The estimation of petrophysical and fluid-filling properties of subsurface reservoirs from seismic data is a crucial component of reservoir characterization. Seismic amplitude variation with offset (AVO) inversion driven by rock physics is an effective approach to characterize reservoir properties. Generally, PP-wave reflection coefficients, elastic moduli and petrophysical parameters are nonlinearly coupled, especially in the multiple type pore-space reservoirs, which makes seismic AVO petrophysics inversion ill-posed. We propose a new approach that combines Biot-Gassmanns poro-elasticity theory with Russells linear AVO approximation, to estimate the reservoir properties including elastic moduli and petrophysical parameters based on multi-trace probabilistic AVO inversion algorithm. We first derive a novel PP-wave reflection coefficient formulation in terms of porosity, stiff-pore volume fraction, rock matrix shear modulus, and fluid bulk modulus to incorporate the effect of pore structures on elastic moduli by considering the soft and stiff pores with different aspect ratios in sandstone reservoirs. Through the analysis of the four types of PP-wave reflection coefficients, the approximation accuracy and inversion feasibility of the derived formulation are verified. The proposed stochastic inversion method aims to predict the posterior probability density function in a Bayesian setting according to a prior Laplace distribution with vertical correlation and prior Gaussian distribution with lateral correlation of model parameters. A Metropolis-Hastings stochastic sampling algorithm with multiple Markov chains is developed to simulate the posterior models of porosity, stiff-pore volume fraction, rock-matrix shear modulus, and fluid bulk modulus from seismic AVO gathers. The applicability and validity of the proposed inversion method is illustrated with synthetic examples and a real data application.
Partition function and open/closed string duality in type IIA string theory on a pp-wave
