Thermoelastic Noise and Homogeneous Thermal Noise in Finite Sized   Gravitational-Wave Test Masses
  An analysis is given of thermoelastic noise (thermal noise due to thermoelastic dissipation) in finite sized test masses of laser interferometer gravitational-wave detectors. Finite-size effects increase the thermoelastic noise by a modest amount; for example, for the sapphire test masses tentatively planned for LIGO-II and plausible beam-spot radii, the increase is less than or of order 10 per cent. As a side issue, errors are pointed out in the currently used formulas for conventional, homogeneous thermal noise (noise associated with dissipation which is homogeneous and described by an imaginary part of the Young's modulus) in finite sized test masses. Correction of these errors increases the homogeneous thermal noise by less than or of order 5 per cent for LIGO-II-type configurations. 
Yuk Tung Liu and Kip S. Thorne (Theoretical Astrophysics, California   Institute of Technology, Pasadena, California)