Highlights • Novel processing of broadband relative permittivity and conductivity logs. • Proposed Markov-chain Monte-Carlo inversion method is robust in shale formation. • Saturation, water conductivity, and surface conductance of clay are continuously estimated. • Estimated hydrocarbon saturation is between 20% and 90%. • Brine conductivity of the shale formation ranges from 0.1 to 0.25 S/m. Abstract An organic-rich shale gas formation generally exhibits high clay content, high total organic carbon (TOC), low porosity, high tortuosity, and the presence of conductive pyrite that adversely affect the well-log-derived hydrocarbon saturation estimations. In the presence of such petrophysical conditions, log-derived hydrocarbon saturation estimates obtained from multi-mineral analysis solver and various subsurface electromagnetic (EM) logs, such as induction resistivity log, dielectric permittivity log, or dielectric dispersion logs, are not consistent and can vary up to 0.5 saturation unit for a single depth. In addition, hydrocarbon saturation estimates derived from EM logs using conventional saturation models tend to break down in organic-rich shale gas formation because of the unaccounted interfacial polarization effects of clays and conductive minerals. Several of the above-mentioned issues can be addressed by processing downhole broadband EM dispersion logs using a mechanistic clay-pyrite interfacial-polarization model to accurately estimate hydrocarbon saturation in organic-rich shale gas formations. EM induction resistivity, logging while drilling (LWD) propagation, and dielectric dispersion logging tools were jointly deployed in a well drilled in an organic-rich shale gas formation to acquire continuous broadband EM dispersion measurements at 7 EM-log-acquisition frequencies for a total depth of 1500 m in the well. This was the first ever acquisition of broadband EM dispersion logs, comprising relative permittivity and conductivity measured at the 7 EM-log-acquisition frequencies. In this paper, a new Markov-chain Monte-Carlo-based (MCMC) stochastic inversion scheme coupled with a clay-pyrite interfacial-polarization (IP) model is used to process the EM broadband dispersion logs, and simultaneously estimate hydrocarbon saturation, connate water conductivity, and surface conductance of clay in the shale gas formation. The proposed Markov-chain Monte Carlo-based stochastic inversion scheme is robust to noise and exhibits fast convergence. The estimated hydrocarbon saturation is also compared against those derived from resistivity log, dielectric dispersion logs, and multi-mineral analysis solver. The estimated hydrocarbon saturation, connate water conductivity, and surface conductance of clay in two specific intervals of the shale gas formation are in the ranges of 0.2–0.9, 0.1 S/m–0.25 S/m, and 1 × 10−7 S–1 × 10−6 S, respectively. [ABSTRACT FROM AUTHOR]