Bayesian lithology/fluid prediction and simulation on the basis of a Markov-chain prior model

Abstract

A technique for lithology/fluid (LF) prediction and simulation from prestack seismic data is developed in a Bayesian framework. The objective is to determine the LF classes along 1D profiles through a reservoir target zone. A stationary Markov-chain prior model is used to model vertical continuity of LF classes along the profile. The likelihood relates the LF classes to the elastic properties and to the seismic data, and it introduces vertical correlation because the seismic data are band-limited. An approximation of the likelihood model provides an approximate posterior model that is a Markov chain. The approximate posterior can be assessed by an exact and efficient recursive algorithm. The LF inversion approach is evaluated on a synthetic 1D profile that is inspired by a North Sea sandstone reservoir. With a realistic wavelet-colored noise model and a S/N ratio of three in the seismic data, the results are reliable. The LF classes and the interfaces between zones are largely correct. The prediction uncertainty increases if the number of zones increases and zone thicknesses decreases. The study clearly demonstrates the impact of a vertically coupled prior Markov model for the LF classes.

Bayesian lithology/fluid inversion—comparison of two algorithms

“…The posterior model contains the complete solution in the Bayesian setting. For Bayesian LF inversion approaches, see Eidsvik et al [5], Avseth et al [2], Larsen et al [8], Hammer and Tjelmeland [7], González et al [6], Buland et al [3], Ulvmoen and Omre [10], and Ulvmoen et al [11]. In the current study, we focus on the approaches in Larsen et al [8] and Hammer and Tjelmeland [7].…”

“…In Hammer and Tjelmeland [7], the seismic inversion is defined using the same prior and likelihood models as in Larsen et al [8]. The inversion is, however, solved using the exact posterior model without any approximation.…”

“…The objective of the study is to evaluate the approximation within the likelihood model in Larsen et al [8]. This is done empirically by comparing inversion results from the methodology in Larsen et al [8] with results from the methodology in Hammer and Tjelmeland [7] using identical seismic data.…”

“…In Larsen et al [8], the prior for the LF classes is defined by a Markov chain model upward through a vertical profile. The likelihood model is defined by a rock physics term relating the LF classes to elastic material properties, and a seismic forward term relating these properties to seismic AVO data.…”

Revealing Multiple Geological Scenarios Through Unsupervised Clustering of Posterior Realizations from Reflection Seismic Inversion

“…In order to handle this, these problems can instead be formulated probabilistically, which leads to a solution described by a typically unknown and non-Gaussian posterior distribution, e.g. (Larsen, Ulvmoen, Omre, & Buland, 2006), (Ulvemoen & Omre, 2010), (Zunino, Mosegaard, Lange, Melnikova, & Hansen, 2014), and (Bosch, Rodrigues, Navarro, & Díaz, 2007). In this way, the solution to the inverse problem can be characterized by a sample from the posterior distribution, which will represent a set of realizations (i.e.…”