Jeremy Wolpert
Geol. 659 – Quantitative Methods
December 11, 2003
2nd Presentation
Abstract
Iron mining is one of the most important mining operations in the world. Since the Middle Ages, iron has been mined in order to manufacture steel products. Statistical analysis was conducted on chemical concentrations that were sampled at an iron carbonate mine near Erzberg, Austria. There were two hypotheses tested in this study. The first one is that iron and manganese oxide have some common cyclic patterns at low and high frequencies with output tonnage from the steel mill. Secondly, that calcium oxide and magnesium oxide have no common cyclic patterns at low and high frequencies with output tonnage.
First, autocorrelations were computed and compared to become better familiar with the data. Fourier transformations with smoothing were conducted on the data to find shared peaks in frequencies. This information was then used to determine the cutoff frequencies for filtering. These filters were then cross-plotted and correlated. From the tests, it is seen that the iron/manganese oxide and calcium oxide/magnesium oxide do not have common cyclic components with tonnage output.
Background
Before Eisenerz, Austria was known as Eisenerz, a man that was carrying water to another village was captured. In order to be released, the man promised to grant one wish to his kidnappers. They would receive either ten years of gold, a hundred years of silver or iron till eternity ( Since the Middle Ages, iron carbonate (siderite) has been mined from this mountain near Erzberg, Austria (Davis, 2002).
Siderite is a carbonate mineral that has the composition of FeCO3. This carbonate mineral is commonly found with other carbonates known as calcite (CaCO3), magnesite (MgCO3) and rhodochrosite (MnCO3). These minerals sometimes have substitution between their metal ions, as well (Klein, 1993).
The iron mine in Eisenerz, Austria is now in the extraction and processing phase of the mining operation. Here inclement winters make mining difficult, so the removal of ore is done in warm weather ( Open pits and underground mining have been used to remove and estimated 200-230 million tons of ore in this century alone ( Also one hundred forty million tons of ore are still projected to be in reserves (
Study Area
At the Eisenerz iron mine near Erzberg, Austria (Figure 1), iron carbonate is mined and taken directly to a beneficiation plant to be processed. Here the iron carbonate that is removed from the mountain is chemically made purer to insure that fewer steps are needed at the steel mill. This in essence keeps costs down at the steel mill itself.
A stream that leaves this plant is sampled every hour to assure that the iron ore being dispatched to a nearby steel mill is consistently similar. Once the composition is determined, the ore is then placed into one of three storage piles. From these piles, the ore is withdrawn and mixed in such a way to insure that the steel mill receives a dependable composition (Davis, 2002).
Voest-Alpine Erzberg Ges.m.b.H helpfully supplied the data to John C. Davis, the author of Statistics and Data Analysis in Geology. The data set includes 3524 average hourly measurements of six different chemical percentages and the hourly tonnage output for the mine. Continuous hourly sampling of the beneficiation stream collected these 3524 data points over a 21-week period in 1996.
Analysis of Ore Composition & Tonnage
Due to the fact the siderite exchanges metal ions with calcite, magnesite, and rhodochrosite these metal concentrations were analyzed. Iron (Fe) and manganese oxide (MnO) were compared to tonnage output for common cyclic components while calcium and magnesium oxides were compared to tonnage output for different cyclic components under the assumption that high iron and manganese oxide will have low calcium and magnesium oxides.
First the raw data was analyzed to find the high and low concentration similarities between concentrations and tonnage (Figure 2). From this, the previous assumptions were correct. That is, the Fe and MnO concentrations are high when the tonnage output is high and the CaO and MgO concentrations are low when the tonnage output is low.
At this point, auto correlations were computed on the five data sets (Figure 3). Due to the fact that the program can only compute a limited number of data points, the first two thousand points were used and compared. Figures 4 through 9 show comparisons of the autocorrelations. Seen again is that the previous assumptions were correct.
Next the data sets were transformed by a Fourier transformation using the forward half function. After looking at the results, smoothing was determined to be essential because of the massive amounts of noise in the graphs (Figures 10 & 11). Averaging the data in increments of five did the smoothing.
Later, the Fourier transformations were filtered to look at the high and low frequencies more closely. A low pass filter was applied to all five of the data sets in order to look at the lower frequency data (Figures 12 – 17). This filter had a cut-off frequency of 0.023. The band pass filter was then applied to the same data sets to look closer at the higher frequency points (Figures 18 – 23). Here the low and high cut-off frequencies were 0.023 and 0.041, respectively.
Results of Analysis
From the autocorrelations, it can be seen that iron and manganese oxide have similar cyclic components. Figure 4 shows a correlation coefficient to be near 87%. This exhibits that the two have similar cyclic components. This can be visually seen in the graph as well. When the iron goes up the manganese oxide does the same, and conversely when one goes down the other follows suite.
Another look at the autocorrelations of iron and manganese oxide shows that when compared to tonnage they have the same relationship to tonnage. Figures 5 and 6 show the correlation coefficients to be both around 46%. This low correlation shows that iron and manganese oxide do not have strong cyclic components with tonnage output.
Further analysis of the relationship between iron and manganese oxide to tonnage is shown in figure 10. Here the Fourier transformations have been smoothed and reveal peaks in both the iron and manganese oxide at the same frequencies. When these peaks are compared to the peaks in the smoothed tonnage, a lag time is exposed.
The common low frequencies are 0.004, 0.01, and 0.017 cycles per hour. These frequencies were filtered with the low pass filter and compared in figures 12, 13, and 14. The cross-plot of Fe and MnO low pass filters (Fig. 12) again shows the common cyclic components between them. But when they are cross-plotted with tonnage (Figs. 13 & 14), there seems to be no common cyclic component at low frequencies. This is quantitatively represented by the low correlation coefficients of 9% for iron and 24% for manganese oxide.
The common high frequencies are 0.029 and 0.034 cycles per hour. These frequencies were filtered with a band pass filter and compared in figures 18, 19, and 20. The cross-plot of Fe and MnO band pass filters (Fig.18) also shows the common cyclic components between them as previously exhibited. But as seen before, there are low correlation coefficients when the two were compared to tonnage. Figures 19 and 20 quantitatively display the Fe correlation to be 16% and the MnO correlation to be 15%.
Again looking at the autocorrelations, it can be seen that calcium and magnesium oxides have similar cyclic components. Figure 7 shows a correlation coefficient to be near 78%. This exhibits that the two have similar cyclic components. This can be visually seen in the graph as well. When the calcium oxide goes up the magnesium oxide does the same, and conversely when one goes down the other follows suite.
A different look at autocorrelations of calcium and magnesium oxides show that when compared to tonnage they have similar relationship to tonnage. Figures 8 and 9 show the correlation coefficients to be both around 40%. This low correlation shows that calcium and magnesium oxides do not have strong cyclic components with tonnage output.
Further analysis of the relationship between calcium and magnesium oxides to tonnage is shown in figure 11. Here the Fourier transformations have been smoothed and reveal peaks in both the calcium and magnesium oxides at the same frequencies. When these peaks are compared to the troughs in the smoothed tonnage, a lag time is exposed.
The common low frequencies are 0.0032, 0.0099, and 0.0177 cycles per hour. These frequencies were filtered with the low pass filter and compared in figures 15, 16, and 17. The cross-plot of CaO and MgO low pass filters (Fig. 15) now shows little common cyclic components between them (r2 = 0.66). But when they are cross-plotted with tonnage (Figs. 16 & 17), there seems to be no common cyclic component at low frequencies. This is quantitatively represented by the low correlation coefficients of 8% for both the calcium and magnesium oxides.
The common high frequencies are 0.028 and 0.033 cycles per hour. These frequencies were filtered with a band pass filter and compared in figures 21, 22, and 23. The cross-plot of CaO and MgO band pass filters (Fig.21) also shows the common cyclic components between them as previously exhibited. But as seen before, there are low correlation coefficients when the two were compared to tonnage. Figures 22 and 23 quantitatively display the CaO correlation to be 18% and the MnO correlation to be 20%.
Conclusions
From this study, cyclic components can be observed between iron and manganese oxide. The autocorrelations between and against a common variable of the two exhibit this relationship. At a closer look though, iron and manganese oxide have no direct common component with tonnage output. At low frequencies the correlations are different but at high frequencies they are similar but with low correlation. These low correlations can be accounted for with the time lag that the tonnage output has to the chemical concentrations. After this statistical analysis, it can be said that there is no direct cyclic component between tonnage output and iron/manganese oxide concentrations, so the hypothesis must be rejected. Again, this is highly influenced by the time lag.
Secondly, there is a universal cyclic component between the calcium and magnesium oxides. The autocorrelations between and against a common variable of the two exhibit this relationship, like before with iron and manganese oxide. Upon further investigations there is no cyclic component shared between tonnage output and the chemical concentrations in question. The low correlations of the filters quantitatively represent this. Hence, the second hypothesis must be accepted. There is no common cyclic component between tonnage output and calcium/magnesium oxides.
Pertinent References and Acknowledgements
Davis, J.C., 2002, Statistics and Data Analysis in Geology – 3rd edition: John Wiley & Sons Inc., New York, 638 pp.
Klein, C., Hurlbut Jr., C., 1993, Manuel of Mineralogy-21st edition: John Wiley & Sons, Inc., New York, 681 pp.
Figure 1: Area picture of Eisenerz, Austria
Figure 2: Raw concentrations and tonnage vs. time
Figure 3: Autocorrelations of the five data sets
Figure 4: Autocorrelation of Fe vs. MnO (r2=0.87)
Figure5: Autocorrelation of Fe vs. Tonnage (r2=0.46)
Figure 6: Autocorrelation of MnO vs. Tonnage (r2=0.46)
Figure 7: Autocorrelation of CaO vs. MgO (r2=0.78)
Figure 8: Autocorrelation of CaO vs. Tonnage (r2=0.43)
Figure 9: Autocorrelation of MgO vs. Tonnage (r2=0.40)
Figure 10: Unsmoothed Spectra vs. Smoothed Spectra
Figure 11: Unsmoothed Spectra vs. Smoothed Spectra
Figure 12: Cross plot of Low pass filters for Fe & MnO (r2=0.81)
Figure 13: Cross plot of Low pass filters for Fe & Tonnage (r2=0.09)
Figure 14: Cross plot of Low pass filters for MnO& Tonnage (r2=0.24)
Figure 15: Cross plot of Low pass filters for CaO & MgO (r2=0.66)
Figure 16: Cross plot of Low pass filters for CaO & Tonnage (r2=0.08)
Figure 17: Cross plot of Low pass filters for MgO & Tonnage (r2=0.08)
Figure 18: Cross plot of Band pass filters for Fe & MnO (r2=0.87)
Figure 19: Cross plot of Band pass filters for Fe & Tonnage (r2=0.16)
Figure 20: Cross plot of Band pass filters for MnO & Tonnage (r2=0.15)
Figure 21: Cross plot of Band pass filters for CaO & MgO (r2=0.79)
Figure 22: Cross plot of Band pass filters for CaO & Tonnage (r2=0.18)
Figure 23: Cross plot of Band pass filters for MgO & Tonnage (r2=0.20)