Value of information analysis and Bayesian inversion for closed skew-normal distributions: Applications to seismic amplitude variation with offset data

Abstract

Information analysis can be used in the context of reservoir decisions under uncertainty to evaluate whether additional data (e.g., seismic data) are likely to be useful in impacting the decision. Such evaluation of geophysical information sources depends on input modeling assumptions. We studied results for Bayesian inversion and value of information analysis when the input distributions are skewed and non-Gaussian. Reservoir parameters and seismic amplitudes are often skewed and using models that capture the skewness of distributions, the input assumptions are less restrictive and the results are more reliable. We examined the general methodology for value of information analysis using closed skew normal (SN) distributions. As an example, we found a numerical case with porosity and saturation as reservoir variables and computed the value of information for seismic amplitude variation with offset intercept and gradient, all modeled with closed SN distributions. Sensitivity of the value of information analysis to skewness, mean values, accuracy, and correlation parameters is performed. Simulation results showed that fewer degrees of freedom in the reservoir model results in higher value of information, and seismic data are less valuable when seismic measurements are spatially correlated. In our test, the value of information was approximately eight times larger for a spatial-dependent reservoir variable compared with the independent case.

Some properties of the unified skew-normal distribution

“…The closed skew-normal and the SUN distributions have been applied in a wide range of applied domains, and their relevance appears to be growing. The following is a non-exhaustive list of methodologies and applied domains where these distributions have been employed: stochastic frontier analysis in the context of productivity analysis, considered by Domínguez-Molina et al (2007), Colombi (2013), Colombi et al (2014), Kumbhakar and Lai (2016); various models for the analysis of spatial data have been introduced by Allard and Naveau (2007), Hosseini et al (2011), Karimi and Mohammadzadeh (2012), Rimstad and Omre (2014), among others; analysis of longitudinal data for the distribution of random effects in work of Ghalani and Zadkarami (2019), and again Colombi (2013); combination of phase II and III clinical trials, by Azzalini and Bacchieri (2010); seismic inversion methodology for geological problems, by Karimi et al (2010) and Rezaie et al (2014); extended formulations of Kalman filter by Kim et al (2014) and Rezaie and Eidsvik (2016); application to small area estimation by Diallo and Rao (2018). In the context of binary data, Durante (2019) has shown that, under Gaussian priors for the probit coefficients, the posterior distribution has an exact unified skew-normal distribution; this formulation lends itself to interesting developments, such as those of Fasano et al (2019) and Fasano and Durante (2020).…”

Simulation–Regression Approximations for Value of Information Analysis of Geophysical Data

“…Albeit clearly useful in practice, in particular when the main uncertainty is related to geologic scenario or special geographic structures, such a discretization might be unnatural if the decision maker has multi-variable spatial alternatives available. Eidsvik et al (2008), Bhattacharjya et al (2010) and Rezaie et al (2014) used parametric models and associated methods to analytically calculate the conditional expectation…”

A Selective Overview of Skew-Elliptical and Related Distributions and of Their Applications

“…An extension of this model to accommodate observed temporal replicates at each geographical location, illustrated by applied work, has been presented by Schmidt et al [98]; see also the subsequent comments by Genton and Hering [99]. [106], and Boojari et al [107], among others.…”