Wavelet analysis of the coherence between Bouguer gravity and topography: application to the elastic thickness anisotropy in the Canadian Shield

Abstract

SUMMARY We use a wavelet transform to compute the local and azimuthal variations of the coherence between Bouguer gravity and topography in eastern Canada. The isotropic coherence is calculated by averaging the wavelet spectra from optimally overlapping 2-D Morlet wavelets having an isotropic spectral envelope in adjacent directions within 180°, defining the so-called ‘fan’ wavelet. The isotropic wavelet coherence spectrum is inverted to obtain local estimates of the elastic thickness (Te) of the lithosphere. We calculate the anisotropic coherence by restricting the fan wavelet over an azimuthal range of 90°. The direction of maximum coherence is diagnostic of the direction of preferred isostatic compensation, or the direction where the lithosphere is weakest. The coherence is inverted using the theoretical response of a thin anisotropic plate model. We have carried out extensive tests on synthetic topography and Bouguer gravity data sets to verify that: (1) the wavelet method can recover Te for simple models with either homogeneous or spatially variable rigidity patterns; and that: (2) the method can determine azimuthal variations in the 2-D coherence for homogeneous models with anisotropic Te. We have used data from the eastern Canadian Shield to infer the variations in Te and the anisotropy of the coherence. The relative variations in Te show trends similar to those obtained in previous studies that used different spectral methods. The wavelet transform gives Te values between 30 and 120 km. Te is generally high (>80 km) throughout eastern Canada. Lower values (30–60 km) are found in the eastern Grenville Province, in the northern Appalachians, and in the Superior Province in the Great Lakes region. The high values found in Hudson Bay are consistent with previous studies of elastic thickness and models of basin subsidence. The direction of maximum coherence obtained from the wavelet method is also consistent with our previous results obtained with the multitaper method and shows that the weak mechanical axis is perpendicular to the fast seismic axis where seismic anisotropy has been detected.