A theoretical approach to thermal noise caused by an inhomogeneously   distributed loss -- Physical insight by the advanced modal expansion
  We modified the modal expansion, which is the traditional method used to calculate thermal noise. This advanced modal expansion provides physical insight about the discrepancy between the actual thermal noise caused by inhomogeneously distributed loss and the traditional modal expansion. This discrepancy comes from correlations between the thermal fluctuations of the resonant modes. The thermal noise spectra estimated by the advanced modal expansion are consistent with the results of measurements of thermal fluctuations caused by inhomogeneous losses. 
Kazuhiro Yamamoto, Masaki Ando, Keita Kawabe, Kimio Tsubono