Frequency domain seismic wave field forward modeling simulation method and device based on PINN

Abstract

The invention relates to the technical field of geophysical exploration, and particularly discloses a PINN-based frequency domain seismic wave field forward modeling method and device, and the method comprises the steps: taking a wave equation which should be satisfied by a background wave field, a scattered wave field and underground medium parameters as a loss function, and building a PINN network; taking part of space point coordinates in the model space as input, and carrying out iterative training on the PINN network until an output scattered wave field meets a wave equation and a boundary condition at the same time; inputting all space point coordinates in the model space into the trained PINN network to obtain scattered wave field response in the whole model space; and adding the background wave field response and the scattered wave field response to obtain a wave field response of a single frequency. According to the method, frequency domain wave field forward modeling simulation is realized, the seismic wave field forward modeling simulation efficiency is improved, the problems of low precision and high calculation cost of a conventional forward modeling simulation method in a complex work area are solved, and a new technical thought is provided for realizing intelligent seismic data processing under physical guidance.

Description

Technical Field

[0001] The invention relates to the technical field of geophysical exploration, and in particular to a frequency domain seismic wave field forward simulation method and device based on PINN. Background Art

[0002] How to properly handle complex geological models and undulating terrain and improve the accuracy and efficiency of numerical simulation has always been the research focus in seismic wave forward modeling. Traditional seismic wave forward modeling methods include finite difference, finite element, pseudospectral method, etc. These methods have their own advantages in the numerical simulation process, but there are still many problems. The finite difference method has small memory requirements, high accuracy, and is easy to implement. It is widely used in seismic wave numerical simulation. However, due to its grid division based on a fixed sampling step, it is difficult to adapt to the situation of complex and fine geological structures and undulating surfaces. The finite element method has flexible grid division and can accurately simulate complex geological bodies, but it is not suitable for high-order algorithms and has a large amount of calculation. The pseudospectral method solves spatial derivatives in the wavenumber domain, has high calculation accuracy and can avoid spatial dispersion, but is not suitable for complex geological models and cannot solve the problem of temporal dispersion. In these traditional numerical simulation methods, most of them require grid division of the model space. The resulting numerical dispersion and the huge number of grids in complex geological models will seriously affect the efficiency and accuracy of wave equation forward modeling. Therefore, it is necessary to explore some new, efficient and high-precision forward modeling technologies.

[0003] Due to its powerful feature extraction and nonlinear mapping capabilities, deep learning models are increasingly being used in seismic exploration. Seismic wave field simulation research based on deep learning has achieved certain results, but it requires a large amount of training data. In addition, since this traditional deep learning algorithm is mainly data-driven, it generally has the problem of poor generalization. When the trained network model is used for underground model wave field simulation other than training data, its applicability is reduced.

[0004] In recent years, neural networks constrained by partial differential equations have become a research hotspot in machine learning, and the corresponding physical field simulation technology based on deep learning has also gradually developed, providing a new technical reference for solving geophysical forward modeling problems. By combining the prior knowledge represented by partial differential equations with traditional machine learning algorithms, Raissi et al. first proposed the concept of physical information neural network PINN. PINN uses physical equations to reduce the demand for labeled training samples. In recent years, research on physical field simulation and inverse problem solving based on PINN has gradually increased, and has been successfully applied in many fields such as heat conduction, fluid dynamics and metamaterial design. The wave equation that describes the relationship between the seismic wave field and the underground medium is a typical partial differential equation. The present invention uses PINN to solve the frequency domain wave equation to achieve fast and efficient frequency domain seismic wave field forward simulation.

[0005] Based on this technical background, the present invention studies a frequency domain seismic wave field forward modeling method and device based on PINN. Summary of the invention

[0006] In view of the shortcomings of the prior art, the present invention provides a frequency domain seismic wave field forward modeling method and device based on PINN, which realizes frequency domain wave field forward modeling, improves the efficiency of seismic wave field forward modeling, solves the problems of low application accuracy and high calculation cost of conventional forward modeling methods in complex working areas, and provides new technical ideas for realizing intelligent seismic data processing under physical guidance.

[0007] In order to achieve the above object, a first aspect of the present invention provides a frequency domain seismic wave field forward modeling method based on PINN, comprising:

[0008] The wave equations that the background wave field, scattered wave field and underground medium parameters should satisfy are used as loss functions to build a PINN network.

[0009] Taking the coordinates of some spatial points in the model space as input, the PINN network is iteratively trained until the scattered wave field outputted by the network satisfies both the wave equation and the boundary conditions;

[0010] Input the coordinates of all spatial points in the model space into the trained PINN network to obtain the scattered wave field response in the entire model space;

[0011] The background wave field and the scattered wave field responses are added together to obtain a wave field response of a single frequency.

[0012] A second aspect of the present invention provides a frequency domain seismic wave field forward simulation device based on PINN, comprising:

[0013] The network building module is used to build the PINN network by taking the wave equations that the background wave field, the scattered wave field and the underground medium parameters should satisfy as loss functions;

[0014] An iterative training module, used for taking the coordinates of some spatial points in the model space as input, and iteratively training the PINN network until the scattered wave field outputted by the network satisfies both the wave equation and the boundary conditions;

[0015] A network inference module, used to input the coordinates of all spatial points in the model space into the trained PINN network to obtain the scattered wave field response in the entire model space;

[0016] The wave field response acquisition module is used to add the background wave field and the scattered wave field response to obtain a wave field response of a single frequency.

[0017] A third aspect of the present invention provides an electronic device, the electronic device comprising:

[0018] A memory storing executable instructions;

[0019] A processor runs the executable instructions in the memory to implement the frequency domain seismic wave field forward modeling method based on PINN according to the first aspect.

[0020] A fourth aspect of the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the PINN-based frequency domain seismic wave field forward modeling method described in the first aspect.

[0021] The beneficial effects of the present invention include:

[0022] (1) The PINN-based frequency domain seismic wave field forward modeling method proposed in the present invention realizes frequency domain wave field forward modeling, improves the efficiency of seismic wave field forward modeling, solves the problem of low accuracy and high computational cost of conventional forward modeling methods in complex work areas, and provides a new technical idea for realizing intelligent seismic data processing under physical guidance.

[0023] (2) The frequency domain seismic wave field forward modeling method based on PINN proposed in the present invention utilizes PINN to solve the frequency domain wave equation to realize intelligent seismic wave field forward modeling, which has high computational efficiency and avoids the problem of large memory usage in conventional numerical simulation. It can be used to improve the forward modeling efficiency in seismic imaging and full waveform inversion.

[0024] (3) The PINN-based frequency domain seismic wave field forward modeling method proposed in the present invention can be applied to any complex surface undulation conditions, has strong universality, and can be easily extended to complex media such as elastic and anisotropic media.

[0025] (4) Compared with the prior art, the PINN-based frequency domain seismic wave field forward modeling method proposed in the present invention has the advantages of high computational efficiency, small memory usage, and applicability to complex work areas such as undulating surfaces.

[0026] Other features and advantages of the present invention will be described in detail in the following detailed description. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] The above and other objects, features and advantages of the present invention will become more apparent through a more detailed description of exemplary embodiments of the present invention with reference to the accompanying drawings.

[0028] Figure 1 This is a flow chart of the frequency domain seismic wave field forward modeling method based on PINN proposed in the present invention.

[0029] Figure 2This is a schematic diagram of the network structure used in a specific implementation of the PINN-based frequency domain seismic wave field forward modeling method proposed in the present invention.

[0030] Figure 3 The Marmousi2 model is a specific implementation of the PINN-based frequency domain seismic wave field forward simulation method proposed in the present invention and is used to test the technical effect of the present invention.

[0031] Figure 4 It is a schematic diagram comparing finite difference forward modeling results and PINN wave field simulation results on the Marmousi2 model in a specific implementation of the PINN-based frequency domain seismic wave field forward modeling method proposed in the present invention. DETAILED DESCRIPTION

[0032] The preferred embodiments of the present invention will be described in more detail below. Although the preferred embodiments of the present invention are described below, it should be understood that the present invention can be implemented in various forms and should not be limited to the embodiments set forth herein.

[0033] The present invention provides a frequency domain seismic wave field forward modeling method based on PINN, such as Figure 1 As shown, including:

[0034] The wave equations that the background wave field, scattered wave field and underground medium parameters should satisfy are used as loss functions to build a PINN network.

[0035] Taking the coordinates of some spatial points in the model space as input, the PINN network is iteratively trained until the scattered wave field outputted by the network satisfies both the wave equation and the boundary conditions;

[0036] Input the coordinates of all spatial points in the model space into the trained PINN network to obtain the scattered wave field response in the entire model space;

[0037] The background wavefield and scattered wavefield responses are added together to obtain the wavefield response of a single frequency.

[0038] The method of the present invention realizes frequency domain wave field forward simulation, improves the efficiency of seismic wave field forward simulation, solves the problems of low application accuracy and high calculation cost of conventional forward simulation methods in complex working areas, and provides a new technical idea for realizing intelligent seismic data processing under physical guidance.

[0039] According to the present invention, the boundary condition is a regularization term of the loss function;

[0040] The wave equation is any one of an acoustic wave equation, an elastic wave equation, an anisotropic medium wave equation, and a fluid-saturated porous medium wave equation.

[0041] According to the present invention, the background wave field is calculated from the velocity at the source point;

[0042] The model space is the range of the target area to be forward modeled;

[0043] The spatial point coordinates are determined by spatially discretizing the target area to be forward modeled.

[0044] According to the present invention, the spatial point coordinates are located at the surface and below the surface.

[0045] Preferably, the PINN network is a fully connected network;

[0046] The network optimizer and network training parameters are selected before iterative training, and the network model is saved after iterative training.

[0047] According to the present invention, the output scattered wave field satisfies the wave equation at the same time: during the training iteration process, the relationship between the scattered wave field output by the PINN network and the underground medium parameters continuously approaches the wave equation.

[0048] In the present invention, PINN is used to solve the frequency domain wave equation to realize intelligent seismic wave field forward simulation, which has high computational efficiency and avoids the problem of large memory usage in conventional numerical simulation. It can be used to improve the forward modeling efficiency in seismic imaging and full waveform inversion.

[0049] Preferably, the boundary conditions are used to process reflections at the boundaries of the region to be forward modeled.

[0050] The method proposed in the present invention can be applied to any complex surface undulations, has strong universality, and can be easily extended to complex media such as elastic and anisotropic media.

[0051] Compared with the prior art, the method proposed in the present invention has the advantages of high calculation efficiency, small memory occupation, and applicability to complex work areas such as undulating surfaces.

[0052] The present invention will be described in more detail below by way of examples.

[0053] Embodiment 1:

[0054] The PINN network framework used in the PINN-based frequency domain seismic wave field forward simulation method proposed in this embodiment is as follows: Figure 2 As shown, the basic model of the network is a fully connected network, which decomposes the seismic wave field into the background wave field u 0 and the scattered field δu, where the velocity at the source point is taken as the background velocity m 0, the background wave field is obtained by analytical expression, and the scattered wave field is solved by PINN network. The scattered wave equation is solved by PINN. The network input is the coordinates of the space point, and the network output is the real part and imaginary part of the scattered wave field at the corresponding space point position. The loss function for network training is established by the scattered wave equation. In order to deal with the reflection problem at the boundary of the area to be forward modeled and further improve the accuracy of seismic wave numerical simulation, boundary condition constraints are introduced. In this embodiment, the boundary condition is used as a regularization term of the loss function and is involved in the PINN wave field simulation. The specific steps of the frequency domain seismic wave field forward simulation method based on PINN in this embodiment are as follows:

[0055] 1) According to the range of the target area to be forward modeled, perform spatial discretization, determine the coordinate position of each spatial point on the grid, and form training samples from these discrete spatial data points. For the wave field simulation problem under the undulating surface, read the undulating surface file and select the spatial data points on and below the undulating surface to form training samples;

[0056] 2) Select the velocity at the earthquake source as the background velocity and use the analytical formula to calculate the background wave field;

[0057] 3) Build a fully connected network to estimate the scattered wave field at any point within the target range to be forward modeled, and establish a loss function based on the wave equation using the background wave field, scattered wave field and underground medium parameters;

[0058] 4) Train the PINN network, select appropriate optimizers and network training parameters, optimize the network model based on the training samples, and save the final trained network model;

[0059] 5) Network model reasoning: input the spatial position of the data points in the target area to be forward modeled into the trained network and output the wave field value at the corresponding position.

[0060] like Figure 2 As shown, the network model used for wave field simulation in this embodiment is a fully connected network with 8 hidden layers, each hidden layer has 80 nodes, and except for the last layer which is a linear activation function, the activation functions of other layers are all sin functions;

[0061] like Figure 3 As shown in the figure, the Marmousi2 velocity model is discretized, and some points are randomly selected to participate in the network training. After the network training is completed, all the discrete points are input to obtain the PINN wave field simulation results. At the same time, the finite difference method is used to calculate the scattered wave field of the velocity model at the corresponding frequency.

[0062] Figure 3In the figure, the seismic wave field with a frequency of 3 Hz, from top to bottom are the finite difference forward simulation results, the PINN wave field simulation results and the absolute error between the two. The rectangular box is the target range to be forward modeled. By comparison, it is found that the PINN wave field simulation results are basically consistent with the conventional numerical simulation results with a small error, which proves the feasibility of PINN wave field simulation.

[0063] Embodiment 2:

[0064] This embodiment provides a frequency domain seismic wave field forward simulation method based on PINN, such as Figure 1 As shown, including:

[0065] The wave equations that the background wave field, scattered wave field and underground medium parameters should satisfy are used as loss functions to build a PINN network.

[0066] The coordinates of some spatial points in the model space are used as input, and the PINN network is iteratively trained until the scattered wave field it outputs satisfies both the wave equation and the boundary conditions.

[0067] Input the coordinates of all spatial points in the model space into the trained PINN network to obtain the scattered wave field response in the entire model space;

[0068] Add the background wave field and scattered wave field responses to obtain the wave field response of a single frequency;

[0069] The boundary condition is the regularization term of the loss function;

[0070] In this embodiment, the wave equation is the acoustic wave equation;

[0071] The background wave field is calculated from the velocity at the source point;

[0072] The model space is the range of the target area to be forward modeled;

[0073] The spatial point coordinates are determined by spatially discretizing the range of the target area to be forward modeled;

[0074] The coordinates of the spatial points are located on the surface and below the ground;

[0075] The PINN network is a fully connected network;

[0076] Before iterative training, the network optimizer and network training parameters are selected, and after iterative training, the network model is saved;

[0077] The output scattered wave field satisfies the wave equation at the same time: During the training iteration process, the relationship between the scattered wave field output by the PINN network and the underground medium parameters continuously approaches the wave equation;

[0078] In this embodiment, the boundary condition is used to process reflections at the boundary of the area to be forward modeled.

[0079] Embodiment three:

[0080] This embodiment provides a frequency domain seismic wave field forward simulation device based on PINN, comprising:

[0081] The network building module is used to build the PINN network by taking the wave equations that the background wave field, the scattered wave field and the underground medium parameters should satisfy as loss functions;

[0082] An iterative training module is used to take the coordinates of some spatial points in the model space as input and iteratively train the PINN network until the scattering wave field outputted by it satisfies both the wave equation and the boundary conditions;

[0083] The network inference module is used to input the coordinates of all spatial points in the model space into the trained PINN network to obtain the scattered wave field response in the entire model space;

[0084] A wave field response acquisition module is used to add the background wave field and the scattered wave field response to obtain the wave field response of a single frequency;

[0085] The boundary condition is the regularization term of the loss function;

[0086] In this embodiment, the wave equation is the acoustic wave equation;

[0087] The background wave field is calculated from the velocity at the source point;

[0088] The model space is the range of the target area to be forward modeled;

[0089] The spatial point coordinates are determined by spatially discretizing the range of the target area to be forward modeled;

[0090] The coordinates of the spatial points are located on the surface and below the ground;

[0091] The PINN network is a fully connected network;

[0092] Before iterative training, the network optimizer and network training parameters are selected, and after iterative training, the network model is saved;

[0093] The output scattered wave field satisfies the wave equation at the same time: During the training iteration process, the relationship between the scattered wave field output by the PINN network and the underground medium parameters continuously approaches the wave equation;

[0094] In this embodiment, the boundary condition is used to process reflections at the boundary of the area to be forward modeled.

[0095] Embodiment 4:

[0096] An embodiment of the present invention provides an electronic device including a memory and a processor.

[0097] A memory storing executable instructions;

[0098] The processor runs the executable instructions in the memory to implement a frequency domain seismic wave field forward modeling method based on PINN.

[0099] The memory is used to store non-temporary computer-readable instructions. Specifically, the memory may include one or more computer program products, which may include various forms of computer-readable storage media, such as volatile memory and / or non-volatile memory. The volatile memory may, for example, include random access memory (RAM) and / or cache memory (cache), etc. The non-volatile memory may, for example, include read-only memory (ROM), hard disk, flash memory, etc.

[0100] The processor may be a central processing unit (CPU) or other forms of processing units with data processing capabilities and / or instruction execution capabilities, and may control other components in the electronic device to perform desired functions. In one embodiment of the present invention, the processor is used to run the computer-readable instructions stored in the memory.

[0101] Those skilled in the art should be able to understand that in order to solve the technical problem of how to obtain a good user experience, the present embodiment may also include well-known structures such as a communication bus and an interface, and these well-known structures should also be included in the protection scope of the present invention.

[0102] For detailed description of this embodiment, reference may be made to the corresponding descriptions in the aforementioned embodiments, which will not be repeated here.

[0103] Embodiment five:

[0104] An embodiment of the present invention provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, a frequency domain seismic wave field forward modeling method based on PINN is implemented.

[0105] The computer-readable storage medium according to the embodiment of the present invention stores non-transitory computer-readable instructions, and when the non-transitory computer-readable instructions are executed by a processor, all or part of the steps of the above-mentioned methods of the embodiments of the present invention are executed.

[0106] The above-mentioned computer-readable storage media include, but are not limited to: optical storage media (e.g., CD-ROM and DVD), magneto-optical storage media (e.g., MO), magnetic storage media (e.g., magnetic tape or mobile hard disk), media with built-in rewritable non-volatile memory (e.g., memory card) and media with built-in ROM (e.g., ROM box).

[0107] The PINN-based frequency domain seismic wave field forward modeling method proposed in the embodiment of the present invention realizes frequency domain wave field forward modeling, improves the efficiency of seismic wave field forward modeling, solves the problems of low application accuracy and high computational cost of conventional forward modeling methods in complex work areas, and provides a new technical idea for realizing intelligent seismic data processing under physical guidance.

[0108] The embodiments of the present invention have been described above, and the above description is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and changes will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments.

Claims

1. A frequency domain seismic wave field forward modeling method based on PINN, It is characterized in that include: The wave equations that the background wave field, scattered wave field and underground medium parameters should satisfy are used as loss functions to build a PINN network. Taking the coordinates of some spatial points in the model space as input, the PINN network is iteratively trained until the scattered wave field outputted by the network satisfies both the wave equation and the boundary conditions; Input the coordinates of all spatial points in the model space into the trained PINN network to obtain the scattered wave field response in the entire model space; The background wave field and the scattered wave field responses are added together to obtain a wave field response of a single frequency.

2. The method according to claim 1, It is characterized in that The boundary condition is a regularization term of the loss function; The wave equation is any one of an acoustic wave equation, an elastic wave equation, an anisotropic medium wave equation and a fluid-saturated porous medium wave equation.

3. The method according to claim 1, It is characterized in that The background wave field is calculated from the velocity at the source point; The model space is the range of the target area to be forward modeled; The spatial point coordinates are determined by spatially discretizing the range of the target area to be forward modeled.

4. The method according to claim 1, It is characterized in that The spatial point coordinates are located on the surface and below the surface.

5. The method according to claim 1, It is characterized in that The PINN network is a fully connected network; The network optimizer and network training parameters are selected before the iterative training, and the network model is saved after the iterative training.

6. The method according to claim 1, It is characterized in that The output scattered wave field satisfies the wave equation at the same time: during the training iteration process, the relationship between the scattered wave field output by the PINN network and the underground medium parameter continuously approaches the wave equation.

7. The method according to claim 1, It is characterized in that The boundary conditions are used to process reflections at the boundaries of the area to be forward modeled.

8. A frequency domain seismic wave field forward simulation device based on PINN, It is characterized in that include: The network building module is used to build the PINN network by taking the wave equations that the background wave field, the scattered wave field and the underground medium parameters should satisfy as loss functions; An iterative training module, used for taking the coordinates of some spatial points in the model space as input, and iteratively training the PINN network until the scattered wave field outputted by the network satisfies both the wave equation and the boundary conditions; A network inference module, used to input the coordinates of all spatial points in the model space into the trained PINN network to obtain the scattered wave field response in the entire model space; The wave field response acquisition module is used to add the background wave field and the scattered wave field response to obtain a wave field response of a single frequency.

9. An electronic device, It is characterized in that The electronic device comprises: A memory storing executable instructions; A processor, wherein the processor runs the executable instructions in the memory to implement the PINN-based frequency domain seismic wave field forward modeling method according to any one of claims 1-7.

10. A computer-readable storage medium, It is characterized in that The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the frequency-domain seismic wave field forward modeling method based on PINN according to any one of claims 1 to 7 is implemented.

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