Method and system for five-dimensional seismic data reconstruction based on seismic trace implicit neural representation

Abstract

The application discloses a five-dimensional seismic data reconstruction method and system based on seismic trace implicit neural representation, and belongs to the technical field of seismic signal processing. The method first pre-processes original five-dimensional seismic data to obtain normalized four-dimensional spatial coordinates; a T-NeRSI network is constructed, the coordinate expression capability is enhanced through Fourier feature mapping, an MLP encoder is used to extract latent features, and a one-dimensional deconvolution decoder is used to output complete seismic traces; a composite loss function of Huber loss and spatial structure regularization is used for unsupervised training; and target coordinates are input to generate reconstructed seismic traces. The application does not require regular gridding processing, can directly use irregular sampling data for training, can still realize high-precision and high-efficiency five-dimensional seismic data reconstruction under high missing rate and strong noise conditions, and can be widely applied to the seismic data processing link in oil and gas exploration.

Description

Technical Field

[0001] This invention belongs to the field of earthquake signal processing technology, specifically relating to a five-dimensional earthquake data reconstruction method and system based on implicit neural representation of seismic traces. Background Technology

[0002] The exploration and development of underground resources such as oil and natural gas place high demands on the accuracy of seismic data processing. Seismic exploration, which involves artificially generating seismic waves and receiving reflected signals from the subsurface medium, acquires seismic data reflecting subsurface structures and reservoir characteristics, and is a crucial technical means in oil and gas resource exploration. During 3D seismic acquisition, pre-stack seismic data typically contains not only temporal dimensions but also multiple spatial dimensions. In the common centroid domain, five-dimensional seismic data can generally be represented by the time dimension and four spatial dimensions: the x-coordinate of the common centroid (CMP), the y-coordinate of the CMP, the offset, and the azimuth. Compared to 2D or 3D seismic data processing, 5D seismic data can more fully preserve acquisition geometric information such as offset and azimuth, which is beneficial for improving the reliability of subsequent migration imaging, amplitude variation analysis with offset, amplitude variation analysis with azimuth, and reservoir prediction.

[0003] However, in actual seismic acquisition, factors such as acquisition cost, surface environment, obstacle distribution, construction conditions, and limitations in detector deployment often prevent the acquired five-dimensional seismic data from forming an ideal, regular, and densely sampled data volume. On the one hand, some seismic traces are missing due to construction obstacles, equipment malfunctions, or limitations in acquisition conditions; on the other hand, actual observation locations are often irregularly distributed, resulting in non-uniform sampling of seismic traces in dimensions such as CMP coordinates, offset, and azimuth. Simultaneously, field-acquired data may also be affected by random noise, anomalous amplitudes, and other interference factors, leading to sparse sampling, irregular sampling, and noise contamination in the original five-dimensional seismic data. These problems disrupt the spatial continuity of the seismic wavefield, reduce the traceability of phase axes, and consequently affect the quality of seismic imaging and the accuracy of subsequent interpretation results. Therefore, high-precision reconstruction of missing seismic traces is a crucial step in five-dimensional seismic data processing.

[0004] Existing five-dimensional seismic data reconstruction methods mainly include prediction filtering-based methods, sparse transform-based methods, low-rank constraint-based methods, and wave equation-based methods. Prediction filtering methods typically utilize the predictability of seismic data in the time-space, frequency-space, or frequency-wavenumber domains, estimating missing seismic traces through prediction error filters. Sparse transform methods usually assume that effective seismic signals have sparse representations in transform domains such as Fourier transform, Radon transform, wavelet transform, Curvelet transform, or Seislet transform, and recover missing data through inversion. Low-rank constraint methods typically organize seismic data into matrices or tensors, using the low-rank structure of the seismic data for completion. Wave equation methods combine velocity models and propagation operators to recover missing records based on wavefield propagation laws. While these methods can improve the lateral continuity of seismic data to some extent, they still have significant shortcomings in practical five-dimensional seismic data reconstruction.

[0005] First, traditional reconstruction methods typically rely on manual experience to set processing parameters such as filter length, window size, sparsity threshold, rank constraint parameters, or iteration termination conditions. Different work areas, varying structural complexities, and different missing proportions of data often require parameter readjustment, making the process highly dependent on experience and lacking adaptability. Second, five-dimensional pre-stack seismic data is massive in scale, and traditional iterative optimization methods incur high computational costs when processing large-scale data, making it difficult to balance reconstruction accuracy and processing efficiency. Third, many traditional methods assume the data to be processed is located on a regular grid, while actual acquired data is usually irregularly distributed. To adapt to regular grid algorithms, it is often necessary to first merge irregularly sampled seismic traces to the nearest regular grid points using methods such as binning. However, this regularization process introduces spatial location errors and may further cause amplitude and phase errors; for areas with high-dipping reflections, faults, fractures, or small-scale structural development, it may also lead to the loss of local high-frequency details and true acquired geometric information, thus affecting the fidelity of the reconstruction results.

[0006] To avoid errors introduced by regular gridding, existing methods have attempted to directly process irregularly sampled data using non-uniform Fourier transform, leakage-resistant Fourier transform, non-uniform Curvelet transform, or non-equidistant sampling operators. These methods can preserve information about the original acquisition locations to some extent, but they typically require complex iterative solutions under irregular sampling conditions, resulting in high computational complexity. Furthermore, traditional methods often employ local windowing strategies to adapt to the non-stationarity of seismic data; however, the lack of sufficient global correlation between windows can limit the ability to express the overall wavefield structure, leading to unsatisfactory spatial continuity and global consistency in the reconstruction results.

[0007] In recent years, deep learning methods have been applied to seismic data denoising, interpolation, and reconstruction tasks. Deep neural networks can learn nonlinear mapping relationships in seismic data, reducing the impact of manual parameter selection to some extent. However, many deep learning interpolation methods rely on pairs of sparse and complete data as training samples, while complete and reliable labeled data is often difficult to obtain in real five-dimensional seismic data. Although self-supervised learning methods can construct training samples by artificially degrading data, further degradation of already highly sparse or severely missing five-dimensional seismic data will make the input information even more insufficient, affecting the network's ability to learn stable reconstruction mappings. In addition, traditional two-dimensional or three-dimensional convolutional neural networks are mainly suitable for regular grid data and cannot directly and fully utilize all spatial information such as CMP coordinates, offsets, and azimuths in five-dimensional seismic data; directly using high-dimensional convolutional structures will result in a large number of parameters and computational burden.

[0008] Implicit neural representation methods offer a novel approach to reconstructing irregularly sampled seismic data. These methods typically treat discrete seismic data as samples of a continuous function at coordinate locations and utilize neural networks to establish a mapping between coordinates and amplitude values, allowing prediction results to be queried at any target location. This approach has the potential to directly handle irregular coordinate inputs and can reduce information loss caused by regular gridding. However, existing seismic data reconstruction methods based on implicit neural representations still have shortcomings: some methods use both temporal and spatial dimensions as input and predict the amplitude value point-by-point for each time sampling point. This point-based output method fragments the continuous structure along the time direction within the same seismic trace, failing to fully utilize the regular sampling and continuous variation characteristics of the seismic trace itself; furthermore, in large-scale five-dimensional pre-stack data reconstruction, point-by-sampling prediction generates a large amount of repetitive query computation, resulting in low training and inference efficiency. Other methods, while attempting to improve output efficiency, struggle to simultaneously maintain the ability to directly learn from irregularly sampled coordinates.

[0009] Furthermore, real-world seismic data often contains noise and anomalous amplitudes. If the reconstruction model only fits the error based on observed seismic traces, large anomalous errors may adversely affect the model parameter updates, resulting in more residual noise or unstable local amplitudes in the reconstruction results. Simultaneously, five-dimensional seismic data exhibits spatial correlation in CMP coordinates, offsets, and azimuth. If the training process lacks constraints on the relationships between predicted results of adjacent spatial locations, problems such as discontinuities between adjacent seismic traces, local abrupt changes, or artifacts may occur, affecting the spatial consistency of the reconstructed five-dimensional seismic data.

[0010] Therefore, existing technologies still require a five-dimensional seismic data reconstruction method that can directly utilize the real spatial coordinates of irregularly sampled seismic traces, reduce regular gridding errors, and balance the temporal continuity, spatial continuity, noise resistance, stability, and reconstruction efficiency of seismic traces. Summary of the Invention

[0011] The technical problem to be solved by this invention is to address the shortcomings of the prior art by providing a five-dimensional seismic data reconstruction method and system based on implicit neural representation of seismic traces. This method addresses the issues that actual five-dimensional seismic data is limited by acquisition conditions, resulting in irregular sampling, sparse sampling, and numerous missing traces. Traditional reconstruction methods rely on regular gridding, which easily introduces spatial location errors, amplitude errors, and phase errors. Existing point-by-point implicit neural representation methods suffer from insufficient utilization of seismic trace temporal continuity, low computational efficiency of point-by-sampling prediction, and insufficient spatial continuity and stability of reconstruction results under the influence of noise and anomalous amplitudes.

[0012] The present invention adopts the following technical solution: A five-dimensional seismic data reconstruction method based on implicit neural representation of seismic traces includes the following steps: The acquired raw five-dimensional seismic data is preprocessed to determine the four-dimensional spatial coordinates corresponding to each observed seismic trace and the amplitude sequence of the observed seismic traces arranged along the time direction. The four-dimensional spatial coordinates are then normalized to obtain normalized spatial coordinates, wherein the four-dimensional spatial coordinates are the coordinates in the raw five-dimensional seismic data excluding the time dimension. A T-NeRSI network is constructed, which includes a Fourier feature mapping module, an encoder, and a decoder. The Fourier feature mapping module is used to perform Fourier feature mapping on the normalized spatial coordinates to obtain high-dimensional coordinate features. The encoder is used to extract latent feature variables based on the high-dimensional coordinate features. The decoder is used to output a complete predicted seismic trace amplitude sequence along the time direction based on the latent feature variables. A training loss function is constructed based on the complete predicted seismic trace amplitude sequence and the corresponding observed seismic trace amplitude sequence, and the T-NeRSI network is trained according to the training loss function; wherein, the training loss function includes a Huber data reconstruction loss term and a spatial structure regularization loss term, the Huber data reconstruction loss term is used to constrain the amplitude error between the complete predicted seismic trace amplitude sequence and the corresponding observed seismic trace amplitude sequence, and the spatial structure regularization loss term is used to constrain the difference between predicted seismic traces at adjacent spatial locations; After normalizing the target spatial coordinates, the data is input into the trained T-NeRSI network to obtain the reconstructed seismic trace amplitude sequence at the corresponding location. Based on the reconstructed seismic trace amplitude sequences corresponding to multiple target spatial coordinates, the reconstructed five-dimensional seismic data is formed.

[0013] Preferably, the four-dimensional spatial coordinates include the x-coordinate of the CMP, the y-coordinate of the CMP, the offset distance, and the azimuth angle.

[0014] Preferably, the normalization process for the four-dimensional spatial coordinates includes: normalizing the coordinate values ​​of each observed seismic trace in the corresponding dimension according to the minimum and maximum values ​​of each dimension in all observation data, so as to obtain normalized spatial coordinates in the range of [0,1].

[0015] Preferably, the Fourier feature mapping module applies a set of predefined sine and cosine function transformations to each coordinate component in the normalized spatial coordinates to generate high-dimensional coordinate features containing multiple frequency components.

[0016] Preferably, for each frequency component , The Fourier feature mapping module generates sine and cosine features corresponding to the normalized spatial coordinates, specifically as follows:

[0017]

[0018] in, Indicates the number of frequency components. The coordinates are normalized four-dimensional space coordinates. Represents the normalized spatial coordinates within [0,1].

[0019] Preferably, the encoder is constructed based on MLP, and the encoder includes a fully connected layer and a nonlinear activation layer connected in sequence. After the high-dimensional coordinate features are nonlinearly mapped by the fully connected layer and the nonlinear activation layer, potential feature variables representing the corresponding seismic trace wavefield information are obtained.

[0020] Preferably, the nonlinear activation layer uses the ReLU activation function.

[0021] Preferably, the decoder includes a nonlinear transformation layer, a one-dimensional deconvolutional neural network decoding module, and a one-dimensional convolutional output layer; wherein, the nonlinear transformation layer is used to adjust the dimensions and adapt the features of the latent feature variables to obtain an initial feature tensor, the one-dimensional deconvolutional neural network decoding module is used to perform layer-by-layer upsampling and nonlinear feature transformation on the initial feature tensor along the time direction, and the one-dimensional convolutional output layer is used to convert the multi-channel feature sequence processed by the one-dimensional deconvolutional neural network decoding module into a single-channel output form to obtain a complete predicted seismic trace amplitude sequence.

[0022] Preferably, the spatial structure regularization loss term is formed by the difference between the predicted seismic trace at a certain spatial location in the constrained upsampling rule grid and the predicted seismic trace at its neighboring spatial locations; wherein, the neighboring spatial locations include the neighborhood coordinates in the x-coordinate, y-coordinate, offset, or azimuth direction of the CMP.

[0023] Secondly, embodiments of the present invention provide a five-dimensional seismic data reconstruction system based on implicit neural representation of seismic traces, including: The preprocessing module is used to preprocess the acquired raw five-dimensional seismic data, determine the four-dimensional spatial coordinates corresponding to each observed seismic trace and the amplitude sequence of the observed seismic traces arranged along the time direction, and normalize the four-dimensional spatial coordinates to obtain normalized spatial coordinates. A T-NeRSI network construction module is used to construct a T-NeRSI network, which includes a Fourier feature mapping module, an encoder, and a decoder. The Fourier feature mapping module is used to perform Fourier feature mapping on the normalized spatial coordinates to obtain high-dimensional coordinate features. The encoder is used to obtain latent feature variables based on the high-dimensional coordinate features. The decoder is used to output a complete predicted seismic trace amplitude sequence along the time direction based on the latent feature variables. The training module is used to construct a training loss function based on the complete predicted seismic trace amplitude sequence and the corresponding observed seismic trace amplitude sequence, and to train the T-NeRSI network according to the training loss function; wherein, the training loss function includes a data reconstruction loss term and a spatial structure regularization loss term, and the data reconstruction loss term adopts the Huber loss function; The reconstruction module is used to input the normalized target grid coordinates into the trained T-NeRSI network to obtain the reconstructed seismic trace amplitude sequence at the corresponding location, and to form the reconstructed five-dimensional seismic data based on the reconstructed seismic trace amplitude sequences corresponding to multiple target grid coordinates.

[0024] Thirdly, a computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the steps of the above-described five-dimensional seismic data reconstruction method based on implicit neural representation of seismic traces.

[0025] Fourthly, embodiments of the present invention provide a computer-readable storage medium including a computer program, which, when executed by a processor, implements the steps of the above-described five-dimensional seismic data reconstruction method based on implicit neural representation of seismic traces.

[0026] Fifthly, a chip includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the steps of the above-described five-dimensional seismic data reconstruction method based on implicit neural representation of seismic traces.

[0027] In a sixth aspect, embodiments of the present invention provide an electronic device, including a computer program, which, when executed by the electronic device, implements the steps of the above-described five-dimensional seismic data reconstruction method based on implicit neural representation of seismic traces.

[0028] Compared with the prior art, the present invention has at least the following beneficial effects: A five-dimensional seismic data reconstruction method based on implicit neural representation of seismic traces decouples discrete five-dimensional seismic data into a continuous mapping relationship from four-dimensional spatial coordinates to a complete time series. The implicit representation of the subsurface wavefield is learned through a T-NeRSI network. This method completely abandons the regular gridding step required by traditional methods, directly using irregularly sampled real spatial coordinates for training. This avoids spatial location errors, amplitude distortion, and phase errors introduced by gridding, and fully preserves the original acquired geometric information. It pioneers a trace-by-trace output mode, replacing the point-by-point amplitude prediction of traditional ISR methods, and models the temporal continuity of the same seismic trace as a whole, significantly improving the continuity of reflection phase axes. The method introduces a composite constraint of Huber loss and spatial structure regularization, simultaneously solving the problems of noise sensitivity and spatial discontinuity, maintaining stable reconstruction quality even under high missing rate and strong noise conditions.

[0029] Furthermore, based on the physical nature of pre-stack seismic data, the spatial dimension is accurately decomposed into the plane coordinates of the common midpoint and the geometric parameters of the shot-receiver distance. These four dimensions comprehensively characterize the spatial location and propagation path information of seismic waves underground. The physical meaning of the network input is clarified, enabling the network to learn mapping relationships that conform to the laws of seismic wave propagation, rather than simply mathematical fitting. The data input format is unified, ensuring that five-dimensional seismic data acquired by different acquisition systems can be standardized. This provides a clear physical basis for the dimensional constraints of subsequent spatial structure regularization, enabling the regularization term to specifically enhance the wavefield continuity in each physical dimension.

[0030] Furthermore, the activation function of the neural network has the best nonlinear expressive power when the input value is within a specific range. Excessive differences in the coordinate range of different dimensions can lead to unstable network training and difficulty in converging to the optimal solution. Eliminating the differences in dimensionality and numerical range between different spatial dimensions allows the network to learn the feature contributions of each dimension equally. Mapping the coordinate values ​​to the optimal input range of the Fourier feature mapping module ensures that subsequent frequency encoding can effectively extract spatial features at different scales. This accelerates the convergence speed of the network and reduces the gradient vanishing or gradient exploding problems during training.

[0031] Furthermore, based on the spectral bias characteristics of neural networks, ordinary MLPs struggle to learn high-frequency variations in the input space. Fourier feature mapping, however, can map low-dimensional spatial coordinates to a high-dimensional frequency space, enabling the network to learn complex high-frequency functions through linear combination. This significantly enhances the network's ability to represent high-frequency details in seismic wavefields, effectively recovering fine structures such as high-dipping reflections, small-scale faults, and fractures. The use of predefined frequency basis functions avoids the network learning frequency features from scratch, reducing the training difficulty of the model. The design of multiple frequency components allows the network to simultaneously capture spatial variations at different scales, balancing the reconstruction accuracy of large-scale structures with small-scale details.

[0032] Furthermore, for each frequency component, corresponding sine and cosine features are generated, with the number of frequency components being K. This clarifies the specific mathematical form of the Fourier feature mapping, making the technical solution clearer and more feasible. The adjustability of the number of frequency components K allows the invention to adapt to seismic data of different complexities and different reconstruction needs. The design of orthogonal basis functions ensures the independence between features, avoids feature redundancy, and improves the learning efficiency of the network.

[0033] Furthermore, by leveraging the nonlinear mapping capability of the multilayer perceptron, high-dimensional coordinate features are compressed into a compact latent representation, which encodes the overall wavefield features of the entire seismic trace at the corresponding spatial location. Encoding the spatially relevant information of an entire seismic trace into low-dimensional latent variables significantly reduces the number of model parameters and computational complexity. The latent feature variables serve as an interface between the encoder and decoder, decoupling spatial and temporal features, allowing the decoder to focus on time series recovery. The global connectivity of the fully connected layers enables the network to learn the global wavefield structure of the entire four-dimensional space, avoiding the locality limitations of traditional windowing methods.

[0034] Furthermore, the computational complexity of the ReLU activation function is much lower than that of activation functions such as Sigmoid and Tanh, which can accelerate the training and inference speed of the network; the one-sided inhibition property of ReLU enables the network to learn sparse feature representations, improving the generalization ability of the model; the linear gradient property of ReLU in the positive interval avoids the gradient vanishing problem, enabling deeper encoder networks to be trained effectively.

[0035] Furthermore, leveraging the upsampling properties of one-dimensional deconvolution, low-dimensional latent feature variables are progressively unfolded into high-resolution seismic trace sequences along the time direction. One-dimensional deconvolution can learn the local correlations between temporal sampling points by sharing convolutional kernels. This replaces the traditional fully connected layer approach of directly outputting seismic traces, significantly reducing the number of decoder parameters; the number of parameters in a decoder with four deconvolution blocks is only 11% of that in a fully connected decoder. The local connectivity of one-dimensional deconvolution effectively maintains the waveform continuity of seismic traces in the time direction, reducing waveform distortion. The layer-by-layer upsampling design enables the network to progressively recover temporal features at different frequencies, improving the reconstruction accuracy of seismic traces.

[0036] Furthermore, prior physical knowledge of seismic wavefields is introduced, enabling the network to make reasonable inferences based on information from adjacent traces in regions with sparse observation data. At the same time, the continuity of the four physical dimensions is constrained to ensure that the reconstructed five-dimensional seismic data has good consistency in all dimensions. Norm is used to calculate the differences between adjacent traces, which has strong robustness to outliers and avoids the impact of individual noisy traces on the overall reconstruction results.

[0037] It is understood that the beneficial effects of the second to sixth aspects mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here.

[0038] In summary, this invention achieves direct reconstruction of irregularly sampled five-dimensional seismic data through a seismic trace-level implicit neural representation architecture, avoiding gridding errors and significantly improving reconstruction accuracy and computational efficiency. It also has excellent noise resistance and spatial continuity, and can adapt to complex practical conditions with high missing rates and strong noise.

[0039] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0040] Figure 1 This is a schematic diagram of the training process for the five-dimensional seismic data network proposed in this invention; Figure 2 A schematic diagram illustrating the processing of seismic data using regularized and irregularized grids; Figure 3 This is a schematic diagram of the T-NeRSI network architecture; Figure 4 Examples of five-dimensional synthesis on a regular grid are shown below; (a) is a three-dimensional display of complete CMP domain data; (b) is thinned data after randomly missing 80% of seismic traces; (c) is the reconstruction result of the ISR method; (d) is the residual error of the ISR method; (e) is the reconstruction result of the T-ISR method; (f) is the residual error of the T-ISR method; (g) is the reconstruction result of the method of the present invention; and (h) is the residual error of the method of the present invention. Figure 5 Examples of five-dimensional synthesis on irregular grids are provided; where (a) is a three-dimensional plot of irregular thinned data with 80% random missing seismic traces in the CMP domain; (b) is the complete regular data to be reconstructed; (c) is the reconstruction result of the ISR method; (d) is the residual error of the ISR method; (e) is the reconstruction result of the T-ISR method; (f) is the residual error of the T-ISR method; (g) is the reconstruction result of the method of the present invention; and (h) is the residual error of the method of the present invention. Figure 6 Given a CMPy channel number of 1, an offset x channel number of 4, and an offset y channel number of 3, the CMPx direction slice results are shown. Among them, (a) is the original irregular data; (b) is the regular coordinates to be queried; (c) and (d) are the reconstruction results and residual errors of the ISR method, respectively; (e) and (f) are the reconstruction results and residual errors of the T-ISR method, respectively; (g) and (h) are the reconstruction results and residual errors of the method of this invention, respectively. Figure 7 T-NeRSI at different deletion rates P and noise levels Q in The quantitative assessment results are as follows; Figure 8 This is a geometric schematic diagram of the actual seismic data acquisition area; Figure 9 The offset gather slice results are given when CMPx=2 and CMPy=4; where (a) is the original measured data; (b) is the reconstruction result of the ISR method; and (c) is the reconstruction result of the method of this invention. Figure 10 This is a diagram showing the coordinate distribution of the midpoint after rotation; Figure 11 The results are offset stacking results given CMPy=4 and azimuth channel number 4; where (a) is the near offset stacking (1–10 channels) before reconstruction; (b) is the mid offset stacking (10–20 channels) before reconstruction; (c) is the full offset stacking (1–25 channels) before reconstruction; (d), (e), and (f) are the corresponding results after reconstruction using the T-NeRSI method, respectively. Figure 12 Large-scale overlay comparison chart of work area data (based on) Figure 9 ); Figure 13 Comparison of signal-to-noise ratio (SNR) Qout variations under different regularization parameters λ; Figure 14 The results show the performance of the T-NeRSI method under different K values; where (a) is the training loss under different K values; and (b) is the test Qout value under different K values. Figure 15 This shows the changes in signal-to-noise ratio, number of parameters, and computational efficiency during the transition from ISR to T-NeRSI. Figure 16 This is a flowchart of the present invention; Figure 17 A schematic diagram of a computer device provided in an embodiment of the present invention; Figure 18 This is a block diagram of a chip provided according to an embodiment of the present invention.

[0041] Among them, 60. Computer equipment; 61. Processor; 62. Memory; 63. Computer program; 600. Electronic device; 610. Processing unit; 620. Storage unit; 6201. Random access memory unit; 6202. Cache memory unit; 6203. Read-only memory unit; 6204. Program / utility; 6205. Program module; 630. Bus; 640. Display unit; 650. Input / output interface; 660. Network adapter; 700. External device. Detailed Implementation

[0042] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0043] In the description of this invention, it should be understood that the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0044] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0045] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes such combinations. For example, A and / or B can represent three cases: A alone, A and B simultaneously, and B alone. Additionally, the character " / " in this invention generally indicates that the preceding and following objects have an "or" relationship.

[0046] It should be understood that although terms such as first, second, third, etc., may be used in the embodiments of the present invention to describe the preset range, these preset ranges should not be limited to these terms. These terms are only used to distinguish the preset ranges from one another. For example, without departing from the scope of the embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0047] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0048] The accompanying drawings illustrate various structural schematic diagrams according to embodiments disclosed in this invention. These drawings are not to scale, and some details have been enlarged for clarity, and some details may have been omitted. The shapes of the various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary and may deviate from reality due to manufacturing tolerances or technical limitations. Furthermore, those skilled in the art can design regions / layers with different shapes, sizes, and relative positions as needed.

[0049] This invention provides a five-dimensional seismic data reconstruction method based on implicit neural representation of seismic traces. First, four-dimensional seismic data (excluding the time dimension) is preprocessed, and a T-NeRSI network architecture is proposed to extract features from the observed seismic data. Input data is normalized on irregular sampled traces and coordinates to enable the network to effectively learn data features. A Fourier feature mapping module is introduced to expand the input data into high-dimensional periodic features, thereby enhancing the network's ability to represent complex data. Based on this, a multilayer perceptron is used to encode the mapped coordinate features to obtain latent variables representing the entire seismic trace. A one-dimensional deconvolutional neural network is used as the decoder to output the complete seismic trace amplitude sequence of the target spatial location. By introducing Huber loss constraints, the error between the predicted and observed traces is optimized, thereby enhancing the network's robustness to anomalous noise; simultaneously, a spatial structure regularization term is introduced to ensure the continuity and smoothness of the reconstruction results across all dimensions. After training, inputting the target grid coordinates generates the complete seismic trace at the corresponding coordinates, achieving missing trace interpolation, regularized reconstruction, and noise suppression. This invention directly utilizes the real spatial coordinates of irregularly sampled seismic traces for training, better preserving the original acquired geometric information. The reconstruction results have good continuity, noise resistance, and stability, thereby effectively improving the accuracy and efficiency of five-dimensional seismic data interpolation reconstruction. By using limited observation data as input and leveraging T-NeRSI to efficiently capture data features, it can perform high-quality reconstruction of missing seismic traces.

[0050] Please see Figure 16 This invention presents a five-dimensional seismic data reconstruction method based on implicit neural representation of seismic traces. Based on deep learning and an ISR network, a T-NeRSI architecture is proposed. An unsupervised learning method is used to learn the distribution relationship of seismic data from observation traces, ultimately effectively improving the accuracy and efficiency of five-dimensional seismic data interpolation and reconstruction. The method includes the following steps: S1. Preprocess the acquired raw five-dimensional seismic data, including removing the time dimension from the five-dimensional seismic data as input and using the time dimension as the output sequence; normalize the other four dimensions after removing the time dimension to facilitate subsequent frequency coding; Please see Figure 2 Traditional methods require mesh regularization before reconstruction, which easily introduces waveform distortion and resolution loss. However, the implicit neural representation (ISR) method can directly utilize irregular observation coordinates for continuous wavefield modeling, avoiding information loss caused by mesh regularization, and supports flexible reconstruction on regular meshes with different spatial sampling intervals. Therefore, this invention is based on the ISR method. This invention proposes determining the spatial coordinates and amplitude sequences of each observed seismic trace based on irregularly sampled actual five-dimensional seismic data. The original five-dimensional seismic data... Remove time dimension information Obtain four-dimensional seismic data ,right Normalization can be performed using the following formula:

[0051] in, and These represent the minimum and maximum values ​​of this dimension across all observed data, respectively. After the above processing, the normalized four-dimensional spatial coordinates can be obtained. ,Right now The x-coordinate of CMP The y-coordinate of CMP It is the offset distance and It is the azimuth angle.

[0052] Furthermore, to address the issue of traditional five-dimensional seismic data reconstruction methods requiring prior regular gridding, this invention represents each observed seismic trace as a combination of spatial coordinates and the corresponding seismic trace amplitude sequence. The spatial coordinates include the x-coordinate and y-coordinate of the CMP (Central Motion Processing Unit), offset, and azimuth. During network training, the actual spatial coordinates of irregularly sampled seismic traces are directly used as input, with the corresponding complete seismic trace amplitude sequence serving as the constraint. This learns the continuous mapping relationship between spatial coordinates and seismic trace data, avoiding spatial positional bias, amplitude error, and phase distortion introduced by the regularization process. This approach is more conducive to preserving the original acquisition geometry and true wavefield characteristics.

[0053] This method removes the time dimension from the input coordinates of five-dimensional seismic data, using only the four dimensions other than time as network input, and outputs the complete amplitude sequence of the corresponding seismic trace along the time direction. This transforms point-by-point reconstruction into trace-by-trace reconstruction, thereby enhancing the continuity in the time direction and improving reconstruction accuracy, noise resistance, and computational efficiency.

[0054] S2. A T-NeRSI network architecture is adopted to extract the characteristics of the observed seismic data; Please see Figure 1This diagram illustrates the training process of the five-dimensional seismic data network proposed in this invention. Existing ISR methods employ an implicit representation with point-by-point input of five-dimensional coordinates and single-point amplitude output. During reconstruction, both the temporal and spatial dimensions need to be used as input, and the amplitude value at each time sampling point needs to be predicted separately. This results in the fragmentation of the continuous structure along the time direction within the same seismic trace, making it difficult to fully utilize the regular sampling and continuously changing prior features of the seismic trace itself. The point-by-point prediction method has a large computational load and low training and inference efficiency when processing large-scale five-dimensional seismic data. Furthermore, under conditions of strong noise and high missing rate, it is prone to problems such as excessive residual noise, insufficient continuity of reflection phase axes, and incomplete recovery of effective signals. To overcome the shortcomings of existing point-by-point implicit representation methods in terms of preserving temporal continuity, feature extraction capability, reconstruction accuracy, and computational efficiency, this invention proposes the T-NeRSI network architecture.

[0055] Specifically, the T-NeRSI network uses four-dimensional spatial coordinates As input, to correspond to the seismic trace The sample pairs, of which These represent the CMPx coordinates, CMPy coordinates, offset, and azimuth angle corresponding to the seismic trace, respectively. This represents the amplitude sequence arranged along the time direction at this spatial location. The T-NeRSI network uses four-dimensional spatial coordinates. As input, to correspond to the seismic trace As a supervisory constraint, it learns the mapping relationship between the two. The spatial variation characteristics and intra-trace time series characteristics of the seismic wavefield are extracted from the sparse and irregular sub-sampled wavefields, thereby establishing an implicit representation of the continuous five-dimensional seismic wavefield.

[0056] Furthermore, to address the low computational efficiency caused by time-sampling point prediction in traditional point-based implicit neural representation methods, this invention employs a reconstruction method using seismic traces as the basic output unit. Specifically, instead of using both time sampling points and spatial coordinates as input to output amplitude values ​​point by point, the network uses only the spatial coordinates of the seismic trace as input and outputs the complete seismic trace amplitude sequence corresponding to that spatial location in one go through a decoder. This approach reduces the amount of point-by-point query computation, improves the efficiency of large-scale five-dimensional seismic data interpolation reconstruction, and simultaneously maintains the continuous waveform structure of the seismic traces in the time direction.

[0057] During training, the T-NeRSI network does not rely on external complete label data, but instead directly utilizes observed irregular seismic traces for unsupervised training. The network continuously adjusts the parameter θ to adjust the input spatial coordinates. Post-output predicted seismic traces Compared with actual observed seismic traces The differences between them are minimized. As shown in the flowchart of the T-NeRSI method, the network learns the distribution patterns of each observation trace in four-dimensional spatial coordinates from the subsampled wavefield and encodes these patterns into the network parameters, enabling the network to represent the continuous subsurface wavefield, rather than just performing discrete fitting on existing sampling points. In this way, T-NeRSI can fully utilize the continuity of seismic traces in the temporal direction and the correlation between seismic traces at different spatial locations to achieve joint extraction of local and global structural features of observed seismic data.

[0058] After training, the T-NeRSI network forms a continuous mapping model from spatial coordinates to complete seismic traces. When inputting arbitrary regular grid coordinates... or higher sampling density upsampling coordinates At any given time, the network can output the reconstructed seismic traces for the corresponding location, thus obtaining a regular grid five-dimensional seismic body. Or reconstruction results at different spatial resolutions The T-NeRSI network architecture proposed in this invention essentially learns irregular seismic observation data as a continuous wavefield function. By extracting and preserving the spatial structure, temporal continuity, and wavefield variation characteristics in the observation data through network parameters, it provides a foundation for subsequent regular grid reconstruction and high-resolution interpolation.

[0059] Please see Figure 3 As shown in the T-NeRSI network architecture diagram, the network consists of a Fourier feature mapping module, a coordinate-based encoding layer, and a decoding module based on a one-dimensional deconvolutional neural network. It establishes a mapping relationship between spatial coordinates and complete seismic trace sequences. This enables the extraction of wavefield structure features and time series features from observed seismic data.

[0060] Specifically, the Fourier feature mapping module applies a set of predefined sine and cosine function transforms to each coordinate component, for each frequency... They will all generate corresponding and Two types of features. The expression is as follows:

[0061]

[0062] Where K represents the number of frequency components. This represents the normalized spatial coordinates within [0,1]. This processing enhances the network's ability to express high-frequency variations, complex structures, and local wavefield differences in seismic data, avoiding the problem that the network struggles to learn high-frequency details when directly using low-dimensional coordinates.

[0063] Furthermore, to address the challenge of conventional implicit neural representation networks failing to express high-frequency details in seismic wavefields, this invention introduces a Fourier feature mapping module at the network input. This module performs multi-frequency sine and cosine transforms on the input low-dimensional spatial coordinates, expanding the original spatial coordinates into high-dimensional coordinate features containing different frequency components. In this way, the network can more fully perceive high-frequency variations in the spatial coordinates, improving its ability to express complex structures, steep-dipping reflections, local waveform changes, and detailed amplitude features, thereby enhancing the precision of the five-dimensional seismic data reconstruction results.

[0064] Specifically, the encoder module is built on an MLP network. The encoder consists of sequentially connected fully connected layers and nonlinear activation layers, with the ReLU activation function preferably used in the nonlinear activation layers. After the high-dimensional coordinate features, after Fourier feature mapping, are input into the encoder, they first undergo a linear transformation through the fully connected layers to achieve a weighted combination of coordinate features at different frequencies. Then, the ReLU activation function introduces nonlinear mapping capabilities, enabling the network to learn the complex nonlinear correspondence between spatial coordinates and the seismic wavefield. The encoder does not directly output the seismic trace amplitude sequence, but rather outputs latent feature variables corresponding to the input spatial coordinates. These latent feature variables characterize the overall wavefield information of the seismic trace at that spatial location and serve as input to the subsequent decoder. Because the encoder only takes spatial coordinates as input, and does not require inputting each time sampling point into the network, it can encode the spatially relevant information of an entire seismic trace into a compact latent representation, thereby reducing the number of model parameters and improving the efficiency of subsequent seismic trace reconstruction.

[0065] Furthermore, to effectively convert spatial coordinate information into wavefield features usable for seismic trace reconstruction, this invention designs an encoder structure. The encoder, positioned after the Fourier feature mapping module, consists of a cascaded fully connected layer and a ReLU activation function, used for nonlinear feature extraction of high-dimensional coordinate features. Through encoder processing, the input spatial coordinates are mapped into latent feature variables, which characterize the overall wavefield information of the seismic trace at the corresponding spatial location. Compared to methods that directly predict time-sampled values ​​point-by-point, this encoding method can express the spatial correlation features of the entire seismic trace in a more compact form, providing a foundation for subsequent efficient decoding and reconstruction.

[0066] Specifically, the decoder is positioned after the encoder to receive the latent feature variables output by the encoder and generate a complete seismic trace amplitude sequence at the corresponding spatial coordinates based on the latent feature variables. The decoder includes a nonlinear transform layer, a one-dimensional deconvolutional neural network (DNN) decoding module, and a one-dimensional convolutional output layer. The nonlinear transform layer is used to adjust the dimensions and adapt the features of the latent feature variables to obtain an initial feature tensor. The one-dimensional deconvolutional neural network decoding module includes multiple sequentially connected one-dimensional deconvolutional blocks. Each one-dimensional deconvolutional block is used to perform layer-by-layer upsampling and nonlinear feature transformation on the initial feature tensor along the time direction. The one-dimensional convolutional output layer is used to perform channel fusion on the multi-channel feature sequence processed by the one-dimensional deconvolutional neural network decoding module and output a single-channel seismic trace amplitude sequence, thereby obtaining a complete predicted seismic trace corresponding to the input spatial coordinates.

[0067] Furthermore, to improve the ability to recover complete seismic trace amplitude sequences from latent feature variables, this invention introduces a one-dimensional deconvolutional neural network structure at the decoding end. The decoder first performs nonlinear transformation and dimensionality adaptation on the latent feature variables output by the encoder, then upsamples and expands the features layer by layer along the time direction through multiple one-dimensional deconvolutional modules, finally obtaining the single-channel seismic trace amplitude sequence through a one-dimensional convolutional output layer. Since the one-dimensional deconvolutional layer can utilize shared convolutional kernels to learn the local correlations between seismic trace time sampling points, compared to directly outputting seismic traces using a large number of stacked fully connected layers, this invention can reduce the number of model parameters and computational complexity, and enhance the continuity of seismic trace waveform recovery.

[0068] S3. Introduce Huber and regularization terms as loss functions to reduce prediction error and prevent overfitting; The loss function is used to constrain the consistency between predicted and observed seismic traces during network training, while simultaneously constraining the spatial continuity of the reconstructed seismic data. The loss function can be decomposed into two components: a data reconstruction loss term and a spatial structure regularization loss term. The training loss function can be expressed as:

[0069] in, Represents network parameters, Represents the spatial coordinates of the j-th observed seismic trace. This represents the observed seismic trace amplitude sequence at this spatial coordinate. This represents the predicted seismic trace amplitude sequence output by the network. Indicates the number of observed seismic traces. This represents the data reconstruction error function. This represents the spatial structure regularization term on the upsampling rule grid. This represents the regularization weight coefficient.

[0070] Furthermore, to balance the accuracy of fitting observed data with the spatial continuity of the reconstructed wavefield, this invention constructs a total loss function composed of a data reconstruction loss term and a spatial structure regularization loss term, and adjusts the relative contributions between the two through regularization weight coefficients. During training, the network learns the true amplitude characteristics of observed seismic traces through the data reconstruction loss, and constrains the prediction results at unobserved areas and adjacent spatial locations through the spatial structure regularization loss. This enables the model to not only accurately fit existing data, but also generate missing seismic traces with good spatial consistency.

[0071] The data reconstruction error is assessed using the Huber loss function, which can be expressed as:

[0072] in, This represents the error between the predicted seismic trace amplitude sequence and the observed seismic trace amplitude sequence. This represents the threshold at which the Huber loss function changes from a quadratic penalty to a single-penalty penalty.

[0073] Spatial structure regularization is used to enhance the spatial continuity of the reconstructed seismic wavefield. This can be achieved by constraining the difference between the predicted seismic trace at a given spatial location within the upsampled regular grid and the predicted seismic traces at adjacent spatial locations. For the spatial coordinates in the upsampled regular grid... Select its adjacent coordinates in the CMPx, CMPy, offset, or azimuth direction. And calculate the difference between the predicted seismic trace amplitude sequences of the two. Norm differences lead to structural regularization constraints. This can be expressed as:

[0074] in, This indicates the number of seismic traces in the upsampling rule grid. Representing coordinates The set of neighborhood coordinates.

[0075] S4. Input the preprocessed four-dimensional seismic data into the network for training. After training, reconstruct the missing seismic traces to obtain high-quality, complete five-dimensional seismic data.

[0076] After data preprocessing and model training are completed, the target spatial coordinates within the reconstruction area are fed into the network, and the output is the complete time-dimensional seismic trace sequence corresponding to the spatial location, thereby achieving high-quality reconstruction of five-dimensional seismic data.

[0077] In another embodiment of the present invention, a five-dimensional seismic data reconstruction system based on implicit neural representation of seismic traces is provided. This system can be used to implement the above-mentioned five-dimensional seismic data reconstruction method based on implicit neural representation of seismic traces. Specifically, the five-dimensional seismic data reconstruction system based on implicit neural representation of seismic traces includes a preprocessing module, a T-NeRSI network construction module, a training module, and a reconstruction module.

[0078] The preprocessing module is used to preprocess the acquired raw five-dimensional seismic data, determine the four-dimensional spatial coordinates corresponding to each observed seismic trace and the amplitude sequence of the observed seismic traces arranged along the time direction, and normalize the four-dimensional spatial coordinates to obtain normalized spatial coordinates. A T-NeRSI network construction module is used to construct a T-NeRSI network, which includes a Fourier feature mapping module, an encoder, and a decoder. The Fourier feature mapping module is used to perform Fourier feature mapping on the normalized spatial coordinates to obtain high-dimensional coordinate features. The encoder is used to obtain latent feature variables based on the high-dimensional coordinate features. The decoder is used to output a complete predicted seismic trace amplitude sequence along the time direction based on the latent feature variables. The training module is used to construct a training loss function based on the complete predicted seismic trace amplitude sequence and the corresponding observed seismic trace amplitude sequence, and to train the T-NeRSI network according to the training loss function; wherein, the training loss function includes a data reconstruction loss term and a spatial structure regularization loss term, and the data reconstruction loss term adopts the Huber loss function; The reconstruction module is used to input the normalized target grid coordinates into the trained T-NeRSI network to obtain the reconstructed seismic trace amplitude sequence at the corresponding location, and to form the reconstructed five-dimensional seismic data based on the reconstructed seismic trace amplitude sequences corresponding to multiple target grid coordinates.

[0079] This invention provides a terminal device comprising a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, graphics processing units (GPUs), tensor processing units (TPUs), digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions to achieve a corresponding method flow or function. The processor described in this embodiment can be used for the operation of a five-dimensional seismic data reconstruction method based on implicit neural representation of seismic traces, including: The acquired raw five-dimensional seismic data is preprocessed to determine the four-dimensional spatial coordinates corresponding to each observed seismic trace and the amplitude sequence of the observed seismic traces arranged along the time direction. The four-dimensional spatial coordinates are then normalized to obtain normalized spatial coordinates, wherein the four-dimensional spatial coordinates are the coordinates in the raw five-dimensional seismic data excluding the time dimension. A T-NeRSI network is constructed, which includes a Fourier feature mapping module, an encoder, and a decoder. The Fourier feature mapping module is used to perform Fourier feature mapping on the normalized spatial coordinates to obtain high-dimensional coordinate features. The encoder is used to extract latent feature variables based on the high-dimensional coordinate features. The decoder is used to output a complete predicted seismic trace amplitude sequence along the time direction based on the latent feature variables. A training loss function is constructed based on the complete predicted seismic trace amplitude sequence and the corresponding observed seismic trace amplitude sequence, and the T-NeRSI network is trained according to the training loss function; wherein, the training loss function includes a Huber data reconstruction loss term and a spatial structure regularization loss term, the Huber data reconstruction loss term is used to constrain the amplitude error between the complete predicted seismic trace amplitude sequence and the corresponding observed seismic trace amplitude sequence, and the spatial structure regularization loss term is used to constrain the difference between predicted seismic traces at adjacent spatial locations; After normalizing the target spatial coordinates, the data is input into the trained T-NeRSI network to obtain the reconstructed seismic trace amplitude sequence at the corresponding location. Based on the reconstructed seismic trace amplitude sequences corresponding to multiple target spatial coordinates, the reconstructed five-dimensional seismic data is formed.

[0080] Please see Figure 17 The terminal device is a computer device. In this embodiment, the computer device 60 includes a processor 61, a memory 62, and a computer program 63 stored in the memory 62 and executable on the processor 61. When executed by the processor 61, the computer program 63 implements the five-dimensional seismic data reconstruction method based on implicit neural representation of seismic traces as described in this embodiment. To avoid repetition, details are omitted here. Alternatively, when executed by the processor 61, the computer program 63 implements the functions of each model / unit in the five-dimensional seismic data reconstruction system based on implicit neural representation of seismic traces as described in this embodiment. To avoid repetition, details are omitted here.

[0081] Computer device 60 can be a desktop computer, laptop, handheld computer, cloud server, or other computing device. Computer device 60 may include, but is not limited to, a processor 61 and a memory 62. Those skilled in the art will understand that... Figure 17 This is merely an example of computer device 60 and does not constitute a limitation on computer device 60. It may include more or fewer components than shown, or combine certain components, or different components. For example, computer device may also include input / output devices, network access devices, buses, etc.

[0082] The processor 61 may be a Central Processing Unit (CPU), or other general-purpose processors, graphics processing units (GPUs), tensor processing units (TPUs), digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0083] The memory 62 can be an internal storage unit of the computer device 60, such as a hard disk or memory of the computer device 60. The memory 62 can also be an external storage device of the computer device 60, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc. equipped on the computer device 60.

[0084] Furthermore, the memory 62 may include both internal storage units of the computer device 60 and external storage devices. The memory 62 is used to store computer programs and other programs and data required by the computer device. The memory 62 can also be used to temporarily store data that has been output or will be output.

[0085] Please see Figure 18 The terminal device is an electronic device 600, which is manifested in the form of a general-purpose computing device. The components of the electronic device may include, but are not limited to: at least one processing unit 610, at least one storage unit 620, a bus 630 connecting different platform components (including storage unit 620 and processing unit 610), a display unit 640, etc.

[0086] The storage unit stores program code, which can be executed by the processing unit 610 to perform the steps described in the method section of this specification according to various exemplary embodiments of the present invention. For example, the processing unit 610 can perform actions such as... Figure 16 The steps are shown in the figure.

[0087] Storage unit 620 may include readable media in the form of volatile storage units, such as random access memory (RAM) 6201 and / or cache memory 6202, and may further include read-only memory (ROM) 6203.

[0088] Storage unit 620 may also include a program / utility 6204 having a set (at least one) program module 6205, such program module 6205 including but not limited to: operating system, one or more application programs, other program modules and program data, each or some combination of these examples may include an implementation of a network environment.

[0089] Bus 630 can represent one or more of several types of bus structures, including a memory cell bus or memory cell controller, a peripheral bus, a graphics acceleration port, a processing unit, or a local bus using any of the multiple bus structures.

[0090] Electronic device 600 can also communicate with one or more external devices 700 (e.g., keyboard, pointing device, Bluetooth device, etc.), and with one or more devices that enable a user to interact with electronic device 600, and / or with any device that enables electronic device 600 to communicate with one or more other computing devices (e.g., router, modem). This communication can be performed via input / output interface 650. Furthermore, electronic device 600 can also communicate with one or more networks (e.g., local area network, wide area network, and / or public network, such as the Internet) via network adapter 660. Network adapter 660 can communicate with other modules of electronic device 600 via bus 630. It should be understood that, although not shown in the figures, other hardware and / or software modules can be used in conjunction with electronic device 600, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage platforms.

[0091] This invention also provides a storage medium, specifically a computer-readable storage medium, which is a memory device in a terminal device for storing programs and data. It is understood that the computer-readable storage medium here can include both built-in storage media in the terminal device and extended storage media supported by the terminal device; it can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, the storage space also stores one or more instructions suitable for loading and execution by a processor, which can be one or more computer programs (including program code). More specific examples of the computer-readable storage medium include: an electrical connection with one or more wires, a portable disk, a hard disk, random access memory, read-only memory, erasable programmable read-only memory, optical fiber, portable compact disk read-only memory, optical storage device, magnetic storage device, or any suitable combination thereof.

[0092] Computer-readable storage media also include data signals propagated in baseband or as part of a carrier wave, carrying readable program code. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable storage medium can also be any readable medium other than a readable storage medium that can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the readable storage medium can be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, radio frequency, etc., or any suitable combination thereof.

[0093] Program code for performing the operations of this invention can be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java and C++, and conventional procedural programming languages ​​such as C or similar languages. The program code can execute entirely on the user's computing device, partially on the user's device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0094] One or more instructions stored in a computer-readable storage medium can be loaded and executed by a processor to implement the corresponding steps of the five-dimensional seismic data reconstruction method based on implicit neural representation of seismic traces in the above embodiments; one or more instructions in the computer-readable storage medium are loaded and executed by the processor in the following steps: The acquired raw five-dimensional seismic data is preprocessed to determine the four-dimensional spatial coordinates corresponding to each observed seismic trace and the amplitude sequence of the observed seismic traces arranged along the time direction. The four-dimensional spatial coordinates are then normalized to obtain normalized spatial coordinates, wherein the four-dimensional spatial coordinates are the coordinates in the raw five-dimensional seismic data excluding the time dimension. A T-NeRSI network is constructed, which includes a Fourier feature mapping module, an encoder, and a decoder. The Fourier feature mapping module is used to perform Fourier feature mapping on the normalized spatial coordinates to obtain high-dimensional coordinate features. The encoder is used to extract latent feature variables based on the high-dimensional coordinate features. The decoder is used to output a complete predicted seismic trace amplitude sequence along the time direction based on the latent feature variables. A training loss function is constructed based on the complete predicted seismic trace amplitude sequence and the corresponding observed seismic trace amplitude sequence, and the T-NeRSI network is trained according to the training loss function; wherein, the training loss function includes a Huber data reconstruction loss term and a spatial structure regularization loss term, the Huber data reconstruction loss term is used to constrain the amplitude error between the complete predicted seismic trace amplitude sequence and the corresponding observed seismic trace amplitude sequence, and the spatial structure regularization loss term is used to constrain the difference between predicted seismic traces at adjacent spatial locations; After normalizing the target spatial coordinates, the data is input into the trained T-NeRSI network to obtain the reconstructed seismic trace amplitude sequence at the corresponding location. Based on the reconstructed seismic trace amplitude sequences corresponding to multiple target spatial coordinates, the reconstructed five-dimensional seismic data is formed.

[0095] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0096] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0097] To quantitatively evaluate the performance of this invention, we conducted systematic simulation experiments and actual data tests. The experimental results are as follows: Comparison of Regular Grid Synthetic Data Reconstruction Experimental setup: The complete synthetic data contains 100×100×25×25×1000 sampling points (CMP x×CMP y×offset×azimuth×time), with 80% of seismic traces randomly missing and 10dB of random noise added. Comparison methods include ISR, T-ISR, and the method of this invention (T-NeRSI).

[0098] Please see Figure 4This paper presents a comparison of the reconstruction effects of different methods on regular grid 5D synthetic seismic data, used to verify the reconstruction capability of the proposed method for 5D seismic data under noisy data conditions with high missing rates. Figure (a) shows the 3D display result of the complete 5D synthetic seismic data in the CMP domain; Figure (b) shows the observation data obtained after adding random noise to the complete data and randomly deleting 80% of the seismic traces. It can be seen that the original continuous phase axis is destroyed by a large number of missing traces, and the spatial continuity is significantly reduced, making it difficult to use directly for subsequent imaging and interpretation. Figures (c) and (d) show the reconstruction results and residuals of ISR, respectively. This method can recover some major reflection events, but the residuals still retain strong structural errors and noise interference, indicating that its point-by-point amplitude modeling method does not fully utilize the temporal continuity within the seismic traces, and the reconstruction results still have significant distortion; Figures (e) and (f) show the reconstruction results and residuals of T-ISR, respectively. Compared with ISR, it enhances the temporal waveform continuity by using the entire seismic trace as the output unit, and the residual energy is reduced, but there are still some signal leakage and detail errors. Figures (g) and (h) show the reconstruction results and residuals of T-NeRSI using the method of the present invention, respectively. It can be seen that the reflection phase axis recovered by the method of the present invention is more continuous and clearer, and the tilt events and local details are more consistent with the complete data.

[0099] The reconstruction signal-to-noise ratio of the method of this invention is the highest, which is 4.91 dB higher than that of the ISR method and 3.72 dB higher than that of the T-ISR method. At the same time, the number of model parameters is only 11% of that of the ISR method, and the training time is comparable to that of the T-ISR method, achieving the best balance between accuracy and efficiency.

[0100] Experimental setup: The sampling coordinates of the synthetic data were randomly perturbed by ±10m to form an irregular grid, while other conditions were the same as in the regular grid experiment.

[0101] Please see Figure 5Figures 1-4 present a comparison of reconstruction results on irregular grid five-dimensional synthetic seismic data, used to verify the adaptability of the method of this invention to actual irregular sampling scenarios. Figure (a) shows the irregular sparse observation data obtained after randomly deleting 80% of the seismic traces in the CMP domain. Its sampling coordinates are randomly perturbed, and the spatial distribution is no longer located on the regular grid. Figure (b) shows the complete regular grid data of the target reconstruction. As can be seen from Figure (a), the loss of a large number of seismic traces leads to a severe disruption of the continuity of the phase axis, and the irregular coordinates further increase the difficulty of wavefield reconstruction. Figures (c) and (d) show the reconstruction results and residuals of the ISR method, respectively. It can recover some reflection events, but there are still obvious structural errors and noise interference in the residuals, indicating that the point amplitude mapping has limited ability to express the continuous wavefield under irregular sampling conditions. Figures (e) and (f) show the reconstruction results and residuals of the T-ISR method, respectively. This method improves the continuity of the time direction by using the entire seismic trace as the output unit. The residuals are lower than those of ISR, but there are still local detail errors. Figures (g) and (h) show the reconstruction results and residuals of T-NeRSI using the method of this invention, respectively. It can be seen that the method of this invention can still effectively recover continuous reflection phase axes under irregular sparse observation conditions. The reconstruction results are more consistent with complete regular grid data, and the residual energy is the lowest with no obvious structural residue. These results demonstrate that this invention can directly utilize irregular sampled coordinates for training without prior gather relocation or gridding, thus improving the fidelity, continuity, and robustness of five-dimensional seismic data reconstruction.

[0102] Under irregular sampling conditions, the advantages of the method of this invention are even more obvious. The reconstruction signal-to-noise ratio remains above 21dB, the spatial continuity index reaches 0.92, and the high-frequency recovery rate is as high as 83%, which is far superior to the comparison method. This shows that the present invention can directly utilize irregular coordinates for training without the need for gridding, effectively avoiding the information loss caused by gridding.

[0103] Please see Figure 6This figure shows the reconstruction results of irregularly sampled five-dimensional seismic data slices extracted along the CMP x direction under the condition of fixed CMP y, offset x, and offset y, which is used to further illustrate the ability of the method of the present invention to recover the continuous wave field in space. Figure (a) is the original irregularly sampled data. Due to the perturbation of the sampling coordinates and the presence of a large number of missing traces, the seismic traces are sparsely distributed and the phase axes are difficult to identify continuously. Figure (b) is the expected regular CMP x coordinate position. Figures (c) and (d) are the reconstruction results and residuals of the ISR method, respectively. It can be seen that although it recovers the main reflection trend, there is local distortion of the phase axes. The residuals still retain a lot of effective signal components, indicating that the point amplitude representation is insufficient to characterize the continuity relationship between traces. Figures (e) and (f) are the reconstruction results and residuals of the T-ISR method, respectively. Compared with the ISR residuals, the residuals are weakened and the waveform continuity is improved, but there is still some signal leakage. Figures (g) and (h) show the reconstruction results and residuals of the method of the present invention, respectively. The reconstructed phase axes are smoother and more continuous, tilt events are well preserved, and the residual energy is the lowest and mainly consists of weak random disturbances. These results indicate that the method of the present invention can learn a continuous five-dimensional seismic wavefield based on irregular observation coordinates and accurately generate complete seismic traces on regular target coordinates, thereby improving the reconstruction accuracy and inter-trace consistency of irregular sampled data.

[0104] Experimental setup: The reconstruction performance of this invention was tested at four missing rates of 50%, 65%, 80%, and 95%, and at five input signal-to-noise ratios of 5dB, 10dB, 15dB, 20dB, and 25dB.

[0105] Please see Figure 7 The figure illustrates the quantitative reconstruction performance of the method of this invention under different seismic trace missing rates and different input signal-to-noise ratios (SNRs). The horizontal axis represents the input SNR, and the vertical axis represents the output SNR. The four regions correspond to seismic trace missing rates of 50%, 65%, 80%, and 95%, respectively. As shown in the figure, at the same missing rate, the overall reconstructed output SNR remains high as the input SNR increases. However, at the same input SNR, the output SNR gradually decreases as the missing rate increases from 50% to 95%, indicating that the sparsity of sampling affects the reconstruction difficulty. Even under high missing rates of 80% and 95%, the method of this invention can still achieve a good output SNR, especially in the extreme case of 95% missing seismic traces and a low input SNR, maintaining usable reconstruction quality. This result demonstrates that the method of this invention, by learning the continuous five-dimensional seismic wavefield through implicit neural representation and combining the output of the entire seismic trace with structural regularization constraints, can maintain good noise resistance and stability under strong noise and high-proportion missing conditions.

[0106] This invention exhibits excellent performance under various missing rates and noise levels. Even with an extremely high missing rate of 95% and a low input signal-to-noise ratio of 5dB, the output signal-to-noise ratio still reaches 12.1dB, meeting basic interpretation requirements. This demonstrates the invention's strong robustness and its ability to adapt to complex real-world acquisition conditions.

[0107] Please see Figure 8 This figure illustrates the geometric distribution of acquired seismic data in the field. The horizontal and vertical axes represent the planar location of the survey area (x and y), respectively. Asterisks indicate the location of the seismic source, and triangles represent the location of the geophones. As can be seen from the figure, the seismic sources and geophones are not completely regularly distributed. The actual five-dimensional seismic data contains irregular sampling and missing traces. This invention can utilize these real spatial coordinates to reconstruct five-dimensional seismic data.

[0108] Please see Figure 9 This figure illustrates the reconstruction effect of offset gather slices from actual field seismic data under fixed CMP x and CMP y conditions. Figure (a) shows the original field data, with numerous missing traces in different azimuths or offset groups, significantly affected by noise, making it difficult to continuously identify reflection phase axes. Figure (b) shows the reconstruction result using the ISR method; although some missing areas are filled, strong random noise and discontinuities still exist in the deep region, resulting in insufficient fidelity of reflection events. Figure (c) shows the reconstruction result using the method of this invention, demonstrating that the reflection phase axes are more continuous and clearer, noise is significantly suppressed, and missing traces are effectively recovered. These results indicate that this invention is applicable to the reconstruction of five-dimensional seismic data under real and complex acquisition conditions, improving the continuity and quality of seismic data in the offset dimension.

[0109] Please see Figure 10 This figure illustrates the distribution of midpoints of the seismic acquisition area in the CMP coordinate system and the spatial selection method of the target reconstruction area. The dot matrix represents the spatial distribution of the observed seismic traces in the CMP x and CMP y directions, showing a large sampling coverage area but with some irregularity. The rectangle in the figure marks the selected study sub-region, with a spatial range of approximately 2000 m × 2000 m, used for subsequent five-dimensional seismic data reconstruction and analysis. This region is located in the middle of the overall sampling area, is representative and has relatively complete coverage, which helps to ensure the stability of training data and the reliability of reconstruction results. In the method implementation, the coordinates of the seismic traces within this rectangular region are used as the input of the implicit neural representation model. By learning the continuous mapping relationship between spatial coordinates and seismic trace amplitudes, high-precision reconstruction from irregular sampling to regular grids is achieved. At the same time, this figure also reflects that the method of this invention does not require regular binning of the original data, but directly uses real coordinates for modeling, thereby effectively avoiding the positional errors and resolution losses caused by gridding in traditional methods, and improving the spatial consistency and fine structure preservation ability of the reconstruction results.

[0110] Please see Figure 11 This figure shows the comparison between the results of stacking at different offsets before and after reconstruction, under the condition of fixed CMP y gather numbers and azimuth numbers. The top row of images (a), (b), and (c) are the original data, in which the near-offset, medium-offset, and full-offset stacked profiles all have obvious problems such as missing traces, random noise, and poor continuity of phase axes. Especially in the area marked by the rectangle, the energy of shallow horizontal events is uneven, the deep tilted reflection structures are interfered with by noise, and the local effective signals are difficult to identify. The bottom row of images (d), (e), and (f) are the results after processing using the five-dimensional seismic data reconstruction method based on the implicit neural representation of seismic traces. It can be seen that the continuity of phase axes within different offset ranges is significantly enhanced after reconstruction, missing traces are effectively filled, and random noise and acquisition footprint are significantly suppressed. The shallow horizontal reflection events in the left rectangle are smoother and more continuous, and the weak reflection energy of the middle and deep layers in the middle rectangle is enhanced. The results show that the present invention can make full use of the five-dimensional correlation between CMP coordinates, offset, azimuth and time dimension to learn the continuous seismic wave field representation, thereby improving the signal-to-noise ratio and spatial consistency of the reconstructed data while maintaining structural details.

[0111] Please see Figure 12 This figure is used to verify the five-dimensional seismic data reconstruction capability of this invention within a large-scale work area. In the figure, (a) is the original stacking result, (b) is the stacking result after T-NeRSI reconstruction at the same spatial sampling interval, and (c) is the reconstruction result obtained by directly doubling the spatial grid after training. It can be seen that some reflection phase axes in the original data are affected by noise, missing traces, and uneven acquisition, resulting in poor continuity and energy stability. After reconstruction, the energy of tilt events within the green box is enhanced, the weak reflection structures within the yellow box are more continuous, and the reflection details previously obscured by noise within the red box are restored. In particular, the doubling upsampling result maintains the main structural morphology without retraining the model and further improves the spatial sampling density. This result demonstrates that this invention, through implicit neural representation of seismic traces, learns the continuous wavefield mapping between CMP coordinates, offsets, azimuth angles, and time sampling. This not only completes missing seismic traces and suppresses noise but also flexibly outputs regularized five-dimensional seismic data according to the target spatial interval, thereby improving the reliability of subsequent imaging, stacking, and structural interpretation.

[0112] Please see Figure 13 The figure shows the structure regularization parameters. The impact on the reconstruction performance of this invention, with the vertical axis representing the output signal-to-noise ratio Q. out The horizontal axis represents the number of training epochs. As shown in the graph, after introducing appropriate structure regularization, the model's convergence speed and final reconstruction quality are significantly better than... In the case where =0, =10 -5 Time Q out The highest value indicates that this parameter can effectively constrain the spatial continuity between adjacent seismic traces and enhance the consistency of the phase axis. When Too large, such as 10 -3 When the reconstruction results are over-smoothed, it is difficult to maintain the complex tilted structure; when When the value is too small or zero, the spatial prior constraints are insufficient, resulting in decreased noise resistance and lane-filling capabilities; this invention addresses this by setting a reasonable value. A balance is achieved between noise suppression, structural preservation, and reconstruction accuracy.

[0113] Please see Figure 14 The figure illustrates the impact of the Fourier feature mapping length K on the training convergence and reconstruction accuracy of this invention. The left figure shows the variation of training loss under different K values. Without Fourier mapping, the model converges slowly and struggles to effectively learn the high-frequency components in the seismic wavefield. After introducing Fourier features, the loss decreases significantly, and increasing the K value accelerates convergence. The right figure shows the test signal-to-noise ratio Q. out The reconstruction accuracy is highest when K=20, indicating that it can better balance high-frequency detail representation and noise suppression. Too small a K value leads to insufficient high-frequency information learning, while too large a K value may learn noise and cause overfitting. This invention improves the ability of implicit neural representations to represent complex seismic wavefields by setting an appropriate K value.

[0114] When λ=10 -5 When λ is too large (e.g., 10), the reconstructed signal-to-noise ratio reaches its highest value of 23.04 dB; when λ is too large (e.g., 10), the signal-to-noise ratio reaches its highest value of 23.04 dB. -3 When λ is too small (e.g., 10), the reconstruction result will be over-smoothed, and the signal-to-noise ratio will drop to 18.7 dB; when λ is too small (e.g., 10), the reconstruction result will be over-smoothed, and the signal-to-noise ratio will drop to 18.7 dB; -7 Due to insufficient spatial constraints, the signal-to-noise ratio dropped to 19.2 dB.

[0115] When K=20, the reconstruction signal-to-noise ratio is the highest; when K is too small (e.g., K=5), high-frequency information is not learned sufficiently, and the signal-to-noise ratio is 17.8dB; when K is too large (e.g., K=50), it is easy to overfit noise, and the signal-to-noise ratio drops to 21.5dB.

[0116] Please refer to Figure 15The figure illustrates the changes in reconstruction accuracy, training time, and model parameter count during the gradual improvement from point-based implicit representation ISR to the T-NeRSI of this invention. The ISR parameter count was approximately 1.23M, and the training time was 38.3 minutes, which was relatively inefficient. After changing to use seismic traces as the output unit, the T-ISR training time decreased to 4.2 minutes, and the signal-to-noise ratio improved to 19.32dB. After further introducing a one-dimensional deconvolution decoding module, the parameter count decreased significantly with the increase of the number of stacked blocks. With 4 decoding blocks, the parameter count was only 0.14M, and the SNR reached a maximum of 23.04dB. These results demonstrate that this invention can achieve high-quality five-dimensional seismic data reconstruction with a lightweight network structure.

[0117] In summary, this invention presents a five-dimensional seismic data reconstruction method and system based on implicit neural representation of seismic traces. Addressing industry pain points such as the requirement for regular gridding, low efficiency of point-by-point reconstruction, and poor noise resistance in traditional methods, it achieves direct, high-precision reconstruction of irregularly sampled data. The reconstruction signal-to-noise ratio is improved by more than 4.9 dB compared to traditional point-based ISR methods, the waveform correlation coefficient increases from 0.82 to 0.94, and the high-frequency detail recovery rate improves to 83%, effectively solving the problem of lost fine structures such as high-dipping reflections and small-scale faults in traditional methods. Employing a channel-by-channel output mode combined with a lightweight one-dimensional deconvolution decoder, training time is reduced by 89%, training efficiency is improved by approximately 9 times, and the number of model parameters is only 11% of that of traditional methods, enabling efficient processing of large-scale industrial data with millions of channels. Even under extreme conditions of a 95% missing rate and a 5 dB low signal-to-noise ratio, usable reconstruction quality is maintained. It also supports arbitrary coordinate queries and multi-resolution output, achieving double spatial upsampling without retraining, providing crucial technical support for oil and gas exploration in deep and complex structural areas in my country.

[0118] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0119] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0120] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this invention can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0121] In the embodiments provided by this invention, it should be understood that the disclosed devices / terminals and methods can be implemented in other ways. For example, the device / terminal embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0122] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0123] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0124] If the integrated module / unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments of the present invention can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, a recording medium, a USB flash drive, a portable hard drive, a magnetic disk, an optical disk, a computer memory, a read-only memory (ROM), a random-access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium, etc.

[0125] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus, and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0126] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0127] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0128] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A five-dimensional seismic data reconstruction method based on implicit neural representation of seismic traces, characterized in that, Includes the following steps: The acquired raw five-dimensional seismic data is preprocessed to determine the four-dimensional spatial coordinates corresponding to each observed seismic trace and the amplitude sequence of the observed seismic traces arranged along the time direction. The four-dimensional spatial coordinates are then normalized to obtain normalized spatial coordinates, wherein the four-dimensional spatial coordinates are the coordinates in the raw five-dimensional seismic data excluding the time dimension. A T-NeRSI network is constructed, which includes a Fourier feature mapping module, an encoder, and a decoder. The Fourier feature mapping module is used to perform Fourier feature mapping on the normalized spatial coordinates to obtain high-dimensional coordinate features. The encoder is used to extract latent feature variables based on the high-dimensional coordinate features. The decoder is used to output a complete predicted seismic trace amplitude sequence along the time direction based on the latent feature variables. A training loss function is constructed based on the complete predicted seismic trace amplitude sequence and the corresponding observed seismic trace amplitude sequence, and the T-NeRSI network is trained according to the training loss function; wherein, the training loss function includes a Huber data reconstruction loss term and a spatial structure regularization loss term, the Huber data reconstruction loss term is used to constrain the amplitude error between the complete predicted seismic trace amplitude sequence and the corresponding observed seismic trace amplitude sequence, and the spatial structure regularization loss term is used to constrain the difference between predicted seismic traces at adjacent spatial locations; After normalizing the target spatial coordinates, the data is input into the trained T-NeRSI network to obtain the reconstructed seismic trace amplitude sequence at the corresponding location. Based on the reconstructed seismic trace amplitude sequences corresponding to multiple target spatial coordinates, the reconstructed five-dimensional seismic data is formed.

2. The five-dimensional seismic data reconstruction method based on implicit neural representation of seismic traces according to claim 1, characterized in that, The four-dimensional spatial coordinates include the x-coordinate of the CMP, the y-coordinate of the CMP, the offset distance, and the azimuth angle.

3. The five-dimensional seismic data reconstruction method based on implicit neural representation of seismic traces according to claim 1, characterized in that, The normalization process for the four-dimensional spatial coordinates includes: normalizing the coordinate values ​​of each observed seismic trace in the corresponding dimension based on the minimum and maximum values ​​of each dimension in all observation data, so as to obtain normalized spatial coordinates in the range of [0,1].

4. The five-dimensional seismic data reconstruction method based on implicit neural representation of seismic traces according to claim 1, characterized in that, The Fourier feature mapping module applies a set of predefined sine and cosine function transformations to each coordinate component in the normalized spatial coordinates to generate high-dimensional coordinate features containing multiple frequency components.

5. The five-dimensional seismic data reconstruction method based on implicit neural representation of seismic traces according to claim 4, characterized in that, For each frequency component , The Fourier feature mapping module generates sine and cosine features corresponding to the normalized spatial coordinates, specifically as follows: in, Indicates the number of frequency components. The coordinates are normalized four-dimensional space coordinates. Represents the normalized spatial coordinates within [0,1].

6. The five-dimensional seismic data reconstruction method based on implicit neural representation of seismic traces according to claim 1, characterized in that, The encoder is constructed based on MLP and includes a fully connected layer and a nonlinear activation layer connected in sequence. The high-dimensional coordinate features are nonlinearly mapped by the fully connected layer and the nonlinear activation layer to obtain potential feature variables that characterize the corresponding seismic trace wavefield information.

7. The five-dimensional seismic data reconstruction method based on implicit neural representation of seismic traces according to claim 6, characterized in that, The nonlinear activation layer uses the ReLU activation function.

8. The five-dimensional seismic data reconstruction method based on implicit neural representation of seismic traces according to claim 1, characterized in that, The decoder includes a nonlinear transformation layer, a one-dimensional deconvolutional neural network decoding module, and a one-dimensional convolutional output layer. The nonlinear transformation layer adjusts the dimensions and adapts the features of the latent feature variables to obtain an initial feature tensor. The one-dimensional deconvolutional neural network decoding module performs layer-by-layer upsampling and nonlinear feature transformation on the initial feature tensor along the time direction. The one-dimensional convolutional output layer converts the multi-channel feature sequence processed by the one-dimensional deconvolutional neural network decoding module into a single-channel output format to obtain a complete predicted seismic trace amplitude sequence.

9. The five-dimensional seismic data reconstruction method based on implicit neural representation of seismic traces according to claim 1, characterized in that, The spatial structure regularization loss term is formed by the difference between the predicted seismic trace at a certain spatial location in the constrained upsampling rule grid and the predicted seismic trace at its neighboring spatial locations; wherein, the neighboring spatial locations include the neighborhood coordinates in the x-coordinate, y-coordinate, offset, or azimuth direction of the CMP.

10. A five-dimensional seismic data reconstruction system based on implicit neural representation of seismic traces, characterized in that, include: The preprocessing module is used to preprocess the acquired raw five-dimensional seismic data, determine the four-dimensional spatial coordinates corresponding to each observed seismic trace and the amplitude sequence of the observed seismic traces arranged along the time direction, and normalize the four-dimensional spatial coordinates to obtain normalized spatial coordinates. A T-NeRSI network construction module is used to construct a T-NeRSI network, which includes a Fourier feature mapping module, an encoder, and a decoder. The Fourier feature mapping module is used to perform Fourier feature mapping on the normalized spatial coordinates to obtain high-dimensional coordinate features. The encoder is used to obtain latent feature variables based on the high-dimensional coordinate features. The decoder is used to output a complete predicted seismic trace amplitude sequence along the time direction based on the latent feature variables. The training module is used to construct a training loss function based on the complete predicted seismic trace amplitude sequence and the corresponding observed seismic trace amplitude sequence, and to train the T-NeRSI network according to the training loss function; wherein, the training loss function includes a data reconstruction loss term and a spatial structure regularization loss term, and the data reconstruction loss term adopts the Huber loss function; The reconstruction module is used to input the normalized target grid coordinates into the trained T-NeRSI network to obtain the reconstructed seismic trace amplitude sequence at the corresponding location, and to form the reconstructed five-dimensional seismic data based on the reconstructed seismic trace amplitude sequences corresponding to multiple target grid coordinates.

Images