Truncated Gaussian and derived methods

Abstract

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

Three Geostatistical Methods for Hydrofacies Simulation Ranked Using a Large Borehole Lithology Dataset from the Venice Hinterland (NE Italy)

“…Because detail and consistency of core descriptions were highly variable, and boreholes were too many to allow for a case-by-case sedimentological interpretation, no other criteria but dominant grain size could be used to define operative facies. As a result, the link between facies and component depositional elements of BRM can be strong (e.g., channel fills are in most cases represented by sands) but by no means exclusive (e.g., sands can occur in levees as well, whereas silts and clays can be locally intercalated within channel-fill sands), potentially undermining all those modelling approaches that rely on fixed facies transition rules and identity between facies and depositional objects, including OBS and TGS, as well as the nowadays highly popular Pluri-Gaussian [17] and the Multiple-Point Statistics [38]. It is therefore concluded that, especially when working with large borehole datasets where definition of operative facies can be weak, using SIS might still represent a pragmatic (it does not require any assumption on spatial relationship among facies) yet decent hydrofacies modelling choice.…”

Lithofacies uncertainty modeling in a siliciclastic reservoir setting by incorporating geological contacts and seismic information

“…One application in reservoir modeling can be found in Liu et al (2016) for stochastic modeling of eight lithofacies in an oilfield. Beucher and Renard (2016) also explained precisely how this methodology is incorporated for digital modeling of geological phenomena. The basic idea of this approach is to define one Gaussian random variable whose spatial continuity is defined by indicator variograms.…”

“…To come up with this problem, Plurigaussian simulation ) is an alternative method designed to adapt to a wider range of complicated types of geological contacts. In particular it has been widely applied to the modeling of petroleum reservoirs (Zagayevskiy and Deutsch 2016;Beucher and Renard 2016;Martinious et al 2017;Cahutru et al 2015;Almeida 2010). The bottom line of the plurigaussian simulation is to extension of one Gaussian random field into two or more ones and using a truncation rule to convert the Gaussian data into lithofacies acting.…”

Geological Modelling and Validation of Geological Interpretations via Simulation and Classification of Quantitative Covariates

“…On a final note, the proposed methodology used for validating the interpreted geological model, based on the calculation of prior and posterior probabilities, and on the definition of heuristic criteria (Sections 2.4 and 2.5), can be applied not only to the geological scenarios obtained from the simulation and classification of quantitative covariates, as set out in Sections 2.2 and 2.3, but also to scenarios obtained from any other geostatistical simulation method, e.g., multiple-point, truncated Gaussian or plurigaussian simulation [17][18][19][20]. …”

“…Another approach to produce gradual transitions near the domain boundaries is to model the quantitative variables of interest with no previous geological domaining by considering the controlling rock types or ore types as cross-correlated covariates [11][12][13][14][15][16]. Geostatistical simulation approaches have been designed to construct several geological scenarios in order to quantify uncertainty in the actual locations and extents of rock types or ore types, accounting for their spatial continuity and proportions (which may vary in space), and contact relationships, including chronological associations, allowable and non-allowable contacts, edge effects (preferential contacts), and directional effects (asymmetrical spatial relationships) between rock types or ore types ( [17][18][19][20] and references therein). However, these approaches are still in their infancy in practical orebody modelling where the geological model often corresponds to a single interpretation of the deposit, rather than multiple scenarios, which does not allow geological uncertainty to be measured.…”