Joint Multi-Mode Dispersion Extraction in Frequency-Wavenumber and Space-Time Domains

In this paper, we present a novel broadband approach for the extraction of dispersion curves of multiple time frequency overlapped dispersive modes from borehole acoustic data. The new approach works jointly in the frequency-wavenumber and space-time domains and, in contrast to existing methods it efficiently handles multiple signals with significant time frequency overlap. The proposed method begins by exploiting the slowness (phase and group) and time location estimates obtained by a broadband dispersion extraction method based on frequency-wavenumber
$( f-k)$
domain sparsity penalization proposed in [A. Aeron, S. Bose, H.-P. Valero, and V. Saligrama, “Broadband dispersion extraction using simultaneous sparse penalization,” IEEE Trans. Signal Process., vol. 50, no. 10, pp. 4821–4837, 2011]. In this context, we first present a Cramér–Rao Bound (CRB) analysis for slowness estimation and show that for the
$ f-k$
domain broadband processing, group slowness estimates have more variance than the phase slowness and time location estimates. In order to improve the group slowness estimates, we exploit the time compactness property of the modes to effectively represent the data as a linear superposition of time compact space-time propagators parameterized by the phase and group slowness. A linear least squares estimation algorithm in the space-time domain is then used to obtain improved group slowness estimates. The performance of the method is demonstrated on real borehole acoustic data sets.