Frederik Simons

Power spectral and coherence estimation methods for multidimensional (non-)stationary geophysical fields

 Abstract:

I will describe robust and unbiased methods for the estimation of spatially, directionally and wavelength-dependent coherence functions between multi-dimensional geophsyical fields.

For stationary fields, the Thomson multi-taper method using Slepian windows is particularly successful because of the low variance of the estimate and the optimal concentration of the measurement in a narrow frequency region, i.e., with low side-lobes. For the correct retrieval of the spatial variation of the coherence, the method must be adapted to account for non-stationarity.

The Slepian multi-taper method can be applied in a sliding window fashion. If the concentration operator is rewritten as band-pass, a class of (Slepian) wavelets is obtained. Spectrogram and scalogram methods based on such windows (or wavelets) provide a mapping of the phase space in terms of rectangular boxes concentrated in time or space and frequency or scale. It is preferable, however, to use a joint optimization for concentration in the time-frequency plane,thereby treating time (or space) and frequency without bias. We implement a multi-spectrogram method that uses orthonormal Hermite functions as windows.

We discuss the properties and advantages of multi-spectrogram and multi-wavelet methods, and apply the Hermite multi-spectrogram method to the coherence estimation between gravity anomalies and topography on the Australian continent in order to characterize the spatial variation of the strength and its anisotropy of the outermost 200 km of the continent.