CN114047548A - Seismic wave impedance inversion uncertainty prediction method based on closed-loop network - Google Patents

Seismic wave impedance inversion uncertainty prediction method based on closed-loop network Download PDF

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CN114047548A
CN114047548A CN202110770021.1A CN202110770021A CN114047548A CN 114047548 A CN114047548 A CN 114047548A CN 202110770021 A CN202110770021 A CN 202110770021A CN 114047548 A CN114047548 A CN 114047548A
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CN114047548B (en
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陆文凯
马绮铭
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Tsinghua University
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    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
    • G01V1/28—Processing seismic data, e.g. analysis, for interpretation, for correction
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Abstract

The invention discloses a seismic wave impedance inversion uncertainty analysis method based on a closed-loop network, which combines the closed-loop network and a depth evidence regression method to provide a new uncertainty analysis network, namely an uncertainty retransmission network (UB-Net), which is used for predicting uncertainty in an inversion process, wherein the predicted uncertainty has better correlation with errors, and meanwhile, by performing uncertainty retransmission on unlabeled data, a prediction result has good transverse continuity, a fault can be predicted more clearly, and the inversion result is more reasonable.

Description

Seismic wave impedance inversion uncertainty prediction method based on closed-loop network
Technical Field
The invention belongs to the field of seismic inversion, and particularly relates to a seismic wave impedance inversion uncertainty analysis method based on a closed-loop network, which is a high-precision seismic inversion analysis method.
Background
Seismic inversion is of great significance in geophysical exploration. Inversion methods can be broadly divided into two categories, namely traditional methods and machine learning based methods. Representative conventional methods such as the trace integral inversion (e.g., document 1: Ferguson, r.j.,&marcgrave, g.f. (1996). a simple algorithm for band-limited impedance inversion. crewes array), recursive inversion (as in document 2: lindseth, R.O. (1979), Synthetic sonic logs-A process for structured interpretation, geophilics, 44(1),3-26), etc., conventional methods generally assume a linear model, while the actual geophysical process is nonlinear, thereby introducing large inversion errors. However, pass throughThe model of the system method has better interpretability, and most of model parameters have more definite physical significance. The machine learning method learns the non-linear mapping from seismic data to wave impedance data by building a neural network,
Figure BDA0003152637380000011
(document 3: G.
Figure BDA0003152637380000012
Tarantola, "Neural networks and extensions of semimic data," Journal of geographic Research: Solid Earth, vol.99, no.B4, pp.6753-6768,1994, doi: https:// doi.org/10.1029/93JB01563), and Lu [ (document 4: "SEISMIC INVERSION USE ERROR-BACK-PROPAGATION NEURAL NETWORK," Chinese Journal of Geophysics,1996) proposed the use of an Artificial NEURAL NETWORK (ANN) and a Convolutional NEURAL NETWORK (CNN) for INVERSION, respectively, which all achieved better results at that time. Wang et al (literature 5: Y.Wang, Q.Ge, W.Lu, and X.Yan. [2020]Well-logging constrained isolated based closed-loop connected seismic network IEEE Transactions on Geoscience and Remote Sensing,2020) proposes using a one-dimensional closed-loop network for seismic inversion, which can introduce label-free data in training and reduce the demand of label samples. Compared with the traditional method, the machine learning method can obtain better inversion results, but the interpretability is not strong.
Kendall et al (document 6: a. Kendall and y. gal, "What incertances Do We Need in Bayesian Deep Learning for Computer Vision," 2017) summarize and propose two kinds of determinism, one is called accidental uncertainty, which is due to inherent noise in the observed data and cannot be eliminated; the other is called perceptual uncertainty, which is model dependent, due to incomplete training. When seismic wave impedance inversion is carried out, multiple solutions exist, one seismic datum corresponds to a plurality of possible wave impedance inversion results, and therefore the inversion process has large uncertainty. Gal et al (document 7: Y.Gal and Z.Ghahranani, "dropping out as a baysian adaptation," in international conference on machine learning,2016: PMLR, pp.1050-1059) estimate the Uncertainty and achieve better results by adding a droout during the training and testing phase, Choi et al (document 8: J.Choi, D.Kim, and J.Byun, "approximation in impedance inversion using Bayesian expression," SEG Technical Program extended interactions 2020: simulation of approximation location, 2020, 300-304) predict the Uncertainty of a single impedance using the impedance of the document 7, but the experimental method predicts the Uncertainty only with less accuracy.
The invention combines a closed-loop network and a depth evidence regression method document 9(A.Amini, W.Schwarting, A.Soleimay, and D.Rus, "Deep empirical regression," arXiv prediction arXiv:1910.02600,2019) to provide a new uncertainty analysis network which is called as an uncertainty back-propagation network (UB-Net) to predict uncertainty of an inversion process, the predicted uncertainty has better correlation with errors, meanwhile, by performing uncertainty back-propagation on unlabeled data, a predicted result has good transverse continuity, a fault can be predicted more clearly, and the inversion result is more reasonable.
Object of the Invention
The invention aims to realize a method for accurately predicting the uncertainty of seismic wave impedance inversion. The invention provides a new uncertainty analysis network based on a closed-loop network and a deep evidence regression method, and the new uncertainty analysis network is called as an uncertainty back propagation network (UB-Net). UB-Net is used to predict the wave impedance uncertainty and further improve the accuracy of the inversion by passing back the uncertainty of the unlabeled data.
Disclosure of Invention
The invention provides a seismic wave impedance inversion uncertainty prediction method based on a closed-loop network, which comprises the following steps of:
step 1: the method comprises the steps of building forward modeling and inversion networks, wherein the built networks are closed-loop network architectures and comprise a forward modeling network and an inversion network, main bodies of the forward modeling and inversion networks are uncertainty retransmission networks U-net and comprise an encoder and a decoder, and all convolution layers are connected by flying wires;
the input of the forward network is one-dimensional wave impedance data, and the output is one-dimensional seismic data;
the inversion network adopts multi-task learning, inputs the data into one-dimensional seismic data, outputs the data into edge distribution of inversion wave impedance, obtains predicted wave impedance and corresponding network uncertainty through calculation, and outputs four parameters determining the edge distribution of the wave impedance;
step 2: preparing data, specifically preparing actual seismic data and logging data, generating interpolation wave impedance data by constraining the logging data and the actual seismic data, and then performing convolution on the interpolation wave impedance data to obtain synthetic seismic data;
and step 3: training a forward modeling network and an inversion network, wherein the forward modeling network training and the inversion network training are divided into a preliminary fitting stage and a reversal uncertain stage;
in the preliminary fitting stage, training a forward and an inverse network by using label data and label-free data in a network training process to obtain forward and inverse models;
in the back propagation uncertainty stage, on the basis of a relatively accurate model obtained in the preliminary fitting stage, aiming at the unlabeled data and the back propagation uncertainty, on one hand, the inversion precision is further improved, and on the other hand, the uncertainty estimation is more accurate;
and 4, step 4: the prediction evaluation specifically comprises the following steps: and in the prediction process, the seismic data is inverted by using the inversion network obtained by training to obtain the edge distribution of the wave impedance, and then the prediction result and the corresponding uncertainty analysis result are obtained by calculation.
Preferably, in the preliminary fitting stage in the step 3, the seismic data are recorded as S and the seismic wave impedance data are recorded as AI, while assuming that the seismic wave impedance data AI satisfy gaussian distribution (μ, σ)2) Where μ, σ2Are all unknown, and have
Figure BDA0003152637380000041
σ2～Γ-1(β, γ), wherein Γ-1Is an inverse gamma distribution;
the forward and inverse network structures each include three closed loops, as follows:
closed loop 1: tagging seismic data
Figure BDA0003152637380000042
Sending into an inversion network, learning to obtain wave impedance edge distribution through a training network, wherein the edge distribution satisfies student distribution
Figure BDA0003152637380000043
Obtaining the predicted wave impedance by calculation according to the edge distribution
Figure BDA0003152637380000044
And uncertainty
Figure BDA0003152637380000045
Will predict the wave impedance mujInputting the data into the forward modeling network to obtain predicted seismic data
Figure BDA0003152637380000046
Closed loop 2: impedance data of logging wave
Figure BDA0003152637380000047
Input into forward network to obtain predicted seismic data
Figure BDA0003152637380000048
Then will be
Figure BDA0003152637380000049
Inputting the data into an inversion network again to obtain predicted wave impedance data
Figure BDA00031526373800000410
Closed loop 3: will not have label seismic data
Figure BDA00031526373800000411
Obtaining predicted wave impedance by inputting inversion network
Figure BDA00031526373800000412
Then will be
Figure BDA00031526373800000413
Input into forward network to obtain predicted seismic data
Figure BDA00031526373800000414
The closed loop 1 and the closed loop 2 are both label data, and the closed loop 3 is label-free data;
wherein each closed loop is trained on different input data using a different loss function including minimizing negative log-likelihood loss LimpMean square error loss LsUncertainty loss Lub；
The loss function used for each closed loop is expressed as shown in equations (1) to (3):
Figure BDA00031526373800000415
Figure BDA0003152637380000051
Figure BDA0003152637380000052
wherein the content of the first and second substances,
Figure BDA0003152637380000053
representing the loss function used for the i-th closed loop, LiWS，LsThe specific form of (c) is not changed, but the data input in different closed loops is different; l isiWS，Ls，LubThe specific expression form of (A) is shown in formulas (4) to (6):
L1mp＝-logp(AIj|(μj,αj,βj,γj))+λ|AIj-fB(Sj|WB)|(2αj+βj) (4)，
Figure BDA0003152637380000054
Figure BDA0003152637380000055
more preferably, in the back propagation uncertainty stage, based on the forward modeling and the inverse network structure obtained by training in the preliminary fitting stage, the uncertainty of the unlabeled data is back propagated as the weight of the loss function, and then L 'is used for the unlabeled data'ubReplacement of LubWherein, L'ubExpressed as shown in formula (7):
Figure BDA0003152637380000056
in the formula (4), lambda is a hyperparameter and is used for balancing the proportion between two losses; in formulae (1) to (7), fFRepresenting a forward network, WFTo forward the network weight, fBRepresenting a forward network, WBFor inverting network weights, (. mu.) in equations (3) - (7)j，αj，βj,γj) To determine parameters of the edge distribution of wave impedance, and the edge distribution of wave impedance obeys the student distribution
Figure BDA0003152637380000057
Drawings
FIG. 1 is a flow chart of a seismic wave impedance inversion uncertainty prediction method of the present invention.
Fig. 2 is a structural diagram of the forward modeling and inversion network constructed by the invention.
FIG. 3 is a data flow diagram of the present invention
FIG. 4 is the inversion result of the present invention on the synthetic data
FIG. 5 shows the inversion result of the present invention on the actual data
Detailed Description
The following further describes embodiments of the present invention with reference to the drawings.
FIG. 1 is a flow chart of a seismic wave impedance inversion uncertainty prediction method of the present invention, which includes four steps, each of which is described below:
step 1: building a forward evolution network and an inversion network;
the network structure mainly comprises two parts: a forward network model and an inverse network model. Both the forward and inverse networks use a modified U-net model, as shown in fig. 2. Mainly comprising an encoder and a decoder. All the coiling layers are connected by flying leads. The inversion network adopts multi-task learning and outputs four parameters for determining the edge distribution of the wave impedance.
Step 2: preparing data;
this step is mainly to provide the network with relevant data for training and testing. Actual seismic data and well log data are first prepared. And then generating interpolated wave impedance data by using the logging data and the actual seismic data, and finally performing convolution on the interpolated wave impedance data to calculate and obtain the synthetic seismic data. The data are one-dimensional data, and synthetic data experiments and actual data experiments are respectively carried out. The input of the synthetic data experiment is synthetic seismic data, and the label is interpolation wave impedance data; the input of the actual data experiment is actual seismic data, and the label is logging data. In particular, in the synthetic data, each synthetic seismic data has a corresponding tag; in actual data, only at the logging location is there corresponding tag data.
And step 3: training forward and inverse networks;
the present invention is trained in two stages. The first stage is a preliminary fitting stage, the main purpose is to train a network to fit input data and learn the edge distribution of wave impedance to obtain more accurate predicted wave impedance and uncertainty, and the second stage is a back propagation uncertainty stage to continue training the network and further improve inversion accuracy by back propagation uncertainty.
To more clearly express the training step, the seismic data are denoted as S and the wave impedance data are denoted as AI. While assuming that the wave impedance data AI satisfy the Gaussian distribution (μ, σ)2) Where μ, σ2Are not known. And is provided with
Figure BDA0003152637380000071
σ2～Γ-1(β, γ), wherein Γ-1Is an inverse gamma distribution. On the basis of the above assumption, the UB-Net training process is introduced in two stages.
And (3) a primary fitting stage: forward and inverse network models are trained. As shown in fig. 3, the network comprises three closed-loop structures, each closed-loop inputting different data.
Closed loop 1: tagging seismic data
Figure BDA0003152637380000072
Sending into an inversion network, learning to obtain wave impedance edge distribution through a training network, wherein the edge distribution satisfies student distribution
Figure BDA0003152637380000073
Obtaining the predicted wave impedance by calculation according to the edge distribution
Figure BDA0003152637380000074
And uncertainty
Figure BDA0003152637380000075
Will predict the wave impedance mujInputting the data into a forward modeling network to obtain predicted seismic data
Figure BDA0003152637380000076
Closed loop 2: impedance data of logging wave
Figure BDA0003152637380000077
Input to forward network to obtain predicted earthquakeData of
Figure BDA0003152637380000078
Then will be
Figure BDA0003152637380000079
Inputting the data into an inversion network again to obtain predicted wave impedance data
Figure BDA00031526373800000710
Closed loop 3: will not have label seismic data
Figure BDA00031526373800000711
Obtaining predicted wave impedance by inputting inversion network
Figure BDA00031526373800000712
Then will be
Figure BDA00031526373800000713
Input into forward network to obtain predicted seismic data
Figure BDA00031526373800000714
Closed loop 1 and closed loop 2 are both labeled data, and closed loop 3 is unlabeled data. The loss function used for each closed loop is as follows:
Figure BDA00031526373800000715
Figure BDA00031526373800000716
Figure BDA00031526373800000717
wherein
Figure BDA00031526373800000718
Representing the loss function used for the i-th closed loop, fFRepresenting a forward network, WFTo forward the network weight, f.Representing a forward network, WBFor inverting network weights, Limp，LsIs not changed, but the data input in the different closed loops is different, the specific input data is as described above, Limp，Ls，LubThe specific expression form of (A) is as follows:
Limp＝-logp(AIj|(μj，αj，βj，γj))+λ|AIj-fB(Sj|WB)|(2αj+βj) (4)
Figure BDA00031526373800000719
Figure BDA0003152637380000081
where λ is the hyperparameter, balancing the ratio between the two losses.
Back propagation uncertainty stage: after the initial fitting stage, more accurate predicted wave impedance and corresponding uncertainty are obtained, and the backward transmission is performed by taking the predicted uncertainty as the weight of the loss term, so that the inversion precision is better improved. At this point all loss functions are still similar to the first stage, but with L'ubReplacement of LubThe weight term of uncertainty is introduced:
Figure BDA0003152637380000082
and 4, step 4: predicting and evaluating;
and obtaining the final forward network weight and the final inversion network weight according to the training process. During prediction, inversion is carried out on the unlabeled seismic data S, the S is input into an inversion network to obtain predicted wave impedance and inversion uncertainty, and the forward network does not participate in prediction evaluation and only plays a semi-supervision role in a training stage.
And (3) experimental simulation results:
in order to verify the effectiveness and superiority of the invention, the UB-Net proposed by the invention is applied to the synthetic data and the actual data respectively. The experimental platform is Intel (R) core (TM) i9-9820X CPU @3.30GHz, 64GB RAM, GeForce RTX 2080 Ti.
In the synthetic data, the synthetic seismic data contained 735 traces, the time sampling rate was 576, 38,329,651 traces were selected as matched-pair samples for training, and in particular, we selected the 500 th trace for single trace analysis. The invention obtains the synthetic wave impedance through interpolation, and the synthetic wave impedance is an inversion target of all the seismic data, so that the average absolute error (MAE) can be calculated for quantitative evaluation. The initial learning rate is 0.0001, and the lambda value is 0.03. All data is trained 1500 times in the first phase, and similarly 1500 times in the second phase. Optimization was performed using an Adam optimizer.
In an actual data experiment, the actual seismic data has 735 tracks, the time sampling rate is 576, wherein 38,329,524,651 tracks are actual logging data, 38,329,651 tracks are selected as matched labeled samples for training, 524 tracks are selected as blind wells for testing, and the rest of the track sets are unlabeled samples. The initial learning rate is 0.0001, and the lambda value is 0.03. All data is trained 1500 times in the first phase, and similarly 1500 times in the second phase. Optimization was performed using an Adam optimizer. The inversion effect of the network in actual data is quantitatively evaluated by calculating the Pearson Correlation Coefficient (PCC).
FIG. 4 is the inversion result of the present invention on synthetic data. FIG. 4(a) is synthetic seismic data, FIG. 4(b) is synthetic wave impedance data, FIG. 4(c) is a one-dimensional closed-loop network inversion result, FIG. 4(d) is a one-dimensional closed-loop network error result, FIG. 4(e) is a depth evidence regression method inversion result, FIG. 4(f) is a depth evidence regression method error result, FIG. 4(g) is an inversion result of the present invention, FIG. 4(h) is an error result of the present invention, FIG. 4(i) is uncertainty of depth evidence regression method prediction, and FIG. 4(j) is uncertainty of the present invention prediction. Comparing FIG. 4(f) with FIG. 4(i), and FIG. 4(h) with FIG. 4(j), it can be seen that the error and prediction are not accurateThere is a strong correlation between the characteristics, and the place with larger uncertainty is usually the place with larger error. By utilizing the correlation, the invention leads the network to pay more attention to learning the region with larger uncertainty through back propagation uncertainty, and the inversion result of the region is better. Comparing fig. 4(c), fig. 4(d) and fig. 4(f), the inversion result of the present invention has better lateral continuity and relatively smaller error compared to the one-dimensional closed-loop network. Meanwhile, after the uncertainty is reversely transmitted, compared with a depth evidence regression method without the uncertainty, the method can obviously improve the inversion accuracy of an area with larger uncertainty originally, as shown by a white arrow in the figure. For better illustration, the 500 th trace is selected for single trace data analysis, fig. 4(k) shows the uncertainty of the 500 th trace predicted by the depth evidence regression method, and fig. 4(l) shows the uncertainty of the 500 th trace predicted by the present invention. It can be seen that, after the back propagation uncertainty, the original place with a large error is reduced in back propagation uncertainty error, and correspondingly, the uncertainty is also reduced. MAE of one-dimensional closed-loop network is 3.2496 × 105The MAE of the depth evidence regression method is 3.2659 × 105The MAE of the present invention is 3.0350X 105. Therefore, the prediction error of the method 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. Fig. 5(a) is actual seismic data, fig. 5(b) is a one-dimensional closed-loop network inversion result, fig. 5(c) is a depth evidence regression method inversion result, and fig. 5(d) is an inversion result of the present invention. FIG. 5(e) is the predicted inversion uncertainty of the depth evidence regression method, and FIG. 5(f) is the predicted inversion uncertainty of the present invention. Compared with a one-dimensional closed-loop network, the inversion result of the method has better transverse continuity, and the fault is predicted more clearly. The comparison depth evidence regression method can make the network pay more attention to learning the region with larger uncertainty, namely the region with larger uncertainty in fig. 5(e), so that the accuracy of the inversion result is higher, and meanwhile, the uncertainty of the part of the region is reduced to different degrees, namely the relative uncertainty value of the same region in fig. 5(f) is reduced compared with that of the same region in fig. 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 invention is 0.8916. Therefore, the predicted wave impedance is better related to the blind well in the blind well test.
Through experiments of synthetic data and actual data, the method and the device for the inversion uncertainty analysis of the data are fully demonstrated that not only can accurate inversion uncertainty analysis be carried out, but also the inversion accuracy can be improved through the back propagation uncertainty.
Compared with the prior art, the invention has the following advantages:
(1) a closed-loop network structure is used, so that label-free data is fully utilized;
(2) uncertainty is estimated by using a depth evidence regression method, time complexity is lower, and estimated uncertainty is more accurate;
(3) and the uncertainty of the tag-free data is reversely transmitted, so that the inversion precision is further improved.

Claims (3)

1. A seismic wave impedance inversion uncertainty prediction method based on a closed-loop network is characterized by comprising the following steps:
step 1: the method comprises the steps of building forward modeling and inversion networks, wherein the built networks are closed-loop network architectures and comprise a forward modeling network and an inversion network, main bodies of the forward modeling and inversion networks are uncertainty retransmission networks U-net and comprise an encoder and a decoder, and all convolution layers are connected by flying wires;
the input of the forward network is one-dimensional wave impedance data, and the output is one-dimensional seismic data;
the inversion network adopts multi-task learning, inputs the data into one-dimensional seismic data, outputs the data into edge distribution of inversion wave impedance, obtains predicted wave impedance and corresponding network uncertainty through calculation, and outputs four parameters determining the edge distribution of the wave impedance;
step 2: preparing data, specifically preparing actual seismic data and logging data, generating interpolation wave impedance data by constraining the logging data and the actual seismic data, and then performing convolution on the interpolation wave impedance data to obtain synthetic seismic data;
and step 3: training a forward modeling network and an inversion network, wherein the forward modeling network training and the inversion network training are divided into a preliminary fitting stage and a reversal uncertain stage;
in the preliminary fitting stage, training a forward and an inverse network by using label data and label-free data in a network training process to obtain forward and inverse models;
in the back propagation uncertainty stage, on the basis of a relatively accurate model obtained in the preliminary fitting stage, aiming at the unlabeled data and the back propagation uncertainty, on one hand, the inversion precision is further improved, and on the other hand, the uncertainty estimation is more accurate;
and 4, step 4: the prediction evaluation specifically comprises the following steps: and in the prediction process, the seismic data is inverted by using the inversion network obtained by training to obtain the edge distribution of the wave impedance, and then the prediction result and the corresponding uncertainty analysis result are obtained by calculation.
2. The method as claimed in claim 1, wherein in the preliminary fitting stage of step 3, the seismic data is recorded as S, the seismic impedance data is recorded as AI, and the seismic impedance data AI is assumed to satisfy gaussian distribution (μ, σ) at the same time2) Where μ, σ2Are all unknown, and have
Figure FDA0003152637370000021
σ2～Γ-1(β, γ), wherein Γ-1Is an inverse gamma distribution;
the forward and inverse network structures each include three closed loops, as follows:
closed loop 1: tagging seismic data
Figure FDA00031526373700000214
Sending into an inversion network, learning to obtain wave impedance edge distribution through a training network, wherein the edge distribution satisfies student distribution
Figure FDA0003152637370000022
Obtaining the predicted wave impedance by calculation according to the edge distribution
Figure FDA0003152637370000023
And uncertainty
Figure FDA0003152637370000024
Will predict the wave impedance mujInputting the data into the forward modeling network to obtain predicted seismic data
Figure FDA0003152637370000025
Closed loop 2: impedance data of logging wave
Figure FDA0003152637370000026
Input into forward network to obtain predicted seismic data
Figure FDA0003152637370000027
Then will be
Figure FDA0003152637370000028
Inputting the data into an inversion network again to obtain predicted wave impedance data
Figure FDA0003152637370000029
Closed loop 3: will not have label seismic data
Figure FDA00031526373700000210
Obtaining predicted wave impedance by inputting inversion network
Figure FDA00031526373700000211
Then will be
Figure FDA00031526373700000212
Input into forward network to obtain predicted seismic data
Figure FDA00031526373700000213
The closed loop 1 and the closed loop 2 are both label data, and the closed loop 3 is label-free data;
wherein each closed loop is trained on different input data using a different loss function including minimizing negative log-likelihood loss LimpMean square error loss LsUncertainty loss Lub；
The loss function used for each closed loop is expressed as shown in equations (1) to (3):
Figure FDA0003152637370000031
Figure FDA0003152637370000032
Figure FDA0003152637370000033
wherein the content of the first and second substances,
Figure FDA0003152637370000038
representing the loss function used for the i-th closed loop, fFRepresenting a forward network, WFIs the forward net weight; l isimp，LsThe specific form of (c) is not changed, but the data input in different closed loops is different; l isimp，Ls，LubThe specific expression form of (A) is shown in formulas (4) to (6):
Limp＝-logp(AIj|(μj,αj,βj，γj))+λ|AIj-fB(Sj|WB)|(2αj+βj) (4)，
Figure FDA0003152637370000034
Figure FDA0003152637370000035
wherein λ is a hyperparameter for balancing the ratio between the two losses; f. ofBRepresenting a forward network, WBTo invert the network weights, (μ)j,αj,βj,γj) To determine parameters of the edge distribution of wave impedance, and the edge distribution of wave impedance obeys the student distribution
Figure FDA0003152637370000036
3. The method as claimed in claim 2, wherein in the back propagation uncertainty stage, based on forward and inverse network structures obtained by training in the preliminary fitting stage, the uncertainty of the unlabeled data is back propagated as the weight of the loss function, and for the unlabeled data, L 'is used'ubReplacement of LubWherein, L'ubExpressed as shown in formula (7):
Figure FDA0003152637370000037
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