All 12 items (silica, alumina, iron oxide, magnesium oxide, calcium oxide, sodium oxide, potassium suboxide, manganese oxide, titanium dioxide, phosphorus oxide, loss on ignition and ferrous oxide content) of these 2 1 rock samples were analyzed by Philips PW2404 X-ray fluorescence spectrometer. The analysis method is GB/T 65438+.
10.4. 1 Quantitative inversion of silica content in surface rocks and construction of spectral index
The emissivity of 2 1 sample is divided into two groups, one group is 15 samples as training samples, and the regression model is established by stepwise regression method, and the other group is 6 samples as test samples for model accuracy evaluation. In order to eliminate high-frequency random noise, baseline offset and multilinear, all samples are subjected to quadratic polynomial filtering noise separation and envelope removal. After removing the envelope, the absorption characteristics of the emissivity curve are more obvious, and they are all normalized to 0 ~ 1, which is more conducive to studying the influence of SiO2 _ 2 content on the transmission and absorption characteristics of the emissivity spectrum. Fig. 10.4 1 shows the comparison of emissivity curves of some rocks before and after pretreatment, with wavelength as abscissa and emissivity as ordinate.
10.4. 1. 1 Construction of regression model
On the training sample set, using SPSS 15.0 (statistical product and service solution) software, the characteristic wavelength of rock is selected by stepwise regression method. Then, based on the selected characteristic wavelength, the regression model of SiO _ 2 content with SCFM(SCFM is the abbreviation of SiO _ 2, CaO, FeO and MgO) index and characteristic band emissivity is established by minimizing the sum of squares of residuals, and the accuracy of the model is verified.
SCFM index reflects the polymerization degree of silica tetrahedron, which is highly correlated with the thermal infrared spectral characteristics of silica minerals in magmatic rocks, and plays an important role in identifying the spectral characteristics of magmatic rocks. The main anions of silicate minerals are SiO4 tetrahedron and its silicon-oxygen tetrahedron skeleton as basic structural units: Si2 O7, Si3 O9, Si4 O 12, SIN-XALXO2n; The cations that constitute silicate are mainly Ca2++, Fe2 ++ and Mg2++. Therefore, the SCFM index is defined as
Figure 10.39 thematic map
Figure 10.40 M304 is used for the spectral test of thermal infrared emissivity of typical minerals.
Fig. 10.4 1 Comparison of spectral envelopes of several silicates before and after treatment.
SCFM = c 1/(c 1+C2+C3+C4)( 10. 18)
Where C 1, C2, C3 and C4 are the percentages of silicon dioxide, calcium oxide, iron oxide and magnesium oxide, respectively.
The relationship between the emissivity and the content of 10.4. 1.2 SiO _ 2 was simulated.
Let the significance level of introduced variables be α in = 0.05, and that of excluded variables be α αout =0. 10. After four steps of stepwise regression, the variables are screened, and the optimal regression equation includes four bands, namely 1 1. 18μm and12.82 μ m. Figure 10.42 shows the correlation between the silica content predicted by the four-band model and the measured value. The results show that the predicted results are ideal, the correlation coefficient between the predicted values and the measured values is 0.942, and the average prediction residual is 3.27, which is 6.6% of the average silica content of all samples (49.59). Among them, the first three bands are in the transmission characteristic band of rock emissivity spectrum, while 9.38μm is the strong absorption characteristic band of rock.
SiO 2 =- 1 17.64-2027.63×b 1+ 1920.24×B2- 100.88×B3+387.77×B4( 10. 19)
R2 = 0.942 ( 10.20)
The emittances of b 1, b2, b3 and b4 are 9.38μm, 1 1. 18μm, 12.36μm and 12.82μm, respectively.
If the significance level of introduced variables is α in = 0. 1, and the significance level of excluded variables is α αout =0. 15, after six-step regression, variable screening is over. Figure 10.43 shows the relationship between model residuals and the number of selected bands, that is, it shows the prediction ability of different models for SiO2 _ 2 content. With the increase of the number of selected bands, the prediction ability of the model is gradually improved. When the number of bands is greater than 4, the model accuracy tends to be stable.
Figure 10.42 Relationship between measured silica content and predicted value of four-band model
Figure 10.43 Relationship between Model Residual and Band Number
Figure 10.44 shows that the model residual of the relationship between the SCFM index of silicate minerals and the emissivity of characteristic bands decreases with the increase of the number of selected bands. When there is only one band, the residual of the model is 0.2, which is 28% of the mean value of SCFM index (0.7 1) of all samples, and the band is1.16 μ m, and the correlation coefficient between the predicted value and the measured value of the model is only 0.52. With the increase of the number of selected bands, the prediction ability of the model is gradually enhanced. When the significance level of introduced variables is α in = 0.05 and the significance level of excluded variables is α out = 0.10, the optimal regression model (00- 1) is obtained when six bands are selected. If the significance level continues to increase, the selected band will continue to increase. However, Figure 10.44 shows that the accuracy tends to be stable when the number of bands is greater than 6 (Table 10.7).
Table 10.7 SCFM exponential optimal regression model to select bands and their coefficients
It is worth noting that the first three selected bands are 1 1. 16μm, 12.82μm and 12.38μm, which are also similar to the first three bands in the SiO2 _ 2 content inversion model. This is not difficult to understand, because SCFM index is also a comprehensive index composed of SiO2 content and several other chemical components, which is significantly affected by SiO2 content. At the same time, there is no band of 9.38μm, which may be that the numerator denominator of SCFM index calculation formula also contains SiO2 content, thus weakening the influence of absorption on SCFM index (Figure 10.45).
Figure 10.44 Relationship between Model Residual and Band Number
Figure 10.45 Comparison between actual SCFM index and predicted value
Construction of spectral index of 10.4. 1.3 SiO 2
Because the thermal infrared hyperspectral imager is expensive and the research and development technology is difficult, it is hoped that fewer bands can be used to achieve the best inversion effect in practical application, so as to design a low-cost instrument. At the same time, the coefficients of the regression model established above are complex, which is not conducive to the practical application of the model. It is necessary to further optimize the combination of these preferred bands and establish the corresponding SiO2 _ 2 spectral index.
This book studies the prediction effect of 12 ratio index and normalized index on silica content. The results show that the correlation coefficient of normalized index is slightly higher than that of ratio index under the same band combination. The correlation coefficient between normalized silica index 1 1. 18μm and 12.36μm and silica content is 0.905, and the correlation coefficient between ratio index and silica content is 0. The second is the normalized index 9.38μm and118 μ m bands, with a correlation coefficient of 0.846 and a ratio index correlation coefficient of 0.84 1 (table10.8; Figure 10.47).
Table 10.8 Different silica indices and their correlation coefficients with silica content
Note: B 1, B2, B3 and B4 represent the emissivity of 9.38μm,1.18 μ m, 12.36μm and 12.82μm respectively.
Figures10.4611.18 μ m and 12.36μm: Relationship between silica index and silica content.
Figures 10.47 9.38μm and11.18 μ m: Relationship between SiO _ 2 index and SiO _ 2 content.
Summary 10.4. 1.4
In this study, the quantitative inversion model and spectral index of silica content based on thermal infrared emissivity spectrum were established. The results show that: ① The silica content can be effectively and quantitatively retrieved by using 1 1. 18μm, 12.82μm, 12.36μm and 9.38 μ m. The correlation coefficient between the predicted value and the measured value is 0.942, and the average prediction residual is 3.27. ② The six bands selected by stepwise regression method can effectively retrieve the SCFM index, and the selected bands116 μ m, 12.82μm and 12.38μm are also important bands for retrieving the silica content. ③ Two kinds of spectral indices of 12 silica were established, among which 1 1. 18μm and 12.36μm bands have the best correlation with silica content, which can be used for geological mapping of silica content.
According to the spectral theory of silicate mineral emissivity, the absorption intensity between 1 1 ~ 14μ m is small, which is mainly caused by the symmetrical vibration of Si-O-Si, Si-O-al, (Si, Al)-O-(Si, Al). In this band, light waves easily enter the interior of rock particles, showing strong. In the model, the 1 1. 18μm, 12.82μm and 12.36μm bands selected according to the stepwise regression method are just within this range. In the spectral range of 8 ~11micron, the strongest absorption characteristic of silicate is caused by the asymmetric stretching vibration of Si-O bond. Silicon dioxide has a strong absorption characteristic in the 8 ~ 9.5 μ m band, which is called Lester-Strong characteristic. However, an important band of the regression model, 9.38μm, is just within this absorption characteristic band.
10.4.2 quantitative estimation of CaO content in surface rocks
Correlation analysis of 10.4.2. 1
Figure 10.48 shows the spectral curves of rock emissivity with different CaO contents measured in the field. It can be seen from figure 10.48 that the emissivity of rocks decreases with the increase of CaO content in the wavelength range of 10.3 ~ 13 micron. In order to quantitatively study the relationship between CaO content and emissivity spectrum in rocks, the following correlation analysis and regression analysis were carried out (Figure 10.49).
Fig. 10.48 spectral curves of rock emissivity with different CaO contents.
Fig. 10.49 correlation between emissivity spectrum and CaO content in rocks
Correlation between (1) emissivity spectrum and CaO content in rocks and minerals
In the experiment, the correlation coefficient between the emissivity spectrum of each band and CaO content in the wavelength range of 8 ~ 14μ m is calculated, and figure 10.49 is the calculation result of the correlation coefficient. The results show that there is a high correlation coefficient between the original emissivity spectrum and CaO content in the range of111.45 micron, and its absolute value is close to 0.8.
(2) Correlation between first-order differential spectrum and CaO content in rocks and minerals.
In order to further reveal the correlation between emissivity spectrum and CaO content, after calculating the first differential of emissivity spectrum, the correlation analysis similar to the original spectrum is carried out, and the result is shown in figure 10.50. The analysis of differential spectrum shows that the first-order differential processing can remove the influence of linear or nearly linear background and noise on the target spectrum and effectively improve the correlation coefficient. This shows that the first-order differential spectrum has high narrow-band prediction ability in estimating CaO content in some characteristic bands. The approximate calculation method of the first-order differential spectrum is as follows:
ε′(λI)=[ε(λI+ 1)-ε(λI- 1)]/2δλ( 10.2 1)
Fig. 10.50 correlation between first-order differential spectrum and CaO content
10.4.2.2 regression analysis
On the basis of correlation analysis, in order to quantitatively estimate the CaO content in surface rocks, a prediction model of CaO content in surface rocks is established, and the regression analysis of CaO content and emissivity spectrum is carried out. In order to find the best prediction model, several typical regression methods are used to model and the modeling results are compared.
On the training sample set, the emissivity characteristic band related to CaO content is selected by SPSS software and Wilks'lambda stepwise method. Then, based on the selected characteristic wavelength, multiple stepwise regression analysis (MLR), principal component analysis (PCR) and partial least squares regression analysis (PLSR) are carried out. The characteristic bands of the original emissivity spectrum are 1 1.28μm, 1 1.23μm and 8.23μm respectively, and the first-order differential spectra are 1 1.40μm and 10 respectively.
Taking the measured CaO content as the abscissa and the predicted value as the ordinate, the regression equations of different models are shown in table 10.9, and the predicted results of different models are shown in figure10.51~10.53. All six models have passed the F test of model linearity and the T test of each regression coefficient, and the determination coefficient of each model is also quite high.
Table 10.9 Regression equation coefficients of different models
Figure 10.5 1 multiple linear regression model
Figure 10.52 principal component analysis model
Figure 10.53 partial least squares regression model
For the original emissivity spectral data, in the MLR model, the sign of the regression coefficient at the wavelength of 1 1.23μm is opposite to the sign of its correlation coefficient, indicating that there are serious multiple correlations among these three bands. Although the correlation coefficient is high, it is not suitable for prediction. Compared with MLR model, the correlation coefficient of PCR model and PLSR model decreased, but there was no sign inversion at 1 1.23μm, which indicated that the model eliminated the influence of multiple correlations and had good prediction effect. PCR model and PLSR model are more suitable for processing original spectral data with multiple correlations.
For the first-order differential spectrum, the prediction effects of all models are greatly improved compared with the original spectrum, and the prediction effects of MLR model and PLSR model are more obvious than those of PCR model, and the determination coefficients are almost equal. This shows that MLR model and PLSR model have the same prediction effect on the first-order differential spectrum.
10.4.2.3 Summary
In this study, the field emissivity spectra of 23 kinds of rock solid samples were measured, and the correlation between CaO content of these samples and the original and first differential spectra of thermal infrared emissivity was analyzed respectively. The results show that it is feasible to retrieve the CaO content of surface rocks by hyperspectral thermal infrared emissivity spectrum, and the CaO content of surface rocks has a good corresponding relationship with the spectral characteristics of thermal infrared emissivity. In the wavelength range of 10.3 ~ 13 micron, the emissivity of rocks decreases with the increase of CaO content. The research results provide a new idea for remote sensing rock and mineral identification.
The modeling results are compared through several typical regression models. The analysis results show that PCR model and PLSR model are more suitable for processing spectral data without differential processing, and the prediction effect of MLR model and PLSR model is better than that of PCR model for first-order differential spectrum.
Some processing methods of hyperspectral data can improve the prediction accuracy of CaO content. The prediction accuracy produced by the first-order differential processing data is obviously different from that produced by the non-differential processing data. Compared with the original emissivity spectrum, the first-order difference spectrum has better prediction effect.