Three-dimensional seismic simulation method based on residual Fourier neural operator

Abstract

The invention discloses a three-dimensional seismic simulation method based on a residual Fourier neural operator. The invention provides an embedded physics data-driven deep learning seismic wave field simulation technology. According to the method, a Fourier wave propagation operator structure is embedded into a convolutional neural network structure, and wave propagation simulation is alternately carried out in a spatial domain and a wavenumber domain. Due to the fact that the network structure conforming to the wave field propagation mode is adopted, and the implied wave field propagation mechanism in the data can be automatically met, the efficiency of the deep learning seismic simulation method is greatly improved, the requirements of the deep learning seismic simulation method for the training data volume and the training time are reduced, and meanwhile the generalization performance of a deep learning model can be enhanced. Compared with a classic finite difference numerical solution, the method has the advantages that the operation efficiency is higher, the occupied storage space is smaller, the method is not restrained by the space grid size and the time step length, and the method is more suitable for large-range high-frequency complex medium seismic wave simulation requirements.

Description

Technical Field

[0001] The invention belongs to the technical field of earthquake simulation, and relates to a three-dimensional earthquake simulation method based on residual Fourier neural operator. Background Art

[0002] Early deep learning earthquake simulations were purely data-driven. Purely data-driven deep learning earthquake simulations do not require any physical information, require a large amount of data and a long training time, and are difficult to be directly applied to earthquake simulations.

[0003] The existing convolutional neural network (CNN) embedded physical deep learning seismic wave field simulation technology adopts the implementation method of embedding the wave equation in the loss function. The computational efficiency is significantly better than the pure data-driven deep learning seismic simulation method, but considering the time to generate training data and the training time, its overall performance is still far inferior to the 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 a certain extent, it will lose the characteristics of deep learning to automatically extract features from data and make predictions. Summary of the invention

[0004] In order to solve the problems existing in the background technology, the present invention proposes a three-dimensional seismic simulation method based on residual Fourier neural operator.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is as follows: A three-dimensional seismic simulation method based on residual Fourier neural operator, comprising: Create a convolutional neural network structure fused with a residual Fourier neural operator; Prepare two data files, corresponding to training data and test data respectively; Add training parameters to the convolutional neural network structure and train the convolutional neural network structure; Three-dimensional earthquake simulation based on the trained convolutional neural network structure.

[0006] Furthermore, the convolutional neural network structure fused with the residual Fourier neural operator embeds the Fourier wave propagation operator structure into the convolutional neural network structure, and performs wave propagation simulation alternately in the spatial domain and the wavenumber domain.

[0007] Furthermore, the specific expression of the Fourier wave propagation operator structure is:

[0008] In the formula, is the output of the i-th layer operator, is the activation function, is the spatial domain convolution operator, is the inverse Fourier transform in the spatial domain, is the beam-domain convolution operator, is the Fourier transform, is the input of the operator.

[0009] Furthermore, the specific architecture of the convolutional neural network based on the residual Fourier neural operator is: The Fourier neural operator earthquake simulation neural network includes two or more fully connected layers, two or more Fourier neural operator layers and two or more activation layers; 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 of the Fourier neural operator earthquake simulation neural network is arrive The output is a snapshot of the wave field at the time A snapshot of TRON at the moment.

[0010] Furthermore, the two data files are prepared, corresponding to the training data and the test data respectively, and include: The geological model is gridded and the excitation points are set at regular intervals in it; Each excitation point uses Ricker wavelet as the excitation function, and uses numerical simulation methods and boundary conditions to perform seismic numerical simulation to obtain wave field snapshots within a period of time, and then uses this part of the wave field snapshots as training data and test data; The training data and test data have the same content.

[0011] Furthermore, the adding of training parameters to the convolutional neural network structure includes: Input and output the number of sampling points in the X direction of the seismic wave field; Input and output the number of sampling points in the Y direction of the seismic wave field; The grid spacing of the seismic wave field in the X direction; Grid spacing in the Y direction of the seismic wave field; The number of sampling points in the wavenumber domain in the X direction after spatial Fourier transform; The number of sampling points in the wavenumber domain in the Y direction after spatial Fourier transform; Deep learning hidden layer width.

[0012] Compared with the prior art, the present invention has the following beneficial effects: The earthquake simulation method provided by the present invention has higher computational efficiency, occupies less storage space, is not constrained by spatial grid size and time step, and is more suitable for the needs of large-scale, high-frequency, complex medium earthquake wave simulation.

[0013] At the same time, the present invention greatly improves the efficiency of the deep learning earthquake simulation method, reduces its demand for training data volume and training time, and also enhances the generalization performance of the deep learning model.

[0014] The earthquake simulation method provided by the present invention breaks through the limitations of traditional numerical algorithms and sampling laws for deep learning earthquake simulation methods, solves the problem of low efficiency of 3D earthquake simulation in complex media, and can increase the simulation speed by more than 1,000 times, reducing computing costs.

[0015] Secondly, the present invention has stronger adaptability to complex geophysical models and can obtain stable solutions to wave equations with higher accuracy, thus improving the flexibility of deep learning technology in the 3D seismic forward modeling process. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 The present invention is a structural diagram of a residual Fourier neural operator; Figure 2 This is the structure diagram of the convolutional neural network layer in the traditional method; Figure 3 This is the structure diagram of the convolutional earthquake simulation neural network in the traditional method; Figure 4 The present invention is a convolutional neural network structure fused with a residual Fourier neural operator; Figure 5 is the linear gradient velocity model adopted in the present invention; Figure 6 It is the simulation result of the present invention using the wave field snapshot of 0.10-0.14s as the training input; Figure 7 It is the simulation result when the method of the present invention uses the 0.15s wave field snapshot as the training input; Figure 8 It is the simulation results, prediction results and their differences when the method of the present invention uses the 0.28s wave field snapshot as the training input; Fig. 9 It is the simulation results, prediction results and their differences when the method of the present invention uses the 0.31s wave field snapshot as the training input; Fig.10 It is the simulation results, prediction results and their differences when the method of the present invention uses the 0.34s wave field snapshot as the training input; Fig.11 It is the velocity model of Dongpu Sag; Fig.12 It is a snapshot of the seismic wave field from 0.05s to 0.09s; Fig.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 operator; Fig.14 It is the comparison of wave field snapshots at different source locations at 0.14s; Fig.15 It is the comparison of wave field snapshots at different source locations at 0.39s; Fig.16 It is the comparison result of wave field records at different earthquake source locations. DETAILED DESCRIPTION

[0017] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0018] Embodiment 1: like Figure 1-Figure 10 As shown, the technical solution adopted by the present invention is as follows: a three-dimensional seismic simulation method based on residual Fourier neural operator, comprising: The Fourier wave propagation operator structure is embedded into the convolutional neural network structure, namely FNO, which simulates wave propagation alternately in the spatial domain and the wavenumber domain.

[0019] Because the network structure conforms to the wave field propagation mode and can automatically meet the wave field propagation mechanism implicit in the data, the efficiency of deep learning earthquake simulation methods is greatly improved, the demand for training data volume and training time is reduced, and the generalization performance of deep learning models is also enhanced.

[0020] Compared with the classical finite difference numerical solution, this method has higher computational efficiency, occupies less storage space, is not constrained by the size of the spatial grid and the time step, and only needs to satisfy the Nyquist sampling theorem, making it more suitable for large-scale, high-frequency, complex medium seismic wave simulation needs. Compared with the existing seismic simulation methods based on embedded physical deep learning, this method is still a data-driven method that does not rely on a specific form of the wave equation. The same network can be directly applied to seismic simulations under various porous media, viscoelastic and anisotropic media conditions.

[0021] like Figure 1 As shown, the Fourier neural operator layer expression is:

[0022] In the formula, is the output of the i-th layer operator, is the activation function, is the spatial domain convolution operator, is the inverse Fourier transform in the spatial domain, is the beam-domain convolution operator, is the Fourier transform, is the input of the operator.

[0023] like Figure 2 As shown, the traditional convolutional neural network layer expression is:

[0024] Traditional convolutional neural network layers are limited by the size of the convolution kernel and usually focus on learning local information, but are not good at processing global information. The Fourier neural operator layer adds a beam domain convolution on the basis of the convolutional neural network, which can learn both local and global information at the same time and is more suitable for wave equation simulation.

[0025] like Figure 3 As shown, the convolutional neural network CNN used for earthquake simulation in this embodiment has a total of 11 layers, including 3 fully connected layers, 4 convolutional neural network layers and 4 activation layers.

[0026] like Figure 4 As shown in FIG. 1 , the Fourier neural operator earthquake simulation neural network FNO used for earthquake simulation in this embodiment also has 11 layers, including 3 fully connected layers, 4 Fourier neural operator layers and 4 activation layers. The inputs of the two earthquake simulation neural networks are arrive The output is a snapshot of the wave field at the time In this embodiment, Prepare two data files, corresponding to training data and test data respectively.

[0027] 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 the training data and the test data respectively.

[0028] The geological model is first gridded and the excitation points are set at regular intervals in it.

[0029] like Figure 5 As shown, 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 shot points are evenly distributed on the model with a spacing of Δx=Δz=80m.

[0030] Next, we construct training data and test data.

[0031] Each excitation point can use Ricker wavelet as the excitation function, and use conventional numerical simulation methods and boundary conditions to perform seismic numerical simulation to obtain a wave field snapshot within a period of time, and then use this part of the wave field snapshot as training data and test data.

[0032] For example, by using the finite difference (FD) method and reflecting boundary conditions for forward modeling, a wave field snapshot of each shot point within the time range of 0.10s to 0.25s can be obtained when the sampling interval Δt=0.5ms.

[0033] Resample the wave field snapshots of the previous step according to a certain spatial sampling interval and time sampling interval. For example, resample the snapshots of Δx=Δz=40m and Δt=10ms to obtain 1024 (shots)×15 (t) snapshots, and the size of each moment is 64 (x)×64 (z). Figure 6 As shown, the wave field snapshots at 0.10s, 0.11s, 0.12s, 0.13s and 0.14s are used as training inputs, as shown in Figure 7 As shown, a wave field snapshot marking the shooting position at 0.15s is taken as the expected output result.

[0034] Among the 1024 stimulus points, 800 stimulus points and their snapshots can be selected for training with a batch size of 25 and the number of epochs of 32, and another 200 stimulus points are selected for testing.

[0035] Save the generated training data and test data in a fixed format, enter the path of the file in the program, configure other parameters and start training. To better illustrate the training process, the relevant parameters of the present invention are described as follows: Sx: the number of sampling points in the X direction of the input and output seismic wave field; Sy: the number of sampling points in the Y direction of the input and output seismic wave field; dx: grid spacing in the X direction of the seismic wave field; dy: grid spacing in the Y direction of the seismic wave field; mode: the number of sampling points in the wavenumber domain in the X direction after spatial Fourier transform; mode2: the number of sampling points in the Y direction wavenumber domain after spatial Fourier transform; width: width of the deep learning hidden layer.

[0036] In this embodiment, Figure 5 Taking the gradient velocity model in as an example, the actual parameters of some settings are given as follows: Sx=31#The number of sampling points in the X direction of the input and output seismic wave field is 31; Sy=8#The number of sampling points in the Y direction of the input and output seismic wave field is 8; dx=40# The grid spacing of the seismic wave field in the X direction is 40m; dy=40# The grid spacing of the seismic wave field in the Y direction is 40m; mode=15#The number of sampling points in the X-direction wavenumber domain after spatial Fourier transform is 15; mode2=4#The number of sampling points in the Y direction wavenumber domain after spatial Fourier transform is 4; width=56#Deep learning hidden layer width 56.

[0037] Using a single GeForceRTX2080 GPU as the test object, the total training time is 372s and the prediction time for each shot point is 0.07s.

[0038] like Figure 8 — Fig.10 As shown, conventional numerical simulation and the convolutional neural network structure provided by the present invention that incorporates the residual Fourier neural operator are used to simulate three-dimensional earthquakes, and the simulation results are compared. The simulation snapshots (finite difference numerical simulation) and predicted snapshots (using the prediction results of this patent) of the shot point (1.2, 0.8) km at 0.28s, 0.31s and 0.34s are compared respectively. It can be found that although the error increases with time, the predicted wave propagation outside the time period of the training data (0.10-0.25s) is similar to the simulated wave. The boundary reflection developed from the initial time period of the training data can be basically predicted, especially the bottom boundary reflection below z=2.0km in the 0.31s and 0.34s snapshots, which is completely developed from the direct wave in the training data. In other words, the method learns the physical principle of boundary reflection from the training data and can predict the wave propagation at subsequent times.

[0039] Embodiment 2: Taking the Cenozoic faulted salt lake basin in Dongpu Sag as an example, the finite difference simulation, CNN simulation and the convolutional neural network structure integrated with the residual Fourier neural operator provided by the present invention were compared.

[0040] like Fig.11 As shown in the figure, the velocity model of Dongpu Sag adopts 501(x)×209(z) discrete grids with a grid spacing of = =5m. We evenly distribute 63(x)×26(z)=1638 earthquake sources on the velocity model, with an interval of = =40m, CNN simulation and FNO simulation were used to obtain wave field snapshots at different source locations at different times. Fig.12As shown in the figure, firstly, the wavefield snapshots at 0.05s, 0.06s, 0.07s, and 0.08s are used as input, and the wavefield snapshot at 0.09s is used as output for training, and then the training is performed recursively at intervals of 0.01s until the training of the wavefield snapshots at all times is completed, and then the training of the wavefield snapshot at the next source position is performed. The training time period is 0.10-0.35s, and the FNO simulation training takes 5643s, which is about 42% of the CNN simulation training time of 13414s. Fig.13 Comparison of training and testing loss functions of CNN simulation and FNO simulation. It can be seen that the convergence speed of FNO simulation is significantly faster than that of CNN simulation, and its loss function convergence value is also significantly lower than that of CNN simulation.

[0041] The prediction time period is 0.10-0.60s, excluding the 0.10-0.35s training time period, and 0.35-0.60s is the newly generated wave field snapshot data. Fig.14 and Fig.15 The comparison results of wave field snapshots at different source locations at 0.14s (within the training time period) and 0.39s (outside the training time period) are shown in Figure 2. Fig.14 From left to right, we can see the finite difference simulation, CNN simulation, FNO simulation, and the residual between the FNO simulation and the finite difference results. Fig.15 From left to right in the figure are the finite difference simulation, CNN simulation, FNO simulation, and the residual between the FNO simulation and the finite difference results. Fig.16 The comparison results of wave field records at different earthquake source locations are shown from left to right, including finite difference simulation, CNN simulation, FNO simulation, and the residual between FNO simulation and finite difference results. It can be seen that the consistency between FNO simulation results and finite difference simulation results is significantly better than that of CNN simulation results, both within and outside the training period. The average time taken for each earthquake source by FNO simulation and CNN simulation is similar, both 0.1s, which is much less than the average time taken for each earthquake source by finite difference simulation, which is about 10s. The efficiency of single-shot simulation is improved by about 100 times. If the spatial grid and time step are further increased, the efficiency of FNO simulation can be improved by more than 1,000 times that of finite difference simulation.

[0042] During the training, the wave field snapshots at the first four moments are taken as input, and the wave field snapshot at the last moment is taken as output, and then the training is repeated at intervals of 0.01s until the training of wave field snapshots at all moments in the training period 0.10-0.35s is completed.

[0043] Although the present invention has been described in detail with reference to the aforementioned embodiments, it is still possible for those skilled in the art to modify the technical solutions described in the aforementioned embodiments, or to make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A three-dimensional seismic simulation method based on residual Fourier neural operator, characterized in that: Included are: Create a convolutional neural network structure fused with a residual Fourier neural operator; Prepare two data files, corresponding to training data and test data respectively; Add training parameters to the convolutional neural network structure and train the convolutional neural network structure; Three-dimensional earthquake simulation based on the trained convolutional neural network structure.

2. A three-dimensional seismic simulation method based on residual Fourier neural operator according to claim 1, characterized in that: The convolutional neural network structure fused with the residual Fourier neural operator embeds the Fourier wave propagation operator structure into the convolutional neural network structure, and performs wave propagation simulation alternately in the spatial domain and the wave number domain.

3. The three-dimensional seismic simulation method based on residual Fourier neural operator according to claim 2 is characterized in that: The specific expression of the Fourier wave propagation operator structure is: In the formula, is the output of the i-th layer operator, is the activation function, is the spatial domain convolution operator, is the inverse Fourier transform in the spatial domain, is the beam-domain convolution operator, is the Fourier transform, is the input of the operator.

4. The three-dimensional seismic simulation method based on residual Fourier neural operator according to claim 2 is characterized in that: The specific architecture of the convolutional neural network based on the residual Fourier neural operator is: The Fourier neural operator earthquake simulation neural network includes two or more fully connected layers, two or more Fourier neural operator layers and two or more activation layers; 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 of the Fourier neural operator earthquake simulation neural network is arrive The output is a snapshot of the wave field at the time A snapshot of TRON at the moment.

5. The three-dimensional seismic simulation method based on residual Fourier neural operator according to claim 1, characterized in that: The two data files prepared, corresponding to the training data and the test data respectively, include: The geological model is gridded and the excitation points are set at regular intervals in it; Each excitation point uses Ricker wavelet as the excitation function, and uses numerical simulation methods and boundary conditions to perform seismic numerical simulation to obtain a wave field snapshot within a period of time, which is then used as training data and test data; The content of training data and test data is the same.

6. The three-dimensional seismic simulation method based on residual Fourier neural operator according to claim 1, characterized in that: The adding of training parameters to the convolutional neural network structure includes: Input and output the number of sampling points in the X direction of the seismic wave field; Input and output the number of sampling points in the Y direction of the seismic wave field; The grid spacing of the seismic wave field in the X direction; Grid spacing in the Y direction of the seismic wave field; The number of sampling points in the wavenumber domain in the X direction after spatial Fourier transform; The number of sampling points in the wavenumber domain in the Y direction after spatial Fourier transform; Deep learning hidden layer width.

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