Prestack seismic inversion based on adaptive mixed-norm constraints

Prior information plays a critical role in seismic inversion, which is used to reduce the ill-posed problem. Most of the inversion methods assume that the noise obeys Gaussian distribution. However, due to the diversity of noise in seismic data, it can hardly meet the prior hypothesis. In this paper, a seismic prestack inversion method based on adaptive mixed-norm constraint is proposed to cope with the different noise distribution, and improve the noise suppressing ability of inversion algorithm in prestack seismic data. First, the noise analysis of actual shale gas is realized through the forward modeling of well logging data. Second, the constraints of the L-2 norm and the L-4 norm are added to the target function. The new algorithm combines the ability of L-2 norm on super-Gaussian and Gaussian noise, and L-4 norm on sub-Gaussian noise. It adaptively regulates the weights between L-2 norm and L(4 )norm through Kurtosis. This method improves the adaptive ability of the algorithm to sub-Gaussian, Gaussian, and super-Gaussian noise. By identifying the types of noise, the adaptive mix-norm inversion method is used to test the model, and the prestack simultaneous inversion is carried out in the actual shale gas data. The results show that the proposed method can obtain better inversion results compared to conventional methods.