Direct Seismic Inversion of a Novel Brittleness Index Based on Petrophysical Modeling in Shale Reservoirs

The brittleness index (BI) is an essential parameter for evaluating rock brittleness, which can effectively guide artificial hydraulic fracturing for shale gas exploitation. However, some conventional BIs often fall short when applied to shale reservoirs with low permeability, low porosity, and high total organic carbon (TOC) content; we proposed a novel BI more sensitive to brittle rock fractions, porosity, and organic matter content, which was corroborated via the constructed petrophysical modeling method for shale reservoirs. Considering the disadvantage of accumulating error in the indirect calculation of elastic parameters, we further derived a new PP-wave reflection coefficient approximation equation incorporating the novel BI, Young’s modulus, and density, named the BYD reflection coefficient approximation equation. Rigorous validation against the exact Zoeppritz equation by four classes of amplitude versus offset (AVO) seismic response models underlines its accuracy and reliability. Furthermore, we enhanced the seismic inversion algorithm using the reweighted
$L_{P}$
(RLP) quasinorm, surpassing the sparsity of the
$L_{P}$
quasinorm. The nonlinear optimization problem was solved by the alternating direction method of multipliers (ADMM) and the
$L_{P}$
quasinorm iterative shrinkage thresholding algorithm (ISTA). Three sets of model tests with different noises have demonstrated the rationality and robustness of the inversion method. Finally, the 3-D seismic inversion of the novel BI parameter applied to a gas-bearing shale reservoir in Sichuan Basin, China, confirmed its effectiveness in characterizing brittleness distribution, facilitating optimal shale gas exploitation.