An accuracy assessment of the fan wavelet coherence method for elastic thickness estimation

Abstract

A variety of methods exist to estimate the elastic thickness (T e ) of the lithosphere. In this contribution, we attempt to provide an indication of how well the fan wavelet coherence method recovers T e , through synthetic modeling. The procedure involves simulating initial topographic and subsurface loads and emplacing them on a thin elastic plate of known T e , generating the postloading topography and gravity. We then attempt to recover that T e distribution from the gravity and topography through the wavelet method, hence discovering where its strengths and weaknesses lie. The T e distributions we use here have elliptical and fractal geometries, while the initial loads are fractal. Importantly, we have found that this widely used synthetic loading calibration method will tend to result in underestimates of T e no matter which recovery method is used. This is due to random correlations between the initial loads which, on average, serve to increase their coherence at all wavelengths and spatial locations. For the fan wavelet method, the degree of underestimation from this “background” source is approximately 10% of the true T e . In addition, the fan wavelet coherence method will provide underestimates of (1) the true T e when the study area size is of the order of the highest flexural wavelength or less, (2) relative T e differences when the T e anomaly is narrow compared to its flexural wavelength, and (3) steep T e gradients. Significantly, we find that the recovery is not greatly affected by the assumption of uniform T e in the inversion of the coherence. We also find that T e recovery from the coherence is only weakly dependent upon the initial subsurface-to-surface loading ratio (f). In contrast to the coherence, T e recovery from the admittance is highly “noisy,” with discontinuities and overestimates of T e frequently arising. This is most likely due to the high sensitivity of the admittance to f and is likely to apply to real data as well.