Estimation of effective elastic thickness and anisotropy

using multitaper spectral analysis

Massachusetts Institute of Technology (MIT)

Cambridge MA 0213 USA

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## The response of gravity to topography provides important insights regarding the degree and mechanisms of isostatic compensation. The azimuthally isotropic coherence function between the Bouguer gravity anomaly and topography evolves from high to low for increasing wave number, a diagnostic that can be predicted for a variety of lithospheric loading models and used in inversions for flexural rigidity thereof. In this study we investigate the isostatic response of continental Australia. We consider the effects of directionally anisotropic plate strength on the coherence. The anisotropic coherence function is calculated for three regions of Australia that have distinctive geological and geophysical properties. The coherence estimation is performed by the Thomson multiple-Slepian-taper spectral analysis method extended to two-dimensional fields. Our analysis reveals the existence of flexural anisotropy in central Australia, indicative of a weaker N-S direction of lower Te. This observation is consistent with the suggestion that the parallel faults in that area act to make the lithosphere weaker in the direction perpendicular to them. It can also be related to the N-S direction of maximum stress and possibly the presence of E-W running zones weakened due to differential sediment burial rates. We also demonstrate that the multitaper method has distinct advantages for computing the isotropic coherence function. The ability to make many independent estimates of the isostatic response that are minimally affected by spectral leakage, particularly at low wavenumbers, results in a more robust estimate of coherence. Our analysis elucidates the reasons for discrepancies in previous estimates of effective elastic thickness, Te, of the Australian lithosphere. In isotropic inversions for Te, we obtain values that are as much as a factor of two less than those obtained in standard inversions using Bouguer gravity and topography, but greater than those obtained by inversions that utilize free-air rather than Bouguer gravity and ignore the presence of subsurface loads. However, owing to the low spectral power of the Australian topography, the uncertainty on any estimate of Te is substantial.

- Figure 01
The necessity of averaging in the coherence calculation.

- Figure 02
One-dimensional Slepian tapers for spectral analysis.

- Figure 03
Two-dimensional Slepian tapers for spectral analysis: spatial domain.

- Figure 04
Two-dimensional Slepian tapers for spectral analysis: spectral domain.

- Figure 05
Synthetic coherence data set: 1-D isotropic case.

- Figure 06
Synthetic coherence data set: 2-D (an)isotropic case.

- Figure 07
Tectonic map of Australia

- Figure 08
Australian gravity and topography data set.

- Figure 09
Coherence calculation for three domains in Australia; one and two dimensions.

- Figure 10
Comparison of free-air anomaly with gravity from uncompensated topography.

- Figure 11
Influence of wavenumber resolution on Central Australia coherence.

- Figure 12
Error in Te determination for the three domains in Australia.

- Figure 13
Coherence calculation for three domains in Australia. Comparison of periodogram and multitaper methods.

Frederik Simons Last modified: Wed Apr 12 23:06:25 EDT 2023