CN114047548A - A Prediction Method for Uncertainty of Seismic Wave Impedance Inversion Based on Closed-loop Network - Google Patents

Abstract

The invention discloses an uncertainty analysis method for seismic wave impedance inversion based on a closed-loop network. Combining the closed-loop network and the deep evidence regression method, a new uncertainty analysis network is proposed, namely the uncertainty back propagation network (UB- Net), which is used to predict the uncertainty of the inversion process. The prediction uncertainty has a good correlation with the error. At the same time, by back-propagating the uncertainty on the unlabeled data, the prediction result has a good horizontal continuity. At the same time, faults can be predicted more clearly, and the inversion results are more reasonable.

Description

A Prediction Method for Uncertainty of Seismic Wave Impedance Inversion Based on Closed-loop Network

technical field

The invention belongs to the field of seismic inversion, and specifically relates to an uncertainty analysis method for seismic wave impedance inversion based on a closed-loop network, which is a high-precision seismic inversion analysis method.

Background technique

(文献3：G.

and A.Tarantola,"Neural networks and inversion of seismicdata,"Journal of Geophysical Research:Solid Earth,vol.99,no.B4,pp.6753-6768,1994,doi:https://doi.org/10.1029/93JB01563)和Lu[(文献4：L.U.Wen-Kai,L.I.Yan-Da,and Y.G.Mu,"SEISMIC INVERSION USING ERROR-BACK-PROPAGATION NEURALNETWORK,"Chinese Journal of Geophysics,1996)分别提出使用人工神经网络(ANN)和卷积神经网络(CNN)进行反演，在当时均取得了较好的效果。Wang等(文献5：Y.Wang,Q.Ge,W.Lu,and X.Yan.[2020]Well-logging constrained seismic inversion based onclosed-loop convolutional neural network IEEE Transactions on Geoscience andRemote Sensing,2020)提出使用一维闭环网络进行地震反演，能够在训练中引入无标签数据，减少了标签样本的需求量。相比于传统方法，机器学习方法可以得到更好的反演结果，但是可解释性不强。Seismic inversion is of great significance in geophysical exploration. Inversion methods can be roughly divided into two categories, namely traditional methods and machine learning-based methods. Representative traditional methods such as channel integral inversion (such as Reference 1: Ferguson, RJ, & Margrave, GF (1996). A simple algorithm for band-limited impedance inversion. CREWES annual), recursive inversion (such as Reference 2: Lindseth, RO (1979). Synthetic soniclogs—A process for stratigraphic interpretation. Geophysics, 44(1), 3-26), etc. Traditional methods usually assume a linear model, while the actual geophysical process is nonlinear, which brings relatively large inversion error. However, the model of the traditional method has good interpretability, and most of the model parameters have a relatively clear physical meaning. The machine learning method learns the nonlinear mapping from seismic data to wave impedance data by building a neural network,

(Document 3: G.

and A. Tarantola, "Neural networks and inversion of seismic data," Journal of Geophysical Research: Solid Earth, vol. 99, no. B4, pp. 6753-6768, 1994, doi: https://doi.org/10.1029/ 93JB01563) and Lu[(Reference 4: LUWen-Kai, LIYan-Da, and YGMu, "SEISMIC INVERSION USING ERROR-BACK-PROPAGATION NEURALNETWORK," Chinese Journal of Geophysics, 1996) proposed the use of artificial neural networks (ANN) and volume The inversion was carried out using the Convolutional Neural Network (CNN), which achieved good results at that time. (Literature 5: Y. Wang, Q. Ge, W. Lu, and X. Yan. [2020] Well-logging constrained seismic inversion based on closed-loop convolutional neural network IEEE Transactions on Geoscience and Remote Sensing, 2020) proposed to use One-dimensional closed-loop network for seismic inversion can introduce unlabeled data in training, reducing the demand for labeled samples. Compared with traditional methods, machine learning methods can obtain better inversion results, but the interpretability is not strong.

(Document 6: A. Kendall and Y. Gal, "What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?," 2017) summarized and proposed two kinds of certainty, one called contingent uncertainty, which is This uncertainty cannot be eliminated due to the inherent noise in the observational data; the other, known as perceptual uncertainty, is related to the model and is due to incomplete training. When seismic wave impedance inversion is performed, there are multiple solutions. One seismic data corresponds to multiple possible wave impedance inversion results, so there is a large uncertainty in the inversion process. Gal et al. (Reference 7: Y. Gal and Z. Ghahramani, "Dropout as a bayesian approximation: Representing model uncertainty in deep learning," in international conference on machine learning, 2016: PMLR, pp. 1050-1059) through the training and testing phases Adding dropout to estimate uncertainty and achieved good results, Choi et al. (Reference 8: J. Choi, D. Kim, and J. Byun, "Uncertainty estimation in impedance inversion using Bayesian deep learning," in SEG Technical Program Expanded Abstracts 2020:Society of Exploration Geophysicists,2020,pp.300-304) People used the method in Literature 7 to predict the uncertainty of single-channel wave impedance, but this method only carried out a single-channel experiment, and the prediction accuracy of wave impedance low, and the uncertainty of the forecast is not very accurate.

The present invention combines closed-loop network and deep evidence regression method Literature 9 (A. Amini, W. Schwarting, A. Soleimany, and D. Rus, "Deep evidential regression," arXiv preprint arXiv: 1910.02600, 2019) proposed a new The deterministic analysis network, called the Uncertainty Backpropagation Network (UB-Net), is used to predict the uncertainty of the inversion process. The prediction uncertainty has a good correlation with the error. Uncertainty is reversed, the prediction results have good lateral continuity, and faults can be predicted more clearly, and the inversion results are more reasonable.

Purpose of invention

The purpose of the present invention is to realize a method for accurately predicting the uncertainty of seismic wave impedance inversion. The present invention proposes a new uncertainty analysis network based on the closed-loop network and the deep evidence regression method, which is called the Uncertainty Backpropagation Network (UB-Net). UB-Net is used to predict the wave impedance uncertainty and further improve the inversion accuracy by back-propagating the uncertainty of the unlabeled data.

SUMMARY OF THE INVENTION

The present invention provides a method for predicting uncertainty of seismic wave impedance inversion based on a closed-loop network, comprising the following steps:

Step 1: Build a forward and inversion network. The built network is a closed-loop network architecture, including a forward network and an inversion network. The forward and inversion network subjects are both uncertain back-propagation networks U- net, including an encoder and a decoder, and each convolutional layer is connected by flying wires;

The input of the forward modeling network is one-dimensional wave impedance data, and the output is one-dimensional seismic data;

The inversion network adopts multi-task learning, the input is one-dimensional seismic data, the output is the edge distribution of the inversion wave impedance, the predicted wave impedance and the corresponding network uncertainty are obtained through calculation, and the four parameters that determine the edge distribution of the wave impedance are output. parameter;

Step 2: preparing data, specifically preparing actual seismic data and logging data, interpolated impedance data generated by the constraints of logging data and actual seismic data, and then convolving the interpolated impedance data to obtain synthetic seismic data;

Step 3: train the forward and inversion network, and the network training of the forward and inversion is divided into two stages: a preliminary fitting stage and an inversion uncertainty stage;

In the preliminary fitting stage, the network training process uses labeled data and unlabeled data to train forward and inversion networks to obtain forward and inversion models;

In the back-propagation uncertainty stage, on the basis of the more accurate model obtained in the preliminary fitting stage, for unlabeled data, back-propagation uncertainty, on the one hand, further improves the inversion accuracy, and on the other hand makes Uncertainty estimates are more accurate;

Step 4: Prediction evaluation, specifically: in the prediction process, use the trained inversion network to invert the seismic data to obtain the edge distribution of the wave impedance, and then calculate the prediction result and the corresponding uncertainty analysis result.

σ²～Γ^-1(β,γ)，其中Γ^-1为逆伽马分布；Preferably, in the preliminary fitting stage in the step 3, the seismic data is denoted as S, the seismic wave impedance data is denoted as AI, and it is assumed that the seismic wave impedance data AI satisfies the Gaussian distribution (μ,σ ² ), wherein μ,σ ² are unknown, and there are

σ ² ～Γ ^-1 (β,γ), where Γ ^-1 is an inverse gamma distribution;

Both the forward and inversion network structures include three closed loops, as follows:

送入反演网络，通过训练网络，学习得到波阻抗边缘分布，其边缘分布满足学生分布

根据边缘分布计算得到预测波阻抗

和不确定性

将预测波阻抗μ_j输入到所述正演网络，得到预测地震数据

Loop 1: Labeling Seismic Data

Send it to the inversion network, and through training the network, learn to obtain the edge distribution of wave impedance, and its edge distribution satisfies the student distribution

Calculate the predicted wave impedance according to the edge distribution

and uncertainty

Input the predicted wave impedance μ _j into the forward modeling network to obtain predicted seismic data

输入到正演网络得到预测的地震数据

然后将

再次输入反演网络得到预测波阻抗数据

Closed loop 2: Convert logging wave impedance data

Input to forward modeling network to get predicted seismic data

followed by

Enter the inversion network again to get the predicted wave impedance data

输入反演网络得到预测波阻抗

然后将

输入到正演网络得到预测的地震数据

Closed Loop 3: Converting Unlabeled Seismic Data

Enter the inversion network to get the predicted wave impedance

followed by

Input to forward modeling network to get predicted seismic data

The closed loop 1 and the closed loop 2 are both labeled data, and the closed loop 3 is unlabeled data;

Wherein, each closed loop uses different loss functions for training on different input data, and the loss functions include minimizing negative log-likelihood loss L _imp , mean square error loss L _s , and uncertainty loss L _ub ;

The loss function used by each closed loop is expressed as equations (1)-(3):

代表第i个闭环所使用的损失函数，L_iWS，L_s的具体形式不变，但是在不同闭环中输入的数据不同；L_iWS，L_s，L_ub的具体表达形式如式(4)-(6)所示：in,

Represents the loss function used in the ith closed loop, the specific form of L _iWS , L _s is unchanged, but the data input in different closed loops is different; the specific expression form of L _iWS , L _s , _Lub is as formula (4)- (6) shows:

L _1mp =-logp(AI _j |(μ _j ,α _j ,β _j ,γ _j ))+λ|AI _j -f _B (S _j |W _B )|(2α _j +β _j ) (4),

More preferably, in the back-propagation uncertainty stage, on the basis of the forward and inversion network structures obtained by training in the preliminary fitting stage, the uncertainty of the unlabeled data is used as the weight of the loss function to back-propagate, At this time, for unlabeled data, L' _ub is used to replace _Lub , where L' _ub is expressed as shown in formula (7):

In equation (4), λ is a hyperparameter, which is used to balance the ratio between the two losses; in equations (1)-(7), f _F represents the forward network, _WF is the weight of the forward network, and f _B represents the positive Inversion network, W _B is the weight of the inversion network, (μ _j , α _j , β _j , γ _j ) in equations (3)-(7) are the parameters that determine the edge distribution of wave impedance, and the edge distribution of wave impedance obeys the students distributed

Description of drawings

FIG. 1 is a flowchart of the method for predicting the uncertainty of seismic impedance inversion according to the present invention.

FIG. 2 is a structural diagram of a forward and inversion network constructed by the present invention.

Fig. 3 is the data flow diagram of the present invention

Fig. 4 is the inversion result of the present invention on synthetic data

Fig. 5 is the inversion result of the present invention on actual data

Detailed ways

The specific embodiments of the present invention will be further described below with reference to the accompanying drawings.

Fig. 1 is the flow chart of the prediction method of seismic wave impedance inversion uncertainty according to the present invention, there are four steps in total, and each step is introduced separately below:

Step 1: Build forward and inversion networks;

The network structure mainly includes two parts: forward network model and inversion network model. Both the forward network and the inversion network use the improved U-net model, as shown in Figure 2. It mainly includes an encoder and a decoder. Each convolutional layer is connected by flying wires. The inversion network adopts multi-task learning and outputs four parameters that determine the edge distribution of wave impedance.

Step 2: Prepare data;

This step is mainly to provide the network with relevant data for training and testing. First prepare actual seismic data and logging data. Then, the interpolated wave impedance data is generated by using the logging data and the actual seismic data, and finally the interpolated wave impedance data is convolved to obtain synthetic seismic data. The above data are all one-dimensional data, and the synthetic data and actual data experiments are carried out respectively. The input of the synthetic data experiment is synthetic seismic data, and the label is the interpolated wave impedance data; the input of the actual data experiment is the actual seismic data, and the label is the logging data. In particular, in the synthetic data, each synthetic seismic data has a corresponding label; in the actual data, only at the logging location, there is corresponding label data.

Step 3: Train forward and inversion networks;

The present invention is trained in two stages. The first stage is the preliminary fitting stage, the main purpose is to train the network to fit the input data, learn the edge distribution of the wave impedance, and obtain a more accurate predicted wave impedance and uncertainty. The second stage is the back propagation uncertainty stage. Continue to train the network while backpropagating uncertainty to further improve the inversion accuracy.

σ²～Γ^-1(β,γ)，其中Γ^-1为逆伽马分布。在以上假设基础上，分两个阶段介绍UB-Net的训练过程。In order to express the training steps more clearly, the seismic data is denoted as S, and the wave impedance data is denoted as AI. At the same time, it is assumed that the wave impedance data AI satisfies the Gaussian distribution (μ,σ ² ), where both μ and σ ² are unknown. and have

σ ² ～Γ ^-1 (β,γ), where Γ ^-1 is an inverse gamma distribution. On the basis of the above assumptions, the training process of UB-Net is introduced in two stages.

Preliminary fitting stage: train forward and inversion network models. As shown in Figure 3, the network consists of three closed-loop structures, each of which inputs different data.

送入反演网络，通过训练网络，学习得到波阻抗边缘分布，其边缘分布满足学生分布

根据边缘分布计算得到预测波阻抗

和不确定性

将预测波阻抗μ_j输入到正演网络，得到预测地震数据

Loop 1: Labeling Seismic Data

Send it to the inversion network, and through training the network, learn to obtain the edge distribution of wave impedance, and its edge distribution satisfies the student distribution

Calculate the predicted wave impedance according to the edge distribution

and uncertainty

Input the predicted wave impedance μ _j into the forward modeling network to obtain the predicted seismic data

输入到正演网络得到预测的地震数据

然后将

再次输入反演网络得到预测波阻抗数据

Closed loop 2: Convert logging wave impedance data

Input to forward modeling network to get predicted seismic data

followed by

Enter the inversion network again to get the predicted wave impedance data

输入反演网络得到预测波阻抗

然后将

输入到正演网络得到预测的地震数据

Closed Loop 3: Converting Unlabeled Seismic Data

Enter the inversion network to get the predicted wave impedance

followed by

Input to forward modeling network to get predicted seismic data

Both closed loop 1 and closed loop 2 are labeled data, and closed loop 3 is unlabeled data. The loss function used for each closed loop is as follows:

代表第i个闭环所使用的损失函数，f_F代表正演网络，W_F为正演网络权重，f_.代表正演网络，W_B为反演网络权重，L_imp，L_s的具体形式不变，但是在不同闭环中输入的数据不同，具体输入数据如上所述，L_imp，L_s，L_ub的具体表达形式为：in

Represents the loss function used by the ith closed loop, f _F represents the forward network, _WF is the weight of the forward network, f _. represents the forward network, and WB is the weight of the inversion network. _The specific form of L _imp , L _s is not However, the input data in different closed loops is different. The specific input data is as described above. The specific expressions of L _imp , L _s , and L _ub are:

L _imp = -logp(AI _j |(μ _j , α _j , β _j , γ _j ))+λ|AI _j -f _B (S _j |W _B )|(2α _j +β _j ) (4)

where λ is a hyperparameter that balances the ratio between the two losses.

Back-propagation uncertainty stage: After the preliminary fitting stage, a more accurate predicted wave impedance and corresponding uncertainty are obtained. Improve inversion accuracy. At this point all loss functions are still similar to the first stage, but L _ub is replaced by L _ub , introducing an uncertain weight term:

Step 4: Predictive evaluation;

According to the above training process, the final forward network weight and inversion network weight are obtained. During prediction, the unlabeled seismic data S is inverted, and S is input into the inversion network to obtain the predicted wave impedance and inversion uncertainty. The forward model network does not participate in the prediction evaluation, and only plays a semi-supervised role in the training phase. effect.

Experimental simulation results:

In order to verify the effectiveness and superiority of the present invention, the UB-Net proposed by the present invention is applied to synthetic data and actual data respectively. The experimental platform is Intel(R) Core(TM) i9-9820X CPU@3.30GHz, 64GB RAM, GeForceRTX 2080Ti.

In the synthetic data, the synthetic seismic data contains 735 traces, the time sampling rate is 576, and 38,329,651 traces are selected as paired samples for training. In particular, we choose the 500th trace for single-trace analysis. The present invention obtains the synthetic wave impedance through interpolation, and the synthetic wave impedance is the inversion target of all traces of seismic data, so we can calculate the mean absolute error (MAE) for quantitative evaluation. The initial learning rate is 0.0001, and the λ value is 0.03. In the first stage, all data are trained for 1500 times, and the second stage is also trained for 1500 times. Optimized using Adam optimizer.

In the actual data experiment, the actual seismic data has a total of 735 traces with a time sampling rate of 576, of which 38,329,524,651 traces are actual logging data, 38,329,651 traces are selected as paired label samples for training, 524 traces are selected for blind well testing, and the rest of the gathers are for unlabeled samples. The initial learning rate is 0.0001, and the λ value is 0.03. In the first stage, all data are trained for 1500 times, and the second stage is also trained for 1500 times. Optimized using Adam optimizer. The invention quantitatively evaluates the inversion effect of the network in actual data by calculating the Pearson correlation coefficient (PCC).

Figure 4 is the inversion result of the present invention on synthetic data. Fig. 4(a) is the synthetic seismic data, Fig. 4(b) is the synthetic wave impedance data, Fig. 4(c) is the inversion result of the one-dimensional closed-loop network, Fig. 4(d) is the error result of the one-dimensional closed-loop network, Fig. 4 (e) is the inversion result of the depth evidence regression method, Fig. 4(f) is the error result of the depth evidence regression method, Fig. 4(g) is the inversion result of the present invention, Fig. 4(h) is the error result of the present invention, Fig. 4 (i) is the uncertainty predicted by the deep evidence regression method, and Fig. 4(j) is the uncertainty predicted by the present invention. Comparing Fig. 4(f) with Fig. 4(i), Fig. 4(h) and Fig. 4(j), it can be seen that there is a strong correlation between the error and the prediction uncertainty, where the uncertainty is usually large It is also the place where the error is large. Using this correlation, the present invention makes the network pay more attention to learning the region with greater uncertainty by back-propagating the uncertainty, and the inversion result of the region will be better. Comparing Fig. 4(c), Fig. 4(d) and Fig. 4(f), compared with the one-dimensional closed-loop network, the inversion result of the present invention has better lateral continuity and relatively smaller error. At the same time, after the uncertainty is back-transmitted, the present invention can significantly improve the inversion accuracy of the original region with large uncertainty compared with the depth evidence regression method without the back-transmission uncertainty, as shown by the white arrow in the figure. For better illustration, the 500th track is selected for single-track data analysis. Figure 4(k) is the uncertainty of the 500th track data predicted by the depth evidence regression method, and Figure 4(l) is the 500th track predicted by the present invention. data uncertainty. It can be seen that after the back-propagation uncertainty, where the original error is large, the back-propagation uncertainty error becomes smaller, and correspondingly, the uncertainty also becomes smaller. The MAE of the one-dimensional closed-loop network is 3.2496×10 ⁵ , the MAE of the deep evidence regression method is 3.2659×10 ⁵ , and the MAE of the present invention is 3.0350×10 ⁵ . Therefore, the prediction error of the present invention is smaller, and the inversion result is closer to the inversion target.

Fig. 5 is the inversion result of the present invention on actual data. Figure 5(a) is the actual seismic data, Figure 5(b) is the one-dimensional closed-loop network inversion result, Figure 5(c) is the inversion result of the deep evidence regression method, and Figure 5(d) is the inversion result of the present invention. Figure 5(e) is the inversion uncertainty predicted by the depth evidence regression method, and Figure 5(f) the present invention is the predicted inversion uncertainty. It can be seen that, compared with the one-dimensional closed-loop network, the inversion results of the present invention have better lateral continuity, and the faults can be predicted more clearly. Comparing the deep evidence regression method can make the network pay more attention to the region with large learning uncertainty, that is, the region with large uncertainty in Figure 5(e), so that the accuracy of the inversion result is higher. The certainty is also reduced to varying degrees, that is, the relative value of uncertainty in the same region in Figure 5(f) is reduced compared to the same region in Figure 5(e). In the quantitative results, the PCC of the one-dimensional closed-loop network blind well is 0.8725, the PCC of the depth evidence regression method is 0.8733, and the PCC of the present invention is 0.8916. Therefore, in the blind well test of the present invention, the predicted wave impedance has a better correlation with the blind well.

Through experiments on synthetic data and actual data, it is fully demonstrated that the present invention can not only perform accurate inversion uncertainty analysis, but also improve inversion accuracy by inverting uncertainty.

Compared with the prior art, the present invention has the following advantages:

(1) Using a closed-loop network structure, making full use of unlabeled data;

(2) Using the deep evidence regression method to estimate uncertainty, the time complexity is lower, and the estimated uncertainty is more accurate;

(3) The uncertainty of back-transmission of unlabeled data further improves the inversion accuracy.

Claims (3)

1. a prediction method based on the uncertainty of seismic wave impedance inversion based on closed-loop network, is characterized in that, comprises the following steps: Step 1: Build a forward and inversion network. The built network is a closed-loop network architecture, including a forward network and an inversion network. The forward and inversion network subjects are both uncertain back-propagation networks U- net, including an encoder and a decoder, and each convolutional layer is connected by flying wires; The input of the forward modeling network is one-dimensional wave impedance data, and the output is one-dimensional seismic data; The inversion network adopts multi-task learning, the input is one-dimensional seismic data, the output is the edge distribution of the inversion wave impedance, the predicted wave impedance and the corresponding network uncertainty are obtained through calculation, and the four parameters that determine the edge distribution of the wave impedance are output. parameter; Step 2: preparing data, specifically preparing actual seismic data and logging data, interpolated impedance data generated by the constraints of logging data and actual seismic data, and then convolving the interpolated impedance data to obtain synthetic seismic data; Step 3: train the forward and inversion network, and the network training of the forward and inversion is divided into two stages: a preliminary fitting stage and an inversion uncertainty stage; In the preliminary fitting stage, the network training process uses labeled data and unlabeled data to train forward and inversion networks to obtain forward and inversion models; In the back-propagation uncertainty stage, on the basis of the more accurate model obtained in the preliminary fitting stage, for unlabeled data, back-propagation uncertainty, on the one hand, further improves the inversion accuracy, and on the other hand makes Uncertainty estimates are more accurate; Step 4: Prediction evaluation, specifically: in the prediction process, use the trained inversion network to invert the seismic data to obtain the edge distribution of the wave impedance, and then calculate the prediction result and the corresponding uncertainty analysis result. 2. The method for predicting uncertainty of seismic wave impedance inversion based on a closed-loop network according to claim 1, characterized in that, in the preliminary fitting stage in the step 3, the seismic data is recorded as S, denote the seismic wave impedance data as AI, and assume that the seismic wave impedance data AI satisfies the Gaussian distribution (μ,σ ² ), where μ,σ ² are unknown, and there are

σ ² ～Γ ^-1 (β,γ), where Γ ^-1 is an inverse gamma distribution; Both the forward and inversion network structures include three closed loops, as follows: Loop 1: Labeling Seismic Data

Send it to the inversion network, and through training the network, learn to obtain the edge distribution of wave impedance, and its edge distribution satisfies the student distribution

Calculate the predicted wave impedance according to the edge distribution

and uncertainty

Input the predicted wave impedance μ _j into the forward modeling network to obtain predicted seismic data

Closed loop 2: Convert logging wave impedance data

Input to forward modeling network to get predicted seismic data

followed by

Enter the inversion network again to get the predicted wave impedance data

Closed Loop 3: Converting Unlabeled Seismic Data

Enter the inversion network to get the predicted wave impedance

followed by

Input to forward modeling network to get predicted seismic data

The closed loop 1 and the closed loop 2 are both labeled data, and the closed loop 3 is unlabeled data; Wherein, each closed loop uses different loss functions for training on different input data, and the loss functions include minimizing negative log-likelihood loss L _imp , mean square error loss L _s , and uncertainty loss L _ub ; The loss function used by each closed loop is expressed as equations (1)-(3):

in,

Represents the loss function used by the ith closed loop, f _F represents the forward network, and _WF is the weight of the forward network; L _imp , the specific form of L _s remains unchanged, but the input data in different closed loops are different; L _imp , The specific expressions of L _s and _{Lu ub} are shown in formulas (4)-(6): L _imp =-logp(AI _j |(μ _j ,α _j ,β _j ,γ _j ))+λ|AI _j -f _B (S _j |W _B )|(2α _j +β _j ) (4),

Among them, λ is a hyperparameter, which is used to balance the ratio between the two losses; f _B represents the forward network, W _B is the weight of the inversion network, and (μ _j ,α _j ,β _j ,γ _j ) is the decisive wave impedance The parameters of the marginal distribution, and the wave impedance marginal distribution obeys the Student distribution

3 . The method for predicting uncertainty of seismic wave impedance inversion based on a closed-loop network according to claim 2 , wherein, in the back propagation uncertainty stage, training is performed in the preliminary fitting stage to obtain positive results. 4 . On the basis of inverting and inverting the network structure, the uncertainty of the unlabeled data is used as the weight of the loss function to be back-transmitted. At this time, for the unlabeled data, L' _ub is used to replace _Lub , where the L' _ub is expressed as As shown in formula (7):

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