and its relation to seismic anisotropy:

Implications for lithospheric deformation

Massachusetts Institute of Technology (MIT)

Cambridge MA 02139, USA

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## 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.

- Figure 01
Five prolate spheroidal
(Slepian) wavelets in the time and frequency domain

- Figure 02
Hermite functions and their eigenvalue

- Figure 03
Concentration of Slepian
wavelets and Hermite functions in the time-frequency plane by their
average Wigner-Ville energy distribution

- Figure 04
Comparison of the Hermite
multiple-spectrogram method with the Slepian multi-wavelet
method

- Figure 05
Coherence estimation with the Hermite method

- Figure 06
Retrieval of spatially varying
anisotropic coherence functions between two synthetic fields

- Figure 07
Predicted and observed coherence
for a realistic loading scenario

- Figure 08
Topography and bathymetry of
Australia and its surrounding areas

- Figure 09
Oceanic and continental Bouguer gravity anomalies

- Figure 10
Coherence anisotropy
between Bouguer gravity and topography: long wavelength response

- Figure 11
Coherence anisotropy for the
shortest wavelengths

- Figure 12a
Major trend directions on
the Australian continent

- Figure 12b
Measurements
of anisotropy in the coherence between Bouguer anomalies and
topography

- Figure 13
Vertically coherent deformation of the
lithosphere

- Figure 14
The relation between seismic and mechanical
anisotropy

- Figure 15
Relationship between
mechanically weak directions and fast axes of seismic
anisotropy

- Figure 16
Error analysis of
coherence-square estimators

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