Combining meta-modeling and categorical indicators for global sensitivity analysis of long-running flow simulators with spatially dependent inputs

Variance-based global sensitivity analysis (GSA) is a powerful procedure for importance ranking of the uncertain input parameters of a given flow model. The application of GSA is made possible for long-running flow simulators (computation (CPU) time more than several hours) by relying on meta-modeling techniques. However, such flow models can involve one or several spatial inputs, for instance, the permeability field of a reservoir and of a caprock formation in the context of CO₂ geological storage. Studying the sensitivity to each of these spatial inputs motivated the present work. In this view, we propose a strategy which combines (1) a categorical indicator (i.e., a pointer variable taking discrete values) assigned to the set of stochastic realizations associated with each spatial input (spatial maps) and (2) meta-modeling techniques, which jointly handle continuous and categorical inputs. In a first application case, a costless-to-evaluate numerical multiphase flow model was used to estimate the sensitivity indices. Comparisons with results obtained using the meta-model showed good agreement using a two-to-three ratio of the number of learning samples to the number of spatial maps. On this basis, the strategy can be recommended for cases where the number of maps remains tractable (i.e., a few hundred), for example, for moderately complex geological settings, or where a set of such maps can be selected in a preliminary stage using ranking procedures. Finally, the strategy was applied to a more complex multiphase flow model (CPU time of a few hours) to analyze the sensitivity of CO₂ saturation and injection-induced pressure build-up to seven homogeneous rock properties and two spatial inputs.     

Multidimensional Map Algebra: Design and Implementation of a Spatio-Temporal GIS Processing Language

Due to the increasing volume of spatio-temporal data generated from remote sensing, sensor networks and computational simulation, there is a need for a generic, domain-independent framework for spatio-temporal data analysis. This research presents a generic set of data processing and manipulation tools for spatio-temporal raster data called multidimensional map algebra (MMA). MMA is an extension of conventional map algebra that operates not only on data that are two-dimensional in space but also on data that are: (1) one-dimensional in time; (2) both two-dimensional in space and one-dimensional in time; (3) three-dimensional in space; and (4) both three-dimensional in space and one-dimensional in time. MMA data types, neighborhoods, lags, and functions are presented, including rules for combining data types of different dimensionality within local, focal, and zonal functions. A prototype implementation in JAVA is provided as a demonstration and syntax specification for the functions. Challenges to continued development of MMA include performance and efficiency issues for processing very large multidimensional data sets.     

Early and Middle Pleistocene river systems in eastern England: evidence from Leet Hill,southern Norfolk,England

Pleistocene sediments at Leet Hill, southern Norfolk are examined in terms of their sedimentary structures, palaeocurrent indicators, clast and heavy mineral lithology and litho- and morphostratigraphic position. Colour of the quartzite and vein-quartz clasts is used to differentiate the Bytham and the Kesgrave sands and gravels, with the Bytham sands and gravels having a significantly higher proportion of coloured material. The Kirby Cane sands and gravels are the lower sedimentary unit and were deposited by the Bytham river, which drained a catchment extending into central England. At Leet Hill, erosion of the Kesgrave Sands and Gravels by the Bytham river has given the Kirby Cane sands and gravels a distinctive lithological assemblage. Trace clast lithologies suggest that the Kesgrave Sands and Gravels in the region of Leet Hill were deposited in a coastal location with an input from northern sources as well as southern and Welsh sources diagnostic of the Thames catchment. The glaciofluvial Leet Hill Sands and Gravels were deposited by outwash from the Anglian Scandinavian ice sheet. Initially the flow direction of the outwash was determined by the Bytham river valley, but this changed to a southerly direction once the valley had been infilled. This paper provides the first indication of the location of the boundary (Early Pleistocene coastline) between the fluvial Kesgrave Sands and Gravels and the marine equivalent reworked by coastal processes, and demonstrates the way the pre-glacial relief initially controlled patterns of glaciofluvial sedimentation during the early part of the Anglian glaciation. Copyright © 1999 John Wiley & Sons, Ltd.     

Optimizing compaction calculation for improved probabilistic 2D mapping

Integration of all available data in reservoir characterization is critically important. 2D mapping is a reliable and robust technique that allows integration of multiple secondary data, including geological and geophysical surfaces and maps, to generate realistic summaries of reservoir quality at each location in an area of interest with an associated measure of uncertainty. This is achieved in 2D mapping with a more straightforward implementation, requiring significantly less time and fewer resources than three-dimensional modelling. In this paper, we propose an approach for the empirical calculation and optimization of differential compaction maps by leveraging existing well control for the use in 2D mapping. Success of the proposal is demonstrated through tests of accuracy, precision and fairness of the local uncertainty distributions for 100 new stratigraphical wells drilled in the Christina Lake and Kirby East area.     

Impact of model free parameters and sea-level rise uncertainties on 20-years shoreline hindcast: the case of Truc Vert beach (SW France)

Shoreline change is driven by various complex processes interacting at a large range of temporal and spatial scales, making shoreline reconstructions and predictions challenging and uncertain. Despite recent progress in addressing uncertainties related to the physics of sea-level rise, very little effort is made towards understanding and reducing the uncertainties related to wave-driven shoreline response. To fill this gap, the uncertainties associated with the long-term modelling of shoreline change are analysed at a high-energy cross-shore transport dominated site. Using the state-of-the-art LX-Shore shoreline change model, we produce a probabilistic shoreline reconstruction, based on 3000 simulations over the past 20 years at Truc Vert beach, southwest France, whereby sea-level rise rate, depth of closure and three model free parameters are considered uncertain variables. We further address the relative impact of each source of uncertainty on the model results performing a Global Sensitivity Analysis. This analysis shows that the shoreline changes are mainly sensitive to the three parameters of the wave-driven model, but also that the sensitivity to each of these parameters is strongly modulated seasonally and interannually, in relation with wave energy variability, and depends on the time scale of interest. These results have strong implications on the model skill sensitivity to the calibration period as well as for the predictive skill of the model in a context of future climate change affecting wave climate and extremes. © 2020 John Wiley & Sons, Ltd.     

40Ar/39Ar ages of L4, H5, EL6, and feldspathic ureilitic clasts from the Almahata Sitta polymict ureilite (asteroid 2008 TC3)

The Almahata Sitta (AhS) meteorite consists of disaggregated clasts from the impact of the polymict asteroid 2008 TC₃, including ureilitic (70%–80%) and diverse non-ureilitic materials. We determined the ⁴⁰Ar/³⁹Ar release patterns for 16 AhS samples (3–1500 μg) taken from three chondritic clasts, AhS 100 (L4), AhS 25 (H5), and MS-D (EL6), as well as a clast of ureilitic trachyandesite MS-MU-011, also known as ALM-A, which is probably a sample of the crust of the ureilite parent body (UPB). Based on our analyses, best estimates of the ⁴⁰Ar/³⁹Ar ages (Ma) of the chondritic clasts are 4535 ± 10 (L4), 4537–4555 with a younger age preferred (H5), and 4513 ± 17 (EL6). The ages for the L4 and the H5 clasts are older than the most published ⁴⁰Ar/³⁹Ar ages for L4 and H5 meteorites, respectively. The age for the EL6 clast is typical of older EL6 chondrites. These ages indicate times of argon closure ranging up to 50 Ma after the main constituents of the host breccia, that is, the ureilitic components of AhS, reached the >800°C blocking temperatures of pyroxene and olivine thermometers. We suggest that these ages record the times at which the clasts cooled to the Ar closure temperatures on their respective parent bodies. This interpretation is consistent with the recent proposal that the majority of xenolithic materials in polymict ureilites were implanted into regolith 40–60 Ma after calcium–aluminum-rich inclusion and is consistent with the interpretation that 2008 TC₃ was a polymict ureilite. With allowance for its 10-Ma uncertainty, the 4549-Ma ⁴⁰Ar/³⁹Ar age of ALM-A is consistent with closure within a few Ma of the time recorded by its Pb/Pb age either on the UPB or as part of a rapidly cooling fragment. Plots of age versus cumulative ³⁹Ar release for 10 of 15 samples with ≥5 heating steps indicate minor losses of ⁴⁰Ar over the last 4.5 Ga. The other five such samples lost some ⁴⁰Ar at estimated times no earlier than 3800–4500 Ma bp . Clustering of ages in the low-temperature data for these five samples suggests that an impact caused localized heating of the AhS progenitor ~2.7 Ga ago. In agreement with the published work, 10 estimates of cosmic-ray exposure ages based on ³⁸Ar concentrations average 17 ± 5 Ma but may include some early irradiation.