An assessment of the accuracy of admittance and coherence estimates using synthetic data

Abstract

Previous work has shown that estimates of the admittance between topography and free-air gravity anomalies are often biased by spectral leakage, even after the application of multiple prolate spheroidal wavefunction data-tapers. Despite this, a number of authors who have used the free-air admittance method to estimate the weighted-average effective elastic thickness of the lithosphere (Te) and to identify topography supported by mantle convection have not tested their methods using synthetic data with a known relationship between topography and gravity. In this paper, I perform a range of such tests using both synthetic surface data and synthetic line-of-sight (LOS) accelerations of satellites orbiting around an extra-terrestrial planet. It is found that spectral leakage can cause the estimated admittance and coherence to be significantly in error—but only if the box in which they are estimated is too small. The definition of ‘small’ depends on the redness of the gravity spectrum. There is minimal error in the whole-box weighted-average estimate of Te if the admittance between surface gravity and topography is estimated within a box at least 3000-km-wide. When the synthetic (uniform) Te is less than 20 km and the coherence is high, the errors in Te are mostly ±5 km for all box sizes greater than 1000 km. On the other hand, when the true Te is greater than 20 km and the box size is 1000 km, the best-fitting Te is likely to be at least 5–10 km less than the true Te. However, even when the coherence is high, it is not possible to use elastic plate admittance models to distinguish between real and spurious small fractions of internal loading when the boxes are smaller than 2000 km in width. Noise in the gravity introduces error and uncertainty, but no additional bias, into the estimates of the admittance. It does, however, bias estimates of Te calculated using the coherence between Bouguer gravity and topography. The admittance at wavelengths between 1000 and 4000 km, which is of interest when studying mantle convection, is only well resolved when the box size is larger than 2000 km, or the synthetic Te is less than 15 km and the true long-wavelength admittance is greater than 30 mGal km−1. When the box size is 1000 km, it is not possible to distinguish between real and spurious convective support of long-wavelength topography. At the altitude of most orbiting satellites (200–400 km), gravity is much redder than it is at ground-level; therefore, it is necessary to use much larger boxes when using LOS accelerations to estimate the admittance than it is when using surface measurements. However, gradual changes in the altitude of the satellite, or even occasional sudden changes, make almost no difference to the estimate of the admittance. Finally, three short investigations are undertaken concerning the effect on the admittance of the application of irregular windows to the data, of lateral variations in Te, and of the infilling of flexural moats by low-density sediment. It is found that the bias due to the application of an irregular window is not significantly greater than the bias due to the application of a regular window of similar size; that the best-fitting Te is strongly biased by the value associated with the highest-amplitude topography; and that sediment infill raises the admittance at wavelengths corresponding to the width of the moat.