We present a new wavelet transform method to map spatial variations in effective elastic thickness T-e and plate loading ratio f. The method assumes a model of thin plate flexural isostasy to describe the mechanical response of the lithosphere to vertical loading. In this model, the rheological properties of the lithosphere are aggregated into the effective elastic thickness T-e of an equivalent thin plate overlying an inviscid fluid. A number of methods have been developed to map spatial variations in T-e in an attempt to assess regional patterns of flexural strength. Our new method first obtains local coherence and local admittance through wavelet cross-spectral analysis of surface topography and Bouguer gravity anomaly. Wavelet coherence is used to obtain the local characteristic wavelength, which is a function of both T-e and the degree of relative loading f of the plate by subsurface loads and surface loads (loading is the combined effect of erosion, sedimentation, intrusion, faulting, and metamorphism). Wavelet admittance, in a normalized form, is used to resolve this f - T-e ambiguity, and maps are made of the spatial variations in T-e and f. We carry out extensive tests of the wavelet method on simulated topography and Bouguer gravity anomaly data that we generate through finite difference simulations of flexural isostasy with spectrally realistic loads and simple spatial variations in T-e. These tests demonstrate that the wavelet inversion method is reasonably robust to uncertainties in loading and in crustal thickness and is able to recover T-e to within +/-25-50% of its correct value. We apply the wavelet method to southern Africa and recover estimates of T-e principally in the range 25 - 50 km, in good agreement with existing estimates from forward modeling and Fourier coherence analyses. We find that our T-e estimates often exceed estimates of crustal thickness, pointing to a strong upper mantle in parts of southern Africa.
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