Maden yataklarının değerlendirilmesinde geliştirilmiş yöntemler: halka ayrışım yöntemi ve uygulaması

Ore deposit evaluation techniques by geostatistical simulation were first introduced some 25 years ago,, it has not fulfilled
its promise as a major toot in the eartksciences. This has been largely due to two main reasons; there are some shortcomings
in the method which, although recognized early on by some practitioners,, have been stow to be acknowledged and rectified,
and alternatively wide usage qfkriging methods (there is although a big difference between kriging and simulation). Â survey
of geostatistical simulation methods is given in Dowd (1992). Amongst proposed methods is Davis" (1987a) LU (lower
and upper) decomposition method and related matrix- polynomial approximation method (Davis,, 1987b). The LU-matrix
(lower and. upper) decomposition method of conditional simulation allows fast generation of stochastic processes on smallmoderate
sized, grids. The method is simple and based on the LU triangular decomposition of the matrix of covariances
between data, locations and simulation grid, locations (Davis, 1987a; Alabert,, 1987).. Covariances matrices are symmetric and
positive-definite and therefore can be decomposed into the product of a lower and an upper triangular matrix,.
The advantages of the LU method are that it is simple to implement, performs conditioning simultaneously with simulation,
is not limited to particular forms of covariance functions and handles anisotropies,. The main drawback of this method
is the amount of storage required which, at least in its general form as presented,, effectively limits its application to less than
1000 grid locations. When there are many data, or when there is a large number of points on which values are to be simulated,
the correspondingiy large matrices cannot he handled by classical decomposition algorithms.This paper shows how ring decomposition can he used to extend the use of LU decomposition to larger simulations.. Ring
decomposition can he applied to reduce significantly this memory-size problem,, and therefore proposed method can he used
fof large grid locations. After introducing the mathematical background of ring decomposition method, conditional simulation
applications using lower-upper and ring decomposition methods are presented in the study. For the purpose of providing
a comparison, simulations on 400 x 400 covariance matrix were pet formed using both LU decomposition and ring decomposition.
The results are shown in Figures 1 and. 2.. The both methods yield satisfactory simulations.. Finally a 1500 x 1500
covariance matrix which is too large for LU decomposition method is solved by ring decomposition and the result is given in
Figure 3.