MATHEMATICAL MODELLING OF OREBODIES – A REVIEW

PROCEEDINGS PIT IAGI RIAU 2006
The 35^th IAGI Annual Convention and Exhibition
Pekanbaru – Riau, 21 – 22 November 2006

MATHEMATICAL MODELLING OF OREBODIES – A REVIEW

By Suharto¹
ABSTRACT

Geometrical analysis of ore body orientation is inspired by one of the mathematical function, which is called eigenvalues and eigenvector matrices. Basically, the function is very simple by transforming the spatial relationship of the 2D or 3D shapes of any object into variance and covariance matrices then extracting its eigenvalues and eigenvector.

In many practices of resource estimation, one of the potential errors is a geologic error that is contributed by lack of knowledge in geometric of ore deposit model and ore continuity (Sinclair, Alastair J and Blackwell, Garston H, 2002). The sophisticated software package cannot guarantee the accurate estimation, unless supported by a better understanding of geological interpretation of geometric and internal ore continuity and other factors. But using the appropriate geological interpretation of the geometrical ore body as constraint variable in estimation will reduce the risk of error due to geometric error during the estimation.

When the interpretation process of geometrical geology is undertaken, a lack of geological understanding and other data supporting can cause some difficulties to determine the principle axis of the ore body. Therefore, some mathematical model is required as basic tools for the interpretation process. The mathematical model is really abstract but it is probably quite understandable and acceptable where in some case difficult to obtain from geological consideration approach.

For this reason, a simple mathematical model is reviewed in order to give more effective way in defining the properties of any spatial geometry such as orientation and continuity.

Hence, having a good understanding of basic mathematical concept in geometrical analysis will give more benefit in geostatistical application. Using the eigenvalues and eigenvector of variance-covariance matrices concept of spatial data point in determining the orientation of ore body or ellipsoid is easy and handy.