A method for generating synthetic seismic data based on multi-scale spectral constraints

Abstract

The application provides a kind of based on multi-scale spectrum constraint's generated synthetic seismic data optimization method, comprising: actual seismic data and original synthetic seismic data are normalized and preprocessed;Actual seismic data is executed two-dimensional discrete wavelet transform, and low-frequency approximation sub-band and multi-stage high-frequency detail sub-band are obtained, and the condition input feature is constructed by channel splicing;Condition generative adversarial network is constructed, generator fuses multi-scale wavelet condition feature and generates optimization data, and discriminator carries out adversarial training;The same wavelet transform is executed to generated data, and multi-scale spectrum constraint loss is constructed, respectively matches low-frequency sub-band and each stage high-frequency detail sub-band, and establishes hierarchical spectrum constraint mechanism;Low frequency and high frequency constraint loss are weighted and fused, and are jointly optimized with adversarial loss to form total loss function, and generator parameter is iteratively updated;KL divergence is calculated to the optimized synthetic seismic data and actual data, and is filtered and output according to distribution similarity.

Description

Technical Field

[0001] This invention relates to the field of seismic exploration data processing technology, and more particularly to a generative synthetic seismic data optimization method based on multi-scale spectral constraints. Background Technology

[0002] Seismic data is a core foundational data source in oil and gas exploration and geophysical interpretation, widely used in tasks such as stratigraphic analysis, reservoir prediction, and structural identification. With the increasing application of deep learning technology in seismic interpretation, the demand for high-quality, large-scale training data is growing. However, actual seismic data acquisition is costly, time-consuming, and significantly affected by geological conditions and the acquisition environment, resulting in a limited availability of high-quality labeled data for model training.

[0003] To alleviate the shortage of real seismic data, existing technologies typically employ wave equation forward modeling to generate synthetic seismic data, thereby expanding the training sample size. However, synthetic data generated based on forward modeling still differs from actual seismic data in terms of spectral structure, multi-scale feature distribution, and statistical properties, particularly in high-frequency detail characterization, tectonic boundary representation, and response characteristics of complex geological bodies. This deficiency affects the generalization performance of models trained on synthetic data in real-world scenarios.

[0004] In recent years, deep learning methods such as generative adversarial networks (GANs) have been gradually applied to the field of seismic data generation and enhancement, improving the distribution matching problem between synthetic and real data to some extent. However, seismic data has significant multi-scale characteristics: low-frequency information reflects the overall stratigraphic structure and trend, while high-frequency information depicts faults and local structural details. Existing methods mostly employ single-scale constraints and lack hierarchical multi-scale modeling mechanisms, making it difficult to simultaneously ensure the consistency of low-frequency structures and the realism of high-frequency details, thus hindering the achievement of collaborative optimization between structure and details.

[0005] Wavelet transform, as a multi-resolution analysis method, can decompose signals scale-by-scale, achieving joint representation of the spatial and frequency domains. It has been widely used in seismic data denoising, attribute analysis, and frequency division processing. Therefore, introducing wavelet transform into the generative model training process to construct a multi-scale spectral constraint mechanism helps improve the structural consistency and detail fidelity of synthetic seismic data at various frequency levels. Summary of the Invention

[0006] To overcome the problems of existing methods lacking multi-scale hierarchical constraints and difficulty in balancing the consistency of overall structure and local details, this invention provides a generative synthetic seismic data optimization method based on multi-scale spectral constraints, which is used to improve the distribution consistency and structural fidelity between synthetic seismic data and real seismic data.

[0007] This invention is achieved through the following technical solution: a generative synthetic seismic data optimization method based on multi-scale spectral constraints, specifically including the following steps: Step S1: Obtain actual earthquake data and raw synthetic earthquake data, and perform normalization preprocessing on the data to uniformly map the data amplitude values ​​to a preset numerical range; Step S2: Perform two-dimensional discrete wavelet transform on the actual seismic data, perform multi-level decomposition, and obtain low-frequency approximation subbands and multi-level high-frequency detail subbands under a unified spectral decomposition system; construct the wavelet coefficients of each scale as conditional input features by channel splicing. Step S3: Construct a conditional generative adversarial network: The generator takes the original synthetic seismic data as input and integrates multi-scale wavelet conditional features to generate optimized synthetic seismic data; the discriminator is trained adversarially using actual seismic data and generated seismic data as input. Step S4: Construct a multi-scale spectral constraint loss during network training. Perform the same two-dimensional discrete wavelet transform as in Step S2 on the generated seismic data. Construct a multi-scale spectral constraint loss during network training, and perform matching calculations on the low-frequency subbands of the generated seismic data and the low-frequency subbands of the actual data to obtain the low-frequency constraint loss. At the same time, perform scale-wise matching calculations on the high-frequency detail subbands of each level of the generated seismic data to obtain the high-frequency constraint loss, thereby establishing a hierarchical spectral constraint mechanism. Step S5: Weight the low-frequency constraint loss and the high-frequency constraint loss to construct a multi-scale spectral constraint loss, and jointly optimize it with the adversarial loss to form the total loss function. Iteratively update the generator parameters through the backpropagation algorithm. Step S6: Compare the optimized synthetic seismic data with the actual seismic data using KL divergence calculation, and filter out the synthetic seismic data based on distribution similarity.

[0008] As a preferred option, step S1 specifically includes the following steps: Step S11: Record the actual earthquake data as The original synthetic seismic data is denoted as ; Step S12: For and Standardization is performed to ensure that the data distribution falls within a uniform scale range.

[0009] Furthermore, step S2 specifically includes the following steps: Step S21: For Multi-scale two-dimensional discrete wavelet decomposition is performed to obtain the low-frequency approximation subband LL and high-frequency detail subbands in three directions, including the horizontal high-frequency subband LH, the vertical high-frequency subband HL, and the diagonal high-frequency subband HH. The low-frequency subband is used to characterize the macroscopic structural information of seismic data, and the high-frequency subband is used to characterize the local texture and edge features, including faults and cracks. Step S22: Since the resolution of sub-bands at different scales may differ, it can be unified to the original resolution through interpolation. Step S23: Stitch together the sub-bands of each scale along the channel dimension to form a conditional feature map. , which serves as one of the inputs to the conditional generative adversarial network generator.

[0010] Furthermore, the two-dimensional discrete wavelet transform can be decomposed into multi-level sub-bands of different scales to obtain low-frequency and high-frequency sub-bands, which can be used to construct the input features of conditional generative adversarial networks.

[0011] Furthermore, the generator in step S3 adopts an encoder-decoder structure, and the discriminator adopts the convolutional discriminant structure PatchGAN, specifically including the following steps: Step S31: Generator G uses the raw synthetic seismic data and conditional characteristics As input, optimized synthetic seismic data is output through feature fusion and multi-scale information transfer mechanisms. ; Step S32: Discriminator D receives and It outputs the authenticity judgment result through the local receptive field discrimination mechanism; Step S33: Construct a loss function based on adversarial training mechanism to measure the distribution difference between generated data and actual data; adopt an adversarial loss form based on Wasserstein distance, and introduce a stability adjustment term as needed; the optimization objective of the discriminator is expressed as:

[0012] in, Represents actual earthquake data Data distribution This represents the data distribution generated by generator G. This represents a data sample obtained from the actual data distribution. This represents a data sample generated by the generator. This represents an intermediate sample obtained by linear interpolation between the actual data sample and the generated data sample. This represents the scoring function output by the discriminator. This represents the gradient of the discriminator output with respect to the input sample. represents the weight coefficient of the gradient penalty term.

[0013] Furthermore, step S4 specifically includes the following steps: Step S41: For Perform multi-scale wavelet decomposition to obtain sub-band features at each scale; Step S42: For each scale, calculate the differences between the generated subband and the actual subband in terms of amplitude spectrum distribution, statistical characteristics, and spatial structure to form the constraint loss for that scale; the multi-scale spectral constraint loss can be expressed as:

[0014] in, and These represent the sub-bands of the generated data and the actual data at the s-th wavelet scale, respectively. Represents a two-dimensional Fourier transform. Indicates amplitude spectrum, and These represent the mean and standard deviation, respectively. Indicators representing structural similarity These are the weighting coefficients for each item.

[0015] Step S43: Perform a weighted summation of the loss terms at each scale to obtain the overall spectral constraint loss, the expression of which is:

[0016] in, The weight of the s-th scale is set according to the frequency importance, and S is the total number of wavelet decomposition scales.

[0017] Furthermore, step S5 specifically includes the following steps: Step S51: The generator loss consists of an adversarial loss term and a multi-scale spectral constraint loss term. The total loss of the generator is expressed as:

[0018] in, and These are the weighting coefficients for the adversarial loss and the spectral constraint loss, respectively. ; Step S52: Iteratively update the parameters of the generator and discriminator using an adaptive optimization algorithm; Step S53: Through multiple rounds of iterative training, the spectral distribution of the generated data gradually approximates the spectral distribution of the actual seismic data. Training stops when the loss function converges or reaches the preset evaluation criteria.

[0019] Furthermore, in the weighted fusion in step S5, the weight of the low-frequency constraint loss is greater than the weight of the high-frequency constraint loss.

[0020] Furthermore, step S6 specifically includes the following sub-steps: Step S61: Extract the amplitude spectrum distribution characteristics of the generated data and the actual earthquake data, construct the corresponding probability distribution function, and quantify the difference between the two in terms of spectrum distribution by calculating the KL divergence. The KL divergence can be expressed as:

[0021] in, and These represent the amplitude spectrum probability distributions of the actual data and the generated data, respectively. Step S62: Filter highly similar samples based on a threshold, and output optimized synthetic seismic data.

[0022] By employing the above technical solutions, this invention has the following beneficial effects compared to existing technologies: 1. This invention constructs a hierarchical representation of low-frequency approximation subbands and multi-level high-frequency detail subbands under a unified wavelet decomposition system, and establishes a scale-by-scale spectrum matching mechanism to optimize the generated seismic data at different frequency components, thereby improving the matching accuracy of multi-scale spectrum components. 2. Relying on the multi-level decomposition characteristics of two-dimensional discrete wavelet transform, adaptive partitioning of frequency components is achieved without the need for manually setting fixed frequency thresholds or complex physical modeling parameters, reducing the method's dependence on human experience and improving the versatility and automation of the technical solution. 3. By constructing low-frequency structural constraints and high-frequency detail constraints separately and co-optimizing them with adversarial loss, we can achieve hierarchical control of overall trend information and local structural features, enhance the ability to characterize details while maintaining the continuity of macroscopic structure, and improve the multi-scale consistency of generated seismic data. 4. The generated optimized synthetic seismic data can be used as high-quality training samples for seismic interpretation, reservoir prediction, and related machine learning model training tasks, showing promising engineering application prospects.

[0023] Additional aspects and advantages of the invention will become apparent in the following description or may be learned by practice of the invention. Attached Figure Description

[0024] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which: Fig. 1 This is a schematic diagram of the overall process of the generative synthetic seismic data optimization method based on wavelet transform multi-scale spectral constraints of the present invention. Fig. 2In the table, (a) represents actual earthquake data, (b) represents original synthetic earthquake data, and (c) represents synthetic earthquake data optimized by the method of this invention. Detailed Implementation

[0025] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0026] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0027] The following is combined with Figs. 1-2 The generative synthetic seismic data optimization method based on multi-scale spectral constraints according to embodiments of the present invention will be described in detail.

[0028] like Fig. 1 , Fig. 2 As shown, this invention proposes a generative synthetic seismic data optimization method based on multi-scale spectral constraints, specifically including the following steps: Step S1: Acquire actual earthquake data and raw synthetic earthquake data, and perform normalization preprocessing on the data to uniformly map the data amplitude values ​​to a preset numerical range, thereby eliminating scale differences between different data sources, improving the numerical stability of model training, and providing a unified input basis for subsequent multi-scale decomposition and adversarial training; specifically including the following steps: Step S11: Record the actual earthquake data as The original synthetic seismic data is denoted as ; Step S12: For and Standardization is performed to ensure that the data distribution is within a uniform scale range.

[0029] Step S2: Perform a two-dimensional discrete wavelet transform on the actual seismic data, performing multi-level decomposition to obtain low-frequency approximation subbands and multi-level high-frequency detail subbands under a unified spectral decomposition system; construct conditional input features by concatenating wavelet coefficients at each scale through channel stitching, providing multi-scale structural prior information for the generative model; the two-dimensional discrete wavelet transform can perform multi-level decomposition to obtain low-frequency and high-frequency subbands at different scales, which are used to construct the input features for the conditional generative adversarial network. Specifically, this includes the following steps: Step S21: For Multi-scale two-dimensional discrete wavelet decomposition is performed to obtain the low-frequency approximation subband LL and high-frequency detail subbands in three directions, including the horizontal high-frequency subband LH, the vertical high-frequency subband HL, and the diagonal high-frequency subband HH. The low-frequency subband is used to characterize the macroscopic structural information of seismic data, and the high-frequency subband is used to characterize the local texture and edge features, including faults and cracks. Step S22: Since the resolution of sub-bands at different scales may differ, it can be unified to the original resolution through interpolation. Step S23: Stitch together the sub-bands of each scale along the channel dimension to form a conditional feature map. , which serves as one of the inputs to the conditional generative adversarial network generator.

[0030] Step S3: Constructing a Conditional Generative Adversarial Network (GAN): The generator takes the original synthetic seismic data as input and integrates multi-scale wavelet conditional features to generate optimized synthetic seismic data; the discriminator uses both actual and generated seismic data as input for adversarial training, improving the consistency of the distribution between the generated and actual data through the adversarial training mechanism; the generator adopts an encoder-decoder structure, and the discriminator adopts a convolutional discriminant structure PatchGAN, achieving synthetic data optimization through adversarial training, specifically including the following steps: Step S31: Generator G uses the raw synthetic seismic data and conditional characteristics As input, optimized synthetic seismic data is output through feature fusion and multi-scale information transfer mechanisms. ; Step S32: Discriminator D receives and The system outputs a realism judgment result through a local receptive field discrimination mechanism to improve the texture consistency of the generated data. Step S33: Construct a loss function based on adversarial training mechanism to measure the distribution difference between generated data and actual data; adopt an adversarial loss form based on Wasserstein distance, and introduce a stability adjustment term as needed; the optimization objective of the discriminator is expressed as:

[0031] in, Represents actual earthquake data Data distribution This represents the data distribution generated by generator G. This represents a data sample obtained from the actual data distribution. This represents a data sample generated by the generator. This represents an intermediate sample obtained by linear interpolation between the actual data sample and the generated data sample. This represents the scoring function output by the discriminator. This represents the gradient of the discriminator output with respect to the input sample, and is the weight coefficient of the gradient penalty term.

[0032] Step S4: During network training, a multi-scale spectral constraint loss is constructed. The same two-dimensional discrete wavelet transform as in Step S2 is performed on the generated seismic data. During network training, a multi-scale spectral constraint loss is constructed, and the low-frequency sub-bands of the generated seismic data are matched with the low-frequency sub-bands of the actual data to obtain the low-frequency constraint loss. Simultaneously, a scale-wise matching calculation is performed on the various levels of high-frequency detail sub-bands of the generated seismic data to obtain the high-frequency constraint loss, thereby establishing a hierarchical spectral constraint mechanism. Specifically, this includes the following steps: Step S41: For Perform multi-scale wavelet decomposition to obtain sub-band features at each scale; Step S42: For each scale, calculate the differences between the generated subband and the actual subband in terms of amplitude spectrum distribution, statistical characteristics, and spatial structure to form the constraint loss for that scale; the multi-scale spectral constraint loss can be expressed as:

[0033] in, and These represent the generated data and the actual data at the [number]th [year]. Subbands at the wavelet scale, Represents a two-dimensional Fourier transform. Indicates amplitude spectrum, and These represent the mean and standard deviation, respectively. Indicators of structural similarity These are the weighting coefficients for each item.

[0034] Step S43: Perform a weighted summation of the loss terms at each scale to obtain the overall spectral constraint loss, the expression of which is:

[0035] in, For the first The weights for each scale are set according to frequency importance. This represents the total number of wavelet decomposition scales.

[0036] Step S5: Weighted fusion of low-frequency constraint loss and high-frequency constraint loss is performed to construct a multi-scale spectral constraint loss. This loss is then jointly optimized with the adversarial loss to form a total loss function. The generator parameters are iteratively updated using the backpropagation algorithm, enabling the generated seismic data to maintain overall structural stability while enhancing its detail representation capabilities, achieving multi-scale spectral collaborative matching. In the weighted fusion, the weight of the low-frequency constraint loss is greater than that of the high-frequency constraint loss. Specifically, this includes the following steps: Step S51: The generator loss consists of an adversarial loss term and a multi-scale spectral constraint loss term, used to simultaneously constrain the authenticity and spectral consistency of the generated data; the total loss of the generator is expressed as:

[0037] in, and These are the weighting coefficients for the adversarial loss and the spectral constraint loss, respectively. ; Step S52: The parameters of the generator and discriminator are iteratively updated using an adaptive optimization algorithm. The specific learning rate and parameter settings can be adjusted according to actual needs. Step S53: Through multiple rounds of iterative training, the spectral distribution of the generated data gradually approximates the spectral distribution of the actual seismic data. Training stops when the loss function converges or reaches the preset evaluation criteria.

[0038] Step S6: Compare the optimized synthetic seismic data with the actual seismic data using KL divergence calculation, and select high-quality synthetic seismic data based on distribution similarity. This specifically includes the following steps: Step S61: Extract the amplitude spectral distribution characteristics of the generated data and the actual seismic data, construct the corresponding probability distribution function, and quantify the difference between the two at the spectral distribution level by calculating the KL divergence, thereby assessing the spectral consistency of the generated data. The KL divergence can be expressed as:

[0039] in, and These represent the amplitude spectrum probability distributions of the actual data and the generated data, respectively. Step S62: Filter highly similar samples based on a threshold, and output optimized synthetic seismic data for downstream tasks such as attribute extraction or machine learning training.

[0040] To demonstrate the effectiveness of the method of the present invention, this embodiment selects actual seismic data and its corresponding original synthetic seismic data, and performs optimization processing according to the process described in steps S1 to S6. Fig. 2 (a) shows the actual earthquake data. Fig. 2 (b) shows the original synthetic seismic data, which differs from the actual seismic data in terms of texture details and spectral distribution. Following steps S1 to S3, the actual seismic data and the original synthetic seismic data are normalized, decomposed into wavelet multi-scale values, and conditional features are constructed. Finally, the original synthetic data is optimized and generated based on a conditional generative adversarial network.

[0041] During the training process, the multi-scale spectral constraint loss described in step S4 is introduced to constrain the amplitude spectrum distribution, statistical characteristics, and structural similarity of the generated data at different frequency scales, so that the generated results gradually approach the actual earthquake data in terms of spectral characteristics.

[0042] Fig. 2 (c) shows the synthetic seismic data optimized by the method of this invention. Compared to Fig. 2 (b) The optimized data, while maintaining the original structural characteristics, exhibits enhanced local details. Furthermore, the optimization results are quantitatively analyzed using the distribution similarity evaluation method described in step S6. The results show that the optimized synthetic seismic data has a lower KL divergence index than the original synthetic data, indicating that its spectral distribution is closer to actual seismic data. The results of this embodiment demonstrate that the method of the present invention can improve the differences in structural characteristics and spectral distribution between the original synthetic seismic data and enhance data quality, making it suitable for subsequent seismic interpretation and machine learning training.

[0043] In this invention, the following terms are explained: "Multi-scale spectral constraint" refers to layer-by-layer spectral matching based on wavelet subbands; "cGAN" refers to conditional generative adversarial network, which is used for description only and does not constitute a limitation on the scheme.

[0044] In the description of this specification, the terms "one embodiment," "some embodiments," "specific embodiment," etc., refer to a specific feature, structure, material, or characteristic described in connection with that embodiment or example, which is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0045] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A generative synthetic seismic data optimization method based on multi-scale spectral constraints, characterized in that... Specifically, it includes the following steps: Step S1: Obtain actual earthquake data and raw synthetic earthquake data, and perform normalization preprocessing on the data to uniformly map the data amplitude values ​​to a preset numerical range; Step S2: Perform two-dimensional discrete wavelet transform on the actual seismic data, perform multi-level decomposition, and obtain low-frequency approximation subbands and multi-level high-frequency detail subbands under a unified spectral decomposition system; construct the wavelet coefficients of each scale as conditional input features by channel splicing. Step S3: Construct a conditional generative adversarial network: The generator takes the original synthetic seismic data as input and integrates multi-scale wavelet conditional features to generate optimized synthetic seismic data; the discriminator is trained adversarially using actual seismic data and generated seismic data as input. Step S4: Construct a multi-scale spectral constraint loss during network training. Perform the same two-dimensional discrete wavelet transform as in Step S2 on the generated seismic data. Construct a multi-scale spectral constraint loss during network training, and perform matching calculations on the low-frequency subbands of the generated seismic data and the low-frequency subbands of the actual data to obtain the low-frequency constraint loss. At the same time, perform scale-wise matching calculations on the high-frequency detail subbands of each level of the generated seismic data to obtain the high-frequency constraint loss, thereby establishing a hierarchical spectral constraint mechanism. Step S5: Weight the low-frequency constraint loss and the high-frequency constraint loss to construct a multi-scale spectral constraint loss, and jointly optimize it with the adversarial loss to form the total loss function. Iteratively update the generator parameters through the backpropagation algorithm. Step S6: Compare the optimized synthetic seismic data with the actual seismic data using KL divergence calculation, and filter out the synthetic seismic data based on distribution similarity.

2. The generative synthetic seismic data optimization method based on multi-scale spectral constraints according to claim 1, characterized in that... Step S1 specifically includes the following steps: Step S11: Record the actual earthquake data as The original synthetic seismic data is denoted as ; Step S12: For and Standardization is performed to ensure that the data distribution falls within a uniform scale range.

3. The generative synthetic seismic data optimization method based on multi-scale spectral constraints according to claim 2, characterized in that... Step S2 specifically includes the following steps: Step S21: For Multi-scale two-dimensional discrete wavelet decomposition is performed to obtain the low-frequency approximation subband LL and high-frequency detail subbands in three directions, including the horizontal high-frequency subband LH, the vertical high-frequency subband HL, and the diagonal high-frequency subband HH. The low-frequency subband is used to characterize the macroscopic structural information of seismic data, and the high-frequency subband is used to characterize the local texture and edge features, including faults and cracks. Step S22: Since the resolution of sub-bands at different scales may differ, it can be unified to the original resolution through interpolation. Step S23: Stitch together the sub-bands of each scale along the channel dimension to form a conditional feature map. , which serves as one of the inputs to the conditional generative adversarial network generator.

4. The generative synthetic seismic data optimization method based on multi-scale spectral constraints according to claim 3, characterized in that... The two-dimensional discrete wavelet transform can be decomposed into multiple levels to obtain low-frequency and high-frequency sub-bands of different scales, which can be used to construct the input features of conditional generative adversarial networks.

5. The generative synthetic seismic data optimization method based on multi-scale spectral constraints according to claim 4, characterized in that... The generator in step S3 adopts an encoder-decoder structure, and the discriminator adopts the convolutional discriminant structure PatchGAN, specifically including the following steps: Step S31: Generator G uses the raw synthetic seismic data and conditional characteristics As input, optimized synthetic seismic data is output through feature fusion and multi-scale information transfer mechanisms. ; Step S32: Discriminator D receives and It outputs the authenticity judgment result through the local receptive field discrimination mechanism; Step S33: Construct a loss function based on adversarial training mechanism to measure the distribution difference between generated data and actual data; adopt an adversarial loss form based on Wasserstein distance, and introduce a stability adjustment term as needed; the optimization objective of the discriminator is expressed as: ， in, Represents actual earthquake data Data distribution Let G represent the data distribution generated by the generator, and x represent a data sample obtained from the actual data distribution. This represents a data sample generated by the generator. This represents an intermediate sample obtained by linear interpolation between the actual data sample and the generated data sample. This represents the scoring function output by the discriminator. This represents the gradient of the discriminator output with respect to the input sample. represents the weight coefficient of the gradient penalty term.

6. The generative synthetic seismic data optimization method based on multi-scale spectral constraints according to claim 1, characterized in that, Step S4 specifically includes the following steps: Step S41: For the input Perform multi-scale wavelet decomposition to obtain sub-band features at each scale; Step S42: For each scale, calculate the differences between the generated subband and the actual subband in terms of amplitude spectrum distribution, statistical characteristics, and spatial structure to form the constraint loss for that scale; the multi-scale spectral constraint loss can be expressed as: ， in, and These represent the sub-bands of the generated data and the actual data at the s-th wavelet scale, respectively. Represents a two-dimensional Fourier transform. Indicates amplitude spectrum, and These represent the mean and standard deviation, respectively. Indicators representing structural similarity These are the weighting coefficients for each item; Step S43: Perform a weighted summation of the loss terms at each scale to obtain the overall spectral constraint loss, the expression of which is: ， in, The weight of the s-th scale is set according to frequency importance, and S is the total number of wavelet decomposition scales.

7. The generative synthetic seismic data optimization method based on multi-scale spectral constraints according to claim 6, characterized in that, Step S5 specifically includes the following steps: Step S51: The generator loss consists of an adversarial loss term and a multi-scale spectral constraint loss term. The total loss of the generator is expressed as: ， in, and These are the weighting coefficients for the adversarial loss and the spectral constraint loss, respectively. ; Step S52: Iteratively update the parameters of the generator and discriminator using an adaptive optimization algorithm; Step S53: Through multiple rounds of iterative training, the spectral distribution of the generated data gradually approximates the spectral distribution of the actual seismic data. Training stops when the loss function converges or reaches the preset evaluation criteria.

8. The generative synthetic seismic data optimization method based on multi-scale spectral constraints according to claim 7, characterized in that, In the weighted fusion in step S5, the weight of low-frequency constraint loss is greater than the weight of high-frequency constraint loss.

9. The generative synthetic seismic data optimization method based on multi-scale spectral constraints according to claim 7, characterized in that, Step S6 specifically includes the following sub-steps: Step S61: Extract the amplitude spectrum distribution characteristics of the generated data and the actual earthquake data, construct the corresponding probability distribution function, and quantify the difference between the two in terms of spectrum distribution by calculating the KL divergence. The KL divergence can be expressed as: ， in, and These represent the amplitude spectrum probability distributions of the actual data and the generated data, respectively. Step S62: Filter highly similar samples based on a threshold, and output optimized synthetic seismic data.

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