The classification in metamorphic rocks using modified fuzzy cluster analysis from geophysical log data: evidence from Chinese Continental Scientific Drilling Main Hole

The classification in metamorphic rocks using modified fuzzy cluster analysis from geophysical log data: evidence from Chinese Continental Scientific Drilling Main Hole Huaijie Yang 0 Heping Pan 0 Miao Luo 0 Gang Li 0 Jing Yao 0 0 Institute of Geophysics and Geomatic, China University of Geosciences , Wuhan 430074, Hubei Province , China Lithology is one of the most important data in evaluating reservoir, and is mainly carried out by cores recovery in laboratory which is very expensive, and its interpretation is time consuming. Accurate identification of lithology is fundamentally crucial to evaluate reservoir from geophysical log data. Pattern recognition and statistical analysis have been proved to be the most powerful methods for constructing optimal model in lithology recognition. To address this issue, a fast and practical K-means clustering algorithm is proposed in order to better deal with lithology recognition from geophysical log data. Based on the traditional K-means clustering algorithm, Euclidean distance is replaced by Mahalanobis distance; the initial cluster centers are acquired from the average of characteristic values but not selected randomly, in addition, adding weight value in each characteristic value of the objective function, and thus a lithology recognition model named modified K-means clustering is established. The method is applied to identify the Chinese Continental Scientific Drilling Main Hole (CCSD-MH) metamorphic rocks. Compared with the traditional K-means clustering, the accurate rate of the modified K-means clustering in lithologic identification has improved for the same 45 samples, raised 11.11 %. According to the modified K-means cluster algorithm, nine kinds of lithology cluster centers are acquired from 45 samples. The classes of the samples can be determined by analyzing the hamming Huaijie Yang Lithology recognition; CCSD-MH; K-means clustering; Hamming approach degree; Cluster center; Geophysical log data; Weight value - approach degree curves, which is calculated by the undetermined samples and 9 cluster centers. The predicted results and the core recovery are exactly the same by comparison. The hamming approach degree can identify the whole well of CCSD-MH lithology effectively and accurately. This model may be made applications to other areas. Fuzzy theory was proposed by cybernetic professor L. A. Zadeh in University of California in 1965 (Gao 2004) and has been widely used in the natural sciences and social sciences fields in the following 50 years. Fuzzy clustering analysis is a branch of fuzzy mathematics, and its range of applications involves time series prediction (Ryoke et al. 1995), neural networks training (Karayiannies and Mi 1997), nonlinear system identification (Runkler et al. 1996), parameter estimation (Gath and Geva 1989), medical diagnosis (Bezdek and Fordon 1979), weather forecast (Newton 1992), food classification (Windham 1985), and water quality analysis (Mukherjee 1995). The limitations of traditional fuzzy clustering analysis are several controlling factors, such as the choice of initial cluster centers, the correlation between samples, the trade-off between iteration times, and solutions accuracy. To solve these problems, many researchers had proposed many modified algorithms, such as K-means clustering, C-means clustering, fuzzy clustering neural network, and fuzzy clustering genetic. Overview of worldwide, the workers had made many researches about the lithology identification of CCSDMH; however, the database of CCSD-MH core data was still incomplete and inaccurate. Xu et al. (2006) analyzed magnetic susceptibility and density of different rocks from CCSD-MH in the depth Section 02000 miles, identified the lithology with SPSS statistical software. Jing et al. (2007) summed up 11 kinds of eclogites into 6 kinds based on multivariate statistic methods. Gu et al. (2009) constructed the lithology recognition model combining the logging response and several well logs of different rocks with the method of cluster analysis and stepwise discriminant analysis. Luo and Pan (2010) used core-log correlation and cross-plotting methods, and the results allowed the authors to conclude that the lithology is mainly comprised orthogneiss, paragneiss, eclogite, amphibolite, and ultramafic rocks. Bosch et al. (2013) used fuzzy logic for lithology prediction from well log data of the German Continental Deep Drilling Program (KTB). Results showed that this fuzzy logic-based method was suited for rapidly and reasonably suggesting a lithology column from KTB well log data. The above authors heavily focused on approaches such as visual inspection, cross-plotting technology, and discriminate function analysis, and not formed a method that can neatly identify the main units and refine the classification of the CCSD-MH whole well. Reservoir evaluation needs the data of many kinds of rocks, which have a much more different porosity and permeability. The well logs have varieties of responses based on different kinds of rocks characteristic. And the lithology data is mainly carried out by cores recovery in lab which is very expensive and its interpretation is time consuming, so accurate identification of lithology from geophysical well log data plays a significant role in reservoir evaluation. In this study, a fast and practical K-means clustering algorithm was proposed in order to better deal with lithology recognition of CCSD-MH from geophysical log data. Based on the traditional K-means clustering algorithm, Euclidean distance was replaced by Mahalanobis distance, and the initial cluster centers were acquired from the average of characteristic values, in addition, added weight value in each characteristic value of the objective function. The model was applied to classify CCSD-MH metamorphic rocks and get the cluster centers of each class. The cluster centers, as well as weight values, were used to calculate the hamming approach degree, which can neatly identify the main units and refine the classification of the CCSD-MH whole well. Modified K-means clustering Cluster center Let us choose m objects, and each object has n characteristic values that may be classified into z classes. According to the fuzzy theory, the fuzzy matrix involving the above objects can be constructed as X xij , (i 1; 2; . . .; m; j 1; 2; . . .; n). The cluster center matrix is defined as C ckj , and k (k 1; 2; . . .; z), j (j 1; 2; . . .; n). And m z. The two matrixes and their compositions are as follows: X fX1; X2; . . .; Xng and C fC1; C2; . . .; Czg and Ck fck1; ck2; . . .; ckng: The traditional K-means algorithm will increase iteration times if initial cluster centers selected inappropriately, and may easily fall into local optimums. In order to alleviate this problem, we acquired the initial cluster centers from the average of characteristics values in matrix X based on the theory of cluster center (Liao 2013). Therefore, an (...truncated)