We model the lithosphere as a uniform elastic plate overlying an inviscid fluid and loaded with both surface and subsurface fractal loads to generate synthetic topography and gravity data. To simulate data having low (topographic) signal to (gravity) noise ratio we use an algebraically larger exponent for the subsurface load in the spectral synthesis fractal algorithm.The gravity power spectrum then decays less rapidly than that of topography, the spectra resembling those for central Australia. We find that the coherence method using multitaper spectral estimation yields significant underestimates of plate thickness for both low and normal signal-to-noise ratio data, unless the data window is larger than several times the true flexural wavelength. We quantify this bias for the parameters used here and apply it as a correction to an effective elastic thickness estimate for central Australia, obtaining a value of 115 ¿ 25 km.