A comparison of Gaussian, Student-t and Vine copulas for modelling geophysical measurements along a rock drill core
Date
2018
Authors
Addo Junior, E.
Metcalfe, A.V.
Chanda, E.
Editors
Clark, A.
Clarke, R.
Clarke, R.
Advisors
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Journal article
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Australia and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal, 2018; 59:216-230
Statement of Responsibility
E Addo Jr, AV Metcalfe, EK Chanda
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Abstract
This case study is a based on measurements made approximately at
20cm lengths along a down-the-hole diamond drill core from a pyrite
mine in South Australia. The measurements are the P-wave velocity,
magnetic susceptibility and impedance. The trivariate distribution is
modelled using Gaussian, Student-t and vine copulas and the results are
compared in terms of goodness of fit and differences in extreme values
from distributions obtained by simulation from the copulas. The vine
copula provides the best fit for the variables. Trivariate linear spatial
Gaussian, Student-t and vine copulas are used to predict magnetic
susceptibility one step below the depth of the drill core. The vine
copula allows for more detailed modelling of the error structure, and so provides more accurate 90% prediction intervals. The 90% prediction
interval for the vine copula is wider than that for the Student-t copula,
and both are wider than the interval obtained with the Gaussian
copula. In general, copulas provides a more realistic modelling of
geological variables and hence allows for accurate assessment of risk
and uncertainty.
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© Austral. Mathematical Soc. 2018.