Direct pre-stack inversion of elastic modulus using the exact Zoeppritz equation and the application in shale reservoir

Abstract

Young’s modulus and Poisson’s ratio are important for reservoir characterization and rock brittleness prediction in unconventional resource exploration and development. Conventional methods can estimate Young’s modulus and Poisson’s ratio by indirect calculations and direct inversion using approximate expressions, which have cumulative errors and limited accuracy of the estimated results, especially at large incident angles. In this study, we derived a new form of the Zoeppritz equation and P-to-P wave reflection coefficient in terms of density and Young’s modulus, Poisson’s ratio. It has the same accuracy as the original Zoeppritz equation over a wide range of incident angles. A robust non-linear inversion method based on the iteratively regularized Levenberg Marquardt (IRLM) algorithm, is used to invert all three parameters based on the new equation directly and simultaneously. Synthetic data and field data are used to test and verify the proposed direct inversion method, ensuring the feasibility and effectiveness of the proposed method and the high accuracy and stability of the inversion results. This study has a great potential and valuable guidance for “sweet spot” evaluation and subsequent horizontal well deployment and hydraulic fracturing.