Global and local isostatic coherence from the wavelet transform

Abstract

A method to compute the variations in lithospheric elastic thickness (Te) has been developed, using the wavelet transform. The technique, which uses a superposition of two-dimensional Morlet wavelets in a geometry named a 'fan' wavelet, is designed to yield isotropic yet complex wavelet coefficients for the co- and cross-spectra of gravity and topography data. These are then used to compute a spatially-varying, isostatic coherence, from which both global and local estimates may be obtained. We appliedthe method to synthetic gravity and topography generated for a thin elastic plate of uniform thickness 20 km, yielding an apparent, spatially variable Te of 24.5 3.5 km. The estimated global coherence for this model appears to fit the theoretical prediction as well as Fourier transform-based estimates, and is smoother than these. We also computed the wavelet coherence, and hence spatially-varying Te, for a plate of non-uniform thickness, yielding a difference with the model of -2.0 1.7 km.