# Statistical models - Geology. Forecasting and search for mineral deposits

## Statistical Models

Statistical models are a variety of geological and geological models - geological, ore-forming, geochemical, geophysical, petrophysical, forecasting, geological, industrial, complex and multifactorial models. The statistical model, in comparison with the qualitative version of the geological structure model, is more accurate in describing the quantitative characteristics and various variations of the features of the modeled object - ore region, ore field, deposit and ore body. Statistical models allow predictions of the probable limits of the oscillations of the parameters of the modeled object and its possible states, which were even observed in the reference sample. The simplest case of such predictions is the estimation of the probability of occurrence of certain ore or ore-controlling bodies or their properties. The statistical model makes it possible to make quantitative calculations in assessing the informativeness of the forecasting criteria, when choosing a complex of geological, geophysical and geochemical methods, and optimal parameters of observation networks when applying them.

Statistical models include the following characteristics [Forecast-Metallogenic ..., 1988]:

1) the mean values ​​ x and the standard deviation a for characteristics whose distribution does not contradict the normal law;

2) mean geometric x and standard deviations for characteristics with a lognormal distribution; to this group of characteristics are all indicators of the sizes, volumes, contents of components; sometimes for lognormal distributions instead of x and є it is more convenient to use the average value of the logarithms lnx and the standard deviation from the logarithm ϭ lnx. There are simple relations between these quantities: Inx - ln (x); ϭlnx = Іпє;

3) for characteristics to which the law of distribution can not be found, only the averages are given; such characteristics in some cases are the percentage values ​​of the area occupied by different rocks,

4) probability of presence of signs; their evaluation is the ratio of a part of the objects (ore fields, deposits, ore bodies) on which this feature was observed to the total number of objects included in the master sample; the confidence limits for these quantities are determined by statistical tables or nomograms;

5) the coordinates of the correlations between the signs;

6) the probabilities of zonal transitions Pc/d characterizing metasomatic or geochemical zoning; The Pc/d estimate is the ratio of the number of deposits at which some metasomatic or geochemical zonation typical for a given type of deposits is replaced in the direction from the center to the periphery of the object by zone d, to the total number of deposits on which zone c is observed; in the matrix of the probabilities of the zonal transitions on the left along the vertical are the zones considered as ci, at the top along the horizon - dj (j * i); Thus, each row of the matrix characterizes for some zone the probability of its transition to any of the bands dj.

An example is the statistical model of the copper-molybdenum-porphyry formation (see Tables 11-13), compiled from a sample of 44 deposits in different regions of the world (Deep, 1981). The estimation of the probability of features in the model (Table II) and the correlation coefficients between them (Table 12) allows to make a quantitative assessment of their informativeness with respect to a particular area, and also to quantify the degree of potentiality of potential ore fields and deposits.

The matrix of the probabilities of zonal transitions (Table 13) characterizes possible zoning variants of productive megasomatites: each row of the matrix describes for some zone the probability of its transition to any of the others. Based on such a statistical model, the probability of presence of quartz-feces and spar zones at a depth of one of the buried copper-molybdenum-porphyry deposits was quantitatively estimated, which allowed us to predict a much larger vertical scale of mineralization than previously thought.

Table 11

Statistical characteristics of geological features of molybdenum-copper-porphyry deposits

 Non-Metric Characteristics ( n = 44) * Magmatic rocks Statistical parameters Acidic and moderately acidic With increased alkalinity Avg and Primary I II I II I II 1 2 3 4 5 6 Probability of presence of a sign 0.58 0.60 0.46 0.35 0.63 0.35 95% confidence limits 0.47 - 0.48 - 0.31 - 0.22 - 0.52 - 0.25 - for the probability 0.69 0.72 0.60 0.48 0.75 0.47 7 8 9 10 II 12 Probability of presence of the sign 95% confidence limits for 0.65 0.95 0.74 1.0 X = 1.07 x = 0.41 Probabilities 0.54 - 0.76 0.88 - 0.99 0.63 - 0.84 0.95-1.0 x = 1.9 x = 2.0

* n - the number of reference objects; I - intrusive rocks; II - rocks composed of small bodies, sometimes subvolcanic; 1,2 ... 12 - feature numbers.

Table 12

Matrix of coefficients between non-metric characteristics

 Numbers Characteristics Characteristic number * 1 2 3 4 5 6 7 8 2 +0.19 3 +0.11 +0.06 4 -0.08 -0.32 +0.18 5 +0.19 -0.15 -0.02 -0.02 6 +0.05 -0.08 -0.22 -0.04 -0.27 7 -0.05 -0.21 -0.07 +0.35 -0.11 -0.18 8 -0.18 +0.05 -0.24 -0.30 -0.17 +0.16 -0.16 9 -0.16 -0.13 0 -0.03 +0.18 0 -0.11 -0.13

* the numbers of the characteristics correspond to the numbers in Table. eleven; the number of observations in sample 44; the threshold value of the correlation coefficient at a significance level of 0.05 is ± 0.30.

Table 13

The matrix of the probabilities of zonal transitions

 The nature of metasomatic changes Kalishpatization and Silicification Quoting and Sericization Chloritization and epidotization (propylitization) Kalishpatization and Silicification - 0.93 (0.82-0.96) * 0.07 (0.03-0.16) Quoting and Sericization 0 (0-0.05) - 0.73 (0.62-0.82) Chloritization and epidotization (propylitization) 0 (0-0.05) 0 (0-0.05) -

* In parentheses, 95% confidence limits of the probability day.

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