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.
Joint Bayesian wavelet and well-path estimation in the impedance domain
ABSTRACTWe addressed the problem of the well-to-seismic tie as a Bayesian inversion for the wavelet and well path in the impedance domain. The result of the joint inversion is a set of wavelets for multiple angle stacks, and a corresponding well path. The wavelet optimally links the impedance data along the well to the seismic data along the optimized well path in the seismic time domain. Starting with prior distribution for wavelet and well path, the method calculates the posterior distribution of conditioning the prior distributions with the seismic and well-log data. This is done by iteratively inverting the seismic data with the current wavelet, to obtain an impedance cube around the well. In a second step, the seismic impedances are projected onto the well path. By minimizing the misfit between the inverted seismic impedances and the impedances derived from the well log, the wavelet and well path are optimized. Comparing the well and seismic data in the impedance domain enables the method to work on ...
Bayesian lithology/fluid inversion—comparison of two algorithms
Algorithms for inversion of seismic prestack AVO data into lithology-fluid classes in a vertical profile are evaluated. The inversion is defined in a Bayesian setting where the prior model for the lithology-fluid classes is a Markov chain, and the likelihood model relates seismic data and elastic material properties to these classes. The likelihood model is approximated such that the posterior model can be calculated recursively using the extremely efficient forward–backward algorithm. The impact of the approximation in the likelihood model is evaluated empirically by comparing results from the approximate approach with results generated from the exact posterior model. The exact posterior is assessed by sampling using a sophisticated Markov chain Monte Carlo simulation algorithm. The simulation algorithm is iterative, and it requires considerable computer resources. Seven realistic evaluation models are defined, from which synthetic seismic data are generated. Using identical seismic data, the approximate marginal posterior is calculated and the exact marginal posterior is assessed. It is concluded that the approximate likelihood model preserves 50% to 90% of the information content in the exact likelihood model.