Self-Supervised Seismic Data Interpolation and Reconstruction Method, System and Device Based on Band Extension

Abstract

The present invention relates to a self-supervised seismic data interpolation and reconstruction method, system and device based on band extension. The method steps include: inputting sparse observation data containing spatial aliasing, and obtaining low-frequency observation data without spatial aliasing through low-pass filtering; obtaining encrypted low-frequency data from the low-frequency data without spatial aliasing in an analytical manner; splitting the encrypted low-frequency data according to the observed channels and missing channels to construct an adaptive training set and a test set for band extension; training a U-net network using the adaptive training set; inputting the test set data into the trained U-net network to obtain full-band data on the missing channels; recombining the reconstructed full-band data of the missing channels with the original sparse observation data to obtain the final interpolation and reconstruction result. Compared with the prior art, the present invention does not rely on labeled data, efficiently and highly accurately completes the interpolation and reconstruction of regularly missing seismic data in a self-supervised manner, and the trained network has a certain degree of scalability.

Description

Technical Field

[0001] The present invention relates to the technical field of self-supervised data reconstruction, and in particular to a self-supervised seismic data interpolation and reconstruction method based on band extension suitable for missing rules. Background Technique

[0002] High-density seismic data without spatial aliasing is of great significance for subsequent seismic data processing to obtain high-quality migration imaging profiles, high-precision inversion results, and accurately depict reservoir distributions. Conventional seismic data acquisition is limited by limited acquisition costs and complex construction environments, resulting in a large trace interval in the acquired data, often containing spatial aliasing. Therefore, efficient and high-precision interpolation and reconstruction of seismic data has become an important part of seismic data processing.

[0003] Conventional seismic data interpolation and reconstruction methods can be divided into prediction filtering methods, low-rank methods, compressive sensing methods based on sparse transforms, and wave equation methods. However, for the case of missing rules, low-rank and compressive sensing methods are not applicable, and the computational cost of the above algorithms increases significantly as the data scale increases. With the development of computer science and technology in recent years, deep learning algorithms have received extensive attention in the field of seismic data interpolation and reconstruction. However, supervised deep learning methods rely on labeled data as training samples, and it is difficult to obtain labeled data in the actual seismic acquisition process; networks trained with simulated data generally have problems such as poor generalization and low interpolation and reconstruction accuracy in the actual data application process. Summary of the Invention

[0004] The purpose of the present invention is to overcome the above-mentioned defects existing in the prior art and provide a self-supervised seismic data interpolation and reconstruction method based on band extension.

[0005] The purpose of the present invention can be achieved through the following technical solutions:

[0006] As the first aspect of the present invention, a self-supervised seismic data interpolation and reconstruction method based on band extension is provided, and the method steps include:

[0007] Input sparse observation data containing spatial aliasing, and obtain low-frequency observation data without spatial aliasing through low-pass filtering.

[0008] Based on the Nyquist sampling theorem, obtain encrypted low-frequency data in an analytical manner from the low-frequency data without spatial aliasing.

[0009] Split the encrypted low-frequency data into observed traces and missing traces, and construct an adaptive training set and a test set for band extension.

[0010] Train the U-net network using the constructed adaptive training set, so that the network has the non-linear mapping ability to map low-frequency data to full-band data;

[0011] Input the low-frequency data in the test set into the trained U-net network to obtain the full-band data on the missing traces;

[0012] Recombine the reconstructed full-band data of the missing traces with the original sparse observation data to obtain the final interpolation reconstruction result.

[0013] Further, the steps for obtaining the low-frequency observation data without spatial aliasing include:

[0014] Use two-dimensional Fourier transform to transform the sparsely acquired observation data d(x,t) into the f-k domain D(f,k x );

[0015] Select the starting frequency f of spatial aliasing in the f-k domain aliase and set the starting frequency f of the Hamming window cut to construct a frequency low-pass filter, the formula is as follows:

[0016]

[0017] Perform frequency-domain low-pass filtering on the sparsely acquired data D to obtain low-frequency data without spatial aliasing

[0018]

[0019] In the formula, ⊙ represents the dot product operator.

[0020] Further, the steps for obtaining the encrypted low-frequency data include:

[0021] Based on the Nyquist sampling law, the f-k spectrum corresponding to the encrypted low-frequency data can be analytically characterized as:

[0022]

[0023] In the formula, represents the low-frequency data without spatial aliasing, k x represents the horizontal wave number, k Nyquist represents the Nyquist wave number;

[0024] Perform two-dimensional inverse Fourier transform on to obtain the encrypted low-frequency data without spatial aliasing

[0025]

[0026] Furthermore, the adaptive training set includes:

[0027] The observed low-frequency data of the encrypted low-frequency data, as sample inputs;

[0028] The original acquired full-band sparse observed data, as labels.

[0029] Furthermore, the test set includes unlabeled low-frequency data on the missing traces.

[0030] Furthermore, the expected output of the U-net network is full-band data, and the following loss function is constructed for network training:

[0031] Loss = ||d obs - f(d low , θ)||1

[0032] In the formula, d obs is the full-band observed data, d low is the low-frequency data input to the network, f(·) is the designed U-net network, θ is the network parameter, and ||·||1 is the L1 norm constraint.

[0033] Furthermore, the U-net network uses the following signal-to-noise ratio formula to quantitatively evaluate the reconstruction result:

[0034]

[0035] In the formula, y is the labeled data, is the network reconstruction result, ||·|| F is the F norm.

[0036] As the second aspect of the present invention, a self-supervised seismic data interpolation and reconstruction system based on frequency band extension is provided, and the system includes:

[0037] Low-pass filtering processing module: used to perform low-pass filtering processing on the input sparse observed data containing spatial aliasing to obtain low-frequency observed data without spatial aliasing;

[0038] Low-frequency data encryption module: based on the Nyquist sampling law, obtain the low-frequency data in an analytical manner from the low-frequency data without spatial aliasing;

[0039] Data set construction module: used to split the encrypted low-frequency data according to the observed traces and the missing traces, and construct an adaptive training set and a test set for frequency band extension;

[0040] U-net network training module: use the constructed adaptive training set to train the U-net network so that the network has the non-linear mapping ability to map low-frequency data to full-band data;

[0041] Missing trace full-band data reconstruction module: Input the low-frequency data in the test set into the trained U-net network to obtain the full-band data on the missing traces;

[0042] Interpolation reconstruction module: Used to recombine the reconstructed full-band data of the missing traces with the original sparse observation data to obtain the final result of interpolation reconstruction.

[0043] As a third aspect of the present invention, there is provided an electronic device, including:

[0044] One or more processors;

[0045] A memory for storing one or more programs;

[0046] When the one or more programs are executed by the one or more processors, the one or more processors implement the self-supervised seismic data interpolation reconstruction method based on band extension as described above.

[0047] As a fourth aspect of the present invention, there is provided a computer-readable storage medium storing a computer program, and when the computer program is executed by a processor, the steps of the self-supervised seismic data interpolation reconstruction method based on band extension as described above are implemented.

[0048] Compared with the prior art, the present invention has the following beneficial effects:

[0049] The present invention provides a self-supervised seismic data interpolation reconstruction method based on band extension, which is applicable to the interpolation reconstruction of regularly missing seismic data. This method transforms the seismic data interpolation reconstruction problem into two sub-problems: low-frequency component reconstruction and band extension. First, encrypted low-frequency seismic data is obtained by low-pass filtering and Nyquist sampling law analysis; then, the full-band data on the missing traces is obtained through self-supervised learning, thereby completing the interpolation reconstruction of seismic data. The solution provided by the present invention does not rely on labeled data, and efficiently and accurately completes the interpolation reconstruction of regularly missing seismic data in a self-supervised manner, and the training network has certain scalability. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is a flowchart of a self-supervised seismic data interpolation reconstruction method based on band extension of the present invention;

[0051] Figure 2 It is a schematic flowchart of the construction of an adaptive training set and data separation operation of the present invention;

[0052] Figure 3 It is a schematic diagram of a U-net network framework for band extension in an embodiment of the present invention;

[0053] Figure 4 Schematic diagram of the interpolation result of the low-frequency component of the simulated data of the present invention; (a) complete data; (b) regularly missing 2 / 3 data; (c) low-frequency complete data; (d) low-frequency data on the observation trace; (e-h) represent the f-k spectra corresponding to the data in (a-d).

[0054] Figure 5 Convergence curves of the loss function and the reconstruction signal-to-noise ratio of the network training set and validation set of the present invention

[0055] Figure 6 Comparison chart of the interpolation reconstruction results of the 80th shot data in an embodiment of the present invention; (a) original complete data; (b) original missing data; (c) reconstruction result of the method of this patent (SNR = 25.3 dB); (d) residual corresponding to (c); (e) reconstruction result of the DIP method (SNR = 15.8 dB); (f) residual corresponding to (e). Detailed implementation manners

[0056] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented on the premise of the technical solution of the present invention, and gives detailed implementation manners and specific operation processes, but the protection scope of the present invention is not limited to the following embodiments.

[0057] Regarding the interpolation reconstruction problem of regularly missing seismic data, the present invention proposes a self-supervised interpolation reconstruction method based on band extension. The core idea of this method is to decompose the seismic data interpolation reconstruction task into two subtasks: low-frequency component interpolation and band extension. As Figure 1 shown, the interpolation reconstruction method is implemented through the following steps:

[0058] (1) Input sparse observation data containing spatial aliasing, and obtain low-frequency observation data without spatial aliasing through low-pass filtering.

[0059] (2) Based on the Nyquist sampling theorem, obtain the encrypted low-frequency data in an analytical manner for the low-frequency data without spatial aliasing.

[0060] (3) Split the reconstructed low-frequency data according to the observation traces and the missing traces.

[0061] (4) After splitting, the low-frequency data on the observation traces and the full-band data on the original observation traces are used as the sample input and label respectively to construct an adaptive training set for band extension, and the low-frequency data on the missing traces are used as the test set.

[0062] (5) Use the adaptive training set constructed in step (4) to train the U-net network, so that the network has the non-linear mapping ability to map low-frequency data to full-band data.

[0063] (6) Input the low-frequency data in the test set into the trained U-net network to obtain the full-band data on the missing channels.

[0064] (7) Recombine the reconstructed full-band data of the missing channels with the original sparse observation data to obtain the final result of interpolation reconstruction.

[0065] The specific steps are as follows:

[0066] Ⅰ. Low-frequency reconstruction based on low-pass filtering and Nyquist sampling theorem

[0067] Based on the Shannon sampling theorem, assuming that the seismic data trace interval is Δx, the corresponding Nyquist wavenumber is shown in formula (1).

[0068]

[0069] When the horizontal wavenumber k x is greater than k Nyquist , the corresponding wavenumber components will fold, resulting in aliasing and generating spatial aliasing in the frequency-wavenumber domain f-k domain. Due to the large trace interval Δx of the sparse acquisition of seismic data, the Nyquist wavenumber is small, and there is strong spatial aliasing in the f-k domain. Since the apparent velocity of seismic data has a certain spread range, and the relationship between the wavenumber k x , frequency f and apparent velocity v is k x = f / v. When the apparent velocity is constant, the wavenumber corresponding to the low-frequency component of seismic data is small and usually does not contain spatial aliasing. Therefore, low-pass filtering of the sparse acquisition data can obtain seismic data without spatial aliasing. Assuming that the sparse acquisition observation data is d(x,t), use the two-dimensional Fourier transform to transform d to the f-k domain D(f,k x ), represents the two-dimensional Fourier transform,

[0070]

[0071] Select the starting frequency f of spatial aliasing in the f-k domain aliase , and set the starting frequency f of the Hamming window cut , and construct a frequency low-pass filter according to formula (3) to avoid the Gibbs phenomenon.

[0072]

[0073] Perform frequency-domain low-pass filtering on the sparse acquisition data D according to formula (4) to obtain low-frequency data without spatial aliasing ⊙ represents the dot product operator,

[0074]

[0075] Based on the Nyquist sampling theorem, any discrete signal without aliasing can be used to obtain its corresponding continuous signal analytically, and then the encrypted discrete signal can be obtained. Assume that the trace interval of the encrypted seismic data is reduced to Δx / n, and its corresponding Nyquist wavenumber becomes nk Nyquist . Based on the Nyquist sampling theorem, the f-k spectrum corresponding to the encrypted low-frequency data can be analytically characterized as

[0076]

[0077] For performing two-dimensional inverse Fourier transform to obtain encrypted low-frequency data without spatial aliasing

[0078]

[0079] II. Band extension based on self-supervised deep learning

[0080] Based on low-pass filtering and the Nyquist sampling theorem, encrypted low-frequency seismic data without spatial aliasing is obtained analytically with high precision, that is, the interpolation reconstruction of the low-frequency component is completed. After completing the interpolation of the low-frequency component, the second processing step of this patent is to use the self-supervised deep learning method to obtain the encrypted full-band data by band extension of the encrypted low-frequency data, that is, the interpolation reconstruction of the sparse seismic data is completed.

[0081] For deep learning algorithms, constructing a reasonable training set is a necessary prerequisite to ensure its effectiveness. For the band extension problem, the encrypted low-frequency data is split according to the observed traces and missing traces. The low-frequency data on the observed traces and the original collected full-band sparse observed data are used as the sample input and label respectively to construct an adaptive training set for band extension, and the unlabeled low-frequency data on the missing traces is used as the test set.

[0082] Adopt Figure 3 the designed U-net network architecture for training. The input of the network is sparse low-frequency data, and the expected output of the network is full-band data. The following loss function is constructed for network training

[0083] Loss = ||d obs - f(d low , θ)||1. (7)

[0084] where d obs is the full-band observed data (label), d lowLet \(x\) be the low-frequency data of the input network, \(f(\cdot)\) be the designed U-net network, \(\theta\) be the network parameters, and \(\|\cdot\|_1\) be the L1 norm. The following signal-to-noise ratio formula is used to quantitatively evaluate the reconstruction results:

[0085]

[0086] where \(y\) is the labeled data, \(\hat{x}\) is the network reconstruction result, and \(\|\cdot\| F is the F norm.

[0087] After the network training is completed, the low-frequency data (test set) on the missing traces is input into the network, and the full-band data corresponding to the missing traces is output. The full-band data on the missing traces is recombined with the original observed data to obtain the encrypted seismic data, thus completing the interpolation reconstruction. The technical process of this invention is as Figure 1 shown.

[0088] Experimental simulation results

[0089] 256 common-shot gather are simulated using the scalar acoustic wave equation. Each gather contains 240 seismic traces, each trace contains 401 time samples, the trace interval is 12.5 m, and the time sampling rate is 4 ms. To simulate regular missing cases, 2 / 3 of the seismic traces in each common-shot gather are regularly missing, the trace interval is expanded to 37.5 m, and the data after regular missing is used as the original observed data for testing. Figure 4 (a), 4(b) respectively show the profiles before and after the seismic data is missing; Figure 4 (e), 4(f) respectively correspond to the f-k spectra of the seismic data before and after missing. After regular missing, the trace interval of the data is expanded, and spatial aliasing appears in the f-k spectrum.

[0090] Based on low-pass filtering and the Nyquist sampling theorem, low-frequency component interpolation reconstruction is performed on the regularly missing seismic data with spatial aliasing to obtain complete low-frequency seismic data ( Figure 4 (c), 4(g)). The low-frequency seismic data on the observed traces and the missing traces are separated to obtain the low-frequency seismic data on the observed traces ( Figure 4 (d)), and it is combined with the full-band data on the original observed traces ( Figure 4 (a)) to construct training pairs for frequency band extension.

[0091] A total of 256 training pairs are constructed from the above 256 common-shot gather. 236 common-shot gather are evenly selected as the training set to train the U-net network, and the remaining 20 common-shot gather are used as the validation set to validate the trained U-net network. During the training process, the reconstruction signal-to-noise ratio and the convergence curve of the loss function are as Figure 5As shown, after 250 iterations, the average signal-to-noise ratios of the training set and the validation set converge to 27.8 dB and 25.7 dB respectively. The low-frequency data on the missing traces is input into the trained network, and the full-band seismic data reconstructed for the missing traces is output and recombined with the observed data on the original observed traces, thereby completing the interpolation reconstruction of the seismic data. Figure 6 The interpolation reconstruction results of the 80th shot data in the dataset are shown in detail and compared with the deep image prior (DIP) deep learning method. Figure 6 (a) is the complete data without missing traces, Figure 6 (b) is the seismic data after regularly missing 2 / 3; after being processed by the method of this patent, the interpolation reconstruction results and their corresponding residuals are as Figure 6 (c) and (d) show. The reconstructed signal-to-noise ratio reaches 25.3 dB; the processing results and residuals of the DIP method are as Figure 6 (e) and (f) show. The reconstructed signal-to-noise ratio is 15.8 dB, which is lower than that of the method of this patent, and the corresponding residuals are greater than those of the method of this patent, further verifying the effectiveness of the method of this patent. The seismic data after interpolation reconstruction is beneficial to improving the accuracy of subsequent migration imaging and inversion methods.

[0092] Embodiment 2

[0093] As the second aspect of the present invention, the present application also provides a self-supervised seismic data interpolation reconstruction system based on band extension. This system applies the self-supervised interpolation reconstruction method based on band extension as described in the above embodiment, and its composition includes:

[0094] Low-pass filtering processing module: used to perform low-pass filtering processing on the input sparse observed data containing spatial aliasing to obtain low-frequency observed data without spatial aliasing;

[0095] Low-frequency data encryption module: based on the Nyquist sampling law, the low-frequency data without spatial aliasing is obtained in an analytical manner;

[0096] Dataset construction module: used to split the encrypted low-frequency data according to the observed traces and the missing traces, and construct an adaptive training set and a test set for band extension;

[0097] U-net network training module: uses the constructed adaptive training set to train the U-net network so that the network has the non-linear mapping ability to map low-frequency data to full-band data;

[0098] Missing trace full-band data reconstruction module: inputs the low-frequency data in the test set into the trained U-net network to obtain the full-band data on the missing traces;

[0099] Interpolation reconstruction module: used to recombine the reconstructed missing channel full-band data with the original sparse observation data to obtain the final result of interpolation reconstruction.

[0100] Embodiment 3

[0101] As the third aspect of the present invention, the present application also provides an electronic device, including: one or more processors; a memory for storing one or more programs; when the one or more programs are executed by the one or more processors, the one or more processors implement the self-supervised interpolation reconstruction method based on band extension as described above. In addition to the processors, the memory, and the interfaces, any device with data processing capabilities where the device in the embodiment is located may generally include other hardware according to the actual functions of the device with data processing capabilities, which will not be elaborated here.

[0102] Embodiment 4

[0103] As the fourth aspect of the present invention, the present application also provides a computer-readable storage medium, on which computer instructions are stored, and when the instructions are executed by a processor, the self-supervised interpolation reconstruction method based on band extension as described above is implemented. The computer-readable storage medium may be an internal storage unit of any device with data processing capabilities described in any of the foregoing embodiments, such as a hard disk or a memory. The computer-readable storage medium may also be an external storage device, such as a plug-in hard disk, a Smart Media Card (SMC), an SD card, a Flash Card, etc. equipped on the device. Further, the computer-readable storage medium may also include both an internal storage unit of any device with data processing capabilities and an external storage device. The computer-readable storage medium is used to store the computer program and other programs and data required by any device with data processing capabilities, and may also be used to temporarily store data that has been output or will be output.

[0104] The preferred specific embodiments of the present invention have been described in detail above. It should be understood that those of ordinary skill in the art can make many modifications and variations based on the concept of the present invention without creative labor. Therefore, all technical solutions that can be obtained by those skilled in the art in the technical field of the present invention through logical analysis, reasoning, or limited experiments based on the concept of the present invention on the basis of the prior art should be within the protection scope determined by the claims.

Claims

1. A self-supervised seismic data interpolation and reconstruction method based on band extension, characterized in that The method steps include: Input sparse observation data containing spatial aliasing, and obtain low-frequency observation data without spatial aliasing through low-pass filtering. Based on the Nyquist sampling theorem, obtain encrypted low-frequency data from the low-frequency data without spatial aliasing in an analytical manner. Split the encrypted low-frequency data according to the observed channels and missing channels, and construct an adaptive training set and a test set for frequency band extension. Use the constructed adaptive training set to train the U-net network so that the network has the non-linear mapping ability to map low-frequency data to full-band data. Input the low-frequency data in the test set into the trained U-net network to obtain full-band data on the missing channels. Recombine the reconstructed full-band data of the missing channels with the original sparse observation data to obtain the final interpolation reconstruction result.

2. A self-supervised seismic data interpolation and reconstruction method based on band extension according to claim 1, characterized in that, The steps for obtaining the low-frequency observation data without spatial aliasing include: Use two-dimensional Fourier transform to convert the sparsely acquired observed data d(x,t) to the f-k domain D(f,k x ); Select the starting frequency \(f\) of spatial aliasing frequency in the \(f - k\) domain aliase and set the starting frequency \(f\) of the Hamming window cut , and construct a low-pass frequency filter with the following formula: Perform frequency-domain low-pass filtering on the sparsely acquired data D to obtain low-frequency data without spatial aliasing. In the formula, ⊙ represents the dot product operator.

3. A self-supervised seismic data interpolation and reconstruction method based on band extension according to claim 1, characterized in that The steps for obtaining the encrypted low-frequency data include: Based on the Nyquist sampling theorem, the f-k spectrum corresponding to the encrypted low-frequency data can be analytically characterized as: In the formula, represents the low-frequency data without spatial aliasing, and k x represents the horizontal wavenumber, and k Nyquist represents the Nyquist wavenumber; Pair Perform a two-dimensional inverse Fourier transform to obtain encrypted low-frequency aliasing-free data 4. A self-supervised seismic data interpolation and reconstruction method based on band extension according to claim 1, characterized in that The adaptive training set includes: The low-frequency data of the observed channels of the encrypted low-frequency data, used as sample inputs. The originally acquired full-band sparse observation data, used as labels.

5. A self-supervised seismic data interpolation and reconstruction method based on band extension according to claim 1, characterized in that The test set includes unlabeled low-frequency data on the missing channels.

6. A self-supervised seismic data interpolation and reconstruction method based on band extension according to claim 1, characterized in that The expected output of the U-net network is full-band data, and the following loss function is constructed for network training: Loss=||d obs -f(d low ,θ)||1 where d obs is the observation data of the full frequency band, d low is the low-frequency data of the input network, f(·) is the designed U-net network, θ is the network parameter, and ||·||1 is the L1 norm constraint.

7. A self-supervised seismic data interpolation and reconstruction method based on band extension according to claim 1, characterized in that The U-net network uses the following signal-to-noise ratio formula to quantitatively evaluate the reconstruction result: where y is the label data, is the network reconstruction result, and ||·|| F is the F-norm.

8. A self-supervised seismic data interpolation and reconstruction system based on band extension, characterized in that, The system includes: A low-pass filtering processing module: used to input sparse observation data containing spatial aliasing and obtain low-frequency observation data without spatial aliasing through low-pass filtering. A low-frequency data encryption module: based on the Nyquist sampling theorem, obtain low-frequency data from the low-frequency data without spatial aliasing in an analytical manner. A data set construction module: used to split the encrypted low-frequency data according to the observed channels and missing channels, and construct an adaptive training set and a test set for frequency band extension. A U-net network training module: uses the constructed adaptive training set to train the U-net network so that the network has the non-linear mapping ability to map low-frequency data to full-band data. A full-band data reconstruction module for missing channels: inputs the low-frequency data in the test set into the trained U-net network to obtain full-band data on the missing channels. An interpolation reconstruction module: used to recombine the reconstructed full-band data of the missing channels with the original sparse observation data to obtain the final interpolation reconstruction result.

9. An electronic device, characterized in that, Includes: One or more processors; A memory for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the self-supervised seismic data interpolation reconstruction method based on frequency band extension according to any one of claims 1-7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the self-supervised seismic data interpolation reconstruction method based on frequency band extension according to any one of claims 1-7.

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