A three-dimensional seismic simulation method based on residual fourier neural operator
By embedding Fourier wave propagation operators into convolutional neural networks for three-dimensional earthquake simulation, the problems of low computational efficiency and insufficient applicability in existing technologies are solved, achieving efficient simulation of seismic waves in complex media and improving simulation speed and model adaptability.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-10
- Publication Date
- 2026-04-07
AI Technical Summary
Existing deep learning earthquake simulation methods are insufficient in terms of computational efficiency and training time, and are difficult to apply to the simulation of seismic waves in complex media. Traditional convolutional neural network methods are inefficient in generating training data and are limited by specific wave equation forms.
A three-dimensional seismic simulation method based on residual Fourier neural operators is adopted. By embedding Fourier wave propagation operators into a convolutional neural network, wave propagation simulation is performed alternately in the spatial domain and wavenumber domain. A neural network structure containing fully connected layers, Fourier neural operator layers and activation layers is constructed, and seismic wavefield simulation is performed using training data.
It improves the computational efficiency of earthquake simulation, reduces storage space requirements, is suitable for large-scale high-frequency seismic wave simulation in complex media, enhances the generalization performance and simulation speed of the model, increasing the simulation speed by more than 1000 times, and reduces computational costs.
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Figure CN119644416B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application belongs to the technical field of seismic simulation and relates to a three-dimensional seismic simulation method based on a residual Fourier neural operator. BACKGROUND
[0002] Early deep learning seismic simulation adopts a pure data-driven mode. Pure data-driven deep learning seismic simulation does not need to provide any physical information, requires a large amount of data and a long training time, and is difficult to be directly applied to seismic simulation.
[0003] Existing convolutional neural network CNN embedded physical deep learning seismic wave field simulation technology all adopts an implementation mode of embedding a wave equation in a loss function, and the calculation efficiency is obviously superior to that of a pure data-driven deep learning seismic simulation method, but in terms of the time for generating training data and the training time, the overall performance is still far inferior to that of a traditional numerical simulation method. Moreover, due to the introduction of a specific wave equation form, this method is usually only applicable to a certain wave equation, and to some extent, the characteristics of deep learning in automatically extracting features from data and making predictions are lost. SUMMARY
[0004] To solve the problems in the background art, the application provides a three-dimensional seismic simulation method based on a residual Fourier neural operator.
[0005] To achieve the above purpose, the application adopts the following technical solutions:
[0006] A three-dimensional seismic simulation method based on a residual Fourier neural operator comprises the following steps:
[0007] A convolutional neural network structure fused with a residual Fourier neural operator is created;
[0008] Two data files are prepared, which correspond to training data and test data respectively;
[0009] Training parameters are added to the convolutional neural network structure, and the convolutional neural network structure is trained;
[0010] Three-dimensional seismic simulation is performed based on the trained convolutional neural network structure.
[0011] Further, the convolutional neural network structure fused with the residual Fourier neural operator is a Fourier wave propagation operator structure embedded in the convolutional neural network structure, and wave propagation simulation is alternately performed in a spatial domain and a wave number domain.
[0012] Further, the specific expression of the Fourier wave propagation operator structure is as follows:
[0013]
[0014] wherein, is the output of the i-th layer operator, is an activation function, is a spatial domain convolution operator, is a spatial domain inverse Fourier transform, is a beam domain convolution operator, is a Fourier transform, is the input of the operator.
[0015] Further, the specific architecture of the convolutional neural network based on the residual Fourier neural operator is:
[0016] The Fourier neural operator seismic simulation neural network comprises two or more fully connected layers, two or more Fourier neural operator layers, and two or more activation layers.
[0017] The Fourier neural operator seismic simulation neural network simulates a seismic wave field through a plurality of fully connected layers, Fourier neural operator layers, and activation layers.
[0018] The input of the Fourier neural operator seismic simulation neural network is a wave field snapshot at time t0, and the output is a wave field snapshot at time t1.
[0019] Further, the preparation of two data files, corresponding to training data and test data respectively, comprises:
[0020] Griding the geological model and setting the shot points at fixed intervals therein;
[0021] Using a Ricker wavelet as a shot function for each shot point, and using a numerical simulation method and boundary conditions to perform seismic numerical simulation to obtain wave field snapshots within a certain time range, and then taking the part of the wave field snapshots as training data and test data;
[0022] The training data and the test data are the same in content.
[0023] Further, the addition of training parameters to the convolutional neural network structure comprises:
[0024] The number of input and output seismic wave field X-direction sampling points;
[0025] The number of input and output seismic wave field Y-direction sampling points;
[0026] The X-direction grid spacing of the seismic wave field;
[0027] The Y-direction grid spacing of the seismic wave field;
[0028] The number of X-direction wave number domain sampling points after spatial Fourier transform;
[0029] The number of Y-direction wave number domain sampling points after spatial Fourier transform;
[0030] The depth learning hidden layer width.
[0031] Compared with the prior art, the present application has the following beneficial effects:
[0032] The seismic simulation method provided by the present application has higher operation efficiency, occupies less storage space, is not restricted by spatial grid size and time step, and is more suitable for large-scale high-frequency complex medium seismic wave simulation requirements.
[0033] At the same time, the present application greatly improves the efficiency of the deep learning seismic simulation method, reduces the demand for training data volume and training time, and also enhances the generalization performance of the deep learning model.
[0034] The seismic simulation method provided by the present application breaks through the limitations of traditional numerical algorithms and sampling laws in deep learning seismic simulation, solves the problem of low efficiency of complex medium 3D seismic simulation, and can improve the simulation speed by more than 1000 times, reducing the calculation cost.
[0035] Secondly, the present application has stronger adaptability to complex geophysical physical models, can obtain stable solutions of wave equations with high precision, and improves the flexibility of deep learning technology in the process of 3D seismic forward simulation. BRIEF DESCRIPTION OF DRAWINGS
[0036] Figure 1 is the residual Fourier neural operator structure diagram of the present application;
[0037] Figure 2 is the convolutional neural network layer structure diagram in the traditional method;
[0038] Figure 3 is the convolutional seismic simulation neural network structure diagram in the traditional method;
[0039] Figure 4 is the convolutional neural network structure of the present application with residual Fourier neural operator;
[0040] Figure 5 is the linear gradient velocity model used in the present application;
[0041] Figure 6 is the simulation result of the present application using 0.10-0.14s wave field snapshots as training input;
[0042] Figure 7 is the simulation result of the present application method using 0.15s wave field snapshots as training input;
[0043] Figure 8The present invention provides simulation results, prediction results, and their differences when the wave field snapshot of 0.28s is used as training input.
[0044] Figure 9 The present invention provides simulation results, prediction results, and their differences when the wave field snapshot of 0.31s is used as training input.
[0045] Figure 10 The present invention provides simulation results, prediction results, and their differences when the wave field snapshot of 0.34s is used as training input.
[0046] Figure 11 It is the velocity model of the Dongpu Depression;
[0047] Figure 12 It is a snapshot of the seismic wave field from 0.05s to 0.09s;
[0048] Figure 13 It is a comparison of the training and testing loss functions of CNN simulation and convolutional neural network structure simulation with residual Fourier neural operators;
[0049] Figure 14 It is a comparison of wavefield snapshots at different source locations at 0.14s;
[0050] Figure 15 It is a comparison of wavefield snapshots at different source locations at 0.39s;
[0051] Figure 16 These are the results of comparing wavefield records from different earthquake source locations. Detailed Implementation
[0052] 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.
[0053] Example 1:
[0054] like Figures 1-10 As shown, the technical solution adopted in this invention is as follows: A three-dimensional seismic simulation method based on residual Fourier neural operators, comprising:
[0055] The Fourier wave propagation operator structure is embedded into the convolutional neural network structure, i.e., FNO, to alternately simulate wave propagation in the spatial domain and the wavenumber domain.
[0056] Due to the network structure conforming to the wave field propagation mode, the wave field propagation mechanism hidden in the data can be automatically met. The efficiency of the deep learning seismic simulation method is greatly improved, the demand for training data volume and training time is reduced, and the generalization performance of the deep learning model is also enhanced.
[0057] Compared with the classical finite difference numerical solution method, the method has higher operation efficiency, occupies less storage space, is not constrained by spatial grid size and time step, only needs to meet the Nyquist sampling theorem, and is more suitable for large-scale high-frequency complex medium seismic wave simulation requirements. Compared with the existing embedded physical deep learning based seismic simulation method, the method is still a data driven method, which does not depend on a specific wave equation form, and the same network can be directly applied to seismic simulation under various porous media, viscoelastic and anisotropic complex medium conditions.
[0058] As shown in Figure 1 , the Fourier neural operator layer expression is:
[0059]
[0060] In the formula, is the output of the i-th layer operator, is an activation function, is a spatial domain convolution operator, is a spatial domain inverse Fourier transform, is a beam domain convolution operator, is a Fourier transform, is the input of the operator.
[0061] As shown in Figure 2 , the expression of the traditional convolutional neural network layer is:
[0062]
[0063] The traditional convolutional neural network layer is limited by the convolution kernel size, and usually focuses on learning local information, and is not good at processing global information. The Fourier neural operator layer adds a beam domain convolution to the convolutional neural network, which can learn local and global information at the same time, and is more suitable for wave equation simulation.
[0064] As shown in Figure 3 , the convolutional neural network CNN used for seismic simulation in the embodiment has 11 layers, including 3 fully connected layers, 4 convolutional neural network layers and 4 activation layers.
[0065] As shown in Figure 4As shown, the Fourier neural operator seismic modeling neural network FNO used for seismic modeling in this embodiment is also 11 layers, including 3 fully connected layers, 4 Fourier neural operator layers and 4 activation layers. The input of the two kinds of seismic modeling neural networks is the wave field snapshot at time , and the output is the wave field snapshot at time
[0066] Two data files are prepared, corresponding to training data and test data respectively.
[0067] Among them, the training data is used for FNO training, and the test data is used for testing during the training process. Two identical files are prepared for each data, corresponding to training data and test data respectively.
[0068] First, the geological model is gridded, and the shot points are set in it at fixed intervals.
[0069] As shown in Figure 5 , the linear gradient velocity model in the figure can be discretized into 256(x)×256(z) grids with a spacing of Δx=Δz=10m, and 32(x)×32(z)=1024 shots are uniformly distributed on the model with a spacing of Δx=Δz=80m.
[0070] Secondly, the training data and test data are constructed.
[0071] Each shot point can use a Ricker wavelet as a shot function, and a conventional numerical simulation method and boundary condition are used for seismic numerical simulation to obtain wave field snapshots within a certain time range, and then the part of the wave field snapshots are used as training data and test data.
[0072] If the finite difference (FD) method and the reflection boundary condition are used for forward modeling, the wave field snapshots of each shot point within 0.10s to 0.25s time are obtained when the sampling interval Δt=0.5ms.
[0073] The wave field snapshots of the last step are resampled according to a certain spatial sampling interval and a time sampling interval, such as resampling the snapshots of Δx=Δz=40m and Δt=10ms, which can obtain 1024(shots)×15(t) snapshots, each time is 64(x)×64(z). As shown in Figure 6 , the wave field snapshots at 0.10s, 0.11s, 0.12s, 0.13s and 0.14s are used as training input, as shown in Figure 7 , the wave field snapshot at 0.15s is marked as the wave field snapshot at the shooting position, which is the expected output result.
[0074] In 1024 shots, 800 shots and their snapshots can be selected for training, the batch size is 25, the number of epochs is 32, and the other 200 shots are selected for testing.
[0075] The generated training data and test data are saved in a fixed format, and the path where the file is input in the program is input, and other parameters are configured to start training. To better illustrate the training process, the parameters related to the application are described as follows:
[0076] Sx: the number of input and output seismic wave field X direction sampling points;
[0077] Sy: the number of input and output seismic wave field Y direction sampling points;
[0078] dx: the grid spacing of the seismic wave field in the X direction;
[0079] dy: the grid spacing of the seismic wave field in the Y direction;
[0080] mode: the number of X direction wave number domain sampling points after spatial Fourier transform;
[0081] mode2: the number of Y direction wave number domain sampling points after spatial Fourier transform;
[0082] width: the width of the deep learning hidden layer.
[0083] In this embodiment, still taking the gradual velocity model in Figure 5 as an example, the actual parameters of part of the settings are as follows:
[0084] Sx=31# the number of input and output seismic wave field X direction sampling points is 31;
[0085] Sy=8# the number of input and output seismic wave field Y direction sampling points is 8;
[0086] dx=40# the grid spacing of the seismic wave field in the X direction is 40m;
[0087] dy=40# the grid spacing of the seismic wave field in the Y direction is 40m;
[0088] mode=15# the number of X direction wave number domain sampling points after spatial Fourier transform is 15;
[0089] mode2=4# the number of Y direction wave number domain sampling points after spatial Fourier transform is 4;
[0090] width=56# the width of the deep learning hidden layer is 56.
[0091] Taking a single GeForceRTX2080 GPU as a test object, the total training time is 372s, and the prediction time of each shot is 0.07s.
[0092] like Figure 8 — Figure 10 As shown, 3D earthquake simulations were performed using conventional numerical simulations and the convolutional neural network structure fused with residual Fourier neural operators provided by this invention, and the simulation results were compared. Simulated snapshots (finite difference numerical simulations) and predicted snapshots (using the prediction results of this patent) at times 0.28s, 0.31s, and 0.34s for the shot point (1.2, 0.8 km) were compared. It can be observed that although the error increases with time, the predicted wave propagation outside the training data time period (0.10-0.25s) is similar to the simulated wave. Boundary reflections developing from the initial time period of the training data are basically predictable, especially the bottom boundary reflection below z=2.0km in the 0.31s and 0.34s snapshots, which are entirely developed from the direct wave in the training data. In other words, this method learns the physical principles of boundary reflections from the training data and can predict wave propagation in subsequent times.
[0093] Example 2:
[0094] Taking the Cenozoic rift basin of the Dongpu Depression as an example, this paper compares the finite difference simulation, CNN simulation and the convolutional neural network structure fused with residual Fourier neural operators provided by this invention.
[0095] like Figure 11 As shown, the velocity model of the Dongpu Depression uses a 501(x)×209(z) discrete grid with a grid spacing of [missing information]. = =5m. We uniformly distributed 63(x)×26(z)=1638 seismic sources on the velocity model, with intervals of 5m. = =40m, wavefield snapshots at different times were obtained from different source locations using CNN simulation and FNO simulation respectively. For example Figure 12 As shown, training is first performed using wavefield snapshots at times 0.05s, 0.06s, 0.07s, and 0.08s as input and a wavefield snapshot at time 0.09s as output. Then, the training is recursively performed at 0.01s intervals until training is complete for all wavefield snapshots at all times. Finally, training begins for the next source location wavefield snapshot. The training period is 0.10-0.35s, and the FNO simulation training time is 5643s, approximately 42% of the CNN simulation training time of 13414s. Figure 13 A comparison of the training and testing loss functions for the CNN simulation and the FNO simulation is presented. It can be seen that the FNO simulation converges significantly faster than the CNN simulation, and its loss function convergence value is also significantly lower than that of the CNN simulation.
[0096] The prediction period is 0.10-0.60s. The training period of 0.10-0.35s is removed, and the period of 0.35-0.60s is the newly generated wave field snapshot data. Figure 14 and Figure 15 Comparison of wavefield snapshots at different source locations at 0.14s (within the training period) and 0.39s (outside the training period), respectively. Figure 14 In the middle, from left to right, are the residuals of the finite difference simulation, CNN simulation, FNO simulation, and the FNO simulation and finite difference results, respectively. Figure 15 From left to right, the results are finite difference simulation, CNN simulation, FNO simulation, and the residuals of the FNO simulation and finite difference simulation. Figure 16 The wavefield records at different source locations are compared, from left to right: finite difference simulation, CNN simulation, FNO simulation, and the residuals of the FNO simulation and finite difference simulation results. It can be seen that, both within and outside the training period, the consistency between the FNO simulation results and the finite difference simulation results is significantly better than that of the CNN simulation results. The average time per source for both FNO and CNN simulations is comparable, at 0.1s, far less than the average time of approximately 10s per source for finite difference simulation, representing an efficiency improvement of about 100 times per shot. If the spatial grid and time step are further increased, the efficiency of FNO simulation can be improved by more than 1000 times compared to finite difference simulation.
[0097] During training, the wave field snapshots at the first four time points are used as input, and the wave field snapshot at the last time point is used as output. Then, the process is repeated at 0.01s intervals until the wave field snapshots at all time points during the training period of 0.10-0.35s are completed.
[0098] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A three-dimensional seismic simulation method based on residual Fourier neural operators, characterized in that, Including: A convolutional neural network structure incorporating residual Fourier neural operators is created, wherein the convolutional neural network structure incorporating residual Fourier neural operators is formed by embedding a Fourier wave propagation operator structure into the convolutional neural network structure, and wave propagation simulation is performed alternately in the spatial domain and the wavenumber domain. Prepare two data files, one for training data and one for testing data; Add training parameters to the convolutional neural network structure to train the convolutional neural network structure; Three-dimensional earthquake simulation based on a trained convolutional neural network structure; The specific architecture of the convolutional neural network based on the residual Fourier neural operator is as follows: The Fourier neural operator earthquake simulation neural network consists of two or more fully connected layers, two or more Fourier neural operator layers, and two or more activation layers; The Fourier neural operator earthquake simulation neural network simulates the seismic wave field through several fully connected layers, Fourier neural operator layers, and activation layers; The input to the Fourier neural operator earthquake simulation neural network is arrive A snapshot of the wave field at time 10:00, the output is... A snapshot of the wave field at a given moment.
2. The three-dimensional seismic simulation method based on residual Fourier neural operators according to claim 1, characterized in that, The specific expression for the Fourier wave propagation operator structure is as follows: ； In the formula, It is the output of the i-th layer operator. It is an activation function. It is a spatial domain convolution operator. It is the inverse Fourier transform in the spatial domain. It is a beam-domain convolution operator. It is a Fourier transform. It is the input of the operator.
3. The three-dimensional seismic simulation method based on residual Fourier neural operators according to claim 1, characterized in that, The preparation of two data files, corresponding to training data and test data respectively, includes: The geological model is gridded, and excitation points are set within it at fixed intervals; Each excitation point uses the Ricker wavelet as the excitation function, and uses numerical simulation methods and boundary conditions to perform seismic numerical simulation to obtain a wavefield snapshot over a period of time. This wavefield snapshot is then used as training data and test data. The training data and test data contain the same content.
4. The three-dimensional seismic simulation method based on residual Fourier neural operators according to claim 1, characterized in that, Adding training parameters to the convolutional neural network structure includes: Input / output number of sampling points in the X direction of the seismic wavefield; Input / output number of sampling points in the Y direction of the seismic wavefield; Grid spacing in the X direction of the seismic wavefield; Seismic wavefield grid spacing in the Y direction; Number of wavenumber domain sampling points in the X direction after spatial Fourier transform; Number of wavenumber domain sampling points in the Y direction after spatial Fourier transform; Width of hidden layers in deep learning.