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The low-frequency attenuation coefficient anomalies of the pulsed Stoneley wave in the borehole can be used to characterize the properties of the formations, guide lateral drilling, and provide information to large scale hydraulic fracturing. This is one of the techniques to increase deep well exploration efficiency. The amplitude of Stoneley wave reaches to the maximum at the borehole wall. It then attenuates gradually from there externally. The lower the frequency, the slower the attenuation. The wavefront exhibits olive-shaped when it penetrates deep into the formation. Attenuation coefficient anomalies show up when the wavefront encounters interfaces or fractures at certain low frequencies. Those low frequency anomalies can be used to characterize the interfaces and fractures at different radial depths. The attenuation coefficient spectrum described in this paper is different from the Stoneley wave attenuation coefficient calculated directly from amplitude. The attenuation coefficient spectrum carries the information about the radial profile of the formation.