Isostatic response of the Australian lithosphere:
Estimation of effective elastic thickness and anisotropy
using multitaper spectral analysis

Frederik J Simons, Maria T. Zuber and Jun Korenaga

Department of Earth, Atmospheric and Planetary Sciences
Massachusetts Institute of Technology (MIT)
Cambridge MA 0213 USA

Abstract

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.

Figures

1. Figure 01 The necessity of averaging in the coherence calculation.
   
2. Figure 02 One-dimensional Slepian tapers for spectral analysis.
   
3. Figure 03 Two-dimensional Slepian tapers for spectral analysis: spatial domain.
   
4. Figure 04 Two-dimensional Slepian tapers for spectral analysis: spectral domain.
   
5. Figure 05 Synthetic coherence data set: 1-D isotropic case.
   
6. Figure 06 Synthetic coherence data set: 2-D (an)isotropic case.
   
7. Figure 07 Tectonic map of Australia
   
8. Figure 08 Australian gravity and topography data set.
   
9. Figure 09 Coherence calculation for three domains in Australia; one and two dimensions.
   
10. Figure 10 Comparison of free-air anomaly with gravity from uncompensated topography.
    
11. Figure 11 Influence of wavenumber resolution on Central Australia coherence.
    
12. Figure 12 Error in Te determination for the three domains in Australia.
    
13. Figure 13 Coherence calculation for three domains in Australia. Comparison of periodogram and multitaper methods.