A seismic wave equation forward modeling acceleration method and system based on deep learning

Abstract

The application discloses a kind of based on deep learning seismic wave equation forward acceleration method and system, the method includes: obtaining velocity field and source location information, velocity field is handled by Z-score normalization and is cropped to preset range, Gaussian distribution coding mask is generated based on source location information, combination is two-channel input tensor, wherein the first channel is normalized velocity field, and the second channel is source mask;Wavefield prediction model is constructed, and the training of model is realized using AdamW optimizer combined with cosine annealing learning rate scheduling strategy, and the optimization of model is realized using multi-loss function joint optimization strategy based on physical information constraint, and each loss term weight is adjusted by stage dynamic weight scheduling strategy;The two-channel input tensor to be predicted is input into the trained wavefield prediction model, and the wavefield prediction result is output.The application effectively solves the long time series prediction accuracy attenuation problem by time attention mechanism and stage dynamic weight scheduling strategy.

Description

Technical Field

[0001] This invention relates to the field of seismic wave numerical simulation technology, and in particular to a method and system for accelerating the forward modeling of seismic wave equations based on deep learning. Background Technology

[0002] Full waveform inversion (FWI) and least squares reverse time migration (LSRTM) have become important tools for velocity modeling and imaging in geophysics, but their high computational cost is a major obstacle to their widespread application. Among these, seismic wave numerical simulation, as the core computational component, is a key factor contributing to the high computational cost.

[0003] In existing technologies, numerical simulation of seismic waves is mainly based on solving the wave equation using the finite difference method, which approximates the propagation of the wave field in the continuous medium through spatial and temporal discretization. However, the finite difference method has the following disadvantages: (1) Large computational load: For complex models and high accuracy requirements, the finite difference method requires a large amount of computational resources, and a single forward modeling simulation takes a long time; (2) Low iteration efficiency: In full waveform inversion and least squares reverse time migration, a large number of forward modeling iterations are required, and traditional methods are difficult to meet the efficiency requirements; (3) Complex boundary condition handling: The traditional perfectly matched layer (PML) absorbing boundary conditions are complex to implement and have a large computational cost; (4) Long-term prediction accuracy decay: The prediction accuracy of existing data-driven methods often decreases significantly in the late time, making it difficult to maintain high-precision predictions throughout the entire time series.

[0004] Despite the continuous development of computing hardware (such as GPUs and TPUs), relying solely on hardware upgrades to meet the near-limitless computing resource demands of applications like Full Waveform Inversion (FWI) is no longer sustainable. Traditional numerical methods are computationally intensive, and their performance improvements heavily depend on the linear increase of hardware computing power, which is facing physical limits. At the same time, the massive computational demands result in extremely high energy costs, making large-scale industrial applications economically unsustainable. The industry urgently needs a new approach that can fundamentally break through the "computing power for accuracy" paradigm.

[0005] Therefore, proposing a deep learning-based method and system for accelerating the forward modeling of seismic wave equations to overcome the difficulties of existing technologies is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] The purpose of this invention is to provide a method and system for accelerating the forward modeling of seismic wave equations based on deep learning. Through the source mask input mechanism, a single model can adapt to wave field prediction at any source location without the need to train multiple models for different source locations.

[0007] To achieve the above objectives, the present invention provides the following solution: A deep learning-based method for accelerating the forward modeling of seismic wave equations includes the following steps: S1. Obtain velocity field and source location information, perform Z-score normalization on the velocity field and trim it to a preset range, generate a Gaussian distribution coded mask based on the source location information, and combine them into a dual-channel input tensor, where the first channel is the normalized velocity field and the second channel is the source mask; S2. Construct a wave field prediction model, including a 3D U-Net encoder-decoder and a lightweight time attention module. Use the AdamW optimizer combined with a cosine annealing learning rate scheduling strategy to train the model. Use a multi-loss function joint optimization strategy based on physical information constraints to optimize the model. Adjust the weights of each loss term through a phased dynamic weight scheduling strategy. S3. Gradually increase the number of time steps during training and optimization, transitioning from short-term training to full-time domain training, and finally complete the training of the wave field prediction model; S4. Input the dual-channel input tensor to be predicted into the trained wave field prediction model, realize unified source perception through the encoder-decoder of 3D U-Net, enhance the late-time feature extraction through the integrated lightweight time attention module, and output the wave field prediction result.

[0008] Preferably, in S1, the velocity field is Z-score normalized and clipped to a preset range, specifically including: The Z-score normalization method is used to calculate the global mean velocity_mean and standard deviation velocity_std of the velocity field, normalize the velocity field, and then prune the normalized values ​​to prevent outliers.

[0009] Preferably, in S2, the encoder-decoder of the 3D U-Net specifically includes: Input layer: Preliminary spatiotemporal features are extracted through 3D convolution operations, and nonlinear transformation is achieved by batch normalization and ReLU activation function; The encoder consists of multiple downsampling blocks, each containing two layers of 3D convolution, batch normalization, ReLU activation, 3D residual blocks, and max pooling operations. It progressively extracts multi-scale spatiotemporal features and preserves skip connections for decoder fusion. Bottleneck layer: Located at the deepest part of the encoder, it includes 3D convolution, batch normalization, double residual blocks and dropout layers, and integrates the first temporal attention module to enhance late feature extraction capabilities; Decoder: Composed of multiple upsampling blocks, it performs upsampling through transposed convolution, and concatenates and fuses the high-resolution features of the corresponding layer of the encoder through skip connections. It then performs 3D convolution, batch normalization, ReLU activation, and residual block processing in sequence to gradually restore the spatial resolution. A second temporal attention module is integrated before the output layer of the decoder. Output layer: The channel features are mapped to single-channel wavefield data through two convolutional layers, and a fixed scaling factor is applied to adjust the output range to match the magnitude of the wavefield values; if the output size is inconsistent with the input, it is restored to the original size through trilinear interpolation.

[0010] Preferably, in S2, the lightweight time attention module specifically includes three stages: The first stage: extracts features along the time dimension through the 3D convolutional layer temporal_conv, compresses the number of channels, ensures that convolution operations are performed only on the time axis, captures the temporal dependencies between adjacent time steps, and introduces non-linearity through ReLU activation; The second stage: The extracted temporal features are mapped to a single-channel attention weight map using the convolutional layer attention_conv, and normalization is achieved through the sigmoid function to output the weight coefficients; The third stage involves multiplying the attention weights element-wise with the original input features to highlight the spatiotemporal regions that the model focuses on, thus giving higher attention to later timeframes.

[0011] Preferably, in S2, a joint optimization strategy using multiple loss functions based on physical information constraints is employed to train and optimize the model, specifically including: The loss function is jointly optimized using seven objectives, and the expression for the total loss function is as follows: ,in, For dynamic weights at each stage, The loss functions are of various types; the seven-objective joint optimization loss function includes: time-weighted mean square error loss, multi-scale correlation loss, global correlation loss, range loss, L1 loss, smoothing loss, physical constraint loss, and late loss.

[0012] Preferably, in S3, the number of time steps is gradually increased during training and optimization, transitioning from short-term training to full-time training. This specifically includes: The Curriculum Learning strategy is adopted to gradually increase the number of training time steps to achieve a learning process from easy to difficult: epochs 0-20 use 70% of the time steps for short-term training; epochs 20-50 use 85% of the time steps for medium-term training; epochs 50-80 use 95% of the time steps for long-term training; and epochs 80+ use 100% of the time steps for full-time domain training.

[0013] Preferably, the forward modeling acceleration method also includes: The MaxAbs normalization method is used to calculate the maximum absolute value of the wave field as the scaling factor wavefield_scale. The wave field prediction results output by the wave field prediction model are multiplied by wavefield_scale and then inversely normalized to obtain wave field data in physical units.

[0014] This invention also provides a deep learning-based forward modeling acceleration system for seismic wave equations, applied to perform any of the above-mentioned deep learning-based forward modeling acceleration methods for seismic wave equations, comprising: The data acquisition module is used to acquire velocity field and source location information, perform Z-score normalization on the velocity field and crop it to a preset range, generate a Gaussian distribution coded mask based on the source location information, and combine them into a dual-channel input tensor. The model building and training module is used to build a wave field prediction model. The AdamW optimizer combined with a cosine annealing learning rate scheduling strategy is used to train the model. The model is optimized by a multi-loss function joint optimization strategy based on physical information constraints. The weights of each loss term are adjusted by a phased dynamic weight scheduling strategy. The model training transition module gradually increases the number of time steps during the training and optimization process, transitioning from short-term training to full-time domain training, and finally completing the training of the wave field prediction model; The prediction output module is used to input the dual-channel input tensor to be predicted into the trained wave field prediction model. It achieves unified source perception through the encoder-decoder of 3D U-Net and enhances the extraction of late-time features through an integrated lightweight time attention module, and outputs the wave field prediction results.

[0015] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements a representation learning method based on a multimodal knowledge graph as described above.

[0016] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects: This invention provides a deep learning-based method and system for accelerating the forward modeling of seismic wave equations. It adopts a 3D U-Net encoder-decoder architecture with a time attention module and combines a multi-loss function optimization strategy based on physical information constraints. It has the following advantages: (1) High computational efficiency: Compared with the traditional finite difference method, this invention can achieve faster and more efficient wave field prediction; (2) Unified multi-source modeling: Through the source mask input mechanism, a single model can adapt to wave field prediction at any source location without training multiple models for different source locations; (3) High late-stage prediction accuracy: Through the time attention module and the phased dynamic weight scheduling strategy, the problem of long-term prediction accuracy decay is effectively solved, and the correlation coefficient at late time can reach above 0.92; (4) Physical constraint guarantee: The introduction of a physical loss term based on the wave equation ensures that the prediction results conform to the physical laws of wave field propagation and avoids the physically unreasonable results that may occur in pure data-driven models; (5) Strong generalization ability: The model has good generalization ability for various velocity field configurations, and the global correlation coefficient is stable above 0.95. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 A schematic diagram illustrating the principle of the deep learning-based forward modeling acceleration method for seismic wave equations provided by this invention. Figure 2 This is a schematic diagram of the unified seismic source sensing 3D U-Net network architecture of the present invention; Figure 3 This is a schematic diagram of the time attention module structure of the present invention; Figure 4 This is a graph showing the weight changes of the phased loss function in this invention. Figure 5 This is a diagram showing the results of the 70×70 mesh velocity model of this invention; Figure 6 This is a comparison diagram of the predicted wavefield and the actual wavefield of this invention; Wherein, (a) is the actual wave field at 250ms, (b) is the actual wave field at 500ms, (c) is the actual wave field at 750ms, (d) is the predicted wave field at 250ms, (e) is the predicted wave field at 500ms, (f) is the predicted wave field at 750ms, (g) is the difference field between the actual wave field and the predicted wave field at 250ms, (h) is the difference field between the actual wave field and the predicted wave field at 500ms, and (i) is the difference field between the actual wave field and the predicted wave field at 750ms. Figure 7 This is a loss curve diagram of the wave field prediction model training process of the present invention; Figure 8 This is a single-channel comparison curve diagram of the present invention; Among them, (a) is the single-channel comparison curve of the actual value and the predicted value at 150ms, (b) is the single-channel comparison curve of the actual value and the predicted value at 350ms, (c) is the single-channel comparison curve of the actual value and the predicted value at 50ms, (d) is the single-channel comparison curve of the actual value and the predicted value at 250ms, (e) is the single-channel comparison curve of the actual value and the predicted value at 500ms, and (f) is the single-channel comparison curve of the actual value and the predicted value at 750ms. Detailed Implementation

[0019] 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 embodiments of the present invention, and not all embodiments. 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.

[0020] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0021] like Figure 1 As shown, the present invention provides a method for accelerating the forward modeling of seismic wave equations based on deep learning, comprising the following steps: S1. Obtain velocity field and source location information, perform Z-score normalization on the velocity field and trim it to a preset range, generate a Gaussian distribution coded mask based on the source location information, and combine them into a dual-channel input tensor, where the first channel is the normalized velocity field and the second channel is the source mask; S2. Construct a wave field prediction model, including a 3D U-Net encoder-decoder and a lightweight time attention module. Use the AdamW optimizer combined with a cosine annealing learning rate scheduling strategy to train the model. Use a multi-loss function joint optimization strategy based on physical information constraints to optimize the model. Adjust the weights of each loss term through a phased dynamic weight scheduling strategy. S3. Gradually increase the number of time steps during training and optimization, transitioning from short-term training to full-time domain training, and finally complete the training of the wave field prediction model; S4. Input the dual-channel input tensor to be predicted into the trained wave field prediction model, realize unified source perception through the encoder-decoder of 3D U-Net, enhance the late-time feature extraction through the integrated lightweight time attention module, and output the wave field prediction result.

[0022] Specifically, the core technical solution of this invention mainly includes: 1. A unified 3D U-Net network architecture for seismic source sensing This invention employs an encoder-decoder architecture based on 3D U-Net, such as... Figure 2 As shown, it specifically includes: (1) Input layer: Receives dual-channel five-dimensional tensor input (B, 2, Z, X, T), where B is the batch size, 2 represents the channel dimension, channel 0 is the normalized velocity field model (normalized to zero mean and unit variance using Z-score), and channel 1 is the Gaussian encoded mask of the seismic source location (using Gaussian distributed weights, sigma=3.0, peak value normalized to 1.0). (Z,X) is the spatial dimension (70×70 grid), and T is the temporal dimension (98 time steps, total duration 980ms, sampling interval 10ms). The input layer extracts preliminary spatiotemporal features through 3D convolution (16 groups of 3×3×3 convolution kernels), and performs nonlinear transformation with batch normalization and ReLU activation.

[0023] (2) Encoder: It consists of 4 downsampling blocks. Each downblock contains two layers of 3D convolution (the number of channels is 16→32→64→128→256 in sequence), batch normalization, ReLU activation, 3D residual block and max pooling operation (pooling kernel 2×2×2), progressively extracting multi-scale spatiotemporal features and retaining skip connections for decoder fusion. The 3D residual block (ResidualBlock3D) contains two layers of 3×3×3 convolution and batch normalization. The input is added to the convolution output through residual connections and then activated by ReLU.

[0024] (3) Bottleneck layer: Located at the deepest part of the encoder, with 512 channels, it includes 3D convolution, batch normalization, double residual block (ResidualBlock3D) and dropout layer (dropout_rate=0.1 to prevent overfitting), and integrates the first temporal attention module to enhance late feature extraction capabilities.

[0025] (4) Decoder: Composed of 4 upsampling blocks, it performs upsampling through transposed convolution (kernel_size=2, stride=2), and splices and fuses the high-resolution features of the corresponding layer of the encoder through skip connections (if the sizes do not match, they are aligned by trilinear interpolation). Then, it performs 3D convolution, batch normalization, ReLU activation and residual block processing in sequence to gradually restore the spatial resolution (the number of channels decreases from 512 to 256→128→64→32). A second temporal attention module is integrated before the output layer of the decoder.

[0026] (5) Output layer: The 32-channel features are mapped to single-channel wavefield data through two convolutional layers (32→16→1, where the first layer is a 3×3×3 convolution with batch normalization and ReLU activation, and the second layer is a 1×1×1 convolution). A fixed scaling factor (fixed_scale=0.002) is applied to adjust the output range to match the magnitude of the wavefield values. If the output size is inconsistent with the input size, it is restored to the original size through trilinear interpolation.

[0027] 2. Time Attention Module This invention designs a lightweight temporal attention module to enhance the model's attention to features at later time points, such as... Figure 3 As shown, it includes three stages: The first stage (temporal feature extraction): Features are extracted along the time dimension using a 3D convolutional layer temporal_conv(kernel_size=(1,1,3), padding=(0,0,1)), compressing the number of channels from C to C / 4, ensuring that convolution operations are performed only on the time axis, capturing the temporal dependencies between adjacent time steps, and introducing non-linearity through ReLU activation.

[0028] The second stage (attention weight generation): The extracted temporal features are mapped to a single-channel attention weight map (B, 1, Z, X, T) using a 1×1×1 convolutional layer attention_conv. The map is then normalized to the [0,1] interval using the Sigmoid function. The output weight coefficients reflect the importance of each spatiotemporal location at different times.

[0029] The third stage (feature weighted fusion) involves element-wise multiplication of the attention weights with the original input features to achieve adaptive feature enhancement, highlighting the spatiotemporal regions that the model needs to focus on, and giving higher attention to later time steps.

[0030] 3. Optimization strategy based on multiple loss functions with physical information constraints This invention employs a seven-objective joint optimization loss function, and the loss curve during the training process is shown in the figure below. Figure 7 As shown, the total loss function expression is: ,in, For dynamic weights at each stage, There are several different loss functions; each loss component includes: (1) MSE loss (L_mse): time-weighted mean square error, using a segmented time-weight strategy: the weight is 1.0 for the early time (0-30%), 1.5 for the middle time (30%-60%), and linearly increases from 2.5 to 5.0 for the late time (60%-100%), thus enhancing the constraint on the accuracy of the late wave field prediction; (2) Correlation loss (L_corr): It consists of multi-scale correlation loss (70% weight) and global correlation loss (30% weight). The multi-scale correlation loss calculates the Pearson correlation coefficient in three time windows (early stage 0-30%, mid-stage 20%-60%, late stage 50%-100%), with weights of 1.0, 1.5, and 3.5 respectively; the global correlation loss calculates the Pearson correlation coefficient between the flattened full-time series prediction and the target, and the correlation loss is defined as 1 minus the correlation coefficient; (3) Range loss (L_range): The predicted amplitude range is constrained to be consistent with the target. The calculation formula is: where pred_range and target_range are the differences between the maximum and minimum values ​​of the predicted and target wave fields, respectively. (4) L1 loss (L_l1): Basic absolute value loss, suppressing outliers; (5) Smoothing loss (L_smooth): Constrains the smoothness of the first and second differences in the time dimension. The first difference calculates the difference between adjacent time steps, and the second difference calculates the difference between the first difference. The weight of the second difference is 0.5 to simulate the continuity of wave field propagation. (6) Physical loss (L_physics): Based on the physical constraints of the acoustic wave equation, the second time derivative u_tt and the second space derivative (Laplace operator u_xx + u_zz) are calculated by finite difference approximation. The mean square value of the residual is calculated, divided by the reference scale, and then multiplied by the scaling factor 200.0. (7) Late Loss (L_late): This is a reinforcement loss specifically for late time intervals. It includes four sub-items: Late MSE (3.0 times weight), Late Smoothness (1.5 times weight), Late Correlation (2.0 times weight), and Late Amplitude Matching (1.5 times weight). The total loss is limited to the interval [0, 20.0].

[0031] 4. Phased dynamic weight scheduling strategy This invention employs a five-stage progressive training strategy, with the weight change curves of the loss function at each stage as shown in the figure. Figure 4 As shown, the weights of each loss term are dynamically adjusted: Phase 1 (epochs 0-30): Prioritize matching amplitude ranges, with the following weights: MSE 25%, Correlation 15%, Range 40%, L1 5%, Smoothing 5%, Physical 5%, and Late 5%. Phase 2 (epochs 30-60): Balancing range and correlation, with the following weighting: MSE 30%, correlation 20%, Range 30%, L1 5%, smoothing 5%, physical 5%, late stage 5%; Phase 3 (epochs 60-100): Increase the weights of MSE and relevance, with the following weight configuration: MSE 35%, relevance 25%, range 25%, L1 5%, smoothing 3%, physical 3%, and late stage 4%; Phase 4 (epochs 100-200): Relevance-driven, with the following weighting: MSE 28%, Relevance 32%, Range 18%, L1 5%, Smoothing 3%, Physical 3%, and Late Stage 11%. Phase 5 (epoch 200+): Focus on strengthening late-stage predictions, with the following weighting: MSE 20%, Correlation 30%, Range 10%, L1 5%, Smoothing 3%, Physical 7%, and Late-stage 25%.

[0032] 5. Course Learning Scheduler This invention employs a Curriculum Learning strategy, gradually increasing the number of training time steps to achieve a learning process from easy to difficult: epochs 0-20 use 70% of the time steps (approximately 68 steps) for short-term training; epochs 20-50 use 85% of the time steps (approximately 83 steps) for medium-term training; epochs 50-80 use 95% of the time steps (approximately 93 steps) for long-term training; and epochs 80+ use 100% of the full time steps (98 steps) for full-time domain training.

[0033] 6. Data Processing and Normalization Strategies The present invention employs the following data processing strategy: (1) Velocity field normalization: The Z-score normalization method is used to calculate the global mean velocity_mean and standard deviation velocity_std of the velocity field in the training set, and the velocity field is normalized. The normalized values ​​are then clipped to the interval [-5, 5] to prevent outliers. (2) Wave field normalization: The MaxAbs normalization method is used to calculate the maximum absolute value of the wave field in the training set as the scaling factor wavefield_scale to normalize the wave field; (3) Source mask generation: Gaussian distribution weights are generated based on the source location (source_x, source_z). The calculation formula is: where sigma=3.0, amplitude=1.0, dist is the Euclidean distance from the spatial point to the source, and after generation, it is normalized to a peak value of 1.0. (4) Velocity field time expansion: The two-dimensional velocity field (nz, nx, 1) is copied and expanded along the time dimension into a three-dimensional tensor (nz, nx, nt), which is aligned with the time dimension of the wave field; (5) Saving statistical information: After training, normalization parameters such as velocity_mean, velocity_std, and wavefield_scale are saved to the model checkpoint file for use during inference.

[0034] 7. Model Inference Process The model reasoning process of this invention includes: (1) Load model checkpoints: Load model_state_dict (model weights) and global_stats (normalized statistics, including velocity_mean, velocity_std, and wavefield_scale) from the .pkl file. (2) Model initialization: Create a UnifiedSourceAwareUNet3D network instance, load the weights and set it to evaluation mode net.eval(), and disable the training behavior of Dropout and BatchNorm; (3) Data preprocessing: The input velocity field is normalized by Z-score using the saved global_stats, a Gaussian mask is created for the specified source location, and the two are combined into a dual-channel input tensor; (4) Inference computation: Use the torch.no_grad() context to disable gradient computation to save memory and support CUDA automatic mixed precision (AMP) to accelerate inference; (5) Post-processing of results: Multiply the model output by wavefield_scale for inverse normalization to obtain the wavefield prediction results for physical units.

[0035] 8. Multi-dimensional evaluation indicator system The present invention uses the following evaluation indicators to comprehensively evaluate the prediction results: (1) Global correlation: Calculate the Pearson correlation coefficient between the predicted wavefield and the target wavefield after flattening; (2) Time dimension assessment: The time series is divided into early stage (first 1 / 3 of the time steps, about 0-330ms) and late stage (second 1 / 3 of the time steps, about 660-980ms), and the early stage correlation and late stage correlation are calculated respectively; at the same time, the time trend similarity is calculated, that is, the correlation coefficient of the energy (spatial sum of squares) sequence of the predicted wave field and the target wave field at each time step; (3) Spatial dimension assessment: Calculate the correlation coefficient of spatial distribution at each time point, and statistically analyze its mean, standard deviation, minimum and maximum values ​​to reflect the stability of spatial prediction; (4) Amplitude accuracy assessment: Calculate the RMS (root mean square value) of the predicted wave field and the target wave field, and calculate the amplitude ratio. The ideal value is 1.0. (5) Error analysis: Calculate the mean absolute error (MAE), root mean square error (RMSE), and maximum absolute error to quantitatively assess the prediction bias.

[0036] like Figure 5 As shown, the 70×70 grid velocity model used for model training is a two-dimensional profile model with spatial dimensions of nz×nx×ny=70×70×1. The sampling intervals in both the lateral and depth directions are 25m. Different colors represent the magnitude of the underground medium velocity values. The overall velocity range of the example is approximately 1510-3520m / s, exhibiting typical layered medium characteristics. This figure is used to characterize the velocity field channels in the input data of this invention, providing a basis for medium parameters for subsequent source mask stacking, wavefield prediction, and physical constraint calculations.

[0037] like Figure 6 As shown in Figures (a)-(i), the comparison results of the actual wavefield, the model-predicted wavefield, and the difference field between the two at different times are presented for the 7th test sample at the source locations x=41 and z=0. The first row shows the actual wavefield obtained through finite-difference forward modeling at 250ms, 500ms, and 750ms, respectively; the second row shows the wavefield predicted by the model at the corresponding times; and the third row shows the difference field between the actual and predicted wavefields at the corresponding times. This figure visually demonstrates the model's ability to recover wavefront morphology, propagation direction, and amplitude distribution in the early, middle, and late stages. The difference field reflects the spatial distribution of the prediction error and can be used to evaluate the model's preservation of the propagation patterns of long-term wavefields.

[0038] like Figure 8 As shown in Figures (a)-(f), when the source location of the 6th test sample is x=31, z=0, the curves comparing the actual and predicted values ​​of the single trace at CDP=40 are presented. The vertical axis in the figures has been normalized. Each sub-figure shows the comparison between the actual and predicted curves at different times, such as 150ms, 350ms, 50ms, 250ms, 500ms, and 750ms. The specific order is as indicated by the labels in the attached figures. This figure verifies the consistency between the model prediction results and the finite difference results in terms of phase, amplitude variation trends, and arrival characteristics from the perspective of single-trace local response. It further illustrates that the present invention can maintain overall correlation not only at the two-dimensional wavefield image level but also maintain good waveform matching effect at the local gather or single-trace scale.

[0039] Example 1 In a specific embodiment, the steps of the method of the present invention are as follows: 1. Data Preparation: Prepare velocity field data with dimensions nz×nx×ny (e.g., 70×70×1), spatial sampling interval dx=dz (e.g., 25m), and a velocity range typically between 1500-4000m / s; prepare wavefield snapshot data with dimensions nz×nx×nt (e.g., 70×70×98), time step dt (e.g., 10ms), and a total duration of 980ms; create a Gaussian-distributed source mask (sigma=3.0) for each source location (e.g., x=21,31,41,51, z=0, located at the Earth's surface). The dataset is divided into a training set of 480 groups and a test set of 120 groups, for a total of 600 data groups.

[0040] 2. Data preprocessing: The velocity field is Z-score normalized (subtract the mean and divide the standard deviation) and clipped to [-5,5]; the wave field data is MaxAbs normalized (divided by the maximum absolute value); the velocity field and source mask are combined into a dual-channel input (B, 2, Z, X, T); the velocity field is copied and extended along the time dimension to match the wave field dimension.

[0041] 3. Model Training: Configure training parameters (initial learning rate 8e-5, weight decay 1e-4, total training epochs 300, batch size 2, gradient accumulation steps 4); use the AdamW optimizer (betas=(0.9, 0.999), eps=1e-8) with a cosine annealing learning rate scheduling strategy (learning rate restart at epochs 70 and 140, with restart factors of 0.5 and 0.3 respectively), a warm-up period of 20 epochs, and a minimum learning rate of 3e-7; use CUDA automatic mixed precision training to accelerate computation, and gradient pruning (max_norm=1.5) to prevent gradient explosion; gradually increase the number of time steps according to the course learning strategy, and dynamically adjust the loss weights according to the phased strategy.

[0042] 4. Model Validation and Saving: Validate every 30 rounds for the first 30 rounds, and then every 5 epochs thereafter, calculating global correlation coefficient, RMS ratio, Range ratio and other indicators; save model checkpoints (including epoch, model_state_dict, global_stats) every 30 epochs; save the best model based on the best correlation coefficient and comprehensive score respectively (file name extensions are _best.pkl and _best_comprehensive.pkl).

[0043] 5. Model Inference and Prediction: Load the pre-trained model checkpoints and set the model to eval mode; disable gradient calculation using torch.no_grad(); input the velocity field to be predicted (normalized using saved global_stats) and a mask for any source location; support CUDA AMP mixed precision to accelerate inference; multiply the model output by wavefield_scale for inverse normalization to obtain the final wavefield prediction result; single-sample prediction time is approximately 0.3 seconds.

[0044] 6. Result Evaluation and Visualization: Calculate multi-dimensional evaluation indicators (global correlation, early / late correlation, RMS ratio, MAE, RMSE, etc.) for the prediction results; generate visualization comparison charts, including velocity field, source mask, and comparison of predictions and targets at early / mid / late time points.

[0045] This invention also provides a deep learning-based forward modeling acceleration system for seismic wave equations, applicable to any of the above-mentioned deep learning-based forward modeling acceleration methods for seismic wave equations, including... The data acquisition module is used to acquire velocity field and source location information, perform Z-score normalization on the velocity field and crop it to a preset range, generate a Gaussian distribution coded mask based on the source location information, and combine them into a dual-channel input tensor. The model building and training module is used to build a wave field prediction model. The AdamW optimizer combined with a cosine annealing learning rate scheduling strategy is used to train the model. The model is optimized by a multi-loss function joint optimization strategy based on physical information constraints. The weights of each loss term are adjusted by a phased dynamic weight scheduling strategy. The model training transition module gradually increases the number of time steps during the training and optimization process, transitioning from short-term training to full-time domain training, and finally completing the training of the wave field prediction model; The prediction output module is used to input the dual-channel input tensor to be predicted into the trained wave field prediction model. It achieves unified source perception through the encoder-decoder of 3D U-Net and enhances the extraction of late-time features through an integrated lightweight time attention module, and outputs the wave field prediction results.

[0046] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements a deep learning-based forward modeling acceleration method for seismic wave equations as described above.

[0047] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0048] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for accelerating the forward modeling of seismic wave equations based on deep learning, characterized in that, Includes the following steps: S1. Obtain velocity field and source location information, perform Z-score normalization on the velocity field and trim it to a preset range, generate a Gaussian distribution coded mask based on the source location information, and combine them into a dual-channel input tensor, where the first channel is the normalized velocity field and the second channel is the source mask; S2. Construct a wave field prediction model, including a 3D U-Net encoder-decoder and a lightweight time attention module. Use the AdamW optimizer combined with a cosine annealing learning rate scheduling strategy to train the model. Use a multi-loss function joint optimization strategy based on physical information constraints to optimize the model. Adjust the weights of each loss term through a phased dynamic weight scheduling strategy. S3. Gradually increase the number of time steps during training and optimization, transitioning from short-term training to full-time domain training, and finally complete the training of the wave field prediction model; S4. Input the dual-channel input tensor to be predicted into the trained wave field prediction model, realize unified source perception through the encoder-decoder of 3D U-Net, enhance the late-time feature extraction through the integrated lightweight time attention module, and output the wave field prediction result.

2. The method for accelerating the forward modeling of seismic wave equations based on deep learning according to claim 1, characterized in that, In step S1, the velocity field is Z-score normalized and clipped to a preset range, specifically including: The Z-score normalization method is used to calculate the global mean velocity_mean and standard deviation velocity_std of the velocity field, normalize the velocity field, and then prune the normalized values ​​to prevent outliers.

3. The method for accelerating the forward modeling of seismic wave equations based on deep learning according to claim 1, characterized in that, In S2, the encoder-decoder of 3D U-Net specifically includes: Input layer: Preliminary spatiotemporal features are extracted through 3D convolution operations, and nonlinear transformation is achieved by batch normalization and ReLU activation function; The encoder consists of multiple downsampling blocks, each containing two layers of 3D convolution, batch normalization, ReLU activation, 3D residual blocks, and max pooling operations. It progressively extracts multi-scale spatiotemporal features and preserves skip connections for decoder fusion. Bottleneck layer: Located at the deepest part of the encoder, it includes 3D convolution, batch normalization, double residual blocks and dropout layers, and integrates the first temporal attention module to enhance late feature extraction capabilities; Decoder: Composed of multiple upsampling blocks, it performs upsampling through transposed convolution, and concatenates and fuses the high-resolution features of the corresponding layer of the encoder through skip connections. It then performs 3D convolution, batch normalization, ReLU activation, and residual block processing in sequence to gradually restore the spatial resolution. A second temporal attention module is integrated before the output layer of the decoder. Output layer: The channel features are mapped to single-channel wavefield data through two convolutional layers, and a fixed scaling factor is applied to adjust the output range to match the magnitude of the wavefield values; if the output size is inconsistent with the input, it is restored to the original size through trilinear interpolation.

4. The method for accelerating the forward modeling of seismic wave equations based on deep learning according to claim 1, characterized in that, In S2, the lightweight time attention module specifically includes three stages: The first stage: extracts features along the time dimension through the 3D convolutional layer temporal_conv, compresses the number of channels, ensures that convolution operations are performed only on the time axis, captures the temporal dependencies between adjacent time steps, and introduces non-linearity through ReLU activation; The second stage: The extracted temporal features are mapped to a single-channel attention weight map using the convolutional layer attention_conv, and normalization is achieved through the sigmoid function to output the weight coefficients; The third stage involves multiplying the attention weights element-wise with the original input features to highlight the spatiotemporal regions that the model focuses on, thus giving higher attention to later timeframes.

5. The method for accelerating the forward modeling of seismic wave equations based on deep learning according to claim 1, characterized in that, In step S2, a joint optimization strategy using multiple loss functions based on physical information constraints is employed to train and optimize the model, specifically including: The loss function is jointly optimized using seven objectives, and the expression for the total loss function is as follows: ,in, For dynamic weights at each stage, The loss functions are varied; the seven-objective joint optimization loss function includes: time-weighted mean square error loss, multi-scale correlation loss, global correlation loss, range loss, L1 loss, smoothing loss, physical constraint loss, and late loss.

6. The method for accelerating forward modeling of seismic wave equations based on deep learning according to claim 1, characterized in that, In S3, gradually increasing the number of time steps during training and optimization to transition from short-term training to full-time training specifically includes: The Curriculum Learning strategy is adopted to gradually increase the number of training time steps to achieve a learning process from easy to difficult: epochs 0-20 use 70% of the time steps for short-term training; epochs 20-50 use 85% of the time steps for medium-term training; epochs 50-80 use 95% of the time steps for long-term training; and epochs 80+ use 100% of the time steps for full-time domain training.

7. The method for accelerating forward modeling of seismic wave equations based on deep learning according to claim 1, characterized in that, The forward modeling acceleration method further includes: The MaxAbs normalization method is used to calculate the maximum absolute value of the wave field as the scaling factor wavefield_scale. The wave field prediction results output by the wave field prediction model are multiplied by wavefield_scale and then inversely normalized to obtain wave field data in physical units.

8. A deep learning-based forward modeling acceleration system for seismic wave equations, applied to the execution of the deep learning-based forward modeling acceleration method for seismic wave equations as described in any one of claims 1-7, characterized in that, include: The data acquisition module is used to acquire velocity field and source location information, perform Z-score normalization on the velocity field and crop it to a preset range, generate a Gaussian distribution coded mask based on the source location information, and combine them into a dual-channel input tensor. The model building and training module is used to build a wave field prediction model. The AdamW optimizer combined with a cosine annealing learning rate scheduling strategy is used to train the model. The model is optimized by a multi-loss function joint optimization strategy based on physical information constraints. The weights of each loss term are adjusted by a phased dynamic weight scheduling strategy. The model training transition module gradually increases the number of time steps during the training and optimization process, transitioning from short-term training to full-time domain training, and finally completing the training of the wave field prediction model; The prediction output module is used to input the dual-channel input tensor to be predicted into the trained wave field prediction model. It achieves unified source perception through the encoder-decoder of 3D U-Net and enhances the extraction of late-time features through an integrated lightweight time attention module, and outputs the wave field prediction results.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements a deep learning-based forward modeling acceleration method for seismic wave equations as described in claims 1-7.

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