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We consider the distributed source coding system of L correlated Gaussian sources Yi, i = 1, 2, ..., L. We assume that YL = t(Y1, Y2, ..., YL) is an observation of the remote source vector XL = t(X1,X2, ..., XL), having the formYL = XK + NL, where NL = t(N1,N2, ..., NL) is a vector of L independent Gaussian random variables also independent of XL. In this system L correlated Gaussian observations are separately compressed by Lencoders and sent to the information processing center. In this paper, we study the multiterminal source coding problem where the decoder wishes to reconstruct the observation YL = XL + NL. In the previous work the author derived inner and outer bounds of the rate distortion region and derived a matching condition of the above two bounds. In this paper, based on this matching condition, we give a detail analysis on a part of the inner bound where it coincides with the outer bound. We further study an explicit characterization of the sum rate part of the rate distortion region when the observed Gaussian sources have a certain symmetric property.