Time-frequency characteristics of P and S waves in fractured igneous formation based on joint EMD and fractional Fourier transform

Key words:  fractured igneous formation  P wave  S wave  time-frequency characteristics  EMD and fractional Fourier transform  Choi-Williams distribution

Abstract:

In order to study the time-frequency characteristics of the primary wave (P wave) and shear wave (S wave) in fractured igneous formation, array acoustic logging signals are filtered by combining EMD and fractional Fourier transform. First, the high-frequency IMFs are extracted from the array acoustic signal by the EMD, and then the P and S waves are separated by using the rotation of fractional Fourier transform. Finally, the Choi-Williams distributions of P and S waves corresponding to different angle fractures are obtained. The results show that the joint EMD and fractional Fourier transform can improve the time-frequency coupling of P and S waves. The energy, dominant frequency and velocity of P and S waves in fractured igneous formation are lower than those in tight formations. Generally, the higher the dip angle of fracture, the greater the attenuation of P wave energy and the smaller the attenuation of S wave energy. The dominant frequency of P and S waves has little difference between low angle fracture and high angle fracture. The velocity attenuation of P and S waves is stronger after passing through the low angle fracture.