The Study Of Uncertainty In Statistical Rock Physics Analysis Of Pre-Stack Seismic

Statistical rock physics establish links between seismic attributes and reservoir parameters, and combining statistical techniques to describe uncertainty of petrophysical model. Imperfect knowledge is the main reason for uncertainty. There exist imperfections in the original data, petrophysical model and lithology prediction model, resulting in quantifying uncertainty difficulty. To overcome the shortage of quantify uncertainty in petrophysical model, we use probability and information entropy to describe, characterize and quantify uncertainty, reducing the risk caused by the uncertainty.First, we describe the raw logging data through probability density, information entropy, to provide data foundation for establishing petrophysical model.Secondly, we establish connections among the reflection coefficient, transmission coefficient and parameters of both sides of the interface, based on the theory of Zoeppritz equation. In this paper, we discuss the applicability of P-wave reflection coefficient of the Zoeppritz equation, Aki-Richard approximation and Shuey approximation in the incident angle, ρ₂/ρ₁, V_P2/V_p1 and V_S2/V_S1,with the model of AI₂< AI₁ and AI₂> AI₁,the two kinds of different lithology combination model. The results show that applicability of the different equations have different fitness, and the approximate equations have high fitting of P-wave reflection coefficient within the range of critical angle; The applicability research of the Zoeppritz equation and its approximate equations establish the foundation for AVO analysis.Based on lithological classification results, we perform Markov Chain Monte Carlo （MCMC） method to simulate AVO response, and estimate the uncertainty of AVO response. The map of AVO probability density shows that there are overlaps between different facies, but most likely response for each facies are definitely separated.Finally, we take advantage of the link established between rock physics and seismic attributes to do facies-guided forward seismic modeling. We perform multi- parameter probabilistic fusion method to predict pre-stack seismic reservoir lithology. The methods not only can effectively discriminate the lithology and distinguish gas-bearing formation from non-gas-bearing formation, but also quantify the uncertainty of reservoir lithology prediction.