Modelling thickness in a stratiform deposit using joint simulation techniques

Eggins, Ronald George (2006). Modelling thickness in a stratiform deposit using joint simulation techniques MPhil Thesis, School of Physical Sciences, The University of Queensland.

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Author Eggins, Ronald George
Thesis Title Modelling thickness in a stratiform deposit using joint simulation techniques
School, Centre or Institute School of Physical Sciences
Institution The University of Queensland
Publication date 2006
Thesis type MPhil Thesis
Supervisor Roussos Dimitrakopoulos
Total pages 179
Collection year 2006
Language eng
Subjects L
260100 Geology
780104 Earth sciences
Abstract/Summary The estimated economic value of a stratiform mineral deposit is often very sensitive to the modelling of thickness in a conformable sequence of beds. A coregionalisation model of thickness expresses the assumed underlying spatial relationships of bedding thickness on a regional scale. Joint simulation of thickness directly models the cross-correlation of bedding thickness in such a model. Many of the current techniques of joint simulation are limited in the number of variables that can be simulated due to the multiplicative increase in processing times, based on the number of variables and number of samples simulated. To minimise processing times some methods make use of simplifying assumptions on the coregionalisation model. For example the Markov model, in which the dependence of one variable on the other is limited to the collocated data, would be unlikely to apply to the thickness of conformable bedding in a stratiform deposit. Transforming the thickness variables to remove correlation, simulating, and then back transforming to original data space offered a possible solution. The Minimum/Maximum Autocorrelation Factor (MAF) technique was chosen as one most likely to successfully decorrelate numbers of thickness variables, if the assumptions regarding a two-structure linear coregionalisation model were reasonably satisfied by the sampled data. The assumptions are that a simple intrinsic model of coregionalisation can represent both a lower correlation (‘noise’) component and a higher correlation (‘signal’) component of the modelled data. This implies that the final coregionalisation model (noise plus signal) is made up of linear combinations of a single basic structure at different spatial scales. In a number of previous applications, this had not proved to be a particularly restrictive requirement of the model. The decorrelated variables can be independently simulated, and back transformed twice; firstly using a MAF back-transformation to obtain correlated Gaussian variables, and finally to original data space. The McArthur River silver/lead/zinc stratiform deposit in the Northern Territory of Australia was chosen as the case study because it had many of the characteristics needed to test and evaluate the MAF technique in a typical stratiform deposit. The orebody model contained seventeen (17) mineralised units forming a conformable sequence which had varying thickness and degrees of mineralisation, and which had good continuity across the deposit. Cross-correlation between the thicknesses of the seventeen stratigraphic units was significant. The deposit was heavily folded in certain areas and true thickness of the bedding was calculated from drillhole log data, and used for the simulation studies. A simple unfolding algorithm was utilised to effectively flatten the deposit to allow the application of 2-D simulation techniques. Drillhole intersections often did not contain the full stratigraphic sequence of beds due to a series of normal faults criss-crossing the deposit. Therefore, incomplete data in the drillhole would need to be removed from the data set, or the number of beds in the joint simulation would need to be reduced, to utilise the MAF technique. A method was developed and validated for the generation of missing thicknesses at a sample point which removed the requirement to delete real incomplete sub-sets of the data when utilising MAF. Sequential Gaussian Simulation (SGS) was used to simulate the MAF decorrelated variables under the assumption that the multi-Gaussian assumptions held. Bedding surface simulations were generated by the addition of true thickness perpendicular to a basal reference surface. The 2-D joint simulations of thicknesses and surfaces were considered successful within a domain of the deposit where drillholes were approximately perpendicular to bedding after unfolding. The univariate, bivariate and spatial statistics of the original thickness data were reproduced accurately in the joint simulation model, including the crossvariograms of original thickness; especially compared to those obtained using independent simulation of thickness. It was concluded that the techniques could be successfully applied to other stratiform deposits if the recommended validation steps were carried out. No further difficulties should be encountered in applying the method to 2-D joint simulation of grades in a stratiform deposit. The full 3-D joint simulation of variables in any deposit using MAF would be assisted by the technique to generate missing variables at a point.

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Created: Fri, 21 Nov 2008, 15:27:14 EST