On the robustness of spectral methods that measure anisotropy in the effective elastic thickness
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Recent studies have inferred patterns of rheological weakness in the lithosphere from analyses of the coherence between gravity and topography data, and related these to tectonic evolution and lithospheric rheology. The methods employed all attempt to estimate the direction of weakest flexural rigidity and the magnitude of the mechanical anisotropy, and their spatial variations whether using the wavelet transform or moving-window multitaper Fourier transform. Here we apply the wavelet transform method to synthetic gravity and topography data derived from plates where the flexural rigidity is known a priori. When analysing plates that replicate the actual topography of North America and Australia, we find that, even when the synthetic plate is isotropic, spurious anisotropy is recovered in which the weak rigidity direction is aligned perpendicular to the strike of major topographic features and continental margins. It appears that strong anisotropy in the gravity and/or topography data is causing the spurious anisotropy in the observed coherence, and that very little artificial anisotropy arises during its inversion. We compare our model weak directions with those from real gravity and topography data over North America and Australia. From synthetic modelling, we also find spurious correlation of the weak rigidity direction with strong gradients in the flexural rigidity. These results suggest that many results of anisotropic spectral analyses of real data should, at best, be treated with caution, and at worst be discarded altogether.
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