Wavelet transform mapping of effective elastic thickness and plate loading

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 sub-surface loads and surface loads (loading is the combined effect of erosion, sedimentation, intrusion, faulting and metamorphism). Wavelet admittance is converted into local pseudo-coherence and is used to resolve this f-T_e ambiguity. 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 the correct values and patterns of T_e to within +/-5 km. 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. The relationship of the apparent variations in T_e and plate loading to regional tectonics are discussed.