CN112085109A - Phase-controlled porosity prediction method based on active learning - Google Patents
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Abstract
The invention discloses a phased porosity prediction method based on active learning, which comprises the following steps: s1, acquiring a seismic sample data set to be predicted; s2, constructing a linear discriminant analysis classifier by using the seismic sample data of the known lithofacies classification and the corresponding labels; s3, performing lithofacies classification on seismic sample data to be predicted by using a linear discriminant analysis classifier; and S4, establishing a linear relation model to predict porosity, and obtaining a prediction result. The invention introduces linear discriminant analysis to classify lithofacies, so that the parameters of a classification model are greatly reduced, and the method has good generalization capability; an active learning framework is introduced to solve the problem of lithofacies classification under the condition of small samples, the defects of the traditional classification method are overcome, and the accuracy of lithofacies classification is improved.
Description
Technical Field
The invention relates to a phased porosity prediction method based on active learning.
Background
The underground physical parameters mainly comprise porosity, permeability, saturation and the like, and the parameters play an important role in the research of the fields of oil reservoir development, hydrogeological survey, mineral reserve prediction and the like. The porosity is one of the most important physical parameters for reservoir characteristic characterization, fluid pattern description and reservoir geological model establishment, and has important significance for predicting the underground porosity parameter.
The accurate porosity parameter estimation method mainly uses core analysis, including mercury intrusion experimental analysis, nuclear magnetic resonance analysis and the like, and the obtained porosity is very accurate, but the experimental means are relatively expensive, the range of the reservoir covered by the observed data is limited, and the research on the large-scale transverse distribution rule of the porosity of the reservoir is difficult to realize. In order to solve the problem of predicting the underground porosity body, some scholars propose a scheme for predicting the porosity by using seismic data, wherein the main technical methods comprise an empirical method, a seismic attribute analysis method, a geostatistical simulation method and the like.
And fitting a regression relationship through a cross plot of the elastic parameter points and the physical property parameter points of the actually measured reservoir in the well by using an empirical porosity prediction method, and applying a fitting formula to actual seismic data. The method has good prediction effect in a single lithofacies, but when the lithofacies are complex in composition, a complex multivariate polynomial fitting formula needs to be constructed, so that a large amount of well data is needed for analysis and prediction, and when the well data are less, an accurate result is often difficult to obtain.
The seismic attribute analysis method adopts deep learning methods such as neural networks to establish a nonlinear deep learning model for seismic attributes and porosity, and then converts seismic attribute bodies in spatial distribution into porosity bodies. Liqu is equal to that of the traditional well logging interpretation, lithology identification and reservoir parameter prediction are carried out by using an artificial neural network, and the introduced BP algorithm simplifies the mathematical means in the traditional well logging interpretation. Cerssomio et al successfully predicted seismic attribute and gamma ray changes using an artificial neural network. And ChenRong and the like utilize the BP neural network to construct mapping correlation between reservoir parameters and logging responses, and predict the porosity of the reservoir. The seismic attribute analysis method can utilize a neural network to establish a complex nonlinear porosity prediction model so as to make up the defects of an empirical method, but parameters in the model are often more, which means that the method needs more samples to train so as to avoid an overfitting phenomenon. When the number of samples is too small, the seismic attribute analysis method may have the phenomenon of neural network overfitting caused by too few samples, and an accurate prediction model is difficult to establish.
The geostatistical simulation method adopts a cokriging interpolation method, uses the well point porosity as a main variable, and interpolates a porosity curve through secondary variable seismic attribute trend constraint. The method requires that the well data are rich and the wells are uniformly distributed on the plane, and when the well data are not rich and uniform, the interpolation method can cause large errors, so the method has large limitation in practical use.
In summary, the existing methods need to consider a large amount of well data for analysis, and also need to predict porosity under lithofacies-distinguishing conditions. However, the drilling is limited by economic cost and is difficult to perform large-scale amplification, and how to perform lithofacies classification under the condition of a small sample becomes a problem to be solved urgently by realizing porosity prediction through less well data on the basis of classification. Aiming at the problems, the invention combines the experience of people and machines through an active learning mechanism to realize the discrimination and the expansion of the samples. By the method, lithofacies classification and phased porosity prediction under the condition of fewer sample wells can be realized.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a phased porosity prediction method based on active learning, which introduces linear discriminant analysis to classify lithofacies, greatly reduces the parameters of a classification model, solves the problem of lithofacies classification under the condition of a small sample through an active learning framework and improves the accuracy of lithofacies classification
The purpose of the invention is realized by the following technical scheme: the phased porosity prediction method based on active learning comprises the following steps:
s1, acquiring a seismic sample data set to be predicted;
s2, constructing a linear discriminant analysis classifier by using the seismic sample data of the known lithofacies classification and the corresponding labels;
s3, performing lithofacies classification on seismic sample data to be predicted by using a linear discriminant analysis classifier;
and S4, establishing a linear relation model to predict porosity, and obtaining a prediction result.
Further, the step S2 includes the following sub-steps:
s21, training a linear discriminant analysis classifier by using the seismic sample data with known phase-controlled porosity and a corresponding label;
s22, predicting unclassified seismic sample data by using a linear discriminant analysis classifier;
s23, selecting the most valuable sample from the unclassified seismic sample data by using a query function, submitting the sample to an expert for labeling, and adding the sample into a classified sample set;
and S24, repeating the steps S21-S23 until the classifier meets the precision requirement.
Further, the step S21 is specifically implemented as follows: by XiSet of samples, μ, representing class iiAverage vector, Σ, representing a set of class i samplesiRepresenting the covariance matrix of the i-th sample set, wherein omega is the projection equation coefficient, and the projection of the centers of the two samples is respectively omegaTμ0And ωTμ1The covariance of the two samples is ωT∑0Omega and omegaT∑1Omega; post-projection intra-class variance VwithinExpressed as:
Vwithin=ωT∑0ω+ωT∑1ω
after-projection inter-class variance VwithoutExpressed as:
to achieve "minimum intra-class variance and maximum inter-class variance after projection", it is only necessary to minimize the objective function J:
μiis the average vector of the i-th sample set, and omega is the coefficient of the projection equation, sigmaiA covariance matrix representing the set of class i samples;
and judging the distance between the projection of the sample center and the projection of each type of sample center, wherein the classification represented by the projection center closest to the projection of the sample center is the classification result of the sample.
Further, the query function in step S23 uses an entropy-based query function, and the probability that a certain sample x belongs to the ith class is set as piThe information entropy H (x) is calculated by the following formula
n is the total number of categories, the larger the information entropy is, the larger the uncertainty is, the richer the contained information quantity is, and the larger the value is.
Further, the specific implementation method of step S4 is as follows: establishing a linear relation model for porosity prediction, and determining the quantitative relation of mutual dependence among multiple variables by using regression analysis in mathematical statistics; the linear regression equation is represented by the following formula:
y=w·x+b
in the above formula, x is a reservoir elastic parameter vector, w represents a coefficient of a corresponding parameter in x, b is a prediction result of linear regression when x is input to be 0, namely 0 input bias, and y is a porosity prediction result.
The invention has the beneficial effects that: the invention introduces linear discriminant analysis to classify lithofacies, so that the parameters of a classification model are greatly reduced, and the method has good generalization capability; an active learning framework is introduced to solve the problem of lithofacies classification under the condition of small samples, the defects of the traditional classification method are overcome, and the accuracy of lithofacies classification is improved.
Drawings
FIG. 1 is a schematic view of LDA dimension reduction;
FIG. 2 is a schematic illustration of a phased porosity prediction process;
FIG. 3 is a flow chart of the active learning based phased porosity prediction method of the present invention;
FIG. 4 is a graph of the change in the classifier accuracy for passive and active learning according to the present invention;
FIG. 5 is a diagram illustrating the actual lithofacies of the well A and the lithofacies results predicted by the different classification methods of this embodiment;
FIG. 6 shows the predicted result of porosity of well A in this example.
Detailed Description
Prior art related to the present invention:
1. multiple linear regression method
Multiple linear regression models are commonly used to study the relationship of a dependent variable to a plurality of independent variables, and if the relationship between the dependent variable and the independent variables can be characterized in a linear form, a multiple linear model can be established for analysis.
For variable y and a set of random variables x ═ x1,x2,…xn) The regression relationship between them can be described by the formula (1):
y=ω0x0+ω1x1+...+ωnxn+b (1)
wherein ω is0,ω1...ωnB is the regression coefficient, and b is the bias of linear regression, i.e. when the input variable x is 0, the value of y corresponds to, also called 0 input bias. If represented by a vector, the above formula may be changed to formula (2):
y=ω·x+b (2)
where ω is the regression coefficient vector and x is the input vector. After the above multiple linear regression equation is determined, parameters which need to be obtained through training are omega and b, so that the multiple linear regression model is predictedThe difference from the real y is minimal. An objective function can thus be constructed as in equation (3):
and training the multiple linear regression model by using the target function to obtain a weight parameter w and a bias parameter b, thereby establishing the multiple linear regression model.
2. Phased porosity regression method
The phased porosity regression method is that lithofacies analysis is carried out by adopting elastic parameters of reservoir intervals, and multivariate regression is carried out in each lithofacies by utilizing the elastic parameters and the porosity to obtain a prediction result.
For each phase, a linear relation model can be established for porosity prediction, and the quantitative relation of mutual dependence among multiple variables is determined by utilizing regression analysis in mathematical statistics. The linear regression equation can be expressed by equation (4)
y=w·x+b (4)
In the above formula, x is a reservoir elastic parameter (shear wave velocity, longitudinal wave velocity, density, etc.) vector, w represents a coefficient of a corresponding parameter in x, b is a prediction result of linear regression when x is input to be 0, namely 0 input offset, and y is a porosity prediction result.
Because the structures such as rock pore structures in different lithofacies are different, the mapping relation between the porosity and the elastic parameters is complex, and meanwhile, the sample acquisition difficulty is high, and the modeling is difficult to be performed by using a complex deep learning model, so that the problem of using the traditional porosity prediction method is difficult to effectively solve. In view of the fact that the mapping relations between the physical property parameters and the porosity in different lithofacies are different, a learner proposes a phased porosity prediction method, namely physical property parameter-porosity prediction models are respectively established in different facies, so that the defects of an empirical method are overcome, and the mapping relations between the physical property parameters and the porosity can be well described.
The phased reservoir physical property parameters need accurate lithofacies to be used as constraints of physical property parameter prediction to train a prediction model, and experiments show that the accuracy of the lithofacies can greatly influence the accuracy of reservoir physical property parameter prediction. The lower the lithofacies accuracy is, the poorer the reservoir physical property parameter prediction effect is, and the lithofacies are often difficult to obtain, which mainly has the reason that the classification model cannot be fully trained and accurate lithofacies prediction is difficult to perform due to the difficulty in obtaining lithofacies samples.
The methods for expanding the samples are as follows: 1. passive learning adds samples. And analyzing the sample and the well curve form by a geological expert so as to determine the lithofacies attribute of the sample. The method can ensure the correctness of a newly added sample, but has higher labor cost and is difficult to label well data in a large scale; 2. semi-supervised learning expands the sample, thereby solving the problem of small samples. And predicting the unlabeled well data by using the conventional classifier, and selecting a sample with higher confidence in the prediction result to be added into the training set, so that the number of training samples is increased. However, in this method, the distribution and the accuracy of the initial samples greatly affect the accuracy of the whole data set, so that it is difficult to achieve a stable and high-accuracy result.
In order to overcome the difficulty brought by small samples to the phase-controlled reservoir physical property parameter prediction method, the invention introduces an active learning framework scheme, as shown in fig. 2. The main content of the scheme is as follows:
(1) and introducing information entropy. And evaluating the credibility of the classification model on the prediction result of the sample through the information entropy so as to determine the reliability of the sample in the classification result.
(2) A query function is introduced. And finding samples meeting the conditions of the query function in the unmarked data pool aiming at the current state of the learner.
(3) And constructing an active learning framework. And aiming at the current state of the learner, selecting a sample from the unmarked data pool by using a query function, and adding the sample into a training set by manual marking, thereby rapidly improving the accuracy of the learner.
The technical scheme of the invention is further explained by combining the attached drawings.
As shown in fig. 3, the phased porosity prediction method based on active learning of the present invention includes the following steps:
s1, acquiring a seismic sample data set to be predicted;
s2, constructing a linear discriminant analysis classifier by using the seismic sample data of the known lithofacies classification and the corresponding labels;
linear Discriminant Analysis (LDA) is a supervised learning dimension reduction technique, where each sample of a data set is classified, unlike Principal Component Analysis (PCA), which is an unsupervised dimension reduction technique that does not consider the output of sample classes. The idea of LDA can be summarized by a sentence, which is "the minimum intra-class variance and the maximum inter-class variance after projection". Consider the simpler case of binary classification, in which case the LDA can be described with figure 1.
The step S2 includes the following sub-steps:
s21, training a linear discriminant analysis classifier by using the seismic sample data with known phase-controlled porosity and a corresponding label; the specific implementation method comprises the following steps: by XiSet of samples, μ, representing class iiAverage vector, Σ, representing a set of class i samplesiRepresenting the covariance matrix of the i-th sample set, wherein omega is the projection equation coefficient, and the projection of the centers of the two samples is respectively omegaTμ0And ωTμ1The covariance of the two samples is ωT∑0Omega and omegaT∑1Omega; post-projection intra-class variance VwithinExpressed as:
Vwithin=ωT∑0ω+ωT∑1ω (5)
after-projection inter-class variance VwithoutExpressed as:
to achieve "minimum intra-class variance and maximum inter-class variance after projection", it is only necessary to minimize the objective function J:
μiis the average vector of the i-th sample set, and omega is the coefficient of the projection equation, sigmaiA covariance matrix representing the set of class i samples;
and judging the distance between the projection of the sample center and the projection of each type of sample center, wherein the classification represented by the projection center closest to the projection of the sample center is the classification result of the sample.
S22, predicting unclassified seismic sample data by using a linear discriminant analysis classifier;
s23, selecting the most valuable sample from the unclassified seismic sample data by using a query function, submitting the sample to an expert for labeling, and adding the sample into a classified sample set;
active learning is one approach to solving the problem of small samples. In the active learning process, firstly, the current classifier is used for predicting an unclassified sample set, then, the most valuable unclassified sample is selected from the unclassified sample set and is labeled by an expert, and the sample is added into a classified sample set to train the classifier again, so that the accuracy of the classifier is rapidly improved. The frame of which can be represented by figure 3. The active learning framework consists of 5 parts: 1. one or a group of classifiers C; 2. a classified sample set L; 3. an unclassified sample set U; 4. a related-art expert S; 5. the function Q is queried. The focus of interest in the active learning framework is on the query function. The query function is used for evaluating the value of a certain sample in the unclassified samples to the classifier, and the active learning framework selects samples meeting conditions from the unclassified samples in a centralized mode according to the current classifier and the query function and submits the samples to an expert for labeling, so that the precision of the classifier is improved. The query function of the invention uses an entropy-based query function, and the probability that a certain sample x belongs to the ith class is set as piThe information entropy H (x) is calculated by the following formula
n is the total number of categories, the larger the information entropy is, the larger the uncertainty is, the richer the contained information quantity is, and the larger the value is.
And S24, repeating the steps S21-S23 until the classifier meets the precision requirement.
Under the active learning framework, the invention firstly trains a linear discriminant analysis classifier by using a small amount of marked sample sets, then selects unmarked samples in the unmarked sample sets by using an inquiry function based on uncertainty, and then submits the samples to experts for lithofacies labeling, thereby leading the classifier to achieve the best classification effect by using the number of training samples as less as possible. Different from passive learning, the classifier actively selects samples from a non-classified sample set according to a query strategy in active learning and submits the samples to an expert for labeling; passive learning only randomly selects samples from an unclassified sample set and delivers the samples to an expert for labeling, so that the result is unstable and the accuracy is improved slowly. Using passive and active learning, the classifier accuracy as a function of the number of samples is shown in FIG. 4
The reason why the accuracy of the active learning training set in fig. 4 decreases as the number of samples increases is that the active learning selects samples which are difficult to judge in the unlabeled sample set and then the samples are labeled by experts, so that the classification of the samples is very difficult, which results in a phenomenon that the accuracy of the training set is low, but the accuracy rapidly increases and stabilizes in the testing set. The rising speed of the passive learning accuracy rate with the number of training samples is not fast than that of active learning, and the result is unstable, which means that the active learning can use fewer samples to achieve better classification effect.
S3, performing lithofacies classification on seismic sample data to be predicted by using a linear discriminant analysis classifier to obtain n lithofacies;
s4, establishing a linear relation model to predict porosity, and obtaining a prediction result; and performing lithofacies analysis on each lithofacies data set by adopting the elastic parameters of the reservoir interval, and performing multiple regression in each lithofacies by utilizing the elastic parameters and the porosity to obtain a prediction result. The specific implementation method comprises the following steps: establishing a linear relation model for porosity prediction, and determining the quantitative relation of mutual dependence among multiple variables by using regression analysis in mathematical statistics; the linear regression equation is represented by the following formula:
y=w·x+b
in the above formula, x is a reservoir elastic parameter vector, w represents a coefficient of a corresponding parameter in x, b is a prediction result of linear regression when x is input to be 0, namely 0 input bias, and y is a porosity prediction result.
The classification effect of the present invention is verified by the following specific examples.
On the well data, the training set only used 0.5% (10/629) of the well data as the initial known label sample, and this example used the following methods for porosity prediction and compares their prediction results: 1. performing linear regression; 2. performing phased regression using the true lithofacies; 3. predicting lithofacies by using a semi-supervised self-training method to perform phased regression; 4. predicting lithofacies by using a passive learning method to perform phased regression; 5. and predicting lithofacies by using an active learning method to perform phased porosity regression. Test data were from a study area with the eastern central depression of the ascharian basin. Experiments were performed with data from well a in the study area. The porosity prediction result is evaluated using a Mean Square Error (MSE) and a decision coefficient (R2), where the smaller the mean square error, the larger the decision coefficient, the more accurate the prediction result and the smaller the error. The lithofacies classification results of well a are shown in fig. 5, the porosity prediction results are shown in fig. 6 (in the figure, the solid line represents the true porosity, and the dotted line represents the predicted porosity), and the correlation errors are shown in table 1.
TABLE 1
MSE | R2 | Rate of accuracy of classification | |
Linear regression | 1.1041 | 0.8975 | - |
True phase-controlled regression | 0.9397 | 0.9128 | 1.000 |
Semi-supervised predictive phased regression | 1.0914 | 0.8987 | 0.712 |
Passive learning predictive phased regression | 1.071 | 0.9006 | 0.753 |
Active learning predictive phased regression | 0.9447 | 0.9123 | 0.932 |
As can be seen from fig. 5 and table 1, the lithofacies prediction accuracy of the semi-supervised learning method and the passive learning method is only 0.712 and 0.753, the lower lithofacies classification accuracy leads to an increase in the phased porosity regression error, while the accuracy of the active learning prediction lithofacies is greatly improved, and the accuracy is 0.932, so that the accuracy of the phased porosity prediction result is improved, which indicates that the problem of too low lithofacies classification accuracy caused by too few lithofacies samples in actual production can be better solved by the active learning, and the problem of too large phased porosity regression error caused by too low lithofacies classification accuracy is further solved.
On the volume data, the training set is trained by only 4% (3/71) of the total well number, the embodiment uses semi-supervised learning and active learning respectively to perform lithofacies prediction, and uses the prediction results of the two methods as phase control constraints to perform phase control porosity regression prediction. Experiments show that the accuracy of the lithofacies predicted by the active learning method reaches 91.91%, and the accuracy of the lithofacies predicted by the semi-supervised method reaches 82.86%.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.
Claims (5)
1. The phased porosity prediction method based on active learning is characterized by comprising the following steps of:
s1, acquiring a seismic sample data set to be predicted;
s2, constructing a linear discriminant analysis classifier by using the seismic sample data of the known lithofacies classification and the corresponding labels;
s3, performing lithofacies classification on seismic sample data to be predicted by using a linear discriminant analysis classifier;
and S4, establishing a linear relation model to predict porosity, and obtaining a prediction result.
2. The active learning based phased porosity prediction method according to claim 1, wherein the step S2 comprises the following sub-steps:
s21, training a linear discriminant analysis classifier by using the seismic sample data with known phase-controlled porosity and a corresponding label;
s22, predicting unclassified seismic sample data by using a linear discriminant analysis classifier;
s23, selecting the most valuable sample from the unclassified seismic sample data by using a query function, submitting the sample to an expert for labeling, and adding the sample into a classified sample set;
and S24, repeating the steps S21-S23 until the classifier meets the precision requirement.
3. The active learning-based facies of claim 2The porosity control prediction method is characterized in that the step S21 is realized by the following specific method: by XiSet of samples, μ, representing class iiAverage vector, Σ, representing a set of class i samplesiRepresenting the covariance matrix of the i-th sample set, wherein omega is the projection equation coefficient, and the projection of the centers of the two samples is respectively omegaTμ0And ωTμ1The covariance of the two samples is ωT∑0Omega and omegaT∑1Omega; post-projection intra-class variance VwithinExpressed as:
Vwithin=ωT∑0ω+ωT∑1ω
after-projection inter-class variance VwithoutExpressed as:
to achieve "minimum intra-class variance and maximum inter-class variance after projection", it is only necessary to minimize the objective function J:
μiis the average vector of the i-th sample set, and omega is the coefficient of the projection equation, sigmaiA covariance matrix representing the set of class i samples;
and judging the distance between the projection of the sample center and the projection of each type of sample center, wherein the classification represented by the projection center closest to the projection of the sample center is the classification result of the sample.
4. The method for predicting phased porosity based on active learning according to claim 2, wherein the query function in step S23 uses an entropy-based query function, and the probability that a sample x belongs to the i-th class is set as piThen the entropy h (x) is calculated using the following equation:
n is the total number of categories, the larger the information entropy is, the larger the uncertainty is, the richer the contained information quantity is, and the larger the value is.
5. The active learning-based phased porosity prediction method according to claim 1, wherein the step S4 is implemented by: establishing a linear relation model for porosity prediction, and determining the quantitative relation of mutual dependence among multiple variables by using regression analysis in mathematical statistics; the linear regression equation is represented by the following formula:
y=w·x+b
in the above formula, x is a reservoir elastic parameter vector, and w represents the coefficient of the corresponding parameter in x; b is the prediction result of linear regression when the input x is 0, namely 0 input offset; and y is a porosity prediction result.
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