Seismic acquisition footprint denoising method based on unsupervised model-driven deep learning

Abstract

The present invention discloses a seismic acquisition footprint denoising method based on unsupervised model-driven deep learning, which is applied to the field of seismic data processing. Aiming at the existing footprint removal methods, when the seismic image has unexpected characteristics beyond its assumptions and relies on manually crafted prior knowledge, the problem of poor footprint removal effect; the present invention proposes a model-driven footprint elimination network FR for unsupervised capture of footprint suppression without any valuable signal assumptions; the FR-Net network designs a unidirectional total variation acquisition footprint model according to the inherent directionality of the noise. By using the UTV model to strongly regularize the deep convolutional autoencoder, it is ensured that the FR-Net network converts the DCAE from completely data-driven to model-driven, inheriting the advantages of the DCAE and the footprint model. The FR-Net network is optimized by the backpropagation algorithm to project the complete separation of the footprint noise and the useful signal in an unsupervised manner.

Description

Technical Field

[0001] The present invention belongs to the field of seismic data processing, and particularly relates to a footprint noise removal technique. Background Art

[0002] Footprint noise is widely recognized as anomalies and periodic amplitude stripes related to acquisition geometry rather than geology, and always appears on time slices or horizontal slices of 3D seismic data. The main causes of footprint noise are diverse and often occur throughout the data acquisition and processing. The presence of footprint noise makes the seismic image unclear, which may affect the identification and analysis of the true subsurface response, undoubtedly increasing the uncertainty of seismic image interpretation. Therefore, footprint noise removal is a very important step in seismic data processing and the focus of this paper.

[0003] In the past few decades, the geophysical community has made great efforts to promote the development of footprint noise elimination. Notably, a large number of paramount methods have been proposed in the seismic literature, which can be roughly divided into two categories: filtering and sparse representation (SR). Filtering methods are the most widely used and can be divided into two categories: wavenumber / frequency domain and time domain filtering. The first category was initially used by Glnay, treating footprints as spatially periodic noise, thus suppressing attempts in the wavenumber space. For example, classical wavenumber filtering, adaptive wavenumber filtering, spectral notch filtering, double-pass frequency wavenumber filtering, and wavenumber notch filtering. The second category is mainly applicable to random noise elimination but can also be applied to footprint elimination. Typical methods include singular value decomposition-based and structure-oriented filtering. However, in actual case studies, the problem lies in that filtering techniques attempt to achieve significant footprint removal while ensuring that the true amplitude is not affected. Compared with the wavenumber / frequency domain, SR can achieve a more compact representation of clear seismic images and footprints, enabling them to be better separated in the sparse domain.

[0004] According to the correct production method of the dictionary, SR can be divided into analytical sparse transformation and data-driven sparse coding (SC). For the case of analytical sparse transformation, it is assumed that noise suppression is based on calculating the sparse coefficients of the footprint and the clear image in a given analytical transformation basis, with different distribution laws, including wavelet transform, 3D complex wavelet transform, stationary wavelet transform (SWT), basis pursuit, and curvelet transform. Specifically, based on the distribution law of the analytical coefficient energy, the complete separation of the footprint and the clear seismic image is achieved by performing threshold or filtering operations on the sparse coefficients. Completely different from the analytical sparse transformation, it is assumed that the atoms of the learned dictionary represent the clear image and the footprint pattern. The denoising method based on SC naturally processes these learned atoms while ignoring the role of the sparse coefficients. In particular, the SC method regards the footprint suppression problem as a binary pattern classification or filtering task for all learned atoms, thereby enabling the separation of the footprint and the clear image at the atomic level. However, although the existing methods have made great progress in footprint removal, their performance must rely on manually crafted prior knowledge, which may reduce the performance if the seismic image has unexpected characteristics beyond its assumptions. Summary of the Invention

[0005] To solve the above technical problems, the present invention proposes a seismic acquisition footprint denoising method based on unsupervised model-driven deep learning, which can remove footprint noise based on deep learning without any ground truth data.

[0006] The technical solution adopted by the present invention is as follows: A seismic acquisition footprint denoising method based on unsupervised model-driven deep learning, comprising:

[0007] S1. Construct an unsupervised training sample according to the 3D seismic data;

[0008] S2. Construct an FR network, and the FR network adopts a U-Net architecture;

[0009] S3. Train the FR network constructed in step S2 with the training sample in step S1;

[0010] S4. Input the seismic data to be processed into the trained FR network, thereby completing footprint removal and obtaining the final result.

[0011] The implementation process of step S1 is as follows: Flatten the 3D seismic data into multiple time slice images; then, crop these time slice images into overlapping or non-overlapping patch images, and obtain the training sample according to these patch images.

[0012] The calculation formula corresponding to step S2 is:

[0013]

[0014] Wherein, Represents the output result of the FR network, D Θ (·) represents the encoder network, Θ represents the training parameters related to the encoder, E Θ (·) represents the decoder network, Represents the input of the FR network.

[0015] Θ is solved by minimizing the cost function, and the cost function is expressed as:

[0016]

[0017] Among them, || ||2 is the 2-norm, || ||1 is the 1-norm, and are the derivative operators in the horizontal and vertical directions respectively, and λ1 and λ2 are regularization parameters.

[0018] The solution process is as follows:

[0019] W in gradient descent l-1 and B l The update expressions are:

[0020]

[0021]

[0022] Among them, α represents the learning rate, div(·) represents calculating the divergence of a given matrix; σ′ is the derivative of σ with respect to the argument, b (k) 、 are the parameters of the gradient descent algorithm.

[0023] Advantages of the present invention: The present invention proposes a model-driven footprint elimination network (referred to as FR-Net) for unsupervised acquisition footprint denoising without any additional signal assumptions. The key of the FR-Net network is to design a unidirectional total variation (UTV) acquisition footprint model according to the inherent directionality of the noise, and strongly regularize the deep convolutional autoencoder (DCAE) by using the UTV model, ensuring that the FR-Net network of the present invention converts the DCAE from completely data-driven to model-driven, inheriting the advantages of the DCAE and the footprint model of the present invention. Subsequently, the FR-Net network is optimized by the backpropagation (BP) algorithm to project the complete separation of footprint noise and useful signals in an unsupervised manner. Through qualitative and quantitative evaluations of three synthetic and field datasets, it shows that the footprint removal effect of the method of the present invention is better than that of the prior art. Description of the Drawings

[0024] Figure 1 It is a schematic diagram of footprint noise;

[0025] Among them, (a) is a seismic image with footprint noise, (b) is the horizontal derivative, and (c) is the V vertical derivative;

[0026] Figure 2 It is a schematic diagram of the FR network model;

[0027] The network is a Unet network with a UTV regularization term.

[0028] Figure 3 It is a synthesis example;

[0029] Among them, (a) and (d) are clean data, (b) and (e) are footprint noise, and (c) and (f) are noisy data;

[0030] Figure 4 It is the result of the synthetic dataset in the single-trace comparison;

[0031] Among them, (a) is the comparison of the clean data and the footprint removal result obtained by the SGRDL method in a single trace, (b) is the comparison of the clean data and the footprint removal result obtained by the CBDNet method in a single trace, (c) is the comparison of the clean data and the footprint removal result obtained by the DRR method in a single trace, and (d) is the comparison of the clean data and the footprint removal result obtained by the FR-Net method in a single trace;

[0032] Figure 5 It is the result of the synthetic dataset in the constant-time slice comparison;

[0033] Among them, (a) is the footprint removal result obtained by the DRR method, (b) is the footprint removal result obtained by the CBDNet method, (c) is the footprint removal result obtained by the SGRDL method, (d) is the footprint removal result obtained by the FR-Net method proposed by the present invention, (e) is the corresponding residual obtained by the DRR method, (f) is the corresponding residual obtained by the CBDNet method, (g) is the corresponding residual obtained by the SGRDL method, and (h) is the corresponding residual obtained by the FR network method proposed by the present invention;

[0034] Figure 6 It is the result of the synthetic dataset in the inline cross-section comparison;

[0035] Among them, (a) is the footprint removal result obtained using the DRR method, (b) is the footprint removal result obtained using the CBDNet method, (c) is the footprint removal result obtained using the SGRDL method, (d) is the footprint removal result obtained using the FR-Net method proposed by the present invention, (e) is the corresponding residual obtained using the DRR method, (f) is the corresponding residual obtained using the CBDNet method, (g) is the corresponding residual obtained using the SGRDL method, and (h) is the corresponding residual obtained using the FR network method proposed by the present invention;

[0036] Figure 7 Results in the constant time slice comparison of the Penobscot dataset;

[0037] Among them, (a) is the constant time slice result of the original noisy Penobscot-3D work area, (b) is the constant time slice and footprint removal result obtained using the FR-Net method proposed by the present invention, (c) is the constant time slice and footprint removal result obtained using the DRR method, (d) is the constant time slice and footprint removal result obtained using the SGRDL method, and (e) is the constant time slice and footprint removal result obtained using the CBDNet method;

[0038] Figure 8 Results in the constant time slice comparison of the Penobscot dataset;

[0039] Among them, (a) is noise removal using the DRR method, (b) is noise removal using the FR-Net method proposed by the present invention, (c) is noise removal using the CBDNet method, and (d) is noise removal using the SGRDL method;

[0040] Figure 9 Results in the inline section comparison of the Penobscot-3D dataset;

[0041] Among them, (a) is the initial 200th inline segment, (b) is the footprint removal result obtained using the FR-Net method proposed by the present invention, (c) is the corresponding residual obtained using the FR-Net method proposed by the present invention, (d) is the footprint removal result obtained using the DRR method, (e) is the corresponding residual obtained using the DRR method, (f) is the footprint removal result obtained using the CBDNet method, (g) is the corresponding residual obtained using the CBDNet method, (h) is the footprint removal result obtained using the SGRDL method, and (i) is the corresponding residual obtained using the SGRDL method;

[0042] Figure 10 Results in the xline section comparison of the Penobscot-3D dataset;

[0043] Among them, (a) is the original 40th xline part, (b) is the footprint removal result obtained by using the FR-Net method proposed by the present invention, (c) is the corresponding residual obtained by using the FR-Net method proposed by the present invention, (d) is the footprint removal result obtained by using the DRR method, (e) is the corresponding residual obtained by using the DRR method, (f) is the footprint removal result obtained by using the CBDNet method, (g) is the corresponding residual obtained by using the CBDNet method, (h) is the footprint removal result obtained by using the SGRDL method, and (i) is the corresponding residual obtained by using the SGRDL method;

[0044] Figure 11 It is the result of the Kerry-3D dataset in the constant time slice comparison;

[0045] Among them, (a) is the constant time slice result of the original noisy Kerry-3D work area, (b) is the constant time slice and footprint removal result obtained by using the FR-Net method proposed by the present invention, (c) is the constant time slice and footprint removal result obtained by using the DRR method, (d) is the constant time slice and footprint removal result obtained by using the SGRDL method, and (e) is the constant time slice and footprint removal result obtained by using the CBDNet method;

[0046] Figure 12 It is the result of the Kerry-3D dataset in the constant time slice comparison;

[0047] Among them, (a) is the removed footprint obtained by using the FR-Net method proposed by the present invention, (b) is the removed footprint obtained by using the FR-Net method proposed by the present invention, (c) is the removed footprint obtained by using the CBDNet method, and (d) is the removed footprint obtained by using the SGRDL method;

[0048] Figure 13 It is the result of the Kerry-3D dataset in the inline cross-section comparison;

[0049] Among them, (a) is the initial 163rd inline segment, (b) is the footprint removal result obtained by using the FR-Net method proposed by the present invention, (c) is the corresponding residual obtained by using the FR-Net method proposed by the present invention, (d) is the footprint removal result obtained by using the DRR method, (e) is the corresponding residual obtained by using the DRR method, (f) is the footprint removal result obtained by using the CBDNet method, (g) is the corresponding residual obtained by using the CBDNet method, (h) is the footprint removal result obtained by using the SGRDL method, and (i) is the corresponding residual obtained by using the SGRDL method;

[0050] Figure 14Results of the Kerry-3D dataset in the xline cross-section comparison;

[0051] Among them, (a) is the original 70th xline section, (b) is the footprint removal result obtained using the FR-Net method proposed in the present invention, (c) is the corresponding residual obtained using the FR-Net method proposed in the present invention, (d) is the footprint removal result obtained using the DRR method, (e) is the corresponding residual obtained using the DRR method, (f) is the footprint removal result obtained using the CBDNet method, (g) is the corresponding residual obtained using the CBDNet method, (h) is the footprint removal result obtained using the SGRDL method, and (i) is the corresponding residual obtained using the SGRDL method. Detailed implementation

[0052] To facilitate the understanding of the technical content of the present invention by those skilled in the art, the following technical terms are first explained:

[0053] 1. Deep convolutional autoencoder

[0054] DCAE (deep convolutional autoencoder) is an end-to-end model consisting of two parts: an encoder with multiple layers of nonlinear functions that maps the input data to latent features, and a decoder with various nonlinear functions that maps the latent features to the reconstruction space. Given the input The representation of the hidden layer is calculated as follows:

[0055]

[0056] where represents the transpose of the matrix, and N represents the number of input sample pairs. Since the decoder is designed in the opposite way to the encoder, feedback can be provided to the decoder for X n,l-1 By minimizing the following reconstruction error cost, the output X of the latter n,l is compared with the original image:

[0057]

[0058] where represents the model parameters of the AE (autoencoder) model.

[0059] 2. Total variation (TV)

[0060] The TV model was originally proposed by Rudin et al. to solve the problem of gray image denoising because it can preserve edge information and effectively promote piecewise smoothing. Later, the TV model has become increasingly crucial for the extrusion of image denoising techniques because its superior performance can naturally be extended to seismic image denoising.

[0061] Formally, for and its derivative and are defined as

[0062]

[0063] where X(i,j) represents the (i,j)-th element of X, and and represent the finite derivative operators in the vertical and horizontal directions respectively. The TV of

[0064]

[0065] After determining the TV norm for image denoising, it can be regarded as a prior and incorporated to constrain the maximum a posteriori (MAP) estimation. Then, the image denoising model can be expressed as:

[0066]

[0067] where ε represents the noise level of Gaussian noise.

[0068] The present invention proposes a model-driven footprint removal network (referred to as FR-Net) as shown in Figure 2 for unsupervised acquisition footprint denoising without the need for additional signal assumptions. The key of the FR-Net network is to design a unidirectional total variation (UTV) acquisition footprint model according to the inherent directionality of the noise. By strongly regularizing the deep convolutional autoencoder (DCAE) using the UTV model, it is ensured that the FR-Net network of the present invention converts the DCAE from completely data-driven to model-driven, inheriting the advantages of the DCAE and the footprint model of the present invention. Subsequently, the FR-Net network is optimized by the backpropagation (BP) algorithm to project out a complete separation of the footprint noise and the useful signal in an unsupervised manner.

[0069] The implementation process of the present invention includes the following steps:

[0070] 1. Problem analysis

[0071] The acquisition footprint is used to represent the linear spatial grid pattern visible on the 3D seismic time or horizontal slice. Therefore, the noisy data is modeled as the superposition of the desired clear image component the acquisition footprint component and the random noise as Figure 1As shown in (a). Further, assuming that the footprint noise and random noise are additive, the degradation process caused by the footprint noise and random noise can be described as

[0072]

[0073] Formally, the task of the present invention is to estimate the potential clear image from the given image in the presence of both footprint and random noise Specifically, by minimizing the following equation

[0074]

[0075] This is a typical inverse problem. The key is to construct an appropriate regularization term to suppress the footprint and random noise as follows:

[0076]

[0077] where and are the priors on the clear image and footprint component respectively, and both τ and λ are regularization parameters. So far, two typical application techniques, namely explicit filtering and sparse representation (SR), have been proposed for footprint suppression. It can be seen from these methods that the key to reducing footprint noise is to establish appropriate models for the clean image and the footprint, which greatly facilitates the separation of the two.

[0078] 2. Footprint noise model

[0079] As Figure 1 (a) shows, the footprint has a distinct directional feature. For this reason, it is considered that the existing TV regularization is not suitable for removing the footprint because the footprint obviously has a directional feature. In Figure 1 , the unidirectional gradients of the degraded seismic image in the horizontal and vertical directions are shown. As Figure 1 (b) and (c) show, the gradient of the vertical footprint is severely affected by the footprint, while the gradient of the footprint along the horizontal direction is completely unaffected. This observation prompts to constrain the vertical footprint gradient while retaining the gradient along the footprint. Therefore, the present invention adopts UTV to remove the footprint noise. The UTV regularization is expressed as

[0080]

[0081] where, and Derivative operators in the horizontal and vertical directions respectively. In the present invention, the direction of the vertical footprint is regarded as the x-axis, while the direction along the horizontal footprint is regarded as the y-axis. λ1 and λ2 are regularization parameters. In this embodiment, the direction passing through the package outline can be called the xline direction, and the yline direction represents the direction along the package outline. Substituting equation (9) into (8), robust stripe removal can be obtained by minimizing the objective function containing unidirectional variation, as follows

[0082]

[0083] To solve equation (10) with respect to it is necessary to construct a model and impose additional constraints on the system equation.

[0084] 3. Model

[0085] In the prior art, the research on modeling mainly relies on manually crafted prior knowledge, and these prior assumptions are not always correct for It is necessary to use DL to model it in a data-driven manner. In this case, the clean image can usually be modeled as a non-linear autoregression:[[]]

[0086]

[0087] where the denoising model h (parameterized by Θ) is approximated by training a DNN on the clean seismic image (i.e., the FR network shown in Figure 2 ). Represent the restoration problem as a regression task:[[]]

[0088]

[0089] Then substitute equation (12) into equation (10), and for incorrect denoising results, a loss function is obtained, which contains the physical model of and the data-driven model of

[0090]

[0091] It can be found from equation (13) that the optimal parameter changes from to Θ, thus successfully deriving a new TDL model. Different from traditional matrix DLs, the challenge of optimizing equation (13) is that it needs to process high-dimensional seismic images, which mainly involves tensor operations rather than matrix operations. Another challenge is to interpret the dedicated DL network structure related to unsupervised footprint removal.

[0092] ​4. Regularize the deep convolutional autoencoder according to UTV

[0093] Use the version of DCAE to recover clear images from corrupted seismic images

[0094]

[0095] In the formula, DΘ(·) represents the encoder network, and Θ represents the training parameters related to the encoder. As follows.

[0096]

[0097] Among them, K represents the total number of iterations;

[0098] In contrast, EΘ(·) represents the decoder network, which upsamples and maps the features of the low-resolution encoder, and is defined as

[0099]

[0100] Substitute Equation (15) into Equation (13) to obtain

[0101]

[0102] 5. Optimize the FR network using BP

[0103] In the parameter learning stage, the present invention uses the BP algorithm to adjust the model parameter θ to minimize the in (17). To study the basic role of the Welsch function in eliminating unstable noise, it is necessary to derive the BP algorithm of RDCAE in detail. First, it is necessary to determine how gradient descent modifies W l-1 and B l :

[0104]

[0105]

[0106] Among them, α represents the learning rate. As the most critical hyperparameter, the learning rate determines the step size of each iteration. These two formulas have two important effects on the working mode of gradient descent. The first is achieved by finding the partial derivative of, while treating B l as a constant. The detailed mathematical form of this term is as follows:

[0107]

[0108] First, is obtained by taking the derivative of (2), and the specific definition is as follows:

[0109]

[0110] where Z = Y n -X n,l represents the reconstruction error between Y n and X n,l .

[0111] Next, is obtained by taking the derivative of (9):

[0112]

[0113] where div(·) calculates the divergence of a given matrix. The second key step is to focus on the calculation of . Similar to , this term can be more specifically defined as:

[0114]

[0115] Now, calculate and Take the derivative of (1) with respect to W l-1 as follows: as follows:

[0116]

[0117] where σ′ is the derivative of σ with respect to the argument, and σ is the function that upsamples and maps its features; then, take the derivative of (1) with respect to the bias B l as follows:

[0118]

[0119] b (k) , are parameters of the gradient descent algorithm, initially assigned 0, and are iteratively updated in the algorithm through equations (18)-(25).

[0120] By deriving the above derivatives, key insights into BP can be obtained. At the same time, it is crucial to understand how to decompose equations (20) and (23) into new robust weighted expressions for alternating updates and Of course, a comprehensive mathematical explanation of this problem far exceeds the scope of the present invention. In addition, it should be noted that the selection of α, C, and λ as the most relevant parameters is discussed in the "Parameter Settings" section below.

[0121] For the function h Θ (·) in equation (17), a convolutional autoencoder can be employed, which takes Y n,lAs the input to obtain the final footprint removal result. The FR network structure of the present invention is as Figure 2 shown, Figure 2 Figure Figure 2 shows the 19-layer U-Net architecture of the FR network, where symmetric skip connections, strided convolutions, and maxpool are used to maximize multi-scale information and widen the receptive field. Then, the rectified linear unit (ReLU)1 non-linearity is applied to each convolutional layer until the final layer, which has a 3×3 dimension. Figure 2 In Figure 2 , Noisy Patches are noise blocks, Denoised Patches are denoised blocks, Encoder is the encoding part, and Decoder is the decoding part.

[0122] The FR network is trained using unsupervised training samples, specifically by cropping the original time-slice image {Y} into overlapping or non-overlapping patch images to obtain sufficient unsupervised training samples; the FR network is trained based on the obtained unsupervised training samples using the backpropagation (BP) algorithm, and the trained FR network is used to completely separate the footprint noise and useful signals.

[0123] The effects of the present invention are described below in conjunction with specific data:

[0124] First, parameter configuration is performed

[0125] In the FR-Net model, there are two trade-off parameters in the objective function that need to be configured: λ1 and λ2. Here, in this embodiment, λ1 = 6×10 4 and λ2 = 4×10 5 are used as synthetic data, λ1 = 4.5×10 4 and λ = 3×10 5 are for the real Penobscot work area data, λ1 = 5×10 4 and λ2 = 3×10 5 are for the real Kerry-3D work area data. To train the FR-Net, in this embodiment, the Adam optimizer is used to minimize the loss function, and its optimal learning rate depends on the FR-Net model structure and the training data set. Generally, for synthetic data and real Kerry-3D work area data, the learning rate of the FR-Net is set to 1.0×10 -5 . For the real Penobscot work area data, the learning rate of the FR-Net is set to 1.0×10 -4 . The standard BP algorithm ensures that the weight updates are performed in batch mode. For synthetic data and real Kerry-3D field data, the batch size is set to 5. For synthetic data and real Kerry-3D field data, as well as real Penobscot field data, the batch size is set to 20.

[0126] Secondly, verify the synthetic data

[0127] The FR-Net model of the present invention was tested on a three-dimensional synthetic dataset, which was generated by the open-source code in "W. Chen, O. M. Saad, H. Wang, and Y. Chen, “Statistics-guided residual dictionary learning for footprint noise removal,” IEEE Trans. Geosci. Remote Sens., vol. 60, pp. 1–11, 2022, Art no. 4502011." Next, a footprint pattern with vertical stripes was added, and the pattern decayed with the decay of the in-line, as Figure 3 (a) and Figure 5 (a) shown. After this coherent noise was added, the signal-to-noise ratio dropped to 1.5 dB. Note that the FR-Net did not see the original seismic image at all because it was only implemented to calculate the signal-to-noise ratio value. In this experiment, the preprocessing of the present invention would have to segment the noisy seismic image into 8x8 patches, and all the patches could be fed into the FR-Net. Figure 3 In which the abscissa is the cross-line seismic interpretation profile (Xline), and the ordinate is the inline seismic interpretation profile (Inline).

[0128] The comparison of two constant slices (at 0.8 seconds) of different datasets is shown in Figure 5 and Figure 6 . Figure 5 and Figure 6 show the comparison of two constant slices of different datasets, Figure 5 and Figure 6 In, it is easy to find that the proposed method results in the fewest residual footprints. While the SOTA method fails in removing footprint noise. In addition, this embodiment also provides a comparison of a single trace contaminated by unstable noise for a more intuitive observation of the signal leakage situation, as Figure 4 shown. It is obvious that the result of RDCAF is closer to the ground truth waveform ratio result than the results of the following: other SOTA methods, which deviate greatly from the data. In addition to the visual comparison. The quantitative comparison between FR-Net and SOTA is shown in Table I. The FR-Net model of the present invention achieved a larger value (36.00 dB) than DRR, CBDNet, and SOTA. The DRR, CBDNet, and SGRDL technical values are 10.29, 20.69, and 20.10 dB respectively. From Figure 5 , Figure 6 ,Figure 4 As shown in Table 1, it can be seen that the proposed method achieves effective footprint suppression without any damage to the structure.

[0129] Figure 4 In [the figure], the abscissa is the time direction (Time) of the seismic data, and the ordinate is the signal amplitude. Figure 5 In [the figure], the abscissa is the seismic interpretation profile of the tie line (Xline), and the ordinate is the seismic interpretation profile of the main survey line (Inline).

[0130] Table 1 Performance comparison of the proposed FR-NET and existing SOTA methods on the synthetic dataset

[0131] Method Synthetic Dataset 1 Synthetic Dataset 2 DRR 10.29 dB 14.82 dB CBDNet 20.69 dB 10.49 dB SGRDL 20.10 dB 20.36 dB Proposed FR-Net 36.00 dB 38.49 dB

[0132] Then, the real Penobscot field data is verified.

[0133] To verify the superiority and effectiveness of the method in practice, the FR network is applied to two different real field datasets: Penobscot-3D and Kerry-3D. As described in Section 5.B, these real field data cover a wide range of footprint noise levels, which helps to demonstrate the adaptability of the proposed FR network to various noise intensities. Therefore, according to the footprint noise level, the entire real field data test currently includes the following two sub-experiments:

[0134] In the first example, the effectiveness and accuracy of the FR network are demonstrated on the Penobscot-3D dataset. As Figure 7 (a) shows, the Kerry3D dataset exhibits significant acquisition footprints, which may pose significant engineering challenges to Penobscot. Specifically, Figure 7 (b)-(e) and Figure 8 (a)-(d) respectively show the denoising results and the corresponding footprints removed by using the proposed FR Net method and the SOTA method. From Figure 7 and Figure 8 it can be clearly seen that the FR network can effectively remove footprints without reducing the resolution of the seismic image, while the SOTA algorithm often produces over-smoothed image edges or leaves residual footprints in the resulting image. To further compare the footprint removal results, two lines in Figure 7 (a) are selected for cross-section inspection, as Figure 9 and Figure 10 shown. Undoubtedly, all the results are as shown in the figure. Figure 9 and Figure 10 repeat the first finding, thus confirming the following conclusion: the FR network method achieves significant footprint attenuation without signal leakage and maintains good edges.

[0135] In the second example, Kerry 3D field data with footprint noise is used to further test the FR network proposed by the present invention. As before, the four methods are first compared in the time slice, as Figure 11 and Figure 12 shown. In terms of visual quality, except for removing the footprint noise, the results generated by the proposed FR network are similar to the original seismic images, which is better than other SOTA methods. Similarly, Figure 13 and Figure 14 show two lines selected from Figure 11 (a) to further study the footprint noise removal performance.

[0136] As Figure 13 and Figure 14 shown. Obviously, FR-Net deletes less meaningful signals in the removed noisy data, while SOTA always causes too much damage to useful signals.

[0137] The present invention only adds a conventional term UTV to the FR-Net cost function. By adding a conventional term UTV to its cost function, the network structure is not changed and no inference overhead is generated, making the FR-Net of the present invention almost remain unchanged compared with the standard U-Net in terms of computational complexity.

[0138] Those of ordinary skill in the art will realize that the embodiments described herein are to assist the reader in understanding the principles of the present invention and should be understood that the scope of protection of the present invention is not limited to such specific statements and embodiments. For those skilled in the art, various changes and modifications can be made to the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the scope of the claims of the present invention.

Claims

1. A seismic acquisition footprint denoising method based on unsupervised model-driven deep learning, characterized in that Including: S1. Construct unsupervised training samples based on 3D seismic data; S2. Construct an FR network, where the FR network adopts a U-Net architecture; the calculation formula corresponding to step S2 is: Among them, represents the output result of the FR network, D Θ (·) represents the encoder network, Θ represents the training parameters related to the encoder, E Θ (·) represents the decoder network, represents the input of the FR network; Θ is solved by minimizing the cost function, and the cost function is expressed as: where, || ||2 is the 2-norm, and || ||1 is the 1-norm, and are the derivative operators in the horizontal and vertical directions respectively, and λ1 and λ2 are regularization parameters; S3. Use the training samples in step S1 to train the FR network constructed in step S2; S4. Input the seismic data to be processed into the trained FR network, thereby completing footprint removal and obtaining the final result.

2. The seismic acquisition footprint denoising method based on unsupervised model-driven deep learning according to claim 1, characterized in that The implementation process of step S1 is: flatten the 3D seismic data into multiple time-slice images; then, crop these time-slice images into overlapping or non-overlapping patch images, and obtain training samples based on these patch images.

3. A seismic acquisition footprint denoising method based on unsupervised model-driven deep learning according to claim 2, characterized in that, Use the BP algorithm to solve the minimization of the cost function, and the solution process is: W in gradient descent l-1 and B l The update expressions are as follows: where α represents the learning rate, and l represents the layer serial number of the FR network; Regarding B l as a constant, solve for as follows: Among them, Z = Y n - X n,l , Y n is the input of the nth iteration, and X n,l is the output of the nth iteration, div(·) represents calculating the divergence of a given matrix; Regarding W l-1 as a constant, solve for : Among them, σ′ is the derivative of σ with respect to the argument, and σ is a function for upsampling and mapping its features. b (k) 、 are parameters of the gradient descent algorithm, and k represents the iteration number.

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