Prestack AVO inversion for brittleness index of shale based on BI_Zoeppritz equation and NSGA II

As one of the evaluation characteristics of shale sweet spots, the brittleness index (BI) of shale formations is of great significance in predicting the range of sweet spots, and guiding hydraulic fracturing. Based on the three elastic parameters of P-wave velocity (V-P), S-wave velocity (V-S) and density obtained by conventional prestack AVO inversion, BI can be calculated indirectly using the Rickman formula. However, the conventional AVO inversion based on Zoeppritz approximation assumes that incident angle is small and elastic parameters change slowly, which affects the inversion accuracy of the three elastic parameters. Additionally, using these three elastic parameters to obtain BI indirectly also leads to cumulative errors of the inversion results. Therefore, we propose an inversion method based on BI_Zoeppritz equation to directly estimateV(P),V(S)and BI. The BI_Zoeppritz equation is an exact Zoeppritz equation for BI, which is used as the forward operator for the proposed method. The multi-objective function of the inversion method is optimized by a fast nondominated sorting genetic algorithm (NSGA II). An initial model and an optimized search window are used to improve the inversion accuracy. The test results of model data and actual data reveal that this method can directly obtain the BI with high precision. In addition, the stability and noise immunity of the proposed method are verified by the seismic data with random noise.