Good Work Deep,
Can you include the equations that you used to calculated these expressions?
The analytical expressions for thermal noise, as calculated by Liu & Thorne and Levin, was plotted as a function of frequency in a log - log plot using Matlab.
The value of the parameters were used from Levin's paper on thermal noise.
phi = 1*10-7 (loss angle)
r0 = 1.56*10-2 (beam radius)
T = 300 K (temperature)
E0 = 7.18*1010 (Young's modulus)
sigma = 0.16 (Poisson ratio)
The value of Sx(100) that given in Levin's paper (8.7*10-40 m2 /Hz) while the Liu-Thorne value is 9.1*10-40 m2 /Hz.
The Liu Thorne expression being
S = 4*kb*T/(pi*f) * (1 - sigma^2) / (2*sqrt(pi)*E*sqrt(2)*r0) * phi
That of Levin goes as
S = 4*kb*T/f * (1 - sigma^2) / (pi^3*E*r0) *I*phi
sigma : Poisson ratio
phi : loss angle
r0 : Beam spot radius
E : Young's modulus
I : This is a sum the value of which is approx. 1.873.22 [Eqn.(A6) of Levin - Internal Thermal Noise]