CN114047548B - Seismic wave impedance inversion uncertainty prediction method based on closed-loop network - Google Patents
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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 the uncertainty of an inversion process, wherein the predicted uncertainty has better correlation with an error, and meanwhile, by performing uncertainty retransmission on unlabelled data, a predicted result has good transverse continuity, a fault can be more clearly predicted, and the inversion result is more reasonable.
Description
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 calculus inversion (e.g., document 1,&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, the model of the traditional method has better interpretability, and most of the model parameters have more definite physical meanings. The machine learning method learns the non-linear 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: "SEISMIC INVERSION USE ERROR-BACK-PROPAGATION NEURAL NETWORK," Chinese Journal of Geophysics, 1996) proposed USING 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 (document 5]Well-logging constrained isolated closed-loop connected nuclear network IEEE Transactions on Geoscience and Remote Sensing, 2020) proposes using a one-dimensional closed-loop network for seismic inversion, which can introduce non-tag data in training and reduce the demand of tag 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 due to inherent noise in the observed data, which 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 data corresponds to a plurality of possible wave impedance inversion results, and therefore the inversion process has larger uncertainty. Gal et al (document 7: y.gal and z.ghahrannani, "Dropout as a baysian adaptation," in international conference on machine learning,2016: pmlr, pp.1050-1059) estimate 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, "unse Technical evaluation in impedance inversion using Bayesian elevation approximation," SEG Technical project extended simulations.
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 predicted arXiv:1910.02600,2019) to provide a new uncertainty analysis network called as an uncertainty back-propagation network (UB-Net) to predict uncertainty of an inversion process, the predicted uncertainty and errors have better correlation, 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;
and 2, step: 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 3, 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, σ 2 Are all unknown, and have
σ 2 ～Γ -1 (β, γ), wherein Γ -1 Is an inverse gamma distribution;
the forward and inverse network structures each include three closed loops, as follows:
closed loop 1: tagging seismic data
Sending into inversion network, learning to obtain edge distribution of wave impedance through training network, wherein the edge distribution satisfies student distribution
Obtaining the predicted wave impedance by calculation according to the edge distribution
And uncertainty
Will predict the wave impedance mu j Inputting the data into the forward modeling network to obtain predicted seismic data
Closed loop 2: impedance data of logging wave
Input into forward network to obtain predicted seismic data
Then will be
Inputting the data into an inversion network again to obtain predicted wave impedance data
Closed loop 3: will not have label seismic data
Obtaining predicted wave impedance by inputting inversion network
Then will be
Input into forward network to obtain predicted seismic data
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 comprising minimizing a negative log-likelihood loss L imp Mean square error loss L s Uncertainty loss L ub ；
The loss function used for each closed loop is expressed as shown in equations (1) to (3):
wherein,
representing the loss function used for the i-th closed loop, L iWS ，L s The specific form of (c) is unchanged, but the data input in different closed loops is different; l is iWS ，L s ，L ub The specific expression form of (A) is shown in formulas (4) to (6):
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, 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, where L 'is used for the unlabeled data' ub Replacement of L ub Wherein, L' ub Expressed as shown in formula (7):
in the formula (4), lambda is a hyperparameter and is used for balancing the proportion between two losses; in formulae (1) to (7), f F Representing a forward network, W F To forward the network weight, f B Representing a forward network, W B For inverting the network weights, (. Mu.) (in equations (3) - (7) j ，α j ，β j ,γ j ) To determine parameters of the edge distribution of wave impedance, and the edge distribution of wave impedance obeys the student distribution
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 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, σ 2 Are not known. And is provided with
σ 2 ～Γ -1 (β, γ), wherein Γ -1 Is an inverse gamma distribution. Based on the above assumptions, the method comprises two stagesThe UB-Net training process is introduced.
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
Sending into an inversion network, learning to obtain wave impedance edge distribution through a training network, wherein the edge distribution satisfies student distribution
Obtaining the predicted wave impedance by calculation according to the edge distribution
And uncertainty
Will predict the wave impedance mu j Inputting the data into a forward modeling network to obtain predicted seismic data
Closed loop 2: impedance data of logging wave
Input into forward network to obtain predicted seismic data
Then will be
Inputting the data into an inversion network again to obtain predicted wave impedance data
Closed loop 3: will not have label seismic data
Obtaining predicted wave impedance by inputting inversion network
Then will be
Input into forward network to obtain predicted seismic data
wherein
Representing the loss function used by the { th closed loop, { f } F Representing a forward network, W F To forward the network weight, f . Representing a forward network, W B For inverting network weights, L imp ，L s Is not changed, but the data input in the different closed loops is different, the specific input data is as described above, L imp ，L s ，L ub The specific expression form of (A) is as follows:
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 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' ub Replacement of L ub The weight term of uncertainty is introduced:
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 was Intel (R) Core (TM) i9-9820X CPU@3.30GHz,64GB RAM,GeForce RTX 2080Ti.
In the synthetic data, the synthetic seismic data contains 735 traces, the time sampling rate is 576, 38,329,651 traces are selected as the matched sample for training, and in particular, the 500 th trace is selected 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 in total, the time sampling rate is 576, 38,329,524,651 tracks are actual logging data, 38,329,651 tracks are selected as matched label samples for training, 524 tracks are selected as blind well tests, and the rest of 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 there is a strong correlation between the error and the prediction uncertainty, and the place with larger uncertainty is also 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 order is selected to be madeFor trace data analysis, FIG. 4 (k) shows the uncertainty of trace 500 data predicted by the depth evidence regression method, and FIG. 4 (l) shows the uncertainty of trace 500 data 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 x 10 5 The MAE of the depth evidence regression method is 3.2659 × 10 5 The MAE of the present invention is 3.0350X 10 5 . 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 contrast 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 result, 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 network and the inversion network 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 uncertainty 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 for predicting seismic wave impedance inversion uncertainty based on closed-loop network according to claim 1, characterized in that in the preliminary fitting stage in the step 3, the seismic data are recorded as S, the seismic wave impedance data are recorded as AI, and meanwhile, the seismic wave impedance data AI are assumed to satisfy Gaussian distribution (μ, σ) 2 ) Where μ, σ 2 Are all unknown, and have
σ 2 ～Γ -1 (β, γ), wherein Γ -1 Is an inverse gamma distribution;
the forward and inverse network structures each include three closed loops, as follows:
closed loop 1: tagging seismic data
Sending into an inversion network, learning to obtain wave impedance edge distribution through a training network, wherein the edge distribution satisfies student distribution
Obtaining the predicted wave impedance by calculation according to the edge distribution
And uncertainty
Will predict the wave impedance mu j Inputting the data into the forward modeling network to obtain predicted seismic data
Closed loop 2: logging wave impedance data
Input into forward network to obtain predicted seismic data
Then will be
Inputting the data into the inversion network again to obtain predicted wave impedance data
Closed loop 3: will not have label seismic data
Obtaining predicted wave impedance by inputting inversion network
Then will be
Input into forward network to obtain predicted seismic data
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 L imp Mean square error loss L s Uncertainty loss L ub ；
The loss function used for each closed loop is expressed as shown in equations (1) to (3):
wherein,
representing the loss function used for the i-th closed loop, f F Representing a forward network, W F Is the forward net weight; l is imp ，L s The specific form of (c) is not changed, but the data input in different closed loops is different; l is imp ，L s ，L ub The specific expression form of (A) is shown in formulas (4) to (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)，
wherein, λ is a hyper-parameter for balancing the ratio between the two losses; f. of B Representing a forward network, W B To invert the network weights, (μ) j ，α j ，β j ，γ j ) To determine parameters of the edge distribution of wave impedance, and the edge distribution of wave impedance obeys the student distribution
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' ub Replacement of L ub Wherein, L' ub Expressed as shown in formula (7):
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