Using PCA and RDA feature reduction techniques for ranking seismic attributes



Optimal attributes are useful in interpretation of seismic data. Two proposed methods are presented in this paper for finding optimal attributes. Regularized Discriminate Analysis(RDA) is based on 2 parameters ë, ? which called regularization parameter. The other method is Principal Component Analysi s(PCA).In this paper gas chimney detection is defined as the subject of study for ranking relevant attributes. For 4817 samples of both classes i.e., gas chimney and non chimney with 28 attributes which are mentioned in table (1). These attributes have been picked by experienced interpreter. Among all of these attributes some of them such as Similarity (time window: [-120,-40]),Similarity (time window: [40,120]), Similarity (time window:[-40,40]), in forward selection algorithm and Similarity (time window: [-120,-40]), Similarity (time window: [-40,40]), Energy (time window:[-120,-40]) in backward selection algorithm in RDA method have the highest ranks. It should be highlighted that because the number of the observations is large so 70% of all observations have been used for train and 30% for test. The discriminate function is:

The classification error rate for RDA with ?=0.01 & ?=0.1 is 0.09 and for ?=0.1 & ?=0.1 is 0.1 and also for ?=0.1 & ?=0.01 is 0.09.
In discriminate matrix form which is shown as:

is covariance matrix of k-th class, is mean vector for k-th class and is prior probability of k-th class where is transpose of .
In PCA method the principal component obtain by calculating of eigenvectors of covariance matrix and also looking for a transformation with least square error .After these calculations we compare scatter plots of PCA. Selected attributes, PCA method are spectral decomposition with Ricker wavelet (center freq.= 60 (Hz), width=2) and Energy (time window: [-40,40]) ,Energy (time window: [-40,40]).
For better judgment and selection of optimal attributes we should combine two methods or more and obtain optimal method and also compare different method two by two.
Finally, using pattern recognition method for interpreting of seismic data is suggested.