Prediction of shear wave velocity based on a statistical rock-physics model and Bayesian theory

Abstract

Shear wave velocity (Vs) is essential for amplitude-variation-with-offset (AVO) analysis and reservoir characterization. However, Vs is unavailable in many well logs due to the cost or the absence of technology for old wells. A common method is to estimate Vs from other measurements through their relationships, but has a large uncertainty. In this study, a statistical method is proposed to predict Vs of wells. Firstly, a statistical rock-physics model is built for the relationship between logging curves and Vs, which is realized by initializing key petrophysical parameters of the Xu–White model by the distributions instead of constants. The distributions come from prior information, which is a knowledge or experience of research area. Secondly, the key petrophysical parameters are calculated in Bayesian inversion framework by comparing the modeled compression wave velocity (Vp) with real data. Then, Vs is estimated based on these parameters and the rock-physics model. The real data test shows that our statistical method gets accurate Vs prediction, whose mean square error is about 0.002. Besides, the correlation coefficient between estimation and real data is about 0.97. The result is better than common methods. Moreover, statistics of the prediction, such as a confidence interval, can be provided by the statistical method. The real velocities are in the 95% confidence interval of the estimation. The estimated values and statistics of well velocities will offer more valuable information for the following processes of reservoir characterization.