Reproduction of secondary data in projection pursuit transformation

Manchuk, John G.; Barnett, Ryan M.; Deutsch, Clayton V.

doi:10.1007/s00477-016-1363-y

Cited by 7 publications

(3 citation statements)

References 23 publications

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“…Then, the geostatistical simulation techniques may be applied to these transformed variables individually without the need for cokriging or the linear model of coregionalisation (Journel and Huijbregts 1978) to reproduce possible cross-correlations among them. The PPMT reproduces well the multivariate relationships between the data (Barnett et al 2014(Barnett et al , 2016Manchuk et al 2017). However, PPMT does not explicitly consider sum and fraction constraints.…”

Section: Introductionmentioning

confidence: 59%

“…The PPMT (Barnett et al 2016; Manchuk et al 2017) involves the following steps: Normal score the variables; Sphere transform the variables; Find an interesting projection of the data; Normal score the data along the projection found in step iii; Repeat steps (3) and (4) until the data is multivariate Gaussian with an identity covariance matrix. …”

Section: Methodsmentioning

confidence: 99%

“…The most common transformations for compositional data are the additive log-ratio (Aitchison 1986), centred log-ratio (Aitchison 1986) and isometric log-ratio (Egozcue et al 2003). Manchuk et al (2017) used the isometric log-ratio followed by PPMT to account for the sum constraint of the data set. In this paper, we used a ratio similar to the additive log-ratio.…”

Section: Introductionmentioning

confidence: 99%

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Multivariate geostatistical simulation with sum and fraction constraints

Bassani

Costa

Deutsch

2018

Applied Earth Science

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Geostatistical modelling of grades in mineral deposits often requires the simulation of multiple related variables that have sum and fraction constraints. Sum constraints occur when the sum of some variables may not exceed or must equal a given constant. Fraction constraints occur when a variable may not exceed another variable. In this case, the geostatistical simulations should reproduce the histograms, variograms, multivariate relationships and honour the constraints. We present a methodology for the geostatistical simulation of multiple related variables that considers sum and fraction constraints. The methodology is illustrated in a case study. The data were obtained from a bauxite deposit. First, the original variables were re-expressed as ratios. Second, the variables were transformed using the Projection Pursuit Multivariate Transform (PPMT). Then the PPMT transformed variables were simulated independently using sequential Gaussian simulation and back-transformed. The simulations reproduced the histograms, variograms and bivariate relationships and honoured the sum and fraction constraints.

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Section: Introductionmentioning

confidence: 59%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multivariate geostatistical simulation with sum and fraction constraints

Bassani

Costa

Deutsch

2018

Applied Earth Science

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Assessment of variogram reproduction in the simulation of decorrelated factors

Erten

Deutsch²

2021

Stoch Environ Res Risk Assess

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Geostatistics in the Presence of Multivariate Complexities: Comparison of Multi-Gaussian Transforms

Abulkhair

Dowd

2023

Math Geosci

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One of the most challenging aspects of multivariate geostatistics is dealing with complex relationships between variables. Geostatistical co-simulation and spatial decorrelation methods, commonly used for modelling multiple variables, are ineffective in the presence of multivariate complexities. On the other hand, multi-Gaussian transforms are designed to deal with complex multivariate relationships, such as non-linearity, heteroscedasticity and geological constraints. These methods transform the variables into independent multi-Gaussian factors that can be individually simulated. This study compares the performance of the following multi-Gaussian transforms: rotation based iterative Gaussianisation, projection pursuit multivariate transform and flow transformation. Case studies with bivariate complexities are used to evaluate and compare the realisations of the transformed values. For this purpose, commonly used geostatistical validation metrics are applied, including multivariate normality tests, reproduction of bivariate relationships, and histogram and variogram validation. Based on most of the metrics, all three methods produced results of similar quality. The most obvious difference is the execution speed for forward and back transformation, for which flow transformation is much slower.

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Reproduction of secondary data in projection pursuit transformation

Cited by 7 publications

References 23 publications

Multivariate geostatistical simulation with sum and fraction constraints

Multivariate geostatistical simulation with sum and fraction constraints

Assessment of variogram reproduction in the simulation of decorrelated factors

Geostatistics in the Presence of Multivariate Complexities: Comparison of Multi-Gaussian Transforms

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