Universal kriging with training images

Li, Lewis; Romary, Thomas; Caers, Jef

doi:10.1016/j.spasta.2015.04.004

Cited by 11 publications

(6 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As such, MPS and covariance-based geostatistics can be seen as competing, and it is not very surprising that in the last decade there have been many cases of fierce debate between the promoters of these two concurrent approaches (Journel and Zhang 2006;Li et al 2015). My view is that in fact, the two sets of methods should not be seen as opposed, but as complementary approaches.…”

Section: Mps Versus Covariance-based Geostatisticsmentioning

confidence: 99%

When Should We Use Multiple-Point Geostatistics?

Mariethoz

2018

Handbook of Mathematical Geosciences

View full text Add to dashboard Cite

Multiple-point geostatistics should be used when there is either too little or too much information available for other types of geostatistics. Under-Informed Versus Over-Informed ModelsFor a long time, the classical geostatistical framework required moderate amounts of knowledge. Too little knowledge (few hard data, poorly distributed, absence of auxiliary information), makes it difficult to infer the parameters of a covariance model. In the other extreme, too much knowledge risks revealing characteristics of the underlying field that are too complex to be represented by a handful of covariance model parameters. These two situations can be denoted respectively under-informed and over-informed models. In-between these extremes, we have the moderately informed case where it is convenient to use the covariance-based geostatistical framework, which has been-and still is-a very solid basis for building models that incorporate spatial and temporal variability.Extreme under-informed and over-informed cases have often presented technical challenges, for which practical workarounds are used. For under-informed cases, standard geostatistical practice consists for example in including interpretative knowledge to guide variogram fitting when too few hard data are available. This is one of the reasons for the common recommendation to fit variograms by hand (e.g. Olea 1999). The question of designing spatial models for over-informed cases (i.e., when large amounts of data are available) is relatively recent, with the development of improved sensors and high-resolution numerical models that triggered the era of "big data".The concept of multiple-point statistics (MPS) appeared in the early 1990s, initially as a means of overcoming extreme under-informed situations. The idea, at

show abstract

Section: Mps Versus Covariance-based Geostatisticsmentioning

confidence: 99%

When Should We Use Multiple-Point Geostatistics?

Mariethoz

2018

Handbook of Mathematical Geosciences

View full text Add to dashboard Cite

show abstract

“…Connections between MPS and Markov random fields [49,50], texture synthesis developed for computer graphics purposes [51], and universal kriging [52] have been investigated. [53] studied the ability of MPS to reproduce statistical properties of a random field by averaging over a large number of MPS realizations obtained from a single training image.…”

Section: Prior Distributions On Parameter Fieldsmentioning

confidence: 99%

On uncertainty quantification in hydrogeology and hydrogeophysics

Linde

Ginsbourger

Irving

et al. 2017

Advances in Water Resources

102

View full text Add to dashboard Cite

Recent advances in sensor technologies, field methodologies, numerical modeling, and inversion approaches have contributed to unprecedented imaging of hydrogeological properties and detailed predictions at multiple temporal and spatial scales. Nevertheless, imaging results and predictions will always remain imprecise, which calls for appropriate uncertainty quantification (UQ). In this paper, we outline selected methodological developments together with pioneering UQ applications in hydrogeology and hydrogeophysics. The applied mathematics and statistics literature is not easy to penetrate and this review aims at helping hydrogeologists and hydrogeophysicists to identify suitable approaches for UQ that can be applied and further developed to their specific needs. To bypass the tremendous computational costs associated with forward UQ based on full-physics simulations, we discuss proxy-modeling strategies and multi-resolution (Multi-level Monte Carlo) methods. We consider Bayesian inversion for non-linear and non-Gaussian state-space problems and discuss how Sequential Monte Carlo may become a practical alternative. We also describe

show abstract

“…Within the field of geostatistics, different methods allow the incorporation of such uncertainties. The results are typically not analytically obtainable but can instead be simulated as realizations through sampling procedures (Journel and Huijbregts 1978;Journel 2002;Lantuéjoul 2002;Remy et al 2009;Mariethoz et al 2010;Chilès and Delfiner 2012;Mariethoz and Lefebvre 2014;Laloy et al 2017). There exist two main types of geostatistical simulation methods: those based on two-point statistics, where the statistical models are assumed as some variant of a multivariate Gaussian model quantified by a mean and a covariance, and those based on multiple-point statistics in which higher-order statistics are inferred from an example model, such as a training image (TI).…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, one also has to address issues of how well simulations from the TI are a reasonable representation of the geology in question (Høyer et al 2017). The issue of quantifying representative geology is also present in the Gaussian case (Li et al 2015). Recent research involves the inclusion of non-stationarity (Sabeti et al 2017;Madsen et al 2020a) and multi-modality (Grana et al 2017;De Figueiredo et al 2019) while maintaining a computationally feasible problem (Zunino and Mosegaard 2019).…”

Section: Introductionmentioning

confidence: 99%

“…TI versus semivariogram based simulation has previously been discussed in the geoscientific community (see e.g. Journel and Zhang 2006;Kessler et al 2013;Li et al 2015). With the separate advantages and disadvantages offered by Gaussian and MPS simulation, it is currently suggested that they should be viewed as complimentary simulation strategies (Mariethoz 2018).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Choosing between Gaussian and MPS simulation: the role of data information content—a case study using uncertain interpretation data points

Madsen

Møller

Hansen

2021

Stoch Environ Res Risk Assess

View full text Add to dashboard Cite

Integration of geophysical data with information such as from boreholes and expert domain knowledge is often performed as cognitive or explicit geological modeling when generating deterministic geological models of the subsurface. However, such cognitive geological models lack the ability to express the uncertainty of layer boundaries. To remedy the shortcomings of this strategy we propose a novel stochastic methodology combining the efforts of probabilistic data integration and cognitive modeling. We treat geological interpretation points from the cognitive model as uncertain “soft” data. These data are then combined with analogous geology in a probabilistic model. We test two ways of combining and sampling from such a probabilistic model. Firstly, a high-entropy setup based on Gaussian distributions simulation. Secondly, lower entropy (and conceivable more realistic) geological solutions are obtained from multiple-point geostatistics (MPS). We apply both ways of solving the problem at a study site near Horsens, Denmark, where airborne transient electromagnetic measurements, seismic data, and borehole information are available and interpreted in cognitive modeling. We explain the complete framework for integrating the uncertain interpretations in geostatistical simulation. Results show that both the Gaussian simulation and multiple-point geostatistical approach allows satisfactory simulations of uncertain geological interpretations and are consistent with prior geological knowledge. Our results suggest that the number of uncertain data points and their information content play a pivotal role in selecting the most appropriate simulation method for the given framework. MPS simulations allow connectivity in scenarios with few data points due to the low entropy of the model. When the number of soft data increases, Gaussian simulation is less prone to produce simulation artifacts, faster to apply, and could be considered preferential to using MPS simulation.

show abstract

Universal kriging with training images

Cited by 11 publications

References 43 publications

When Should We Use Multiple-Point Geostatistics?

When Should We Use Multiple-Point Geostatistics?

On uncertainty quantification in hydrogeology and hydrogeophysics

Choosing between Gaussian and MPS simulation: the role of data information content—a case study using uncertain interpretation data points

Contact Info

Product

Resources

About