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In acoustic logging, the acoustic attenuation coefficient of the stratigraphy is an important parameter for assessing the fractures and fluid properties of the formation. Therefore, accurately estimating the attenuation coefficient of the formation has become one of the core subjects of geophysical research. The attenuation of Stoneley wave, characterized by large amplitude, low frequency, and less velocity than P- and S-waves in logging signals, is more sensitive to the reflection of cracks. Consequently, we proposed a method—iterative maximum posterior probability with empirical mode decomposition and Choi-Williams distribution (ECIMAP) workflow to estimate the attenuation coefficient of the Stoneley wave from an array of acoustic logging signals. The synthetic Stoneley wave verifies the high accuracy and noise immunity of the IMAP. The Stoneley wave can be adaptively separated by combining EMD and CWD from the actual acoustic logging data, which contains multiple frequency components. By doing this, the problem of parameter selection relying on manual experience in conventional methods can be avoided. The results show that the attenuation coefficient calculated by ECIMAP and LSRM are more sensitive than those computed by the mentioned commercial software. Moreover, the ECIAMP is more stable than the LSRM.