Computerized Modeling of Rock-Varnish Dating
Xl =Na - elemental concentration of Na, weight %
x2=Mg - elemental concentration of Mg, weight %, etc.
423
The calculated model for dating on rock-varnish chemistry in terms of resultant coefficients is as follows:
Y =330. 1418Na-8.63694Mg+6.604966Al+ 1.998514Si+ 39.39983K +
+ 108.7927Ti+223.1224Cr++5.85118Mn+ 1.642149Fe+8.874461 NaMg+
+88.80886Na/Mg+0.452191Mg/Na-2.092061NaAI-9.667416NaSi-3378.058Na/Si-0.012379Si/Na-6.70379NaK-0.809987K/Na+
+ 1.719279NaCa+ 1O.34105Na/Ca-0.774867Ca/Na-15.83823NaTi-1.599621Na/Ti-0.433843Ti/Na+ 119.9918NaCr+0.020519Na/Cr+
+5.903579Cr/Na-1.789714NaMn+0.289843Na/Mn-0.016879Mn/Na+
+ 1.262028NaFe+ 124.2728Na/Fe+O.220534Fe/Na+0.462026Mg/ Al+
+2.743229Al/Mg+416.4457Mg/Si-3.283021Si/Mg+ 1.199073MgK+
+9.77944 7Mg/K -36.083020K/Mg+5.5 70085MgCa-0.244911MglCa +
+48.72757Ca/Mg-7.275502MgTi+1.444417Mg/Ti-70.54765Ti/Mg-20.59409MgCr-35.18291Cr/Mg+0.544135MgMn+0.171234Mg/Mn+
+2.117619Mn/Mg-10.85525Mg/Fe+3.731436Fe/Mg-119.314500Al/Si+
+91. 18935K/AI-0.728109AICa-0.584765Al/Ca-0. 10423Al/Ti-0.002248Al/Cr+6707. 978Cr/ AI-26.432950Mn/ AI-3.347590Fe/ AI-0.569367SiK+0.619844Si/Ca-0.984085SiTi-6.243132SiCr+
+0.00 1532Si/Cr-0.083056SiMn -1.3 789Mn/Si-0.008665SiFe+5.
-0.458225KFe-2.144309Fe/K-3.705322CaTi-86.225500CaCr-0.0 18887Ca/Cr-0.088510CaMn-0.960711 CaFe-126.143700TiCr+
-12.71956CrMn-11.0507Cr/Mn-0.000828Mn/Cr-15.80915CrFe-0.097761 MnFe-11.19832Mn/Fe-69 .23621.
Calculating the coefficients with a precision of six signs after the point insures
estimation of absolute age by this model with an accuracy of several thousand
years. The new elementary functions needed to describe this relationship testify
to the complicated relation between absolute age and ten variables - the elemental concentrations. An attempt to construct a correct model for rock-varnish
dating without considering the pairs ratio of elements revealed great deviations
from the initial dating data. Therefore all combinations of primary signs should
be considered. As a result of the mathematical analysis, a data base for a system
which allows dating of geomorphic levels on the chemistry of varnish coating
was built. For a verification of this model, control samples without allocation
from different geomorphic levels were analyzed and the geological age was calculated on the basis of developed the model. The results obtained correspond to
TL determinations and geological data (Fig. 4). The value calculated by a given
programming operation was considered as the generalized geochemical indicator of rock-varnish dating (see Table 3). This indicator reflects the relation be-
Xl =Na - elemental concentration of Na, weight %
x2=Mg - elemental concentration of Mg, weight %, etc.
423
The calculated model for dating on rock-varnish chemistry in terms of resultant coefficients is as follows:
Y =330. 1418Na-8.63694Mg+6.604966Al+ 1.998514Si+ 39.39983K +
+ 108.7927Ti+223.1224Cr++5.85118Mn+ 1.642149Fe+8.874461 NaMg+
+88.80886Na/Mg+0.452191Mg/Na-2.092061NaAI-9.667416NaSi-3378.058Na/Si-0.012379Si/Na-6.70379NaK-0.809987K/Na+
+ 1.719279NaCa+ 1O.34105Na/Ca-0.774867Ca/Na-15.83823NaTi-1.599621Na/Ti-0.433843Ti/Na+ 119.9918NaCr+0.020519Na/Cr+
+5.903579Cr/Na-1.789714NaMn+0.289843Na/Mn-0.016879Mn/Na+
+ 1.262028NaFe+ 124.2728Na/Fe+O.220534Fe/Na+0.462026Mg/ Al+
+2.743229Al/Mg+416.4457Mg/Si-3.283021Si/Mg+ 1.199073MgK+
+9.77944 7Mg/K -36.083020K/Mg+5.5 70085MgCa-0.244911MglCa +
+48.72757Ca/Mg-7.275502MgTi+1.444417Mg/Ti-70.54765Ti/Mg-20.59409MgCr-35.18291Cr/Mg+0.544135MgMn+0.171234Mg/Mn+
+2.117619Mn/Mg-10.85525Mg/Fe+3.731436Fe/Mg-119.314500Al/Si+
+91. 18935K/AI-0.728109AICa-0.584765Al/Ca-0. 10423Al/Ti-0.002248Al/Cr+6707. 978Cr/ AI-26.432950Mn/ AI-3.347590Fe/ AI-0.569367SiK+0.619844Si/Ca-0.984085SiTi-6.243132SiCr+
+0.00 1532Si/Cr-0.083056SiMn -1.3 789Mn/Si-0.008665SiFe+5.
-0.458225KFe-2.144309Fe/K-3.705322CaTi-86.225500CaCr-0.0 18887Ca/Cr-0.088510CaMn-0.960711 CaFe-126.143700TiCr+
-12.71956CrMn-11.0507Cr/Mn-0.000828Mn/Cr-15.80915CrFe-0.097761 MnFe-11.19832Mn/Fe-69 .23621.
Calculating the coefficients with a precision of six signs after the point insures
estimation of absolute age by this model with an accuracy of several thousand
years. The new elementary functions needed to describe this relationship testify
to the complicated relation between absolute age and ten variables - the elemental concentrations. An attempt to construct a correct model for rock-varnish
dating without considering the pairs ratio of elements revealed great deviations
from the initial dating data. Therefore all combinations of primary signs should
be considered. As a result of the mathematical analysis, a data base for a system
which allows dating of geomorphic levels on the chemistry of varnish coating
was built. For a verification of this model, control samples without allocation
from different geomorphic levels were analyzed and the geological age was calculated on the basis of developed the model. The results obtained correspond to
TL determinations and geological data (Fig. 4). The value calculated by a given
programming operation was considered as the generalized geochemical indicator of rock-varnish dating (see Table 3). This indicator reflects the relation be-