A comparison of Gaussian, Student-t and Vine copulas for modelling geophysical measurements along a rock drill core

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.