Habilitation Thesis
DOI
https://doi.org/10.11606/T.44.2013.tde-22072013-111953
Document
Author
Full name
Jorge Kazuo Yamamoto
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 1995
Committee
Bettencourt, Jorge Silva (President)
Amaral, Gilberto
Duarte, Uriel
Landim, Paulo Milton Barbosa
Suslick, Saul Barisnik
Title in Portuguese
Desenvolvimento dos métodos de interpolação para avaliação de jazidas
Keywords in Portuguese
Depósitos Minerais (avaliação)
Abstract in Portuguese
Keywords in English
Not available.
Abstract in English
This paper presents a systematic revision, followed by a critical analysis, of a part of our scientific production in the research program centered on problems of mathematical interpolation of geological data for ore-body modelling and ore-reserve estimation. The main interpolation functions studied in this research program were: hyperpolynomials, multiquadric equations, ordinary kriging, new method of interpolation and inverse of weighted distance. The problem of estimation variance of interpolated value was also studied, which resulted in the proposition of interpolation variance as a dispersion measure of sampling points in relation to the interpolated value. Because of its simple statistical and mathematical formulation, interpolation variance can be applied to all the methods of interpolation based on the principle of weighted average. The origin of a new method of interpolation, developed during the research program, is restudied in this work in relation to the multiquadric equations and it is concluded that the efficiency of this method for a small number of sampling points is the result of the normalization of its coefficients. Thus the new method shall be referred to henceforth as "normalized multiquadric equations". The main characteristic of our research is the use of practical approaches to problems of ore-body modelling and ore-reserve estimation, such as: a) the method of "normalized multiquadric equations"; b) interpolation variance; and c) the inverse of weighted distance method adapted to block estimation. The improvement of multiquadric equations by means of normalization of their coefficients opens a new perspective to their application, because now they can be used as a local interpolation function, while maintaining the same characteristics of accuracy and smoothness of the interpolated surface. However, the correct choice of a multiquadric constant as a function of natural variability of geological data continues as an open question for future research. Besides its versatility in the estimation of dispersion variance for punctual and block evaluations, interpolation variance presents the advantage of being combinable in order to compute the global variance of a deposit associated with its global average grade, which is impossible in geostatistics. The inverse of weighted distance method for block evaluation is an important practical contribution to mining, because it has been extensively used when the ordinary kriging technique cannot be applied, for instance, when representative variograms cannot be computed.