A seismic wave velocity inversion method based on function smoothing noise suppression technology

Abstract

The application discloses a seismic wave velocity inversion method based on function smooth noise suppression technology, comprising the following steps: defining seismic wave motion equation parameters and boundary conditions; generating a training data set; constructing a full connection neural network; defining a total loss function L; training the full connection neural network to convergence by using the training data set to minimize L, and obtaining a seismic wave propagation velocity solving model; and solving the predicted seismic wave propagation velocity of any space-time point in a research area by using the seismic wave propagation velocity solving model. The method can fully utilize observation data to quickly and accurately calculate the predicted seismic wave propagation velocity of any space-time point in the research area, can dynamically adapt to the performance of the space-time point in training, does not need to preset noise prior knowledge, avoids subjective estimation of noise level, effectively reduces the influence of noise, can obtain results at a lower calculation cost even in a high-dimensional case, and reduces the overfitting risk while retaining physical consistency.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of seismic data processing, and particularly relates to a seismic wave velocity inversion method based on function smoothing noise suppression technology. BACKGROUND

[0002] The seismic wave differential equation describes the physical law of the propagation of seismic waves in the earth medium, and the forward problem aims to calculate the corresponding seismic response and predict the propagation behavior of seismic waves in the underground medium. Compared with the forward problem, the inverse problem has significant complexity. In the related research of solving the inverse problem of the seismic wave differential equation, data noise is an important challenge. In actual problems, the observation data obtained is very limited and contains noise, and the noise in the observation data will directly affect the stability and accuracy of the solution. Noise may not only cause the model to overfit the observation data, making the solution highly sensitive to noise, but also may cause instability problems, i.e., small measurement errors will cause large fluctuations in the solution. Therefore, how to effectively process the noise in the observation data, enhance the resistance of the solution to noise, and at the same time ensure that the solution of the inverse problem has physical meaning and stability, has become one of the core problems to be solved in the research of the inverse problem of the seismic wave differential equation.

[0003] With the rapid development of machine learning and deep learning technology, more and more researchers have begun to use neural networks to solve partial differential equation problems, trying to combine the powerful fitting ability of machine learning with the precise constraints of physics to form a new type of solving framework. PINNs (Physics-informed Neural Networks) is an important breakthrough in this field. PINNs directly incorporate physical information such as control equations, boundary conditions, etc. of partial differential equations into the model training process by introducing physical constraints into the loss function of neural networks. This method greatly ensures that the trained model follows the prior knowledge and enhances the model's learning of known physical information.

[0004] Currently, two commonly used PINNs methods for solving inverse problems with noise are Bayesian Physics-Informed Neural Networks (B-PINNs) and Energy-Based Model Physics-Informed Neural Networks (EBM-PINN).

[0005] Bayesian Physics-Informed Neural Networks (B-PINNs) is an algorithm that deeply integrates Bayesian Neural Networks (BNN) and Physics-Informed Neural Networks (PINN) to solve partial differential equation (PDE) problems with noisy observation data. This method has the following problems:

[0006] (1) High computational complexity

[0007] B-PINN uses HMC method or VI method to estimate the posterior distribution, while HMC method usually requires a large number of sampling iterations in practical applications and is accompanied by complex numerical integration operations, which leads to large computational overhead and prolongs the training time. In addition, when dealing with complex partial differential equation problems, the computational resource demand for uncertainty modeling using BNN increases significantly, and the computational overhead grows rapidly with the increase of model complexity.

[0008] (2) Uncertainty of prior distribution selection

[0009] The performance of B-PINN depends largely on the selection of the prior distribution in the Bayesian neural network (BNN). The setting of the prior distribution is essentially a hypothesis about unknown parameters, and whether this hypothesis accurately reflects the actual situation of the problem directly affects the early performance of the model. In practical problems, it is often difficult to accurately express the prior distribution. If the prior distribution set has a large deviation, it may cause the model to deviate from the true value in the early stage, thereby affecting the prediction accuracy.

[0010] (3) Difficult to extend to high-dimensional problems

[0011] Although B-PINNs have shown good adaptability and robustness in dealing with low-dimensional PDE problems, when they are extended to high-dimensional problems, the computational complexity of the model will increase dramatically. This complexity mainly manifests in two aspects: on the one hand, with the increase of the dimension of the parameter space, the number of parameters that BNN needs to process grows continuously, leading to rapid expansion of the demand for computational resources; on the other hand, although the HMC method can provide relatively accurate posterior estimation, the sampling efficiency in high-dimensional space decreases significantly, which not only directly affects the efficiency of posterior estimation, but also greatly increases the training time of the model, further reducing the operability and practicality of B-PINNs in high-dimensional problems. Thus the extensibility of B-PINNs in high-dimensional PDE problems is limited, and it must rely on more iterations and higher computational resources, increasing the difficulty and cost of its application.

[0012] Energy model physics information neural network EBM-PINN combines physics information neural network PINNs and energy model EBM to construct a framework that can learn the prior information of physical equations and adaptively model noise distribution. This method has the following problems:

[0013] (1) High computational cost

[0014] The joint training strategy of EBM-PINN needs to optimize two networks simultaneously, which greatly increases the computational complexity and training time. In practical applications, when dealing with high-dimensional PDEs or complex noise distributions, the training time of the model may be significantly prolonged.

[0015] (2) Dependence on large-scale data and EBM model

[0016] Although EBM can effectively estimate the noise distribution, its training process relies on a large number of data samples, and the hyperparameters of the EBM model itself also need to be finely adjusted. If EBM fails to correctly estimate the noise distribution, it may affect the training effect of the entire model. SUMMARY

[0017] The purpose of the present application is to provide a seismic wave velocity inversion method based on function smoothing noise suppression technology that can suppress the interference of noise in data on the solution, simplify the training process, reduce the demand for computing resources, and adapt to high-dimensional space.

[0018] To achieve the above purpose, the technical scheme adopted by the present application is as follows: a seismic wave velocity inversion method based on function smoothing noise suppression technology, comprising the following steps:

[0019] S1, defining the control condition of the seismic wave equation for solving the seismic wave propagation velocity and boundary conditions , including S11-S12;

[0020] S11, establishing a yz coordinate system in the study area and defining a geometric domain , boundary ;

[0021] ;

[0022] ;

[0023] Wherein y and z are points in the horizontal direction and vertical direction of the yz coordinate system, respectively, and a and c are the far boundaries in the horizontal direction and vertical direction, respectively. The space-time point , t is the time;

[0024] S12, obtaining the control condition of the seismic wave equation and boundary conditions according to the following formula;

[0025] , ,

[0026] ,

[0027] where v is the seismic wave propagation velocity, and u is the seismic wave field;

[0028] S2, generating a training data set ;

[0029] Obtaining a number of spatiotemporal points x in the geometric domain Ω to form a point set , obtaining a number of spatiotemporal points x on the boundary to form a point set , reading the observation data of the study area to obtain a number of spatiotemporal points x and the corresponding seismic wave field , obtaining an observation data set ;

[0030] S3, constructing a fully connected neural network for inputting the spatiotemporal point x and outputting the corresponding predicted seismic wave field , and predicting the seismic wave propagation velocity ;

[0031] S4, defining a total loss function L;

[0032] ,

[0033] ,

[0034] ,

[0035] ,

[0036] ,

[0037] wherein is the seismic wave equation residual, is the boundary condition residual, is the data residual, is the regularization loss of function smoothing, , , , are weight parameters of , , , , , , are the number of spatiotemporal points in , , , , are the fully connected neural network input x, and the outputs and , and are substituted into , The calculated value;

[0038] The The i-th space-time point in the interior, around which normal distribution sampling is performed to obtain a plurality of sampling space-time points, constituting a sampling point set , The The sampling space-time point in the interior, The fully connected neural network outputs the predicted seismic wave field;

[0039] S5, using the training data set T to train the fully connected neural network to minimize L to convergence, obtaining a seismic wave propagation velocity solving model;

[0040] S6, using the seismic wave propagation velocity solving model to solve;

[0041] Obtain any space-time point in the study area , input the seismic wave propagation velocity solving model, output its corresponding predicted seismic wave field And the predicted seismic wave propagation velocity .

[0042] As preferred: the observation data includes space-time points, space-time points corresponding to the seismic wave field.

[0043] As preferred: in S5, when training the fully connected neural network, the Adam optimizer and the L-BFGS optimizer are mixed to optimize the total loss function L.

[0044] In the present application, regarding each component in the total loss function L, wherein, The seismic wave equation residual is The boundary condition residual is , , The space-time points in the interior participate in the calculation of And , used to constrain the model to follow the prior physical information; The data residual is only The space-time points in the interior participate in the calculation, used to measure the degree to which the model satisfies the observation data, and to ensure that the model follows the physical constraints while not deviating from the true data. The regularization loss of the function smoothing is based on the sampling point set And the observation data point set ​, for processing local small range noise problems. In the real spatiotemporal point in the observation data set, unknown noise often has a greater impact on the corresponding area of the model training, under the joint constraint of physical information loss term and data loss term, by dynamically sampling nearby spatiotemporal points in the observation data set and calculating the difference between the adjacent points and the data points, the local fitting result can be effectively avoided from large deviation caused by data point noise without losing the original data information, and the solving result in the region is kept smooth.

[0045] In the present application: after determining the research area, The observation data from the research area contains spatiotemporal points x and corresponding seismic wave field , 、 A series of defined spatiotemporal point sets. Based on 、 、 Train the full connection neural network for solving the velocity of the spatiotemporal point corresponding to any position and time in the research area.

[0046] Compared with the prior art, the present application has the advantages that:

[0047] (1) Make full use of the information of the observation data. This method does not need additional data preprocessing steps, avoids information loss, and realizes the maximum use of effective information in the observation data.

[0048] (2) Without noise modeling, it has good adaptability. Traditional methods often rely on the preset or modeling of noise distribution, and this method discards the dependence on noise modeling by combining regularization and adaptive adjustment. This design makes the model not need to preset the noise level or assume the distribution form of the noise, so that the model can adaptively adjust the fitting strategy during the training process according to the real-time performance of the spatiotemporal point, thereby avoiding the problem of model performance decline caused by inaccurate prior assumptions. This flexible adaptability enables the model to adaptively adjust and maintain high robustness when dealing with more complex data.

[0049] (3) Local noise processing effect is better, and the smoothness of the prediction solution is enhanced. By dynamically sampling and predicting error adjustment around the spatiotemporal point during the model training process, this method can better capture the influence of small range noise, effectively process local small range noise problems, and realize more natural noise smoothing processing without losing the original data information, while maintaining data integrity and reducing the instability caused by single point error.

[0050] (4) Reducing the computational complexity, easier to deal with high-dimensional problems. The design of the regularization term helps to limit the complexity of the solution in high-dimensional space, preventing overfitting of the model under high-dimensional data. In addition, the dynamic sampling mechanism preferentially concentrates computing resources on key spatiotemporal points according to the local characteristics of the data, avoiding the problem of global computational redundancy. The model reduces the computational cost by simplifying the loss space exploration process. This scheme significantly shortens the training time while maintaining high accuracy, providing a practical solution path for high-dimensional PDE problems. BRIEF DESCRIPTION OF DRAWINGS

[0051] Figure 1 The flowchart of the present application. DETAILED DESCRIPTION

[0052] The present application will be further described below in conjunction with examples and drawings.

[0053] Example 1: see Figure 1 A seismic wave velocity inversion method based on function smooth noise suppression technology, comprising the following steps:

[0054] S1, defining the control condition of the seismic wave equation for solving the seismic wave propagation velocity And the boundary condition , including S11~S12;

[0055] S11, establish a yz coordinate system in the study area, define the geometric domain , boundary ;

[0056] ;

[0057] ;

[0058] Wherein, y, z are points in the yz coordinate system, horizontal direction, vertical direction, a, c are the far end boundary of the horizontal direction, vertical direction; Spatiotemporal point , t is time;

[0059] S12, get the control condition of the seismic wave equation And the boundary condition ;

[0060] , ,

[0061] ,

[0062] In the formula, v is the seismic wave propagation velocity, u is the seismic wave field;

[0063] S2, generate training data set ;

[0064] Obtain several spatio-temporal points x in the geometric domain Ω to form a point set , obtain several spatio-temporal points x on the boundary to form a point set , read the observation data of the study area to obtain several spatio-temporal points x and corresponding seismic wave fields , obtain an observation data set ;

[0065] S3, construct a fully connected neural network for inputting the spatio-temporal points x and outputting the corresponding predicted seismic wave fields , and predicting the seismic wave propagation velocity ;

[0066] S4, define a total loss function L;

[0067] ,

[0068] ,

[0069] ,

[0070] ,

[0071] ,

[0072] In the formula, is a seismic wave equation residual, is a boundary condition residual, is a data residual, is a regularization loss of function smoothing, , , , are weight parameters of , , , respectively, , , are the number of spatio-temporal points in , , respectively, , are the fully connected neural network input x, output and , and the values calculated by substituting , ;

[0073] for ​In the i th space-time point, normal distribution sampling is performed around the space-time point, a plurality of sampling space-time points are obtained, and a sampling point set is formed , is the sampling space-time point in the i th space-time point, is the predicted seismic wave field output by the fully connected neural network .

[0074] S5, using the training data set T to minimize L to train the fully connected neural network to convergence, obtaining a seismic wave propagation velocity solving model;

[0075] S6, using the seismic wave propagation velocity solving model to solve

[0076] Obtain any space-time point in the study area , input the seismic wave propagation velocity solving model, output its corresponding predicted seismic wave field and predicted seismic wave propagation velocity .

[0077] In the embodiment, the observation data includes space-time points and seismic wave fields corresponding to the space-time points. In S5, when training the fully connected neural network, the Adam optimizer and the L-BFGS optimizer are used to optimize the total loss function L.

[0078] In the observation data, noise cannot be avoided, the noise level is unknown, and the noise rule is not clear. In this case, the traditional seismic wave velocity inversion method cannot effectively filter out noise data in the calculation process, so the inversion result will be affected by noise to some extent, making it difficult to guarantee the credibility of the inversion result and the accuracy of some areas is low. Other deep learning methods need to estimate the noise rule when inverting the velocity, which is difficult to estimate in actual scenarios. The method uses regularization method and physical information network to constrain noise, and smooths the area with large noise through regularization without noise rule estimation, which can ensure that the model meets the physical prior and guarantees the accuracy of the model with low calculation cost, meeting the actual application requirements.

[0079] The above only describes the preferred embodiments of the present application and is not intended to limit the present application. Any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the present application.​

Claims

1. A seismic wave velocity inversion method based on function smoothing noise suppression technology, characterized in that: Includes the following steps; S1 defines the governing conditions for solving the seismic wave equation for seismic wave propagation velocity. and boundary conditions Including S11~S12; S11, Establish a yz coordinate system in the study area and define the geometric domain. ,boundary ; ； ； Where y and z are points in the horizontal and vertical directions of the yz coordinate system, respectively, and a and c are the far boundaries in the horizontal and vertical directions, respectively; spatiotemporal points t is time; S12, the governing conditions of the seismic wave equation are obtained according to the following formula. and boundary conditions ; ， ， ， In the formula, v is the propagation velocity of the seismic wave, and u is the seismic wave field; S2, Generate the training dataset ; Within the geometric domain Ω, obtain several spatiotemporal points x to form a point set. At the border A point set is formed by obtaining several spatiotemporal points x. By reading observational data of the study area, several spatiotemporal points x and their corresponding seismic wavefields were obtained. , to obtain the observation dataset ; S3. Construct a fully connected neural network to take a spatiotemporal point x as input and output its corresponding predicted seismic wavefield. Predicting the propagation speed of seismic waves ; S4, Define the total loss function L; ， ， ， ， ， In the formula, For data residuals, The regularization loss is for function smoothing. , , , They are respectively , , , The weight parameters, , , They are respectively , , The number of spatiotemporal points in the middle, the input x is processed by a fully connected neural network and the output is... and ,Will and Substitute u and v , The formula yields the governing conditions and boundary conditions of the seismic wave equation, which are denoted as follows: , ; right For the i-th spatiotemporal point, perform normal distribution sampling around it to obtain multiple sampling spatiotemporal points, which constitute the sampling point set. , for Sampling spatiotemporal points within, For fully connected neural networks The output is the predicted seismic wave field; S5. Using the training dataset T, train a fully connected neural network to minimize L until convergence, and obtain the seismic wave propagation velocity solution model. S6, solve the model using the seismic wave propagation velocity; Obtain any spatiotemporal point within the study area Input the seismic wave propagation velocity solution model and output its corresponding predicted seismic wave field. And predicting the propagation speed of seismic waves .

2. The seismic wave velocity inversion method based on function smoothing noise suppression technology according to claim 1, characterized in that: In S5, when training a fully connected neural network, the Adam optimizer and the L-BFGS optimizer are used to optimize the total loss function L.

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