CN113128623B - Robust K-means algorithm for seismic facies analysis - Google Patents

Robust K-means algorithm for seismic facies analysis Download PDF

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CN113128623B
CN113128623B CN202110524286.3A CN202110524286A CN113128623B CN 113128623 B CN113128623 B CN 113128623B CN 202110524286 A CN202110524286 A CN 202110524286A CN 113128623 B CN113128623 B CN 113128623B
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宋承云
李凌轩
李琳
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Chongqing University of Technology
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Abstract

The invention relates to a robust K-means algorithm for seismic facies analysis. The method comprises the following steps: selecting original amplitude data; setting a maximum phase adjustment parameter and a time window to extract a seismic waveform of a target interval; establishing a target function and carrying out iterative update on parameters in the function; and continuously training the target function by adjusting the phase parameters, and finishing parameter training when the training is carried out until R is smaller than a threshold value or the training frequency reaches the maximum iteration frequency to obtain a final classification result. By adopting the algorithm and the corresponding optimization method provided by the invention, the influence caused by horizon noise can be effectively overcome, and the seismic facies classification result is more accurate.

Description

Robust K-means algorithm for seismic facies analysis
Technical Field
The invention relates to a seismic data technology, in particular to a robust K-means algorithm for seismic facies analysis.
Background
Seismic facies analysis is intended to describe and interpret extracted seismic reflection parameters, including geometry, continuity, amplitude, frequency, velocity, and coherence. Because the coverage area of the three-dimensional seismic data is large, a great deal of time and energy are needed for manually explaining the seismic facies, and even under the help of user-friendly software, subjective results can be generated depending on the experience of interpreters, so that the seismic facies automatic analysis technology is continuously developed in recent decades, and similar seismic reflection signals are divided into one type by using some pattern recognition methods to represent a deposition characteristic, and the seismic facies can also be defined as the seismic facies.
In general, machine learning methods for seismic facies analysis can be divided into supervised and unsupervised methods. The supervision technology needs to mark data to train a classification model to identify unlabeled seismic data, however, well data or seismic interpretation of a new exploration area is limited, and the occurrence of incomplete and unbalanced problems of labels brings challenges to supervised learning; in contrast, unsupervised seismic facies analysis uses a clustering algorithm to generate a seismic facies graph, which is a data-driven method that allows for good reservoir prediction without the aid of specialized interpreters. Common unsupervised methods include K-means algorithms, self-organizing maps, neural networks, Generating Topological Maps (GTM), deep learning, etc.
From the input of the clustering method, the unsupervised seismic facies analysis mainly comprises two research branches of seismic waveform classification and multi-attribute clustering. Seismic attributes extracted from the original seismic waveform data are robust to seismic noise, hidden reservoir information can be revealed, however, how to select proper attributes from numerous redundant attributes is a main challenge of multi-attribute analysis; attributes optimized by adopting multi-feature fusion technologies such as Principal Component Analysis (PCA) and deep learning may lose the physical significance of original seismic attributes and are difficult to interpret; therefore, waveform classification methods are commonly used for seismic facies analysis because of their simplicity and effectiveness. In addition, although the seismic reflection patterns such as strong amplitude reflection, weak amplitude reflection, continuous reflection, and discontinuous reflection can be easily identified from the model seismic trace of the final seismic facies analysis result, there are problems to be solved such as time window selection and seismic data noise in waveform classification in order to improve the effectiveness of the analysis. Xie et al extract mel-frequency cepstral coefficients (MFCCs) based on the bottom and top horizons, avoiding the use of fixed-size time windows. Song et al, proposes a new similarity measurement method that can directly calculate the distance between unequal waveforms. Saraswat and Sen introduced an artificial immune system and self-organizing map (AI-SOM) for unsupervised seismic facies analysis, which is robust in the presence of noise in seismic data. Furthermore, Song et al (2017a) and Song et al (2017b) take into account formation continuity to overcome the effects of noise.
Another important issue in seismic waveforms is horizon interpretation noise. Gao (2008,2011) proposes Texture Model Regression (TMR) to perform seismic facies analysis, and uses a variable phase model to distinguish seismic facies features, however, when facing sparse and labeled accurate data, the selection and training of the model is difficult; therefore, Song et al propose an adaptive-phase K-means algorithm (Ap-K-means) for unsupervised waveform classification to reduce horizon interpretation noise. The Ap-K-means algorithm proposes a method of extracting waveforms along a target horizon by using a sliding window, and represents the characteristics of reflection points by using waveforms most matched with model seismic traces (i.e. clustering centroids). This method actually fine-tunes the interpretation horizon through an iterative optimization process of the algorithm.
However, the difficulty of horizon interpretation varies from geological structure to geological structure, and in the case of a larger coverage of seismic data, inconsistent horizon noise may be generated at different reflection times. Thus, when a large sliding window maximum offset is used to tolerate different horizon noise, the problem of "horizon crossing" may occur, resulting in unreliable seismic phase diagrams.
Disclosure of Invention
Aiming at the problems in the prior art, the technical problems to be solved by the invention are as follows: because the difficulty of geological horizon interpretation is different due to different geological structures, the horizon interpretation is not accurate, and the ability of horizon adjustment needs to be improved.
In order to solve the technical problems, the invention adopts the following technical scheme: a robust K-means algorithm for seismic facies analysis, comprising the steps of:
s100: selecting data obtained by seismic exploration, wherein the data is original amplitude data;
s200, setting a maximum phase adjustment parameter pmaxSelecting a target layer to be analyzed, selecting a time window according to the main frequency of the seismic exploration signal of the target layer section, and adjusting a parameter p through a phase aiming at the original amplitude datalObtaining a waveform sample set comprising N samples, using the weighted adaptive phase distanceClassifying the samples, which comprises the following steps:
s210: randomly selecting K samples from the N samples as the initial centroid mu of the data setiThere are K initial centroids, each corresponding to a cluster center;
s220: selecting j sample, making i equal to 1,2, …, K, calculating j sample and i initial centroid muiThe weighted distance between them, the calculation expression of the weighted distance is as follows:
Figure BDA0003065162780000021
wherein D iswAn adaptive phase distance representing the fusion weight, i.e. a weighted distance; mu.siRepresents the ith initial centroid, i.e., the cluster center for the ith cluster; x is the number ofjRepresents j-th sample data, j ═ 1,2, …, N; p represents a phase adjustment parameter, and w (p) represents a phase weight;
s230: selecting the initial centroid with the smallest weighted distance value with the jth sample as the cluster center of the jth sample according to the result obtained in step S220, wherein the clustering result of the jth sample is represented as zkj；
Figure BDA0003065162780000031
S240: repeating the steps S220 and S230, and clustering and dividing the N samples to obtain a clustered data set;
s300: establishing an objective function, wherein the specific expression is as follows:
Figure BDA0003065162780000032
where R represents the minimum sum of distances from sample points of all classes to their class centers, zijRepresenting a clustering result;
s400: updating the ith initial centroid, i.e. let μi＝μi', theMu is describedi' calculation using equation (4-1):
Figure BDA0003065162780000033
s500: updating the phase adjustment parameter p, i.e. order plP, calculated using equation (5-1);
Figure BDA0003065162780000034
s600: presetting a maximum iteration number and a threshold value of R, and finishing parameter training when the training time is less than the threshold value or the training time reaches the maximum iteration number; otherwise, executing the next step;
s700: adjusting a parameter p by phase for a geological waveformlA new waveform sample set is obtained, the new waveform sample set includes N samples, the waveform sample set is updated by the new waveform sample set, and the process returns to step S220.
Preferably, the step of obtaining the weighted distance calculation expression in S220 includes the following steps:
s221: and calculating the weight of the phase by using a Gaussian algorithm, wherein the specific expression is as follows:
Figure BDA0003065162780000035
wherein σ represents a standard deviation of the gaussian function;
s222: calculating the self-adaptive phase distance by using W (p) to obtain the self-adaptive phase distance D of the fusion weightw。
A sliding, shiftable time window is employed in extracting waveform samples to obtain the ability to tolerate horizon noise. Since it is more reliable that the center point of the time window is closer to the horizon, the weight of the gaussian is chosen such that the further the offset, the heavier the penalty.
Preferably, the S400 calculates μiThe specific steps of' are:
s410: when p and z are fixed values, the objective function is simplified as:
Figure BDA0003065162780000041
wherein, the specific expression of J is as follows:
Figure BDA0003065162780000042
s420: j to muiTaking the derivative, the specific expression is as follows:
Figure BDA0003065162780000043
wherein, the formula (4-4) is equal to 0, and the updated centroid mu is obtained by calculationi′。
This method is used here to match the centroid μ of the K-means algorithmiThe updates of (a) remain substantially consistent.
Compared with the prior art, the invention has at least the following advantages:
1. by introducing Gaussian weight into the adaptive phase distance, a new robust K-means (R-K-means) waveform classification algorithm is provided, and the problem of inaccurate layer bit interpretation under the influence of layer bit noise is solved.
2. The method has good horizon adjusting capability, can generate a satisfactory waveform classification effect, and can be applied to a data work area with large horizon interpretation errors.
3. Compared with the existing algorithm, the seismic facies classification result obtained by the method is more reliable
Drawings
Fig. 1 explains the noise for horizons. a) Line 1 represents the original horizon; Ap-K-means has the ability to modify a given horizon to the horizon labeled line 2. b) The horizontal line noise of the oval area is large, so that the maximum offset of the sliding window is difficult to set.
Fig. 2 is a portion of the F3 data.
Fig. 3 is an initial centroid used in all comparison methods.
FIG. 4 is a correlation image generated by the R-K-means algorithm proposed by the present invention. FIG. 4a is a seismic facies diagram and FIG. 4b is a model seismic trace.
FIG. 5 is a seismic facies diagram and model seismic traces generated by the Ap-K-means algorithm and the conventional K-means algorithm.
FIG. 6 is a comparison of seismic data profiles along line AB and seismic facies analysis results.
Detailed Description
The present invention is described in further detail below.
Different weights are used for different sliding windows, and a Gaussian weight is adopted to punish a farther sliding window so as to ensure that the adjusted window is close to the original level; meanwhile, the algorithm has certain adjustment capability in a longer time range. If the waveform is close to the horizon and can not be well matched with the model seismic channel, on the basis, a weighted adaptive phase distance is provided to calculate the similarity between the waveform extracted around the interested horizon and the model seismic channel, and an objective function of a robust K-means (R-K-means) algorithm is constructed; finally, an alternative method for solving the R-K-means optimization problem is provided.
The invention creatively provides the weight of selecting the Gaussian, so that the farther the deviation is, the heavier the punishment can be obtained; firstly, selecting original amplitude data; setting a maximum phase adjustment parameter and clustering data samples; secondly, establishing a target function and carrying out iterative update on parameters in the function; and finally, continuously training the target function by adjusting the phase parameters, and finishing parameter training when the training is carried out until R is smaller than a threshold value or the training times reach the maximum iteration times to obtain the trained target function.
A robust K-means algorithm for seismic facies analysis, comprising the steps of:
s100: selecting data obtained by seismic exploration, wherein the data is original amplitude data;
s200, setting a maximum phase adjustment parameter pmaxSelecting the object to be analyzedAccording to the main frequency of the seismic exploration signal of the target interval, selecting a time window, and adjusting a parameter p by a phase aiming at the original amplitude datalObtaining a waveform sample set, wherein the waveform sample set comprises N samples, and the samples are classified by using a weighted adaptive phase distance, and the method specifically comprises the following steps:
s210: randomly selecting K samples from the N samples as the initial centroid mu of the data setiThere are K initial centroids, each corresponding to a cluster center;
s220: selecting j sample, making i equal to 1,2, …, K, calculating j sample and i initial centroid muiThe weighted distance between them, the calculation expression of the weighted distance is as follows:
Figure BDA0003065162780000051
wherein D iswAn adaptive phase distance representing the fusion weight, i.e. a weighted distance; mu.siRepresents the ith initial centroid, i.e., the cluster center for the ith cluster; x is the number ofjRepresents j-th sample data, j ═ 1,2, …, N; p represents a phase adjustment parameter, and w (p) represents a phase weight;
in specific implementation, the weighted distance calculation expression comprises the following specific steps:
s221: and calculating the weight of the phase by using a Gaussian algorithm, wherein the specific expression is as follows:
Figure BDA0003065162780000052
wherein σ represents a standard deviation of the gaussian function;
s222: calculating the self-adaptive phase distance by using W (p) to obtain the self-adaptive phase distance D of the fusion weightw。
S230: selecting the initial centroid with the smallest weighted distance value with the jth sample as the cluster center of the jth sample according to the result obtained in step S220, wherein the clustering result of the jth sample is represented as zkj；
Figure BDA0003065162780000061
S240: repeating the steps S220 and S230, and clustering and dividing the N samples to obtain a clustered data set;
s300: establishing an objective function, wherein the specific expression is as follows:
Figure BDA0003065162780000062
where R represents the minimum sum of distances from sample points of all classes to their class centers, zijRepresenting a clustering result;
s400: updating the ith initial centroid, i.e. let μi＝μi', said mui' calculation using equation (4-1):
Figure BDA0003065162780000063
in specific implementation, mu is calculatediThe specific steps of' are:
s410: when p and z are fixed values, the objective function is simplified as:
Figure BDA0003065162780000064
wherein, the specific expression of J is as follows:
Figure BDA0003065162780000065
s420: j to muiTaking the derivative, the specific expression is as follows:
Figure BDA0003065162780000066
wherein, the formula (4-4) is equal to 0, and the updated centroid mu is obtained by calculationi′。
S500: updating the phase adjustment parameter p, i.e. order plP, calculated using equation (5-1);
Figure BDA0003065162780000067
s600: presetting a maximum iteration number and a threshold value of R, and finishing parameter training when the training time is less than the threshold value or the training time reaches the maximum iteration number; otherwise, executing the next step;
s700: adjusting the parameter p by phase for the raw amplitude datalA new waveform sample set is obtained, the new waveform sample set includes N samples, the waveform sample set is updated by the new waveform sample set, and the process returns to step S220. When z and μ are fixed, the objective function R has the same solution as the weighted distance Dw, since p represents the window offset, the accuracy of which is related to the sampling ratio, at pmaxThe solution space is relatively small, so p, l ═ 1,2, …, max can be directly solved by an exhaustive search method in general.
Experimental verification
To further demonstrate the effectiveness of the method of the present invention, the method proposed by the present invention was applied to published actual data in the F3 block of the netherlands.
Referring to fig. 1, this figure explains the noise for the horizon. a) Line 1 represents the original horizon, Ap-K-means has the ability to modify a given horizon to one marked as line 2; that is, line 1 in FIG. 1a is the original horizon, with some explanatory noise; Ap-K-means can modify a given horizon to the horizon indicated by line 2 in figure 1a, thus generating a satisfactory seismic facies map. b) The horizontal line noise of the oval area is large, so that the maximum offset of the sliding window is difficult to set; that is, the noise of the elliptical region in fig. 1b is larger than that of other positions, which is mainly due to the strong discontinuity of the elliptical region.
Referring to FIG. 2, which is a cross-section, in the present invention, an MFS4 horizon is selected to analyze seismic facies, as shown; the sampling interval is 4 ms. To achieve high-precision adjustment, interpolation is necessary before extracting the waveform; extracting seismic waveforms in a time range of [ -8ms, +42ms ]; the maximum offset of horizon adjustment is 10ms, the σ of the Gaussian function is 15, and the number of seismic facies is 6. On the basis of the parameter setting, the traditional K-means (T-K-means), the self-adaptive K-means (Ap-K-means) and the proposed method (R-K-means) are adopted for seismic phase analysis.
Referring to FIG. 3, the present invention uses the same seismic signals due to the sensitivity of these methods to the initial centroid.
Referring to FIG. 4, a final phase diagram (FIG. 4a) and model seismic traces (FIG. 4b) based on the R-K-means algorithm. From which major seismic facies (e.g., channels and faults) can be readily identified.
Referring to FIG. 5, in contrast, the Ap-K-means and R-K-means algorithm-generated phases exhibit some discontinuities and noise classification, especially in the regions marked as white ellipses. Meanwhile, the river shown in fig. 5 is not easily distinguished in the drawing. Additionally, the first peak of the model trace in FIG. 4 is around 12ms, similar to FIG. 3.
Thus, it can be said that the algorithm employs gaussian weights so that the adjustment of horizons is slight.
Referring to fig. 6, which is a graph of the AB line section and the results of seismic phase analysis using various methods, it can be readily observed that the method can identify river channels located near inline 665 and 700. Wherein line 1 represents the original horizon and lines 3 and 2 represent the horizon adjusted by the R-K-means algorithm and the Ap-K-means algorithm, respectively.
A novel robust K-means (namely R-K-means) waveform classification algorithm is provided by introducing Gaussian weight into adaptive phase distance, and the problem of inaccurate layer bit interpretation under the influence of layer bit noise is solved. Compared with the existing algorithm, the seismic facies classification result obtained by the method is more reliable. Experimental results show that the method has good horizon adjusting capability, can generate a satisfactory waveform classification effect, and can be applied to data work areas with large horizon interpretation errors.
Finally, the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting, although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all of them should be covered in the claims of the present invention.

Claims (2)

1. A robust K-means algorithm for seismic facies analysis, comprising: the method comprises the following steps:
s100: selecting data obtained by seismic exploration, wherein the data is original amplitude data;
s200, setting a maximum phase adjustment parameter pmaxSelecting a target layer to be analyzed, selecting a time window according to the main frequency of the seismic exploration signal of the target layer section, and adjusting a parameter p through a phase aiming at the original amplitude datalObtaining a waveform sample set, wherein the waveform sample set comprises N samples, and the samples are classified by using a weighted adaptive phase distance, and the method specifically comprises the following steps:
s210: randomly selecting K samples from the N samples as the initial centroid mu of the data setiThere are K initial centroids, each corresponding to a cluster center;
s220: selecting j sample, making i equal to 1,2, …, K, calculating j sample and i initial centroid muiThe weighted distance between them, the calculation expression of the weighted distance is as follows:
Figure FDA0003532062890000011
wherein D iswAn adaptive phase distance representing the fusion weight, i.e. a weighted distance; mu.siRepresents the ith initial centroid, i.e., the cluster center for the ith cluster; x is the number ofjRepresents j-th sample data, j ═ 1,2, …, N; p represents a phase adjustment parameter, and w (p) represents a phase weight;
s221: and calculating the weight of the phase by using a Gaussian algorithm, wherein the specific expression is as follows:
Figure FDA0003532062890000012
wherein σ represents a standard deviation of the gaussian function;
s222: calculating the self-adaptive phase distance by using W (p) to obtain the self-adaptive phase distance D of the fusion weightw；
S230: selecting the initial centroid with the smallest weighted distance value with the jth sample as the cluster center of the jth sample according to the result obtained in step S220, wherein the clustering result of the jth sample is represented as zkj；
Figure FDA0003532062890000013
S240: repeating the steps S220 and S230, and clustering and dividing the N samples to obtain a clustered data set;
s300: establishing an objective function, wherein the specific expression is as follows:
Figure FDA0003532062890000014
where R represents the minimum sum of distances from sample points of all classes to their class centers, zijRepresenting a clustering result;
s400: updating the ith initial centroid, i.e. let μi＝μi', said mui' calculation using equation (4-1):
Figure FDA0003532062890000021
s500: updating the phase adjustment parameter p, i.e. order plP, calculated using equation (5-1);
Figure FDA0003532062890000022
s600: presetting a maximum iteration number and a threshold value of R, and finishing parameter training when the training time is less than the threshold value or the training time reaches the maximum iteration number; otherwise, executing the next step;
s700: adjusting the parameter p by phase for the raw amplitude datalA new waveform sample set is obtained, the new waveform sample set includes N samples, the waveform sample set is updated by the new waveform sample set, and the process returns to step S220.
2. A robust K-means algorithm for seismic facies analysis as claimed in claim 1 wherein: s400 calculating muiThe specific steps of' are:
s410: when p and z are fixed values, the objective function is simplified as:
Figure FDA0003532062890000023
wherein, the specific expression of J is as follows:
Figure FDA0003532062890000024
s420: j to muiTaking the derivative, the specific expression is as follows:
Figure FDA0003532062890000025
wherein, the formula (4-4) is equal to 0, and the updated centroid mu is obtained by calculationi′。
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