Seismic wave velocity inversion method based on function smoothing noise suppression technology

Abstract

The invention discloses a seismic wave velocity inversion method based on a function smoothing noise suppression technology. The method comprises the following steps: defining seismic wave equation parameters and boundary conditions; generating a training data set; constructing a full-connection neural network; defining a total loss function L; using the training data set to train the full-connection neural network with the minimum L until convergence, and obtaining a seismic wave propagation speed solving model; and solving the predicted seismic wave propagation speed of any time-space point in the research area by using the seismic wave propagation speed solving model. The method can fully utilize observation data to quickly and accurately calculate the predicted seismic wave propagation speed of any time-space point in a research area, can dynamically adapt to the performance of the time-space point in training, does not need to preset noise priori knowledge, avoids subjective estimation of the noise level, effectively reduces the noise influence, and can improve the prediction accuracy even under a high-dimensional condition. And the result can be obtained with relatively low calculation cost, and the over-fitting risk is reduced while the physical consistency is kept.

Description

Technical Field

[0001] The invention relates to the technical field of seismic data processing, and in particular to a seismic wave velocity inversion method based on function smoothing noise suppression technology. Background Art

[0002] The seismic wave differential equation describes the physical laws of seismic wave propagation in the earth's medium. Its direct problem aims to calculate the corresponding seismic response and predict the propagation behavior of seismic waves in the underground medium; the inverse problem compares the actual seismic data with the simulated data to infer the spatial distribution and physical properties of the underground medium. Compared with the direct problem, the inverse problem is significantly more complex. In the related research on solving the inverse problem of the seismic wave partial differential equation, data noise is an important challenge. The observation data obtained in the actual problem is very limited and the data contains noise. 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, that is, small measurement errors will cause large fluctuations in the solution. Therefore, how to effectively deal with the noise in the observation data, enhance the solution's resistance to noise, and ensure that the solution to the inverse problem is both physically meaningful and stable, has become one of the core problems that need to be solved in the inverse problem of the seismic wave partial differential equation.

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

[0004] Currently, the two commonly used PINNs methods for dealing with inverse problems in noisy conditions are Bayesian physical information neural networks (B-PINNs) and energy model physical information neural networks (EBM-PINN).

[0005] Bayesian Physical Information Neural Networks (B-PINNs) is an algorithm that deeply integrates Bayesian Neural Networks (BNN) and Physical Information Neural Networks (PINN) to solve partial differential equations (PDE) when the observed data contains noise. This method has the following problems: (1) High computational complexity

[0006] B-PINN uses the HMC method or the VI method to estimate the posterior distribution. However, the HMC method usually requires a large number of sampling iterations and is accompanied by complex numerical integration operations in practical applications, which leads to large computational overhead and prolongs the training time. In addition, when dealing with complex partial differential equation problems, the computational resource requirements for uncertainty modeling using BNN increase significantly. As the model complexity increases, the computational overhead increases significantly.

[0007] (2) Uncertainty in the selection of prior distribution The performance of B-PINN depends largely on the choice of prior distribution in the Bayesian neural network (BNN). The setting of prior distribution is essentially an assumption about unknown parameters, and whether this assumption can accurately reflect the actual situation of the problem is directly related to the early performance of the model. In practical problems, it is often difficult to accurately express the prior distribution. If the set prior distribution has a large deviation, it may cause the model to deviate from the true value in the early stage, thereby affecting the prediction accuracy.

[0008] (3) Difficult to extend to high-dimensional problems Although B-PINNs show good adaptability and robustness when dealing with low-dimensional PDE problems, the computational complexity of the model will increase dramatically when it is extended to high-dimensional problems. This complexity is mainly reflected 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 continues to grow, resulting in a rapid expansion of computing resource requirements; on the other hand, although the HMC method can provide more accurate posterior estimates, the sampling efficiency in high-dimensional space is significantly reduced, which not only directly affects the efficiency of the 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. Therefore, the scalability of B-PINNs in high-dimensional PDE problems is subject to certain limitations, and it must rely on more iterations and higher computing resources, which increases the difficulty and cost of its application.

[0009] Energy model physical information neural network EBM-PINN combines physical information neural network PINNs with energy model EBM to build a framework that can not only learn the prior information of physical equations but also adaptively model the noise distribution. This method has the following problems: (1) High computational cost The joint training strategy of EBM-PINN requires optimizing two networks simultaneously, which greatly increases the computational complexity and training time. When dealing with high-dimensional PDEs or complex noise distributions in practical applications, the training time of the model may be significantly extended.

[0010] (2) Dependence on large-scale data and EBM models 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 fine-tuned. If EBM fails to correctly estimate the noise distribution, it may affect the training effect of the entire model. Summary of the invention

[0011] The purpose of the present invention is to provide a seismic wave velocity inversion method based on function smoothing noise suppression technology, which 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.

[0012] In order to achieve the above object, the technical solution adopted by the present invention is as follows: a seismic wave velocity inversion method based on function smoothing noise suppression technology, comprising the following steps; S1, define the control conditions of the seismic wave equation for solving the seismic wave propagation velocity and boundary conditions , including S11~S12; S11, establish the yz coordinate system in the study area and define the geometric domain ,boundary ; ; ; Among them, y and z are the points in the horizontal and vertical directions in the yz coordinate system, a and c are the far boundaries in the horizontal and vertical directions respectively; space-time point , t is time; S12, the control condition of the earthquake wave equation is obtained according to the following formula and boundary conditions ; , , , In the formula, v is the propagation velocity of seismic waves, and u is the seismic wave field; S2, generate training data set ; Get several space-time points x in the geometric domain Ω to form a point set , at the border Get several space-time points x to form a point set , read the observation data of the study area, and obtain several time-space points x and the corresponding seismic wave fields , get the observation data set ; S3, construct a fully connected neural network to input a space-time point x and output its corresponding predicted seismic wave field , predicting the speed of seismic wave propagation ; S4, define the total loss function L; , , , , , In the formula, is the residual of the seismic wave equation, is the boundary condition residual, is the data residual, is the regularization loss of function smoothing, , , , They are , , , The weight parameter, , , They are , , The number of time and space points, , The fully connected neural network input x and output and , substitute , The calculated value; right The i-th time-space point in the sample is sampled in a normal distribution around it to obtain multiple sampling time-space points, forming a sampling point set , for The sampling time and space points within For a fully connected neural network Output predicted seismic wavefield; S5, using the training data set T to minimize L to train the fully connected neural network until convergence, and obtain the solution model for the seismic wave propagation velocity; S6, solve the model using the seismic wave propagation velocity; Get any time and space point in the study area , input the seismic wave propagation velocity solution model, and output its corresponding predicted seismic wave field and predicting the speed of seismic wave propagation .

[0013] Preferably, the observation data include time-space points and seismic wave fields corresponding to the time-space points.

[0014] As a preferred embodiment: in S5, when training the fully connected neural network, the total loss function L is optimized by mixing the Adam optimizer and the L-BFGS optimizer.

[0015] In the present invention, regarding the components in the total loss function L, among which, is the residual of the seismic wave equation, is the boundary condition residual, , , All time and space points participate and Calculation is used to constrain the model to follow prior physical information; is the data residual, only The mid-spacetime points participate in the calculation and are used to measure the extent to which the model satisfies the observed data, ensuring that the model does not deviate from the real data while following the physical constraints. is the regularization loss of function smoothing, which is based on the sampling point set and the set of observed data points , which is used to deal with local small-scale noise problems. In the real spatiotemporal points in the observation data set, unknown noise often has a great impact on the training of the corresponding area of ​​the model. Under the joint constraints of the physical information loss term and the data loss term, by dynamically performing local sampling near the spatiotemporal points in the observation data set and calculating the difference between the adjacent points and the data points, it is possible to effectively avoid large deviations in the local fitting results caused by data point noise without losing the original data information, and ensure that the solution results in the region remain smooth.

[0016] In the present invention: after determining the research area, The source is the observation data of the study area, including the time and space point x and the corresponding seismic wave field , , is a set of defined points that only contain space-time points. , , A fully connected neural network is trained to solve the velocity corresponding to a space-time point at any position and time in the study area.

[0017] Compared with the prior art, the advantages of the present invention are:

[0018] (1) Make full use of the information of the observation data. This method does not require additional data preprocessing steps, avoids information loss, and maximizes the use of effective information in the observation data.

[0019] (2) No need for noise modeling, with good adaptability. Traditional methods often rely on the preset or modeling of noise distribution. This method abandons the reliance on noise modeling by combining regularization with adaptive adjustment. This design allows the model to adaptively adjust the model's fitting strategy according to the real-time performance of the time and space points during training without the need to preset the noise level or assume the distribution of the noise, thereby avoiding the problem of model performance degradation caused by inaccurate prior assumptions. This flexible adaptability enables this method to adaptively adjust the model when processing more complex data, maintaining a high degree of robustness.

[0020] (3) Better local noise processing effect and enhanced prediction solution smoothness. By dynamically performing real-time local sampling and prediction error adjustment around the spatiotemporal point during model training, this method can better capture the impact of small-scale noise and effectively deal with local small-scale noise problems. By calculating the error between the sampling point and the real spatiotemporal point, a more natural noise smoothing process is achieved without losing the original data information, maintaining data integrity while reducing the instability that may be caused by single-point errors.

[0021] (4) Reduce computational complexity and make it easier to handle high-dimensional problems. The design of regularization terms helps to limit the complexity of the solution in high-dimensional space and prevent the model from overfitting under high-dimensional data. In addition, the dynamic sampling mechanism prioritizes the concentration of computing resources at key time and space points based on the local characteristics of the data, avoiding the problem of global computational redundancy. The model reduces computational costs by simplifying the loss space exploration process. This solution enables the model to significantly shorten the training time while maintaining high accuracy, providing a practical solution path for solving high-dimensional PDE problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0023] The present invention will be further described below in conjunction with embodiments and drawings.

[0024] Example 1: See Figure 1 , a seismic wave velocity inversion method based on function smoothing noise suppression technology, comprising the following steps; S1, define the control conditions of the seismic wave equation for solving the seismic wave propagation velocity and boundary conditions , including S11~S12; S11, establish the yz coordinate system in the study area and define the geometric domain ,boundary ; ; ; Among them, y and z are the points in the horizontal and vertical directions in the yz coordinate system, a and c are the far boundaries in the horizontal and vertical directions respectively; space-time point , t is time; S12, the control condition of the earthquake wave equation is obtained according to the following formula and boundary conditions ; , , , In the formula, v is the propagation velocity of seismic waves, and u is the seismic wave field; S2, generate training data set ; Get several space-time points x in the geometric domain Ω to form a point set , at the border Get several space-time points x to form a point set , read the observation data of the study area, and obtain several time-space points x and the corresponding seismic wave fields , get the observation data set ; S3, construct a fully connected neural network to input a space-time point x and output its corresponding predicted seismic wave field , predicting the speed of seismic wave propagation ; S4, define the total loss function L; , , , , , In the formula, is the residual of the seismic wave equation, is the boundary condition residual, is the data residual, is the regularization loss of function smoothing, , , , They are , , , The weight parameter, , , They are , , The number of time and space points, , The fully connected neural network input x and output and , substitute , The calculated value; right The i-th time-space point in the sample is sampled in a normal distribution around it to obtain multiple sampling time-space points, forming a sampling point set , for The sampling time and space points within For a fully connected neural network Output predicted seismic wavefield; S5, using the training data set T to minimize L to train the fully connected neural network until convergence, and obtain the solution model for the seismic wave propagation velocity; S6, solve the model using the seismic wave propagation velocity; Get any time and space point in the study area , input the seismic wave propagation velocity solution model, and output its corresponding predicted seismic wave field and predicting the speed of seismic wave propagation .

[0025] In this embodiment, the observation data includes a space-time point and a seismic wave field corresponding to the space-time point. In S5, when training the fully connected neural network, the total loss function L is optimized by mixing the Adam optimizer and the L-BFGS optimizer.

[0026] The existence of noise is usually unavoidable in observation data, and the data noise level is unknown and the noise law is unclear. In this case, the traditional seismic wave velocity inversion method cannot effectively screen out the noise data during the calculation process, so the inversion result will be affected by the noise to a certain extent, making it difficult to guarantee the credibility of the inversion result and the accuracy in some areas is low; other deep learning methods need to estimate the noise law when inverting the velocity, which is difficult to estimate in actual scenarios; this method uses regularization methods and physical information networks to constrain the noise, and smoothes the noisy areas through regularization. There is no need to estimate the noise law, and it can ensure that the model conforms to the physical prior, ensuring the accuracy of the model, with low computational cost, which meets the actual application needs.

[0027] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A seismic wave velocity inversion method based on function smoothing noise suppression technology, characterized in that: The steps include: S1, define the control conditions of the seismic wave equation for solving the seismic wave propagation velocity and boundary conditions , including S11~S12; S11, establish the yz coordinate system in the study area and define the geometric domain ,boundary ; ； ； Among them, y and z are the points in the horizontal and vertical directions in the yz coordinate system, a and c are the far boundaries in the horizontal and vertical directions respectively; space-time point , t is time; S12, the control condition of the earthquake wave equation is obtained according to the following formula and boundary conditions ; ， ， ， In the formula, v is the propagation velocity of seismic waves, and u is the seismic wave field; S2, generate training data set ; Get several space-time points x in the geometric domain Ω to form a point set , at the border Get several space-time points x to form a point set , read the observation data of the study area, and obtain several time-space points x and the corresponding seismic wave fields , get the observation data set ; S3, construct a fully connected neural network to input a space-time point x and output its corresponding predicted seismic wave field , predicting the speed of seismic wave propagation ; S4, define the total loss function L; ， ， ， ， ， In the formula, is the residual of the seismic wave equation, is the boundary condition residual, is the data residual, is the regularization loss of function smoothing, , , , They are , , , The weight parameter, , , They are , , The number of time and space points, , The fully connected neural network input x and output and , substitute , The calculated value; right The i-th time-space point in the sample is sampled in a normal distribution around it to obtain multiple sampling time-space points, forming a sampling point set , for The sampling time and space points within For a fully connected neural network Output predicted seismic wavefield; S5, using the training data set T to minimize L to train the fully connected neural network until convergence, and obtain the solution model for the seismic wave propagation velocity; S6, solve the model using the seismic wave propagation velocity; Get any time and space point in the study area , input the seismic wave propagation velocity solution model, and output the corresponding predicted seismic wave field and predicting the speed of seismic wave propagation .

2. The seismic wave velocity inversion method based on function smoothing noise suppression technology according to claim 1 is characterized in that: The observation data include time-space points and seismic wave fields corresponding to the time-space points.

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

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