Wang, C., Yin, C., Shi, X.W., Pan, S.L., Guo, Q.Y., Zhang, D.J., Zeng, C.W. and Fang, C.Y., 2022. Direct prediction method of fracturing ability in shale formations based on pre-stack seismic inversion. Journal of Seismic Exploration, 31: 407- 424. The prediction of brittleness is an important research field for shale gas exploration and development. Currently, the most common way to evaluate the brittleness is calculating the average of the sum of normalized Young’s modulus and Poisson’s ratio. But this method needs pre-stack seismic inversion, petrophysics model calculation and normalization which is not an efficient way to obtain brittleness index directly and may introduce iterative error in the process. This paper derives a novel elastic impedance (EI) approximation which establishes a direct relationship with brittleness index. After that, we discussed the accuracy of EJ approximation in Goodway’s model, the results show the approximation is very close to Zoeppritz matrix when the incident angle is less than 30 degrees. Then we establish a method under Bayesian framework for improving the accuracy of brittleness index prediction. We find the predicted brittleness index fits very well with the real model data even SNR = 3. Finally, we apply our theory to shale gas block in southern Sichuan Basin, it shows that the predicted brittleness index not only fits well with well-logging, but also indicates the highest brittleness layer which is consistent with the rock core experiment results.