Leaky modes and the first arrivals in cased boreholes with poorly bonded conditions

The generation mechanism of the first arrivals in the cased boreholes for the poorly bonded conditions is investigated. Based on the analyses of the Riemann surface structure of the characteristic function, the dispersion features, excitation spectra and contributions of modes excited in the cased boreholes with different cementing types are studied. The phase velocity dispersion studies of leaky modes show that high-order modes form “plateau” regions with one approximate velocity denoted by v separated by their cutoff frequencies, in which the phase velocity changes little with a considerable frequency range, while the group velocity keeps a relatively constant high value. Usually, the operation frequency range of a specific cementing evaluation acoustic logging tool is covered by such a “plateau” region. Mode excitation and contribution analyses show that the first arrivals in the cased boreholes for the poorly bonded conditions are the contributions from leaky modes, where the traveling velocity of the first arrivals processed by slowness time coherence (STC) method is equal to the approximated velocity v. Analyses on generation of leaky modes in the cased boreholes supplement the understanding of the generation mechanism of the first arrivals.