Effects of loads in the upper crust on estimates of the elastic thickness of the lithosphere

Abstract

Summary The admittance function and coherence relating gravity and topography are important constraints on the elastic thickness (Te) of the lithosphere. Forsyth (1985) modelled them with a lithosphere loaded both externally by topography and internally by density contrasts such as initial undulations on the Moho. His approach has yielded thicknesses as high as 150 km for the continental lithosphere. McKenzie & Fairhead (1997) argued that this method can only supply an upper bound on Te because the response is biased by ‘noise’ due to density variations in the upper crust. We have used Forsyth's approach to analyse the effect of shallow heterogeneities such as sedimentary basins and igneous intrusions, simulating them by a thin layer with a laterally variable density. The information content of the admittance and coherence is concentrated in the wavenumbers at which the two responses roll‐off to half their zero‐wavenumber values. These two parameters are used to explore the interdependence of the retrieved elastic thickness and internal/external loading ratio f. Provided the internal load is less than 10 per cent of the external, it does indeed bias the response so that Te is overestimated. However, for predominantly internal loads, the reverse is the case, and the value of Te obtained by assuming equal internal and external loads is actually a lower bound. It is particularly important to allow for the flexure due to upper‐crustal loads when the lithosphere is old and topography subdued due to prolonged erosion. Application of our approach to McKenzie & Fairhead's (1997) Western Australia data shows that the loading ratio depends strongly on wavenumber, but that it is still possible to use the response data to constrain Te, which must be at least 90 km if the results obtained by conventional spectral estimation are accepted, at least 40 km using the multitaper method.

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

“…As for the Forsyth approach with a variable z m (x), the wavelet-adapted equations for the Banks method can account for a variable z l (x) if this information is known. Generally speaking, the inclusion of a thin layer between the surface and Moho serves to reduce T e estimates, though not significantly, with 1999] and Flück et al [2003] finding their results to be fairly insensitive to the magnitude of the density contrasts or depth of the interface, albeit using different approaches to that of Banks et al [2001].…”

“…In support of this argument, performing the coherence inversion using a wavelet adaptation of the Banks et al [2001] deconvolution method gives a relatively constant f (at least for shallow internal loads), because the (implied) downward continuation is to a shallower depth (see equation (C13)). …”

“…[99] In the Banks et al [2001] formulation of the thin plate model, the internal loading occurs at a thin layer at depth z l (<z m ) within the crust. Importantly, the actual magnitude of the thin layer's density does not need to be known.…”

“…[92] To invert the observed wavelet coherence (or admittance), at each grid node, in order to obtain estimates of effective elastic thickness, T e , and subsurface-to-surface loading ratio, f, we use wavelet transform adaptations of the thin elastic plate models of Forsyth [1985] and Banks et al [2001]. Owing to the relationship between Morlet wavelet spectra and Fourier spectra, equation (B6), the wavelet versions of their equations are identical to the Fourier equations, but with Fourier transforms replaced by Morlet wavelet transforms, and wave number replaced by equivalent Fourier wave number, equation (B3).…”

“…However, in the work by Swain and Kirby [2006] we extended the method of Forsyth [1985] to compute a predicted wavelet coherence, which provides both T e and f estimates directly from the observed gravity and topography data: the ''wavelet-Forsyth method.'' For completeness, in Appendix C2 we give the wavelet versions of the Banks et al [2001] equations, because we used this method in the work by Tassara et al [2007]. Finally, we also present a new algebraic method to estimate the coherence transition wavelength (Appendix D).…”