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With an axisymmetric connected fracture model, this paper discovers that the resonance of acoustic waves within the connected fractures yields reflected Stoneley waves of many oscillation cycles. The inherent frequency of the resonant waves changes with the extension length of the fracture and with the depth of mud invasion for gas layer. Stemming from these discoveries, this paper proposes a method for identifying connected fractures and gas layers using the attenuation coefficient of Stoneley waves