AVO impedance three-parameters non-linear inversion method based on gradient calculation of adjoint state equation

Seismic pre-stack inversion is the key method to obtain the elastic parameters of underground media. The conventional non-linear AVO inversion methods often utilize gradient descent-based optimization algorithms, which require the computation of gradient equation for the objective function, resulting in relatively low accuracy and efficiency. To solve this problem, a three-parameters inversion method of P-wave impedance, S-wave impedance and density based on the gradient calculation of adjoint state equation is proposed in this paper. In this method, the adjoint state equation of the objective function gradient is derived based on the AVO inversion formula. Furthermore, a quasi-Newton optimization algorithm with Limited memory-BFGS (L-BFGS) is introduced to solve the inverse objective function. The 1-D, 2-D model and actual logging data is used to test the method, and the results show that this method can obtain accurate P-wave, S-wave impedance, density and P-Swave velocity ratio. Additionally, noise resistance testing demonstrated that the method can tolerate a signal-to-noise ratio (SNR) above approximately 8 ~ 15 dB. Finally, the method is applied to the actual seismic data of tight sandstone reservoir, and the results exhibited a high consistency with well logging data and effectively captured the lateral distribution patterns of the strata, thereby validating the effectiveness of the method.