Cramér–Rao Bounds for Broadband Dispersion Extraction of Borehole Acoustic Modes

The estimation of slowness (the reciprocal of velocity) and attenuation dispersion of borehole acoustic and surface seismic data is key to a variety of applications. The emerging broadband approach for dispersion extraction of multiple modes has shown significant advantages over traditional narrowband approaches. In this letter, Cramér-Rao bounds (CRBs) are established to characterize the best achievable performance of any unbiased broadband estimator of the dispersion. One noteworthy observation from the derived CRBs is that the same estimation accuracy can be achieved between the angular wavenumber and the attenuation and, between the group slowness and the attenuation rate. The broadband CRB is also shown to include the narrowband CRB as a special case and it quantifies the performance benefit of the broadband approach.