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.
On the use of the Hardening Soil Small Strain model in geotechnical practice
This article highlights the importance of using advanced constitutive soil models in numerical modelling as daily geotechnical practice. In this context, the Hardening Soil (HS) model is presented as the most advanced soil model implemented in the ZSoil finite element code. The article recalls the basic features of the HS model and it explains their role in numerical simulations. The role of pre-failure non-linear behaviour of soils is also discussed. An application of the HS model is illustrated on typical geotechnical problems such as retaining wall excavation, tunnel excavation and undrained loading followed by consolidation.