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Abrahamsen, Petter; Benth, Fred Espen

doi:10.1023/a:1011078716252

Cited by 43 publications

(11 citation statements)

References 11 publications

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“…In this work, a methodology was explored where information was retrieved from images, combined with expert knowledge and conditional expectations at image points were calculated. Other methodologies discussed here are available, some of which could potentially have been used for the presented purpose, e.g., kriging with inequalities presented by Abrahamsen and Benth (2001). None of the kriging indicators can alone be used directly as a classification indicator.…”

Section: Discussionmentioning

confidence: 99%

“…Wackernagel et al (2002) presented approaches to take advantage of auxiliary information including kriging with external drifts where a primary variable typically at borehole location is combined with a secondary variable providing low(er) frequency/resolution information about the variable(s) under study. Abrahamsen and Benth (2001) presented a methodology to estimate trend coefficients given both exact data and inequality constraints. Omre (1987) developed Bayesian kriging as a generalized form of kriging with an external drift.…”

Section: Using Auxiliary Information In Resource Estimationmentioning

confidence: 99%

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Application of Soft Data in Nodule Resource Estimation

Ellefmo

Kühn

2020

Nat Resour Res

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Minerals and metals are of uttermost importance in our society, and mineral resources on and beneath the deep ocean floor represent a huge potential. Deciding whether mining from the deep ocean floor is financially, environmentally and technologically feasible requires information. Due to great depths and harsh conditions, this information is expensive and time and resource consuming to obtain. It is therefore important to use every piece of data in an optimum way. In this study, data retrieved from images and expert knowledge were used to estimate minimum and maximum nodule abundances at image locations from an area in the Clarion-Clipperton-Zone of the equatorial North East Pacific. From the minimum and maximum values, box cores and the spatial correlation quantified through variogram, a conditional expectation and associated uncertainty were obtained through the Gibbs sampler. The conditional expectation and the uncertainty were used with the assumed certain abundance data from the box cores in a kriging exercise to obtain better informed estimates of the block by block abundance. The quality assessment of the estimations was done based on distance criterion and on kriging quality indicators like the slope of regression and the weight of the mean. From the original image locations, alternative image configurations were tested, and it was shown that such alternatives produce better estimates, without extra costs. Future improvements will focus on improving the estimation of the minimum and the maximum values at image locations.

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Section: Discussionmentioning

confidence: 99%

Section: Using Auxiliary Information In Resource Estimationmentioning

confidence: 99%

Application of Soft Data in Nodule Resource Estimation

Ellefmo

Kühn

2020

Nat Resour Res

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“…This phenomenon frequently occurs in datasets due to some reasons such as geological formation (i.e., different minerals), instrumental devices for assaying the grades and chemical components restrictions. This type of constraint, for instance, can be investigated by some defined bounds on the dataset, which restrict the variables to be adjusted to predefined intervals [23]. Particularly in mineral resource evaluation, inequality constraint is related to the grades that are smaller than a detection limit (e.g., censor samples) or when working with soft data defined by lower and upper bounds [24].…”

Section: Inequality Constraintmentioning

confidence: 99%

A Hybrid Approach for Joint Simulation of Geometallurgical Variables with Inequality Constraint

2019

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Geometallurgical variables have a significant impact on downstream activities of mining projects. Reliable 3D spatial modelling of these variables plays an important role in mine planning and mineral processing, in which it can improve the overall viability of the mining projects. This interdisciplinary paradigm involves geology, geostatistics, mineral processing and metallurgy that creates a need for enhanced techniques of modelling. In some circumstances, the geometallurgical responses demonstrate a decent intrinsic correlation that motivates one to use co-estimation or co-simulation approaches rather than independent estimation or simulation. The latter approach allows us to reproduce that dependency characteristic in the final model. In this paper, two problems have been addressed, one is concerning the inequality constraint that might exist among geometallurgical variables, and the second is dealing with difficulty in variogram analysis. To alleviate the first problem, the variables can be converted to new variables free of inequality constraint. The second problem can also be solved by taking into account the minimum/maximum autocorrelation factors (MAF) transformation technique which allows defining a hybrid approach of joint simulation rather than conventional method of co-simulation. A case study was carried out for the total and acid soluble copper grades obtained from an oxide copper deposit. Firstly, these two geometallurgical variables are transferred to the new variables without inequality constraint and then MAF analysis is used for joint simulation and modelling. After back transformation of the results, they are compared with traditional approaches of co-simulation, for which they showed that the MAF methodology is able to reproduce the spatial correlation between the variables without loss of generality while the inequality constraint is honored. The results are then post processed to support probabilistic domaining of geometallurgical zones.

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“…With this distribution, the probability of the fault surface being on the wrong side of the well path point is approximately 0.01. An alternative for conditioning the well path points is the use of inequality conditioning (Abrahamsen and Benth 2001). This would ensure that the fault surface realizations are on the correct side of the well path point, and would also ensure that the location of the fault surface inside the well path point follows the desired distribution, a truncated version of (z|x i , y i ).…”

Section: Well Path Pointsmentioning

confidence: 99%

An Uncertainty Model for Fault Shape and Location

2014

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Fault models are often based on interpretations of seismic data that are constrained by observations of faults and associated strata in wells. Because of uncertainties in depth migration, seismic interpretations and well data, there often is significant uncertainty in the geometry and position of the faults. Fault uncertainty impacts determinations of reservoir volume, flow properties and well planning. Stochastic simulation of the faults is important for quantifying the uncertainties and minimizing the impacts. In this paper, a framework for representing and modeling uncertainty in fault location and geometry is presented. This framework can be used for prediction and stochastic simulation of fault surfaces, visualization of fault location uncertainty, and assessments of the sensitivity of fault location on reservoir performance. The uncertainty in fault location is represented by a fault uncertainty envelope and a marginal probability distribution. To be able to use standard geostatistical methods, quantile mapping is employed to construct a transformation from the fault surface domain to a transformed domain. Well conditioning is undertaken in the transformed domain using kriging or conditional simulations. The final fault surface is obtained by transforming back to the fault surface domain. Fault location uncertainty can be visualized by transforming the surfaces associated with a given quantile back to the fault surface domain.

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Untitled

Cited by 43 publications

References 11 publications

Application of Soft Data in Nodule Resource Estimation

Application of Soft Data in Nodule Resource Estimation

A Hybrid Approach for Joint Simulation of Geometallurgical Variables with Inequality Constraint

An Uncertainty Model for Fault Shape and Location

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