Direct inversion for shale brittleness index using a delayed rejection adaptive Metropolis-Markov chain Monte Carlo method

The reservoir brittleness index can characterize the relative brittleness of shale oil and gas reservoirs, which provides guidance for hydraulic fracturing in the later stage of oil and gas exploration and development. It is a significant index to evaluate the sweet spot of oil and gas reservoirs. Most research on the brittleness index involves laboratory measurements and petrophysical quantitative analysis, but few studies directly predict the reservoir brittleness index from prestack seismic data. The Markov chain Monte Carlo (MCMC) probabilistic algorithm incorporating the delayed rejection adaptive Metropolis (DRAM) strategy has been developed to invert the reservoir brittleness index directly. The different brittleness indexes are analyzed and compared by using the constructed rock-physics model of the shale gas exploration area to select the most sensitive one. Based on the chosen brittleness index, the approximate equation of the PP-wave reflection coefficient for the brittleness index is deduced, and the correctness and achievability of the modeling operator are indicated by theoretical analysis. To analyze the uncertainty of the brittleness index and enhance computational efficiency, an improved MCMC probabilistic inversion algorithm is introduced, which aims to optimize the sampling process of the general MCMC algorithm by delayed rejection and adaptive Metropolis strategies. Our study finds that the DRAM strategy improves the efficiency of the algorithm by nearly 30%. Synthetic examples and field seismic data verify the applicability and effectiveness of our inversion method.