Estimation of fracture parameters and in-situ stress parameter based on extended azimuthal elastic impedance

Accurate estimation of fracture parameters and Differential Horizontal Stress Ratio (DHSR) is of great significance for subsurface fracture prediction and hydraulic fracturing. Extended Elastic Impedance (EEI) is an effective tool for the estimation of elastic parameters and physical parameters in isotropic media. However, EEI in isotropic media does not consider the influence of anisotropy. Here, we extend the EEI in isotropic media to Horizontal Transverse Isotropic (HTI) media, introduce the concept of Extended Azimuthal Elastic Impedance (EAEI), and propose a novel approach to estimate fracture parameters and DHSR using the Fourier Coefficient (FC) of EAEI. First, we derive the EAEI equation and FCs equation in HTI media. The analysis shows that the second FC of EAEI has a good correlation with fracture parameters and DHSR. Secondly, we propose a novel seismic Bayesian inversion with the regularization of the Cauchy-sparse constraint and smoothing model constraint to estimate intercept impedance, gradient impedance, and curvature impedance. Finally, we integrate the optimal rotation angles and the second FC of EAEI to estimate fracture parameters and DHSR, respectively. A synthetic data example and a field data application show that the proposed approach can provide reasonable and reliable inversion results of fracture parameters and DHSR, which help to guide the lateral identification of fracture development areas and favorable fracturing areas.