Flexural Isostasy
Specific interests ...
Elastic Thickness from the Wavelet Transform
The "fan" wavelet (Kirby, 2005), or at least its geometry, can be used in place of the Fourier transform
to estimate the coherence and admittance between gravity and topography (Kirby & Swain, 2004). It also lends itself to a
wavelet adaptation of Forsyth's method by which to compute the predicted coherence and admittance.
These are then compared via least squares to give the elastic thickness (Te) and the initial
subsurface-to-surface laoding ratio (f) at each grid node of the study area.
We have applied this method to the Australian (Swain & Kirby, 2006) and South American
(Tassara et al., 2007) continents, and to North America, Europe, and Africa (unpublished).
The results show that most cratonic regions are characterised by 'core' of high Te.
Mechanical Anisotropy
The fan wavelet can also be rotationally-restricted so that it reveals directional variations in elastic
thickness (or rather, in the flexural rigidity): that is, a mechanical anisotropy.
In order to interpret the resulting weak directions and % anisotropy, we developed an orthotropic elastic plate model
(Swain & Kirby, 2003b). When used together with the Forsyth-wavelet approach, the inversion yields the anisotropic
parameters at each location of the area (Kirby & Swain, 2006).
Results for Precambrian Australia show a strong correlation with seismic anisotropy data (Kirby & Swain, 2006).
The weak axes are approximately at right angles to the fast axes of the seismic anisotropy, suggesting that
they arise from the same source.
Synthetic Modelling
Two initial loads (surface and subsurface) are constructed from fractally-distributed surfaces generated from a random seed. These then flex a thin elastic
plate which has a known variable Te distribution (or Tx, Ty and weak direction for orthotropic plates). The resulting surface topography
and Bouguer anomaly after flexure are obtained by a finite difference solution of the partial differential equation for the flexure of such a plate.
The topography and Bouguer anomaly can then be used in Te-recovery software (or the anisotropic equivalent) to test the accuracy of the chosen
method when reproducing the input Te distribution.
Beware though, many Te-recovery methods assume that surface and subsurface loads are uncorrelated, whereas by the very nature of the fractal-load
generation method, random correlations within the space and wavenumber domains do exist.
Complex Admittance & Coherence
As mentioned above, most spectral Te estimation methods assume that the initial loads on the plate are uncorrelated. This assumption renders
the admittance a real-valued variable. However, if this assumption is not made, then the admittance and correlation coefficient become complex-valued,
with their real components differing from the 'uncorrelated-load' admittance by an amount depending upon the phase relationship between the initial
loads.
The isowave software suite, for computation of isotropic and anisotropic elastic thickness
variations, via the wavelet transform, is available upon
request.
CRICOS provider code 00301J