Truncation Map Estimation for the Truncated Bigaussian Model Based on Bivariate Unit-lag Probabilities

Астракова, А. С.; Oliver, Dean S.

doi:10.3997/2214-4609.20141830

Cited by 3 publications

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“…Because lithotype rule, proportions and variogram models are interdependent, their fitting could be delicate. Concerning the lithotype rule, Deutsch et al (2014) and Astrakova and Dean (2014) propose new procedures to fit complex lithotype arrangements, using sequential and automatic procedures. For the GRF variogram fits, Desassis et al (2014) have developed a methodology to compute the experimental variograms of the underlying GRFs starting from lithotypes at sample points and knowing the lithotype rule and the proportions; then the fit in a Gaussian framework is easier (stationary case and classical approach).…”

Section: Discussionmentioning

confidence: 99%

Truncated Gaussian and derived methods

Beucher

Renard

2016

Comptes Rendus. Géoscience

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International audienceThe interest of a digital model to represent the geological characteristics of the field is well established. However, the way to obtain it is not straightforward because this translation is necessarily a simplification of the actual field. This paper describes a stochastic model called truncated Gaussian simulations (TGS), which distributes a collection of facies or lithotypes over an area of interest. This method is based on facies proportions, spatial distribution and relationships, which can be easily tuned to produce numerous different textures. Initially developed for ordered facies, this model has been extended to complex organizations, where facies are not sequentially ordered. This method called pluri-Gaussian simulation (PGS) considers several Gaussian random functions, which can be correlated. PGS can produce a large variety of lithotype setups, as illustrated by several examples such as oriented deposits or high frequency layering

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Section: Discussionmentioning

confidence: 99%

Truncated Gaussian and derived methods

Beucher

Renard

2016

Comptes Rendus. Géoscience

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“…It is often the case vertically through the vertical proportion curves (Felletti, 2004) but also laterally, for instance when using an auxiliary information as seismic data in the model. Other authors concentrate on the estimation of more complex coding functions constant in space (Astrakova and Oliver, 2014). Finally, Allard et al (2012) estimate complex coding function varying in space by using auxiliary information.…”

Section: Introductionmentioning

confidence: 99%

A pairwise likelihood approach for the empirical estimation of the underlyingvariograms in the plurigaussian models

Desassis,

Renard,

Beucher

et al. 2015

Preprint

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The plurigaussian model is particularly suited to describe categorical regionalized variables. Starting from a simple principle, the thresholding of one or several Gaussian random fields (GRFs) to obtain categories, the plurigaussian model is well adapted for a wide range of situations. By acting on the form of the thresholding rule and/or the threshold values (which can vary along space) and the variograms of the underlying GRFs, one can generate many spatial configurations for the categorical variables. One difficulty is to choose variogram model for the underlying GRFs. Indeed, these latter are hidden by the truncation and we only observe the simple and cross-variograms of the category indicators. In this paper, we propose a semiparametric method based on the pairwise likelihood to estimate the empirical variogram of the GRFs. It provides an exploratory tool in order to choose a suitable model for each GRF and later to estimate its parameters. We illustrate the efficiency of the method with a Monte-Carlo simulation study . The method presented in this paper is implemented in the R package RGeostats.

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“…The choice between the two methods should depend on the case study and further work on this topic is required. It should also be noted that some methods that create automatic truncation rules have been developed Astrakova et al 2015). It would be interesting to generalise these methods by incorporating the shift between the Gaussian functions in order to match asymmetric transition probabilities.…”

Section: Adapting the Truncation Rule For More Faciesmentioning

confidence: 99%

Geostatistical modelling of cyclic and rhythmic facies architectures

Blévec

Dubrule

John

et al. 2017

Preprint

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A Pluri-Gaussian method is developed for facies variables in three dimensions to model vertical cyclicity related to facies ordering and rhythmicity. Cyclicity is generally characterised by shallowing-upward or deepening-upward sequences and rhythmicity by the repetition of facies at constant intervals along sequences. Both of these aspects are commonly observed in shallow-marine carbonate successions, especially in the vertical direction. A grid-free spectral simulation approach is developed, with a separable covariance allowing a dampened hole-effect to capture rhythmicity in the vertical direction and a different covariance in the lateral plane along strata, as in space-time models. In addition, facies ordering is created by using a spatial shift between two latent Gaussian functions in the Pluri-Gaussian approach. Rapid conditioning to data is performed via Gibbs sampling and kriging using the screening properties of separable covariances. The resulting facies transiograms can show complex patterns of cyclicity and rhythmicity. Finally, a three dimensional case study of shallow-marine carbonate deposits at outcrop shows the applicability of the modelling method.

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Truncation Map Estimation for the Truncated Bigaussian Model Based on Bivariate Unit-lag Probabilities

Cited by 3 publications

References 0 publications

Truncated Gaussian and derived methods

Truncated Gaussian and derived methods

A pairwise likelihood approach for the empirical estimation of the underlyingvariograms in the plurigaussian models

Geostatistical modelling of cyclic and rhythmic facies architectures

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