Wavelet transform mapping of effective elastic thickness and plate loading: Validation using synthetic data and application to the study of southern African tectonics

Abstract

[1] 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 À 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. Citation: Stark, C. P., J. Stewart, and C. J. Ebinger, Wavelet transform mapping of effective elastic thickness and plate loading: Validation using synthetic data and application to the study of southern African tectonics,

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

“…[36] The preprocessing technique of mirroring the gravity/topography data before performing a Fourier transform has been performed in many studies [e.g., Zuber et al, 1989;Lowry and Smith, 1994;Macario et al, 1995;Hartley et al, 1996;McKenzie and Fairhead, 1997;Poudjom Djomani et al, 1999;Ojeda and Whitman, 2002;Stephen et al, 2003;Stark et al, 2003]. Authors using mirroring with Fourier-based coherence methods, such as periodogram, maximum entropy and multitaper methods, have reported that the recovered T e is usually overestimated when mirroring is performed [e.g., Lowry and Smith, 1994;Ojeda and Whitman, 2002;Stephen et al, 2003].…”

“…The initial load at the Moho causes a deflection of amplitude h B at the surface, resulting in a new Moho topography of w B . Here we use the sign convention used by Forsyth [1985], though not by Stark et al [2003], that all deflections away from the center of the Earth are positive, whether they occur at the surface or at the Moho. Therefore, the final surface topography after flexure is:…”

“…[18] Both the uniform f wavelet method and the wavelet-Forsyth method assume the independence of adjacent spectra: the ''decoupling assumption'' [Stark et al, 2003;Kirby and Swain, 2004;Swain and Kirby, 2006]. This enables the inversion of the observed wavelet coherence at each grid node independently of the coherence at neighboring nodes.…”

“…[7] Then, rather than performing two separate analyses and inversions on land and ocean areas, as did Pérez-Gussinyé et al [2004], we scale oceanic bathymetry to an equivalent topography before wavelet transformation, as was done by Stark et al [2003], and compute T e for the whole area (in one run) using only the land-loading equations. We did this because we found that using actual bathymetry and mixed-loading inversion equations gave T e discontinuities at the coastlines.…”

“…This feature lends itself to flexural analyses, where the flexural rigidity of the lithosphere can vary spatially. Stark et al [2003] based their analysis upon the derivative of Gaussian (DOG) wavelet family, while Kirby and Swain [2004] used rotated Morlet wavelets in a socalled ''fan'' geometry. Applications of these methods were made to southern Africa by Stark et al [2003], and to the Irish Atlantic margin by Daly et al [2004] using the DOG wavelets; and by Swain and Kirby [2006] to Australia, and Tassara et al [2007] to South America using the fan wavelet.…”