Ultrasonic attenuation estimation based on time-frequency analysis

The quality factor (or Q value) is an important parameter for characterizing the inelastic properties of rock. Achieving a Q value estimation with high accuracy and stability is still challenging. In this study, a new method for estimating ultrasonic attenuation using a spectral ratio based on an S transform (SR-ST) is presented to improve the stability and accuracy of Q estimation. The variable window of ST is used to solve the time window problem. We add two window factors to the Gaussian window function in the ST. The window factors can adjust the scale of the Gaussian window function to the ultrasonic signal, which reduces the calculation error attributed to the conventional Gaussian window function. Meanwhile, the frequency bandwidth selection rules for the linear regression of the amplitude ratio are given to further improve stability and accuracy. First, the feasibility and influencing factors of the SR-ST method are studied through numerical testing and standard sample experiments. Second, artificial samples with different Q values are used to study the adaptability and stability of the SR-ST method. Finally, a further comparison between the new method and the conventional spectral ratio method (SR) is conducted using rock field samples, again addressing stability and accuracy. The experimental results show that this method will yield an error of approximately 36% using the conventional Gaussian window function. This problem can be solved by adding the time window factors to the Gaussian window function. The frequency bandwidth selection rules and mean slope value of the amplitude ratio used in the SR-ST method can ensure that the maximum error of different Q values estimation (Q > 15) is less than 10%.