Nonlinear elastic impedance inversion in the complex frequency domain based on an exact reflection coefficient

Abstract

The low-frequency information is extremely crucial to the stability, reliability, and enhanced resolution of the elastic impedance (EI) inversion. Bandwidth of seismic data has been extended during the development of seismic acquisition technology (especially for the acquisition of low-frequency components). In new exploration areas without sufficient prior geological information and drilling, low-frequency initial models are difficult to be established. In order to overcome the model dependence problem in conventional EI inversion, the Bayesian framework, in the complex frequency domain, is utilized to estimate the low-frequency information. The inverted parameters (EI) and likelihood function are considered to obey the Cauchy and Gaussian probability distribution, respectively. Linear EI equations has two disadvantages: low accuracy of reflection coefficient and poor applicability when the elastic parameters of the upper and lower media vary dramatically (high contrast situations), so we derived a novel nonlinear EI equation in terms of compressional wave (P-wave) impedances, shear wave (S-wave) impedances, and density. Its accuracy is basically consistent with the exact Zoeppritz equation. The P-and S-wave impedances and density can be extracted from the direct inversion algorithm Artificial Neural Network Inversion Tool (ANNIT) and EI data, and the sensitivity analysis of the novel EI equation indicates that the inversion results of impedances will be better than density. The feasibility of this method is verified by the model tests and field data examples.