CN112163611A - Feature tensor-based high-dimensional seismic data interpolation method - Google Patents

Feature tensor-based high-dimensional seismic data interpolation method Download PDF

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CN112163611A
CN112163611A CN202011014635.9A CN202011014635A CN112163611A CN 112163611 A CN112163611 A CN 112163611A CN 202011014635 A CN202011014635 A CN 202011014635A CN 112163611 A CN112163611 A CN 112163611A
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陈尧
贾永娜
顾军华
常光耀
李一凡
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Abstract

The invention discloses a feature tensor-based high-dimensional seismic data interpolation method which comprises the steps of preprocessing data, extracting training feature tensors, training and learning a tensor regression model and carrying out interpolation reconstruction. The tensor regression model is applied to seismic data interpolation reconstruction, the tensor is used as the input feature for training, the original feature is directly input into the tensor regression model, the structural information of high-dimensional data is not damaged, the structural information in the original feature is effectively reserved, the structural information utilization rate of the high-dimensional seismic data is improved, the interpolation effect of a machine learning method is improved, the seismic data recovery quality is improved, the seismic data interpretation accuracy is improved, and the universality capacity of different types of different-dimension seismic data is realized.

Description

Feature tensor-based high-dimensional seismic data interpolation method
Technical Field
The invention relates to the field of seismic data processing, in particular to a feature tensor-based high-dimensional seismic data interpolation method.
Background
At present, the traditional energy sources such as natural gas, petroleum and the like which the national people rely on for survival are exploited without exploring physics, and the acquired data are called seismic data. High density complete seismic data is of great importance in subsequent steps such as offset imaging and multiple suppression. On one hand, the arrangement of the detectors is restricted by natural conditions, so that the phenomenon of column alignment loss of the acquired data is caused; on the other hand, in order to save mining cost, the distance between adjacent detectors is increased, so that data are too sparse, and the phenomenon of data loss of the acquired data is caused. The purpose of seismic data interpolation is to complement missing data completely or encrypt sparse data by a mathematical algorithm to densify the data. In recent years, the exploration industry has become more concerned with the acquisition of high dimensional seismic data. The high-dimensional seismic data refers to data acquired by multiple detectors and multiple shot points at different moments. Information among data space coordinate axes is closely connected under the constraint of complex physical wave characteristics, so that the high-dimensional seismic data can contain more structural information, and more basis is provided for the correct interpretation of the underground medium. However, due to the limitation of economic conditions and natural conditions, the problem of interpolation reconstruction of high-dimensional seismic data is particularly important.
When the traditional algorithm processes the interpolation problem of high-dimensional seismic data, such as sparse transformation, dictionary learning, tensor completion and the like, the high-dimensional seismic data are often converted into low-dimensional seismic data by depending on dimension reduction conversion in an unfolding mode, and the interpolation is carried out by adopting a low-dimensional interpolation algorithm, so that the physical correlation relationship of the seismic data among different dimensions is destroyed, and the interpolation effect needs to be further improved. The original machine learning method usually expands high-dimensional data into vectors according to a certain dimension, which destroys the rich multi-dimensional characteristics of high-dimensional seismic data, and as the dimension is increased, the training parameters are increased, which results in low efficiency and unsatisfactory interpolation effect in training the high-dimensional data. Emerging machine learning algorithms exhibit universality and powerful learning capabilities for different types of seismic data, but still do not achieve the capability of learning structural information. When solving the high dimensional data, the interpolation is still carried out by adopting a low dimensional algorithm after the expansion.
In recent years, tensor regression models such as a support tensor machine, a generalized tensor linear regression model, a low-rank sparse tensor regression model and the like are applied to the application fields such as the image field, neuroimaging, hyperspectral remote sensing imaging and the like. With the tensor decomposition, the model has significant advantages in the processing of high-dimensional data. In the seismic data interpolation technology, the existing algorithm lacks the universality capability of high-dimensional data, and the research of the universality interpolation algorithm suitable for the high-dimensional data is necessary.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a feature tensor-based high-dimensional seismic data interpolation method.
The technical scheme for solving the technical problem is to provide a feature tensor-based high-dimensional seismic data interpolation method, which is characterized by comprising the following steps of:
step one, preprocessing data: selecting original training data, and then carrying out deletion processing on the original training data to obtain deletion training data; performing pre-interpolation processing on the missing training data and the missing seismic data respectively by adopting an interpolation algorithm to obtain pre-interpolation training data and pre-interpolation reconstruction data;
step two, extracting a training feature tensor: selecting step length and scale, and respectively carrying out local cutting processing on pre-interpolation training data and pre-interpolation reconstruction data to obtain a training feature tensor and a predicted feature tensor;
step three, training and learning of a tensor regression model: determining a mapping point of a training feature tensor and original training data in the original training data, wherein the mapping point is a training label, and a training set consisting of the training label and the training feature tensor is obtained; each training feature tensor and the corresponding training label form a group of training point pairs in a training set; sequentially inputting each group of training point pairs to a tensor regression model, and training and learning the tensor regression model to obtain a trained tensor regression model;
step four, interpolation reconstruction: sequentially inputting the predicted feature tensors into a trained tensor regression model to obtain a predicted label set; and then according to the mapping relation between the training feature tensor determined in the third step and the original training data, performing interpolation operation on the missing seismic data by using the prediction labels in the prediction label set to obtain reconstructed seismic data.
Compared with the prior art, the invention has the beneficial effects that:
(1) the tensor regression model is applied to seismic data interpolation reconstruction, the tensor is used as the input feature for training, the original feature is directly input into the tensor regression model, the structural information of high-dimensional data is not damaged, the structural information in the original feature is effectively reserved, the structural information utilization rate of the high-dimensional seismic data is improved, the interpolation effect of a machine learning method is improved, the seismic data recovery quality is improved, the seismic data interpretation accuracy is improved, and the universality capacity of different types of different-dimension seismic data is realized.
(2) When high-dimensional data is interpolated, by means of CP decomposition, the high-dimensional data is decomposed into a plurality of matrixes on the premise of not destroying the structural information of the high-dimensional data, so that training parameters can be effectively reduced, and the interpolation efficiency is further improved.
(3) In the model parameter training process, the alternating least square method is adopted, each wheel retrains the correlation matrix of each dimension, the multi-dimensional structure correlation property of the seismic data is repeatedly considered, and the utilization capacity of the structure information is obviously improved.
Drawings
FIG. 1 is a complete seismic data plot of example 1 of the present invention;
FIG. 2 is 8 graphs of original training data according to example 1 of the present invention;
FIG. 3 is a graph of missing seismic data at a sampling rate of 50% for example 1 of the present invention;
fig. 4 is a pre-interpolation reconstruction data graph obtained through a Bicubic interpolation algorithm in embodiment 1 of the present invention;
FIG. 5 is a flow chart of data preprocessing of the present invention;
FIG. 6 is a flow chart of training learning of the tensor regression model of the present invention;
FIG. 7 is a flow chart of CP decomposition of the three-dimensional tensor;
FIG. 8 is a flow chart of an interpolation reconstruction of the present invention;
fig. 9 is a recovery result of the tensor regression algorithm of embodiment 1 of the present invention;
fig. 10 shows the recovery result of the support vector machine algorithm according to embodiment 1 of the present invention.
Detailed Description
Specific examples of the present invention are given below, and the specific examples are only for illustrating the present invention in further detail, and do not limit the scope of protection of the claims of the present application.
The invention provides a feature tensor-based high-dimensional seismic data interpolation method (short method), which is characterized by comprising the following steps of:
step one, preprocessing data: selecting original training data from the existing seismic database, and then performing missing processing on the original training data to obtain missing training data; performing pre-interpolation processing on the missing training data and the missing seismic data respectively by adopting an interpolation algorithm to obtain pre-interpolation training data and pre-interpolation reconstruction data;
selecting seismic data with proper scale and similar landform structure from the original training data, wherein the quality of the original training data is closely related to the interpolation recovery result; missing seismic data are obtained during actual exploration; the missing condition of the missing training data is consistent with the missing seismic data;
step two, extracting a training feature tensor: selecting step length and scale, and respectively carrying out local cutting processing on pre-interpolation training data and pre-interpolation reconstruction data to obtain a local feature tensor for training and learning, namely a training feature tensor, and a local feature tensor for interpolation reconstruction, namely a prediction feature tensor;
step three, training and learning of a tensor regression model: determining a mapping point of a training feature tensor and original training data, namely a training label, in the original training data to obtain a training set consisting of the training label and the training feature tensor; each training feature tensor and the corresponding training label form a group of training point pairs in a training set; sequentially inputting each group of training point pairs to a tensor regression model, and training and learning parameters of the tensor regression model, namely adjusting coefficient tensor and bias to obtain a trained tensor regression model;
step 3.1, determining a mapping point of the training feature tensor and the original training data in the original training data, wherein the mapping point is a training label, and further obtaining a training set consisting of the training label and the training feature tensor
Figure BDA0002698636890000031
Wherein
Figure BDA0002698636890000032
For the ith training feature tensor, yiThe ith training label; each training feature tensor and the corresponding training label form a group of training point pairs in a training set;
step 3.2: sequentially inputting each group of training point pairs to a tensor regression model, and training and learning parameters of the tensor regression model, namely adjusting coefficient tensor and bias to obtain a trained tensor regression model;
the training and learning method of the parameters of the tensor regression model comprises the following steps:
the tensor regression model is shown in equation 1):
Figure BDA0002698636890000033
in the formula 1), the reaction mixture is,
Figure BDA0002698636890000034
is a tensor argument; operator, euclidean inner product of the representation tensor; the parameters of the tensor regression model are coefficient tensors
Figure BDA0002698636890000035
And an offset b;
tensor of coefficient
Figure BDA0002698636890000036
Performing CP decomposition to obtain
Figure BDA0002698636890000037
(FIG. 6 shows the CP decomposition process of the three-dimensional tensor, which is a mature tensor decomposition technique, and the regression model is built on the basis of tensor decomposition), and the regression model is substituted into the formula 1) to obtain:
Figure BDA0002698636890000041
in the formula 2), the reaction mixture is,
Figure BDA0002698636890000042
is a factor matrix;
passing pair coefficient tensor
Figure BDA0002698636890000043
The CP decomposition is performed so that the number of parameters of the tensor regression model is determined by
Figure BDA0002698636890000044
Is reduced to
Figure BDA0002698636890000045
R denotes the CP rank of the coefficient tensor W; p is a radical ofiThe variable number of the coefficient tensor in the ith dimension;
converting equation 2) to equation 3 by separability of the Khatri-Rao product):
Figure BDA0002698636890000046
in formula 3), X(n)N-mode expansion for χ; "" indicates the product of Khatri-Rao;
therefore, in each training and learning process, the coefficient tensor W does not need to be adjusted, and only each factor matrix W needs to be adjustednMaking adjustments, i.e. to the factor momentsArray WnAdjustment with offset b:
Figure BDA0002698636890000047
in formula 4), L (-) is a loss function, Xi(n)Is xiN-mode unfolding of (1);
solving n +1 optimization problems in the formula 4) by an alternating least square method to obtain an optimal estimation value of the coefficient tensor
Figure BDA00026986368900000411
Optimal estimation of bias
Figure BDA00026986368900000412
Obtaining a trained tensor regression model:
Figure BDA0002698636890000048
preferably, the method for solving the n +1 optimization problems in equation 4) by the alternating least squares method is as follows:
given the error accuracy, the input error accuracy and the training set { X }i,y i1, …, M; for bias b and factor matrix WnInitialization is performed according to equations 6) and 7), respectively:
Figure BDA0002698636890000049
Figure BDA00026986368900000410
in formulae 6) and 7), b(0)And Wn (0)Representing the bias and factor matrix obtained from the 0 th training turn, namely the initial bias and initial factor matrix; operator rand (p)nR) represents the generation of pnA random number matrix of x R;
training in the t-th roundIn practice, the factor matrix W of the t-th round is obtained according to the following formulai (t)I is 1, …, N, and then the coefficient tensor W of the t round is obtained(t)Offset from round t b(t)：
Figure BDA0002698636890000051
Figure BDA0002698636890000052
Figure BDA0002698636890000053
Calculating the loss function value L (b) of the t round(t),W(t))；
When L (b)(t),W(t))-L(b(t-1),W(t-1)) Stopping training when the error precision is less than or equal to the error precision; order to
Figure BDA0002698636890000055
Obtaining the optimal estimated value of the coefficient tensor
Figure BDA0002698636890000056
And bias
Figure BDA0002698636890000057
The optimal estimated value of (a).
Step four, interpolation reconstruction: sequentially inputting the predicted feature tensors into a trained tensor regression model to obtain a predicted label set; and then according to the mapping relation between the training feature tensor determined in the third step and the original training data, performing interpolation operation on the missing seismic data by using the prediction labels in the prediction label set to obtain reconstructed seismic data.
Example 1
In this embodiment, a support vector machine algorithm (SVR algorithm) and the interpolation method (i.e., a tensor regression algorithm (TR algorithm)) are used to perform interpolation operation on missing seismic data, so as to obtain reconstructed seismic data respectively.
In the SVR algorithm, a piece of two-dimensional complete seismic data (as shown in fig. 1) is selected from the existing seismic database, and the missing seismic data is obtained by performing missing processing on the piece of two-dimensional complete seismic data. The missing seismic data size is 128 x 128. Selecting 8 pieces of seismic data which are 128 multiplied by 128 in size and have similar landform structures with missing seismic data from an existing seismic database as original training data (as shown in figure 2); as can be seen in fig. 2, the landform structure of the original training data is similar to the complete seismic data.
In the interpolation method, the selection of complete seismic data, missing seismic data and original training data is the same as that of the SVR algorithm.
In the first step of the interpolation method, as can be seen from fig. 3, the missing seismic data rule is missing, and the sampling rate is 1/a which is 50%;
the interpolation algorithm adopts Bicubic interpolation technology. It can be seen from fig. 4 that the pre-interpolated reconstructed data is only simply reconstructed and restored; the signal-to-noise ratio S/N of the pre-interpolation reconstruction data obtained in the step is 25.03dB, the reconstruction result is not ideal, and still needs to be further improved;
in the second step of the interpolation method, the step length is selected to be 1, the scale is 3 multiplied by 3, and the pre-interpolation training data and the pre-interpolation reconstruction data are subjected to local cutting processing to obtain 127008 training feature tensors and 15876 predicted feature tensors.
And quantifying the recovery quality according to the signal-to-noise ratio, wherein the signal-to-noise ratio is calculated according to the following formula:
Figure BDA0002698636890000054
wherein I is complete seismic data, InTo reconstruct seismic data;
the selected sampling rate was 50%, the recovery effects of the SVR algorithm and the TR algorithm of the present invention were compared, and the signal-to-noise ratio of the interpolation results is listed in table 1.
TABLE 1
Figure BDA0002698636890000061
In table 1, the percentage refers to the percentage ratio of the training set used in the process of training and learning the parameters of the model to the total training set. As can be seen from fig. 9, the recovery result of the TR algorithm at 100% is the signal-to-noise ratio S/N of 33.9dB, and as can be seen from fig. 10, the recovery result of the SVM algorithm at 100% is the signal-to-noise ratio S/N of 32.16 dB. As can be seen from the reconstruction results of fig. 9 and 10 and the signal-to-noise ratios in table 1, the reconstruction effect of the tensor regression algorithm using tensor as argument is better than the reconstruction effect of the support vector machine algorithm using vector as argument.
The embodiments are only for illustrating the invention and not for limiting the invention, and those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention, so all equivalent technical solutions also belong to the scope of the invention, and the scope of the invention should be defined by the claims.
Nothing in this specification is said to apply to the prior art.

Claims (4)

1. A feature tensor-based high-dimensional seismic data interpolation method is characterized by comprising the following steps:
step one, preprocessing data: selecting original training data, and then carrying out deletion processing on the original training data to obtain deletion training data; performing pre-interpolation processing on the missing training data and the missing seismic data respectively by adopting an interpolation algorithm to obtain pre-interpolation training data and pre-interpolation reconstruction data;
step two, extracting a training feature tensor: selecting step length and scale, and respectively carrying out local cutting processing on pre-interpolation training data and pre-interpolation reconstruction data to obtain a training feature tensor and a predicted feature tensor;
step three, training and learning of a tensor regression model: determining a mapping point of a training feature tensor and original training data in the original training data, wherein the mapping point is a training label, and a training set consisting of the training label and the training feature tensor is obtained; each training feature tensor and the corresponding training label form a group of training point pairs in a training set; sequentially inputting each group of training point pairs to a tensor regression model, and training and learning the tensor regression model to obtain a trained tensor regression model;
step four, interpolation reconstruction: sequentially inputting the predicted feature tensors into a trained tensor regression model to obtain a predicted label set; and then according to the mapping relation between the training feature tensor determined in the third step and the original training data, performing interpolation operation on the missing seismic data by using the prediction labels in the prediction label set to obtain reconstructed seismic data.
2. The feature tensor-based high-dimensional seismic data interpolation method as recited in claim 1, wherein the third step is specifically:
step 3.1, determining a mapping point of the training feature tensor and the original training data in the original training data, wherein the mapping point is a training label, and further obtaining a training set consisting of the training label and the training feature tensor
Figure FDA0002698636880000011
Wherein
Figure FDA0002698636880000012
For the ith training feature tensor, yiThe ith training label; each training feature tensor and the corresponding training label form a group of training point pairs in a training set;
step 3.2: and sequentially inputting each group of training point pairs to a tensor regression model, and training and learning the parameters of the tensor regression model to obtain the trained tensor regression model.
3. The feature tensor-based high-dimensional seismic data interpolation method as recited in claim 2, wherein the parameters of the tensor regression model are trained and learned as follows:
the tensor regression model is shown in equation 1):
Figure FDA0002698636880000013
in the formula 1), the reaction mixture is,
Figure FDA0002698636880000014
is a tensor argument; operator<·>A euclidean inner product representing the tensor; the parameters of the tensor regression model are coefficient tensors
Figure FDA0002698636880000015
And an offset b;
tensor of coefficient
Figure FDA0002698636880000016
Performing CP decomposition to obtain
Figure FDA0002698636880000017
And substituting it into formula 1) to obtain:
Figure FDA0002698636880000018
in the formula 2), the reaction mixture is,
Figure FDA0002698636880000019
is a factor matrix;
passing pair coefficient tensor
Figure FDA0002698636880000021
The CP decomposition is performed so that the number of parameters of the tensor regression model is determined by
Figure FDA0002698636880000022
Is reduced to
Figure FDA0002698636880000023
R denotes the CP rank of the coefficient tensor W; p is a radical ofiIs coefficient sheetThe number of variables measuring in the ith dimension;
converting equation 2) to equation 3 by separability of the Khatri-Rao product):
Figure FDA0002698636880000024
in formula 3), X(n)Is composed of
Figure FDA0002698636880000025
N-mode unfolding of (1); "" indicates the product of Khatri-Rao;
therefore, in each training learning process, the tensor of the coefficient is not required to be processed
Figure FDA0002698636880000026
The adjustment is carried out only by each factor matrix WnMaking adjustments, i.e. to the factor matrix WnAdjustment with offset b:
Figure FDA0002698636880000027
in formula 4), L (-) is a loss function, Xi(n)Is composed of
Figure FDA0002698636880000028
N-mode unfolding of (1);
solving n +1 optimization problems in the formula 4) by an alternating least square method to obtain an optimal estimation value of the coefficient tensor
Figure FDA0002698636880000029
Optimal estimation of bias
Figure FDA00026986368800000210
Obtaining a trained tensor regression model:
Figure FDA00026986368800000211
4. the feature tensor-based high-dimensional seismic data interpolation method as recited in claim 3, wherein the method for solving n +1 optimization problems in the formula 4) by the alternating least square method is as follows:
given error accuracy, input error accuracy and training set
Figure FDA00026986368800000212
For bias b and factor matrix WnInitialization is performed according to equations 6) and 7), respectively:
Figure FDA00026986368800000213
Figure FDA00026986368800000214
in formulae 6) and 7), b(0)And
Figure FDA00026986368800000215
representing the bias and factor matrix obtained from the 0 th training turn, namely the initial bias and initial factor matrix; operator rand (p)nR) represents the generation of pnA random number matrix of x R;
in the training of the t-th round, the factor matrix of the t-th round is obtained according to the following formula
Figure FDA00026986368800000216
Further, the coefficient tensor of the t round is obtained
Figure FDA00026986368800000217
Offset from round t b(t)：
Figure FDA00026986368800000218
Figure FDA0002698636880000031
Figure FDA0002698636880000032
Calculating the loss function value of the t round
Figure FDA0002698636880000033
When L (b)(t),W(t))-L(b(t-1),W(t-1)) Stopping training when the error precision is less than or equal to the error precision; order to
Figure FDA0002698636880000034
Obtaining the optimal estimated value of the coefficient tensor
Figure FDA0002698636880000035
And bias
Figure FDA0002698636880000036
The optimal estimated value of (a).
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