a seismic survey, wherein the seismic image includes at least one seismic trace with data that is unavailable from the acquired data set;
b) training a convolutional neural network to predict values for the unavailable data of the at least one trace, the convolutional neural network includes at least one layer having a kernel function configured to evaluate a bounded domain that defines a blind-trace receptive field, wherein the blind-trace receptive field encompasses data corresponding to a plurality of traces in the seismic image that are adjacent to, but exclude, the at least one trace having unavailable data;
c) predicting values for the unavailable data of the at least one trace by inputting the seismic image into the trained convolutional neural network;
d) reconstructing the at least one trace having unavailable data using the data values predicted in step c); and
e) generating a reconstructed seismic image with the at least one trace reconstructed in step d).
2. The method according to claim 1 , wherein the convolutional neural network is a U-net.
3. The method according to claim 2 , wherein training the convolutional neural network includes using a converging criterion based on an approximation error estimation E s for measuring an interpolation loss when predicting the reconstructed trace, and the approximation error estimation E s being determined as a linear combination of a misfit loss and a regularization loss, the regularization loss being determined by the following steps:
determining a main energy area of the seismic image; and
calculating a norm of the reconstructed seismic image in the frequency domain limited to an area outside of the main energy area based on a predetermined norm.
4. The method according to claim 3 , wherein the linear combination determining the approximation error estimation is:
E s =∥misfit loss∥+α∥regularization loss∥
wherein α is a positive weighting value and ∥·∥ the predetermined norm.
5. The method according to claim 4 , wherein the misfit loss is determined as a difference between the seismic image and the reconstructed seismic image after removing the at least one reconstructed trace.
6. The method according to claim 1 , wherein the at least one layer is a down-sampling layer.
7. The method according to claim 1 , wherein the blind-trace receptive field of the kernel function is determined by the following processing steps:
limiting a receptive field to one adjacent side of the at least one trace having unavailable data, the one adjacent side being determined based on a direction of the at least one trace having unavailable data;
generating a first copy of the seismic image and a second copy of the seismic image, the second copy of the seismic image being rotated 180° with respect to the first copy of the seismic image; and
inputting the first copy and the second copy of the seismic image into the convolutional neural network with the one-adjacent-sided receptive field resulting in two output images that are subsequently combined to form a single image.
8. The method according to claim 7 , wherein the at least one layer with the blind-trace receptive field is a down-sampling layer and wherein any layer of the convolutional neural network includes an output for outputting a feature map and, wherein:
before inputting a feature map, output of a previous layer or the image if the current layer is the first layer, into the current layer, the feature map is padded by adding rows of zeros at the end of the feature map located at one side of the trace;
carrying out a convolution operation; and
cropping out the same number of rows previously added wherein cropping the output feature map is carried out on the side opposite to the side on which rows were previously added.
9. A method for deblending seismic data in a receiver domain, the method comprising:
deploying a plurality of n s acoustic sources in the upper surface of the reservoir domain wherein the plurality of n s acoustic sources are grouped into B groups σ l , l=1 . . . B, and wherein each of the n s acoustic sources is a member of only one of the groups σ l and is positioned at a location x i s , i=1 . . . n s , and deploying a plurality of n r acoustic receivers in the upper surface of the reservoir domain at a location x j r , j=1 . . . n r ;
a) within each group σ l , each of the acoustic sources fires a shot with a random delay time τ li and responses thereto are received at the acoustic receivers and stored in a data structure represented by P ljk b =(x i s , x j r , t k −τ li ); wherein t k is the k th time sample in a time domain;
b) calculating, for each group σ l , the Fourier-transform Π b (:,:,ω k )=F {P ljk b } wherein ω k is the k th frequency and “:” denoting variables depending in index i or index j;
c) for each frequency ω k , determining Π LS (:,:,ω k )=Γ*ø b (:,:,ω k ) wherein Γ* is
Γ*=Γ k H D
wherein D is a diagonal matrix and Γ k H is the conjugate transpose of a blending matrix Γ k calculated from the random delay times τ li as
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d) calculating an Inverse Fourier Transform of F −1 (Π LS (:,:, ω k ))=P ljk ;
e) a shot-gather ordering in the output P ljk is sorted to get an image I j of trace data in a common-receiver domain, a common-midpoint receiver, or a common-offset receiver, and the time domain; and
f) for each trace, carrying out a deblending step by reconstructing a coherent signal of the traces using the reconstructing method according to claim 1 .
10. The method for deblending seismic data according to claim 9 , wherein D=(Γ k Γ k H ) −1 .
11. The method for deblending seismic data according to claim 9 , wherein D=I, wherein I denotes the identity matrix.
12. The method for deblending seismic data according to claim 9 , wherein each source is shot once and wherein for all m≠n, σ m ∩σ n =Ø.
13. A non-transitory computer program product stored on a computer-readable medium and comprising computer-implementable instructions, which, when executed by a computer, cause the computer to carry out the method according to claim 1 .
14. A computer system having a processor and a non-transitory computer-readable medium storing computer-executable instructions which, when executed by the processor, cause the processor to carry out the method according to claim 1 .