A method for reconstructing low-frequency signals of marine seismic data based on a transformer
By constructing alternating cascaded Transformer coding unit groups and a multi-head self-attention mechanism, the problem of missing low-frequency signals in marine seismic data was solved, achieving high-precision low-frequency signal reconstruction and model convergence. This method is applicable to various marine seismic data acquisition methods and improves the accuracy and efficiency of seismic data processing.
Patent Information
- Application Number
- CN202611375347.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-09-07
- Publication Date
- 2026-11-03
AI Technical Summary
Existing technologies for marine seismic data processing suffer from the problem of missing low-frequency signals, resulting in poor convergence of full waveform inversion and difficulty in achieving high-precision modeling of the distribution of subsurface medium physical parameters. Furthermore, existing Transformer models have limited ability to capture multi-scale waveform features of seismic signals, are difficult to train deep networks, and have an imbalance between computational efficiency and long-range modeling capability, lacking a dedicated architecture for marine seismic data.
The architecture of 'input convolutional module - alternating cascaded Transformer coding unit group - output convolutional module' is adopted. It combines the windowed multi-head self-attention mechanism (W-MSA) and the shifted windowed multi-head self-attention mechanism (SW-MSA) to run alternately. Through multi-head self-attention calculation and Pre-LN double residual structure, a training sample set is constructed and gradient backpropagation training is performed to realize the low-frequency signal reconstruction of marine seismic data.
It significantly improves the relative error and time-domain waveform correlation coefficient of spectral reconstruction of 0–8 Hz seismic data, enhances the convergence speed and computational efficiency of the model, and is applicable to towed cable and submarine cable seismic data, with good generalization and practicality.
Smart Images
Figure CN123029599A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of seismic data processing technology, and in particular relates to a method for reconstructing low-frequency signals from marine seismic data based on Transformer. Background Technology
[0002] In seismic exploration, due to limitations imposed by surface conditions and acquisition costs, acquired data often suffers from irregularities, missing data, or insufficient sampling, affecting the accuracy of migration imaging and inversion. Therefore, data reconstruction is crucial. Traditional reconstruction methods, including wave equation methods, low-rank constraint methods, predictive filtering methods, and sparse transform methods (such as Curvelet transform), while effective to some extent, have limitations when handling irregular or irregularly missing data. In recent years, deep learning, due to its powerful nonlinear mapping capabilities, has been widely applied to seismic data processing. Existing research has utilized generative adversarial networks, residual networks, and convolutional autoencoders to achieve interpolation and reconstruction.
[0003] Full Waveform Inversion (FWI) technology utilizes all kinematic and dynamic information (amplitude, phase, travel time, etc.) in seismic data and is currently the most accurate method for modeling the distribution of subsurface media properties. Based on the first-order Born approximation of weak scattering, FWI is a strongly nonlinear inverse problem solved within a local optimization framework, and its convergence is highly dependent on low-frequency signals in the measured seismic data. However, in actual marine seismic data acquisition, due to the high-frequency wavefield excited by airguns and the physical limitations of detectors, it is difficult to effectively respond to low-frequency signals, resulting in the frequent absence of low-frequency signals in measured marine seismic data. This lack of low-frequency data can cause "cycle skipping" problems in FWI, making the inversion prone to getting trapped in local minima and leading to unreliable inversion results.
[0004] To address the problem of missing low-frequency signals, some scholars have proposed methods based on modulation and demodulation model theory to reconstruct the corresponding low-frequency signals from the missing high-frequency signals. However, this process requires nonlinear demodulation operators and involves changes in the global wavefield distribution, making it difficult to implement. In recent years, the Transformer model has been introduced into the field of seismic data processing due to its powerful global feature extraction capabilities. However, existing methods still have shortcomings in the following aspects: (1) They have limited ability to capture multi-scale waveform features of seismic signals, making it difficult to simultaneously consider local waveform details and long-period low-frequency trends; (2) Deep network training is difficult and convergence is slow, affecting model performance; (3) The balance between computational efficiency and long-range modeling capability needs to be optimized; (4) Dedicated architectures for low-frequency signal reconstruction of marine seismic data (towed cables, submarine cables) are not yet perfect. Summary of the Invention
[0005] The purpose of this invention is to provide a method for reconstructing low-frequency signals from marine seismic data based on Transformer, aiming to solve the problems mentioned in the background art.
[0006] The present invention is implemented as follows: a method for reconstructing low-frequency signals from marine seismic data based on Transformer, comprising the following steps:
[0007] Step 1: Construct a low-frequency reconstruction network;
[0008] The low-frequency reconstruction network adopts an architecture of "input convolutional module - alternating cascaded Transformer coding unit group - output convolutional module"; the input convolutional module uses a 3×1 one-dimensional convolutional kernel to perform initial feature extraction and channel dimensionality upscaling of the seismic traces; the alternating cascaded Transformer coding unit group consists of 8 to 12 layers of coding units stacked alternately to achieve multi-scale feature extraction from shallow to deep; the output convolutional module uses convolutional kernels of the same size to map high-dimensional features back to the original seismic trace dimension;
[0009] Step 2: Establish an attention calculation mode in the coding unit that alternates between W-MSA and SW-MSA;
[0010] The seismic feature sequence is divided into non-overlapping equal-length windows along the time axis using W-MSA, and self-attention is calculated independently only within the window; the feature sequence is then cyclically shifted by half the window length using SW-MSA, and the windows are re-divided and self-attention calculations are performed within the window; the two methods are stacked alternately.
[0011] Step 3: Perform multi-head self-attention calculation;
[0012] The input features are divided into multiple subspaces along the channel dimension, with each subspace corresponding to an independent attention head; each head is independently transformed linearly to generate the query matrix. Key matrix Sum matrix ;calculate and The attention weights are obtained by transposing the dot product, dividing by the square root of the single-head dimension for scaling, and then normalizing using Softmax. Weighted summation yields the single-head attention output; the outputs of each attention head are concatenated along the channel dimension and then fused through linear transformation, combined with the LN double residual structure to output the final feature.
[0013] Step 4: Construct the training sample set;
[0014] A 0-8Hz high-pass filter is applied to the complete frequency band label samples to remove the low-frequency components to be reconstructed, resulting in network input samples. The input samples and label samples correspond one-to-one to form "input-label" sample pairs, which are divided into training set, validation set and test set according to a preset ratio.
[0015] Step 5: Train the low-frequency reconstruction network;
[0016] The training set samples are input into the low-frequency reconstruction network in batches. The total loss between the output and the label is calculated. Gradient backpropagation is performed based on the total loss. An adaptive optimization algorithm is used to update the weights of each layer of the network. After each round of complete training, the network performance is tested on the validation set. The relative error of the low-frequency band spectrum and the correlation coefficient of the time-domain waveform are used as evaluation indicators. The weights with the best validation performance are saved.
[0017] Step 6: Preprocess the data to be reconstructed;
[0018] The marine seismic data volume to be reconstructed is split into single-channel seismic data sequences, and random noise suppression and intra-channel amplitude normalization are performed sequentially on each channel:
[0019] Step 7: End-to-end reasoning reconstruction;
[0020] The preprocessed single-channel data is input into the trained low-frequency reconstruction network. After feature upscaling is completed by the input convolution module, it is sequentially processed through 8 to 12 layers of W-MSA and SW-MSA cascaded coding units to extract multi-scale global features layer by layer. Finally, it is mapped back to the original dimension by the output convolution module to output the reconstructed 0-8Hz low-frequency seismic signal.
[0021] In a further technical solution, the marine seismic data includes towed cable seismic data and submarine cable seismic data.
[0022] In a further technical solution, in step 6, random noise suppression employs an adaptive filtering method.
[0023] In a further technical solution, the alternating cascaded Transformer coding unit group of the low-frequency reconstruction network is composed of 8, 10, or 12 layers of coding units stacked alternately.
[0024] The present invention provides a method for reconstructing low-frequency signals from marine seismic data based on Transformer, which has the following advantages:
[0025] (1) For the spectral reconstruction of 0-8Hz seismic data, the relative error can be significantly reduced, the correlation coefficient of time-domain waveform can be improved, and the low-frequency phase and amplitude fidelity can be significantly optimized.
[0026] (2) For conventional seismic traces of more than 1,000 points, the single-trace data inference speed is 3 to 5 times faster than the global Transformer architecture, and the memory usage is reduced by more than 60%.
[0027] (3) The Pre-LN dual residual structure effectively solves the problems of difficult training and slow convergence of deep Transformer networks, and the convergence speed of the model is significantly improved.
[0028] (4) It is applicable to various marine seismic data (towed cable, submarine cable) and has good generalizability and practicality. Attached Figure Description
[0029] Figure 1 For Transformer multi-head self-attention architecture;
[0030] Figure 2 Network structure for low-frequency reconstruction networks;
[0031] Figure 3 The data consists of marine towed seismic exploration data and low-frequency signals (where (a) is the missing low-frequency seismic profile actually acquired, (b) is the true low-frequency component obtained by applying a 0-8Hz low-pass filter to the original data, and (c) is the reconstruction result output by this method).
[0032] Figure 4 The data includes seismic exploration data and low-frequency signals for submarine cables (where (a) is the actual profile under the geometry of fixed receiving point on the seabed and sea surface source under sea-based excitation, (b) is the real low-frequency label obtained by low-pass filtering from 0 to 8 Hz, and (c) is the reconstruction result of this method).
[0033] Figure 5 This is a flowchart illustrating a method for reconstructing low-frequency signals from marine seismic data based on Transformer, provided as an embodiment of the present invention. Detailed Implementation
[0034] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.
[0035] The specific implementation of the present invention will be described in detail below with reference to specific embodiments.
[0036] like Figure 1 , Figure 2 and Figure 5 As shown, an embodiment of the present invention provides a method for reconstructing low-frequency signals from marine seismic data based on Transformer, comprising the following steps:
[0037] Step 1: Construct a low-frequency reconstruction network;
[0038] The low-frequency reconstruction network adopts an architecture of "input convolutional module - alternating cascaded Transformer coding unit group - output convolutional module". The input convolutional module uses a 3×1 one-dimensional convolutional kernel to perform initial feature extraction and channel dimensionality upscaling of the seismic traces; the alternating cascaded Transformer coding unit group consists of 8 to 12 layers of coding units stacked alternately (specifically, it can be 8, 10, or 12 layers of coding units stacked alternately), realizing multi-scale feature extraction from shallow to deep; the output convolutional module uses convolutional kernels of the same size to map high-dimensional features back to the original seismic trace dimension.
[0039] Step 2: Establish an attention calculation mode in the encoding unit where window multi-head self-attention mechanism (W-MSA) and shift window multi-head self-attention mechanism (SW-MSA) operate alternately;
[0040] W-MSA divides the seismic feature sequence into non-overlapping windows of equal length along the time axis, and self-attention is calculated independently only within the window, reducing the global computational complexity to the local window level. SW-MSA performs a half-window length cyclic shift on the feature sequence and then re-divides the windows and performs self-attention calculation within the window, enabling information exchange between adjacent windows. The two methods are stacked alternately to balance computational efficiency and long-range modeling capabilities.
[0041] Step 3: Perform multi-head self-attention calculation;
[0042] The input features are divided into multiple subspaces along the channel dimension, with each subspace corresponding to an independent attention head; each head is independently transformed linearly to generate the query matrix. Key matrix Sum matrix ;calculate and The attention weights are obtained by transposing the dot product, dividing by the square root of the single-head dimension for scaling, and then normalizing using Softmax. Weighted summation yields the single-head attention output; the outputs of each attention head are concatenated along the channel dimension and then fused through linear transformation. Combined with the LN (layer normalization) double residual structure (LN is placed before the attention and MLP sub-layers, and the two recursive formulas correspond to the sum of the residuals of the attention branch and the MLP branch, respectively), the final feature is output.
[0043] Step 4: Construct the training sample set;
[0044] A 0-8Hz high-pass filter is applied to the complete frequency band label samples to remove the low-frequency components to be reconstructed, simulating the low-frequency loss caused by the high-frequency excitation of the air gun and the physical limitations of the detector in actual acquisition, thus obtaining the network input samples. The input samples and label samples correspond one-to-one to form "input-label" sample pairs, which are divided into training set, validation set and test set according to a preset ratio of 8:1:1, and used for weight update, optimal model selection and final quantitative evaluation, respectively.
[0045] Step 5: Train the low-frequency reconstruction network;
[0046] The training set samples are input into the low-frequency reconstruction network in batches, the total loss value between the output and the label is calculated, gradient backpropagation is performed based on the total loss, and the weights of each layer of the network are updated using an adaptive optimization algorithm. After each round of complete training, the network performance is tested on the validation set, with the relative error of the low-frequency spectrum as the core evaluation index, and the correlation coefficient of the time-domain waveform is monitored. The optimal weights for validation performance are continuously saved until the performance no longer improves or reaches the preset number of rounds.
[0047] Step 6: Preprocess the data to be reconstructed;
[0048] The marine seismic data volume to be reconstructed is split into single-channel seismic data sequences by channel. Random noise suppression and intra-channel amplitude normalization are performed sequentially for each channel: noise suppression uses adaptive filtering to remove random interference from acquisition and improve the input signal-to-noise ratio; amplitude normalization maps the amplitude range of a single channel to the input distribution range during training to ensure that the inference input is consistent with the distribution of training data and matches the network input format.
[0049] Step 7: End-to-end reasoning reconstruction;
[0050] The preprocessed single-channel data is input into the trained low-frequency reconstruction network. After feature upscaling by the input convolution module, it is sequentially passed through 8 to 12 layers of W-MSA and SW-MSA cascaded coding units to extract multi-scale global features and discard redundant information. Finally, it is mapped back to the original dimension by the output convolution module to output the reconstructed 0-8Hz low-frequency seismic signal, thus obtaining the low-frequency prediction results of towed cable data and submarine cable data.
[0051] Figure 3 The reconstruction results are compared using the towed cable acquisition method at sea. A total of 150 channels were recorded, with a recording time of 0 to 4.8 seconds. The horizontal axis represents the channel number, and the vertical axis represents the time (s). The red and blue colors alternate to indicate the positive and negative phases of the waveform amplitude. Figure 3 (a) is the missing low-frequency seismic profile acquired in practice. The phase axis is generally inclined and has rich waveform details, but it is mainly composed of mid-to-high frequency components. The phase axis in the deep layer (below 4.0s) is weak in energy and has poor continuity due to the limitation of the main frequency. This corresponds to the situation in actual acquisition where the high main frequency excitation of the air gun and the low frequency response of the detector are insufficient. This is used as the network input. Figure 3 (b) The real low-frequency components obtained by applying a 0-8Hz low-pass filter to the original data are used as training labels and comparison benchmarks. It can be seen that the low-frequency profile in phase axis is significantly smooth, coarse and continuous, and the macroscopic trend of the tilted wave group is clear. The yellow box in the figure marks the deep weak reflection area of 4.0-4.8s as the key area for investigation. Figure 3 (c) shows the reconstruction result output by this method. (and) Figure 4 (b) Comparison shows that the travel position, bending shape, and phase change of the tilted phase axis are highly consistent, and the amplitude distribution is consistent; the deep weak low-frequency signal within the yellow box is also stably recovered, with no obvious artifacts or phase axis breaks. Quantitatively, the time-domain correlation coefficient between the reconstructed waveform and the actual low frequency reaches over 0.95, and the relative error of the 0~8Hz spectrum is reduced by over 40%, indicating that the network has achieved high-fidelity low-frequency reconstruction of the tow cable data.
[0052] Figure 4 This section compares the reconstruction results obtained using submarine cable acquisition methods, totaling 223 channels with a recording duration of 0–3.5 seconds. The coordinate axes have the same meaning as... Figure 3 Consistent. Figure 4 (a) is the actual profile under the geometry of the fixed receiving point on the seabed and the sea surface source under the excitation of the observation. The phase axis is generally arc-shaped (bent upward), which is significantly different from the tilted linear phase axis shape of the towed cable data. The wave field is more complex due to the seabed coupling and the influence of converted waves, and it also lacks low-frequency components as network input. Figure 4 (b) is the true low-frequency label obtained by low-pass filtering from 0 to 8 Hz. The macroscopic low-frequency trend of the arc-shaped phase axis is continuous and smooth, and the outline of the arc-shaped wave group in the middle and deep parts is clear. Figure 4 (c) shows the reconstruction result of this method. (and) Figure 4 (b) Comparison shows that the curvature, vertex position, wing extension range, and phase of the arc-shaped phase axis all match the actual low-frequency data. The low-energy arc-shaped wave group in the middle and deep regions is completely recovered without waveform distortion or spurious phase axes. This result indicates that the network accurately captures the arc-shaped low-frequency wave field patterns that differ from those of towed cable data without designing a separate structure for OBC data. Figure 3 The results collectively validate the adaptability of this method to both towed cable and OBC, two mainstream marine data acquisition methods, and its ability to generalize across observation systems.
[0053] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A method for reconstructing low-frequency signals from marine seismic data based on Transformer, characterized in that, Includes the following steps: Step 1: Construct a low-frequency reconstruction network, which adopts an architecture of "input convolutional module - alternating cascaded Transformer coding unit group - output convolutional module"; Step 2: Establish an attention calculation mode in the coding unit that alternates between W-MSA and SW-MSA; Step 3: Perform multi-head self-attention computation; divide the input features into multiple subspaces along the channel dimension, with each subspace corresponding to an independent attention head; each head independently performs a linear transformation to generate the query matrix. Key matrix Sum matrix ;calculate and The attention weights are obtained by transposing the dot product, dividing by the square root of the single-head dimension for scaling, and then normalizing using Softmax. Weighted summation yields the single-head attention output; the outputs of each attention head are concatenated along the channel dimension and then fused through linear transformation, combined with the LN double residual structure to output the final feature. Step 4: Construct the training sample set; Step 5: Input the training set samples into the low-frequency reconstruction network in batches, calculate the total loss value between the output and the label, perform gradient backpropagation based on the total loss, and update the weights of each layer of the network using an adaptive optimization algorithm; test the network performance after each round of complete training, using the relative error of the low-frequency spectrum and the correlation coefficient of the time-domain waveform as evaluation indicators, and save the weights with the best verification performance. Step 6: Divide the marine seismic data volume to be reconstructed into single-track seismic data sequences by track, and perform random noise suppression and intra-track amplitude normalization on each track in sequence: Step 7: Input the preprocessed single-channel data into the trained low-frequency reconstruction network. After feature upscaling by the input convolution module, the Transformer coding unit groups are alternately cascaded to extract multi-scale global features layer by layer. Finally, the output convolution module maps the data back to the original dimension and outputs the reconstructed 0~8Hz low-frequency seismic signal.
2. The method for reconstructing low-frequency signals from marine seismic data based on Transformer according to claim 1, characterized in that, In step 1, the input convolutional module uses a 3×1 one-dimensional convolutional kernel to perform initial feature extraction and channel dimensionality upscaling on the seismic traces; the alternating cascaded Transformer coding unit group consists of 8 to 12 layers of coding units stacked alternately to achieve multi-scale feature extraction from shallow to deep; the output convolutional module uses a convolutional kernel of the same size to map the high-dimensional features back to the original seismic trace dimension.
3. The method for reconstructing low-frequency signals from marine seismic data based on Transformer according to claim 2, characterized in that, In step 2, the seismic feature sequence is divided into non-overlapping equal-length windows along the time axis using W-MSA, and self-attention is calculated independently only within the window; the feature sequence is then cyclically shifted by half the window length using SW-MSA, and the windows are re-divided and self-attention calculation within the window is performed; the two are stacked alternately.
4. The method for reconstructing low-frequency signals from marine seismic data based on Transformer according to claim 1, characterized in that, The specific steps of step 4 are as follows: A 0-8Hz high-pass filter is applied to the complete frequency band label samples to remove the low-frequency components to be reconstructed, resulting in network input samples. The input samples and label samples correspond one-to-one to form "input-label" sample pairs, which are then divided into training set, validation set, and test set according to a preset ratio.
5. The method for reconstructing low-frequency signals from marine seismic data based on Transformer according to claim 2, characterized in that, The alternating cascaded Transformer coding unit group of the low-frequency reconstruction network is composed of 8, 10 or 12 layers of coding units stacked alternately.
6. The method for reconstructing low-frequency signals from marine seismic data based on Transformer according to claim 1, characterized in that, The marine seismic data includes towed cable seismic data and submarine cable seismic data.
7. The method for reconstructing low-frequency signals from marine seismic data based on Transformer according to claim 1, characterized in that, In step 6, random noise suppression employs an adaptive filtering method.