Extracting array acoustic logging signal information by combining fractional Fourier transform and Choi–Williams distribution

• We obtain the desired Choi–Williams distribution by changing the order.
• In a stratum with no obvious tectonics, every component wave showes no clear attenuation.
• In the stratum with a fracture, the Stoneley wave will significantly, even completely, attenuate.
• The longitudinal wave is sensitive to high angle fracture and the shear wave is sensitive to low angle fracture.
• Lithology will influence time of signal components.

Array acoustic logging signals are non-linear. When these signals are processed with traditional methods, such as time-domain methods and frequency-domain methods, they have some drawbacks. In order to improve the situation, this study combines the fractional Fourier transform and Choi–Williams distribution in the signal processing. By this method, the regularities of the distribution of every component wave can be obtained. In the strata with no obvious tectonics, the energy of every component wave showed no significant attenuation. In the strata with fractures, the energy of the Stoneley wave will significantly attenuate and its attenuation will increase with the increasing fracture degree. If the fracture is vertical or high angle to the horizontal, the energy of the longitudinal wave will attenuate some and the energy of the shear wave will change little. If the fracture is parallel or low angle to the horizontal, the energy of the longitudinal wave will attenuate a little and the energy of the shear wave will attenuate obviously. Besides, by comparing the time of components that do not attenuate completely, different lithology can be distinguished.

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