Improved implementation of the fk and Capon methods for array analysis of seismic noise

Abstract

The frequency–wavenumber (fk) and Capon methods are widely used in seismic array studies of background or ambient noise to infer the backazimuth and slowness of microseismic sources. We present an implementation of these techniques for the analysis of microseisms (0.05–2 Hz) which draws on array signal processing literature from a range of disciplines. The presented techniques avoid frequency mixing in the cross-power spectral density and therefore yield an accurate slowness vector estimation of the incoming seismic waves. Using synthetic data, we show explicitly how the frequency averaged broad-band approach can result in a slowness-shifted spectrum. The presented implementation performs the slowness estimations individually for each frequency bin and sums the resulting slowness spectra over a specific frequency range. This may be termed an incoherently averaged signal, or IAS, approach. We further modify the method through diagonal loading to ensure a robust solution. The synthetic data show good agreement between the analytically derived and inferred error in slowness. Results for real (observed) data are compared between the approximate and IAS methods for two different seismic arrays. The IAS method results in the improved resolution of features, particularly for the Capon spectrum, and enables, for instance, Rg and Lg arrivals from similar backazimuths to be separated in the case of real data.