Comparison and research of multidimensional analysis for array acoustic logging in fractured formations

Currently, array acoustic logging data processing is mainly achieved by calculating only the velocity variation of each component wave. This provides a little formation information; thus, it is difficult to identify all fractures. We have analyzed the array acoustic logging signals by combining their times, frequencies, or amplitudes. First, we decomposed the array acoustic logging signals into main and secondary signals by improving the singular value decomposition. We then analyzed the characteristics of the array acoustic logging signals in fractured formations and compared them using three multidimensional analysis methods: the 2D Fourier transform, the 2D wavelet transform, and the Choi-Williams distribution. The results showed that the frequency characteristics of the compressional waves (P-waves), shear waves (S-waves), and Stoneley waves in the [Formula: see text]-[Formula: see text] domain of the fracture formations can be obtained by the 2D Fourier transform method. The multiresolution time characteristics of these waves can be realized by the 2D wavelet transform method, and their time-frequency characteristics can be observed via the Choi-Williams distribution. The times, frequencies, and amplitudes of the P-waves, S-waves, and Stoneley waves change from the tight formation to the fractured formation. The three methods introduced here can comprehensively use eight arrays, time, frequency, or amplitude to improve the information usage rate of array acoustic logging and provide new ways to interpret it.