Christopher Swain

The effect of ‘noise’ on estimates of the elastic thickness of the continental lithosphere by the coherence method

[1] We model the lithosphere as a uniform elastic plate overlying an inviscid fluid and loaded with both surface and subsurface fractal loads to generate synthetic topography and gravity data. To simulate data having low (topographic) signal to (gravity) noise ratio we use an algebraically larger exponent for the subsurface load in the spectral synthesis fractal algorithm.The gravity power spectrum then decays less rapidly than that of topography, the spectra resembling those for central Australia. We find that the coherence method using multitaper spectral estimation yields significant underestimates of plate thickness for both low and normal signal-to-noise ratio data, unless the data window is larger than several times the true flexural wavelength. We quantify this bias for the parameters used here and apply it as a correction to an effective elastic thickness estimate for central Australia, obtaining a value of 115 ± 25 km. INDEX TERMS: 8110 Tectonophysics: Continental tectonics—general (0905); 8159 Tectonophysics: Rheology—crust and lithosphere; 1236 Geodesy and Gravity: Rheology of the lithosphere and mantle (8160). Citation: Swain, C. J., and J. F. Kirby, The effect of ‘noise’ on estimates of the elastic thickness of the continental lithosphere by the coherence method, Geophys. Res. Lett., 30(11), 1574, doi:10.1029/2003GL017070, 2003.

Improving the spatial resolution of effective elastic thickness estimation with the fan wavelet transform

Abstract We show here a simple technique to improve the spatial resolution of the fan wavelet method for effective elastic thickness ( T e ) estimation that we have previously developed. The technique involves reducing the number of significant oscillations within the Gaussian window of the Morlet wavelet from approximately five to three or fewer (while making an additional correction for its no-longer-zero mean value). Testing with synthetic models and data over South America indicates that the accompanying reduction in wavenumber resolution does not seriously affect the accuracy of the T e estimates. Comparison against the more widely-used multitaper Fourier transform approach shows that the enhanced wavelet method not only improves upon the multitaper methods spatial resolution, but also is computationally much faster and requires the arbitrary variation of only one parameter compared to three for the multitaper method. Finally, we present a modified method to compute the predicted coherence using the multitaper method that, while not improving its spatial resolution, does improve the bias of recovered T e estimates.

The long-wavelength admittance and effective elastic thickness of the Canadian Shield

The strength of the cratonic lithosphere has been controversial. On the one hand, many estimates of effective elastic thickness (Te) greatly exceed the crustal thickness, but on the other the great majority of cratonic earthquakes occur in the upper crust. This implies that the seismogenic thickness of cratons is much smaller than Te, whereas in the ocean basins they are approximately the same, leading to suspicions about the large Te estimates. One region where such estimates have been questioned is the Canadian Shield, where glacial isostatic adjustment (GIA) and mantle convection are thought to contribute to the long-wavelength undulations of the topography and gravity. To date these have not been included in models used to estimate Te from topography and gravity which conventionally are based only on loading and flexure. Here we devise a theoretical expression for the free-air (gravity/topography) admittance that includes the effects of GIA and convection as well as flexure and use it to estimate Te over the Canadian Shield. We use wavelet transforms for estimating the observed admittances, after showing that multitaper estimates, which have hitherto been popular for Te studies, have poor resolution at the long wavelengths where GIA and convection predominate, compared to wavelets. Our results suggest that Te over most of the shield exceeds 80 km, with a higher-Te core near the southwest shore of Hudson Bay. This means that the lack of mantle earthquakes in this craton is simply due to its high strength compared to the applied stresses.

Correction to “An accuracy assessment of the fan wavelet coherence method for elastic thickness estimation”

Kirby, J. F., and C. J. Swain (2008), An accuracy assessment of the fan wavelet coherence method for elastic thickness estimation, Geochem. Geophys. Geosyst., 9, Q03022, doi:10.1029/ 2007GC001773. Simons, F. J. (2002), Structure and evolution of the Australian continent: Insights from seismic and mechanical heterogeneity and anisotropy, Ph.D. thesis, 261 pp., Mass. Inst. of Technol., Boston, Mass. Simons, F. J., and R. D. van der Hilst (2003), Seismic and mechanical anisotropy and the past and present deformation of the Australian lithosphere, Earth Planet. Sci. Lett., 211, 271–286. G Geochemistry Geophysics Geosystems