Wavelet estimation in seismic convolved hidden Markov models
Inversion of seismic AVO-data is an important part of reservoir evalua- tion. These data are convolved but the convolution kernel and the associated error- variances are largely unknown. We aim at estimating these model parameters with- out using calibration observations in wells. This constitu tes the first step in socalled blind deconvolution. We solve the seismic inverse problem in a Bayesian setting and perform the associated model parameter estimation by an approximate marginal maximum likelihood method. A small test study indicate that bell-shaped wavelets with smooth edges are identified well, even for approximatio ns of low orders.
Approximate posterior distributions for convolutional two-level hidden Markov models
A convolutional two-level hidden Markov model is defined and evaluated. The bottom level contains an unobserved categorical Markov chain, and given the variables in this level the middle level contains unobserved conditionally independent Gaussian variables. The top level contains observable variables that are a convolution of the variables in the middle level plus additive Gaussian errors. The objective is to assess the categorical variables in the bottom level given the convolved observations in the top level. The inversion is cast in a Bayesian setting with a Markov chain prior model and convolved Gaussian likelihood model. The associated posterior model cannot be assessed since the normalizing constant is too computer demanding to calculate for realistic problems. Three approximate posterior models based on approximations of the likelihood model on generalized factorial form are defined. These approximations can be exactly assessed by the forward-backward algorithm. Both a synthetic case and a real seismic inversion case are used in an empirical evaluation. It is concluded that reliable and computationally efficient approximate posterior models for convolutional two-level hidden Markov models can be defined.
Mapping lithofacies and pore‐fluid probabilities in a North Sea reservoir: Seismic inversions and statistical rock physics
Reliably predicting lithologic and saturation heterogeneities is one of the key problems in reservoir characterization. In this study, we show how statistical rock physics techniques combined with seismic information can be used to classify reservoir lithologies and pore fluids. One of the innovations was to use a seismic impedance attribute (related to the VP/VS ratio) that incorporates far‐offset data, but at the same time can be practically obtained using normal incidence inversion algorithms. The methods were applied to a North Sea turbidite system. We incorporated well log measurements with calibration from core data to estimate the near‐offset and far‐offset reflectivity and impedance attributes. Multivariate probability distributions were estimated from the data to identify the attribute clusters and their separability for different facies and fluid saturations. A training data was set up using Monte Carlo simulations based on the well log—derived probability distributions. Fluid substitution by Ga...