  In this paper we present a novel broadband approach for the extraction of
dispersion curves of multiple time frequency overlapped dispersive modes such
as in borehole acoustic data. The new approach works jointly in the Fourier and
space time domains and, in contrast to existing space time approaches that
mainly work for time frequency separated signals, efficiently handles multiple
signals with significant time frequency overlap. The proposed method begins by
exploiting the slowness (phase and group) and time location estimates based on
frequency-wavenumber (f-k) domain sparsity penalized broadband dispersion
extraction method as presented in \cite{AeronTSP2011}. In this context we first
present a Cramer Rao Bound (CRB) analysis for slowness estimation in the (f-k)
domain and show that for the f-k domain broadband processing, group slowness
estimates have more variance than the phase slowness estimates 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.
