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THE USE OF FRACTAL GEOMETRY AND CHAOS THEORY TO QUANTIFY AND PREDICT MINERALIZED FRACTURE AND VEIN SYSTEMS

Objective

The objective of this research project is to design and evaluate procedures for the application of fractal geometry and chaos theory in the quantification and prediction of mineralized fracture and vein systems with the aim of improving the accuracy of ore reserve calculations of vein hosted mineral deposits.
Use of frequency plot of vein parameters such as thickness, length and spacing are powerful methods for describing and quantifying vein systems. Although this study has been a pilot one, every economically mineralized vein system studied had fractal size frequency distributions of both minerals and veins. While it is unlikely that all mineralized vein systems are fractal, the studied ones were gold mineralized. The gold must have been transported in very large, high permeability fluid systems. It seems a reasonable inference, therefore, that large scale vein plumbing systems with a high degree of connectivity are typically fractal. In contrast, vein systems which are confined to small scale layers which are typically not fractal are also less likely to be interconnected on a large scale.

Data collection does not require highly skilled personnel. A detailed knowledge of statistical methods is not required and the results can be readily displayed on most desktop computers.

Cumulative frequency distributions (length, thickness and area) of large vein systems are commonly fractal. Exponents range from -0.5 to -1.1. Spacing frequencies are most commonly distributed lognormally. Fractal veins are clustered and this leads to enriched areas of mineralization.

Fractal statistics may be used to quantify certain mineral distributions. Spectral analysis is a useful technique for confirming that the mineral has a fractal texture, but the cumulative area distribution is a better predictive tool. The investigations indicate some mineral distributions conform well to a fractal description and that through the publication of the Manual and further case studies, the application and use of the technique will assist the prediction of mineralized vein systems.
Geologists have been aware for decades that the geometries of fracture systems have some common features over a large range of scales (from a single outcrop to major tectonic units). Recently, developments in mathematical chaos theory have generated a potentially useful tool for the analysis and systematization of fracture and fault systems.

The rationale of this project is based on firm indications that vein systems have comparable geometrical systematics and constraints for the reason that they can be envisaged as dilatant faults with their net displacement gradient mimicked by their thickness. The nature of the empirical relationship is a rheological function and, once established for a particular vein set, it may be used predictively.

The work programme can be subdivided into 3 phases of investigation, which will roughly follow a chronological sequence: acquisition and compilation of geological data (mapping on various scales, evaluation of existing data collections); statistical analysis of the data (empirical characterization); and field testing of predictive models and compilation of results.

The result of the study will be the development of a new approach to the generation and handling of both exploration and mining data which will enable the optimization of the quality of interpretation and thereby maximize the value of such data. For instance, it would be possible to make an immediate, statistically quantified, predictive statement about the minimum volume of a vein from a single intersection on a borehole core.

The following results should be achieved:
analysis and systematization of the geometrical features of natural fracture systems using techniques based on mathematical chaos theory;
definition of the nature of the empirical relationship between shape, displacement and size of dilatant faults;
analysis of the geometrical systematics and constraints of vein systems and the relationship between the thickness and net displacement gradient of a vein;
formulation of immediate, statistically quantified, predictive statements about the minimum volume of a vein from a single intersection on a borehole core;
and development of a new approach to the generation and handling of both exploration and mining data which will enable progress to be made towards the optimization of the quality of interpretation and thereby maximize the value of such data.

Fieldwork will comprise the mapping of vein hosted precious and base metal ore deposits from Ireland, Great Britain and northern Spain, concentrating on parameters such as vein length, height, width, shape, incremental geometry, spacing, vein array orientation, ore distribution and localization. Additional data on these deposits will be provided by the industrial partners. These will include borehole cores on which similar parameters will be measured. From the collected data fractional dimensions and attractors will be derived. As a control, brittle ductile shear zones which do not contain ore grade mineralization will also be examined from an equivalent range of geological settings. In all cases the examination will be carried out over the maximum possible range of scales, ideally from micrometric to kilometric (approximately 7 orders of magnitude). The data will be computerized and subjected to rigorous parametric and nonparametric testing.

Funding Scheme

CSC - Cost-sharing contracts

Coordinator

Mineral Industry Research Organisation
Address
Expert House 6 Sandford Street
WS13 6QA Lichfield
United Kingdom

Participants (2)

University of Dublin - Trinity College
Ireland
Address

2 Dublin
University of Liverpool
United Kingdom
Address

L69 3BX Liverpool