Joint multi-mode dispersion extraction in Fourier and space time domains

摘要

In this paper we present a novel broadband approach for the extraction ofdispersion curves of multiple time frequency overlapped dispersive modes suchas in borehole acoustic data. The new approach works jointly in the Fourier andspace time domains and, in contrast to existing space time approaches thatmainly work for time frequency separated signals, efficiently handles multiplesignals with significant time frequency overlap. The proposed method begins byexploiting the slowness (phase and group) and time location estimates based onfrequency-wavenumber (f-k) domain sparsity penalized broadband dispersionextraction method as presented in \cite{AeronTSP2011}. In this context we firstpresent 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 slownessestimates have more variance than the phase slowness estimates and timelocation estimates. In order to improve the group slowness estimates we exploitthe time compactness property of the modes to effectively represent the data asa linear superposition of time compact space time propagators parameterized bythe phase and group slowness. A linear least squares estimation algorithm inthe space time domain is then used to obtain improved group slowness estimates.The performance of the method is demonstrated on real borehole acoustic datasets.