Spatiospectral localization of isostatic coherence anisotropy in Australia
and its relation to seismic anisotropy:
Implications for lithospheric deformation

Frederik J Simons, Rob D. van der Hilst, and Maria T. Zuber

Department of Earth, Atmospheric and Planetary Sciences
Massachusetts Institute of Technology (MIT)
Cambridge MA 02139, USA

Abstract

We investigate the two-dimensional (2-D) nature of the coherence between Bouguer gravity anomalies and topography on the Australian continent. The coherence function or isostatic response is commonly assumed to be isotropic. However, the fossilized strain field recorded by gravity anomalies and their relation to topography is manifest in a degree of isostatic compensation or coherence which does depend on direction. We have developed a method that enables a robust and unbiased estimation of spatially, directionally, and wavelength-dependent coherence functions between two 2-D fields in a computationally efficient way. Our new multispectrogram method uses orthonormalized Hermite functions as data tapers, which are optimal for spectral localization of nonstationary, spatially dependent processes, and do not require solving an eigenvalue problem. We discuss the properties and advantages of this method with respect to other techniques. We identify regions on the continent marked by preferential directions of isostatic compensation in two wavelength regimes. With few exceptions, the short-wavelength coherence anisotropy is nearly perpendicular to the major trends of the suture zones between stable continental domains, supporting the geological observation that such zones are mechanically weak. Mechanical anisotropy reflects lithospheric strain accumulation, and its presence must be related to the deformational processes affecting the lithosphere integrated over time. Three-dimensional models of seismic anisotropy obtained from surface wave inversions provide an independent estimate of the lithospheric fossil strain field, and simple models have been proposed to relate seismic anisotropy to continental deformation. We compare our measurements of mechanical anisotropy with our own model of the azimuthally anisotropic seismic wave speed structure of the Australian lithosphere. The correlation of isostatic anisotropy with directions of fast wave propagation gleaned from the azimuthal anisotropy of surface waves decays with depth. This may support claims that above 150-200 km, internally coherent deformation of the entire lithosphere is responsible for the anisotropy present in surface wave speeds or split shear waves.

Figures

1. Figure 01 Five prolate spheroidal (Slepian) wavelets in the time and frequency domain
   
2. Figure 02 Hermite functions and their eigenvalue
   
3. Figure 03 Concentration of Slepian wavelets and Hermite functions in the time-frequency plane by their average Wigner-Ville energy distribution
   
4. Figure 04 Comparison of the Hermite multiple-spectrogram method with the Slepian multi-wavelet method
   
5. Figure 05 Coherence estimation with the Hermite method
   
6. Figure 06 Retrieval of spatially varying anisotropic coherence functions between two synthetic fields
   
7. Figure 07 Predicted and observed coherence for a realistic loading scenario
   
8. Figure 08 Topography and bathymetry of Australia and its surrounding areas
   
9. Figure 09 Oceanic and continental Bouguer gravity anomalies
   
10. Figure 10 Coherence anisotropy between Bouguer gravity and topography: long wavelength response
    
11. Figure 11 Coherence anisotropy for the shortest wavelengths
    
12. Figure 12a Major trend directions on the Australian continent
    
13. Figure 12b Measurements of anisotropy in the coherence between Bouguer anomalies and topography
    
14. Figure 13 Vertically coherent deformation of the lithosphere
    
15. Figure 14 The relation between seismic and mechanical anisotropy
    
16. Figure 15 Relationship between mechanically weak directions and fast axes of seismic anisotropy
    
17. Figure 16 Error analysis of coherence-square estimators
    

Frederik Simons