Since the end of last century, Ф. юлевинсонлессинг (1897). Looking at these methods, Some of these methods, such as Pi Negri (19 19) [5], анзаварицкий. At present. The author tries to explore the theory, method and significance of using mathematical geology to explore the genetic information of rock constant typomorphic components in practice. I sincerely hope that readers will correct me if there is something wrong.
2 Functional relationship between chemical composition (C) and temperature (T) and time (T)
In the process of magma crystallization with time passing (t) and temperature decreasing (t), if the pressure (p) remains relatively stable under plutonic conditions, the Si∶O ratio in magma gradually increases (from 0.25 to 0.5) due to the decrease of temperature, which shows that the polymerization degree of silica tetrahedron is a function of temperature. Moreover, silica tetrahedrons with different polymerization degrees have different negative voltage differences, so cations with different positive electricity prices, such as Mg2+, Fe2+, Ca2+, Na 1+ and K 1+, can be attracted according to the order of ion potential and ionization potential from high to low, so as to balance the electricity prices, thus forming different components, and minerals with different structural types can be precipitated in order of decreasing temperature, forming different rock types. The famous K.Rosenbuch( 1898) rule and N.L.Bowen( 1922) reaction series are actually the embodiment and generalization of this objective law.
In this way, in the process of the formation of intrusive rocks, especially plutonic rocks, T is the derivative constant of T, and the change of magma composition C is determined by T. It is concluded that T is a function of T, C is a function of T, and C and T are composite functions. Namely:
Selected works of Fu Debin's geological papers
In a word, the temperature of molten slurry is different at different time, which leads to the precipitation of minerals with different components in turn, so that the chemical composition of molten slurry depends on the temperature change law. This law reflects the change of physical and chemical conditions that depend on diagenesis and mineralization, so it can be used as a theoretical basis for studying the genetic information of rock components.
3. Selection of indicator elements of genetic information
According to the above theory, it is necessary to compare and identify the geochemical properties, thermodynamic characteristics and petrochemistry of constant rock-forming elements in order to select the indicator elements that are most sensitive to temperature conditions and to study genetic information.
Si4+, Al3+ and Fe3+ are high valence cations, which mainly exist in the form of complexes in magma. In particular, Si4+ with ionic potential greater than 10 always forms [SiO 4]4- silica complex with oxygen ions, which forms the anion skeleton of silicate minerals, while Al3+ mainly coordinates and binds with silica complex four or six times by replacing Si4+ in rocks. The substitution of Al3+ for Si4+ produces a negative price difference, which attracts K 1+ and Na 1+ to form feldspar minerals. If the alkali content in the molten slurry is insufficient, Al3+ will combine with Ca2+ to form anorthite molecules of plagioclase. If the elements of K, Na and Ca in the molten slurry are poor, Al3+ will appear in garnet, pyroxene, amphibole and other minerals in the form of sixth coordination with silica complex. In the rare case that aluminum in molten slurry is strongly supersaturated, Al3+ forms special alumina-corundum and spinel minerals. Obviously, the change of Al3+ content during the evolution of molten magma is increasing and decreasing with time, and it is not sensitive to temperature change, and the change range is not large in intermediate-acid rocks, so it does not have the function of indicating components. Similarly, Fe3+ can exist in silicate and aluminosilicate, and can also form its own oxide minerals-magnetite, hematite, etc. Therefore, it is not suitable to be selected as an indicator element.
The low-valent cations of K 1+ and Na 1+ are characterized by the weakest bond energy, large ionic radius and small nuclear charge and ionic potential.
Ca2+, Mg2+ and Fe2+ are all between the two groups of ions in bond energy, ionic potential and bonding degree with oxygen. The ion radius is moderate, the ion potential is between 1.9 ~ 2.7, and the splitting bond energy with oxygen is 99 ~ 1 16 kcal/mol. Among them, Mg2+ and Fe2+ have higher ionic potentials than alkali metals, so they first enter pyroxene and magnetite in alkaline molten slurry. Compared with Si4+ and Al3+, Mg2+ and Fe2+ have lower ionic potential and bond energy with oxygen, so oxygen cannot be extracted from Si-O and Al-O structures, but weak cations in silicic acid complexes with simple structures can be squeezed out, so that olivine and pyroxene composed of the simplest island or chain-like silica complexes can be combined at the earliest time of slurry crystallization, and then banded or layered amphiboles with complex structures can be formed. Only in this way, in the process of magma crystallization evolution, the contents of magnesium and ferrous iron decrease with the decrease of temperature, so they are a pair of main rock-forming elements sensitive to temperature and other conditions, and both of them can be used as indicator elements. However, due to the different ionization degrees of Mg2+ and Fe2+ connected with anions, Fe2+ tends to form compounds with S2- anions which are easily polarized, and their electronegativity is quite different. Secondly, Fe2+ mainly exists in dark rock-forming minerals in the form of isomorphism with Mg2+ replacement in molten magma. Mg2+ can replace the fossilization of Fe2+ to some extent, so Fe2+ can not be considered in indicator elements. As for Ca2+, with the increase of SiO _ 2 content during the evolution of molten magma, its content curve is parabolic, and the peak value is located at SiO _ 2 = 45%, that is, just at the boundary between ultrabasic rocks and basic rocks, which is sensitive to temperature, so it has a special function of indicating genetic information.
To sum up, K 1+, Na 1+, Ca2+, Mg2+ and other major constant rock-forming elements are low-valent cations in molten magma, which have strong affinity with oxygen and appear in the lattice of rock-forming minerals in the form of free ions, and are most sensitive to the changes of physical and chemical conditions such as temperature during the crystallization of molten magma, so it is ideal to choose them as typomorphic components or indicator elements for studying genetic information.
Drawing parameters and describing function images
The following parameters (calculated by atomic number) are formulated according to the actual distribution law of major rock-forming constant elements cations Mg2+, Ca2+, Na 1+ and K 1+ during the evolution of molten magma, their internal relations in rocks, their functions in minerals and the rock genetic information to be reflected.
Selected works of Fu Debin's geological papers
As mentioned above, t is determined by t, so the temperature gradient of molten slurry cooling is:
Selected works of Fu Debin's geological papers
For rocks of the same genetic series, the relationship between constant canonical component parameters and temperature gradient is functional. that is
Selected works of Fu Debin's geological papers
Therefore, these parameters are also functional relationships:
Selected works of Fu Debin's geological papers
Because the main parameter is the function relation, it can be represented by some function images [8]. Just like most things in nature develop by curves, there is also a curve relationship between two pairs of variables, namely parameters M and A and parameters M and C. Graphical representation can provide an intuitive possibility for studying the changing laws and processes between functions by geometric methods, which is helpful to reveal the genetic information contained in each component function.
The calculated parameter values are displayed on the plane rectangular coordinate system with horizontal axis M, vertical axis A and vertical axis C, and then on the basis of geological and petrological research, the coordinate points are fitted into two functional curves of ma and mc according to a certain functional relationship. The two curves represent the distribution law of constant typomorphic components of rocks with temperature change (Figure 1, Figure 2 and Figure 3).
Because the curves of ma and mc represent the changing trend of magnesium-alkali ratio and magnesium-calcium ratio respectively, it is conceivable that the curves of ma and mc are also functional.
It should be pointed out that, according to the author's statistics, although the deviation of equivalent M value of two same rocks invaded at the same time is less than 1, and the corresponding deviation of A and C values is less than 2, due to the influence of some random factors, it is necessary to fit the curve. Therefore, the author adopts the following two empirical curve equations:
Selected works of Fu Debin's geological papers
Representing ma and mc curves respectively.
Where: ya stands for parameter a; Yc stands for parameter c; X represents the parameter m; E is the base of natural logarithm, which is equal to irrational number 2.7183 ...; A, b and c are undetermined constants. In practice, the above two empirical equations fit the curve well.
In order to express the relationship between m and a, m and c with more accurate quantitative relationship, it is necessary to determine the correlation equation of the curve. The method and steps are as follows:
(1) Make a scatter plot.
(2) Throw the calculated values of parameters M, A and C into rectangular coordinate system to get scattered points, and then press M to connect points A and C into ma and mc function curves.
(3) Find the undetermined constants A, B and C, and specifically determine the curve type.
Because these two curve equations cannot be directly transformed into linear functions, A, B and C can be easily obtained by multiple regression methods.
Selected works of Fu Debin's geological papers
(1) Converts a curve function into a straight line function. Take two sides of the equation as the natural logarithm with E as the base:
Selected works of Fu Debin's geological papers
Let y=lnya, x 1=lnx, x2=x, b0=lna, B 1 =-c, B2 =-b, and rewrite the equation y = lnya = lna-clnx-bx as follows:
(2) According to the value list of x and ya, find: y=lna, x 1=lnx, x2=x, x2 1, x22, x 1x2, x 1y, x2y, and find their sum and arithmetic mean respectively.
(3) Find variance and mean square error:
Selected works of Fu Debin's geological papers
(4) Column normal equation:
Selected works of Fu Debin's geological papers
Solve the normal equation to get b 1, b2.
(5) Find b0:
Selected works of Fu Debin's geological papers
(6) According to b0=lna, find a=eb.
Selected works of Fu Debin's geological papers
(7) Since B2 =-b and B 1 =-c, it can be concluded that B =-B2 and c =-b. After finding A, B and C, the curve type can be determined in detail.
(8) Substitute the x value of each point into the specific curve formula to calculate the corresponding ya value. Connect ya points to get the fitting curve.
Yc=c+bx+ax2 curve
(1) let b0=c, b 1=b, b2=a, x 1=x, x2=x2, then the equation yc=c+bx+ax2 can be rewritten as:
Selected works of Fu Debin's geological papers
(2) The following steps (2), (3), (4), (5), (6), (7) and (8) of the homography algorithm.
(3) The quadratic curve yc=c+bx+ax2 has a maximum value, and the x value of the maximum point can be obtained by derivation:
set up
Selected works of Fu Debin's geological papers
rule
Selected works of Fu Debin's geological papers
Substituting the x value of the maximum point into the equation yc=c+bx+ax2, the corresponding yc value can be obtained.
Cause information of five-function images
Because the original solid composition of magma is different, the initial temperature of molten magma formation is also different, which determines that the initial molten magma composition is not uniform. In addition, the differences in the depth, shape, size, surrounding rock composition and structural conditions of the molten magma abyss or magma chamber make it impossible for the compound rock mass invaded twice or more to have the same temperature gradient and other formation conditions. There will be no difference in the composition of the rock mass invaded continuously in the same place (even if the rock mass invaded for the first time has not been cooled or completely cooled, the molten slurry invaded for the second time), especially in the physical and chemical conditions such as temperature gradient, which is the premise of analyzing and judging the genetic information of the function image. 5. 1 Genetic information provided by discontinuity and continuity of function curve image
From practice, the author sums up four types of constant regular component parameter function curve images (Figure 1). One is a single pair of continuous curves (figure 1(a)), which shows the evolution characteristics of the initial invasion and crystallization of molten slurry of the same genetic series, that is, the temperature gradient and other medium conditions of molten slurry are gradually changed during condensation. The other is a double pair continuous curve (figure 1(b)), which shows that the rock mass studied belongs to two genetic series or two stages of magmatic intrusion products, and each stage has perfect continuous evolution characteristics. The third type is a pair of discontinuous curves which are discontinuous on the same slope (Figure 1(c)). If the sample is fully representative, this discontinuity indicates that the rock mass intruded from the same source, at the same time and at different times, which is closely related to the pulsating activity of diagenetic control structures and is also a sign that deep magma experienced liquid melting. The last one is a step discontinuity or two pairs of discontinuous curves (figure 1(d)), which indicates that the rock mass was formed by two periods or two genetic series of molten magma activities.
The genetic information provided by the discontinuity and continuity of the curve image of the canonical component parameter function of rock constant is of great significance to identify the hidden contact relationship, determine the single and composite rock mass, study the genesis of related contemporaneous deposits, and is also conducive to metallogenic prediction and prospecting. A large number of facts repeatedly show that in the same tectonic-magmatic cycle, it is often the late intrusive body (or phase) with high ore-bearing probability; In the same complex rock mass, it is superior to the late intrusive lithofacies, especially taking the basic-ultrabasic copper-nickel deposit as an example.
Figure 1 constant standard component parameter function curve image
5.2mc genetic information of extreme points of mc curve
As mentioned above, petrochemical research shows that the change law of calcium content in magmatic rocks has special indicating significance. With the maximum value CMax of mc curve as the boundary, one side is poor in alkali, and the alkali content increases slowly in the process of magma crystallization, and the chemical action of calcium in the rock gradually increases to the peak along mc curve, while magnesium is the opposite; The other side is far away from the peak point and the alkalinity increases sharply, so its petrochemical action quickly surpasses that of Fe-Mg plasma, and the calcium content gradually decreases. Therefore, the extreme point (CMax) is essentially the critical composition point of calcium. So CMax provides some data of rock composition and magma crystallization temperature.
Genetic information of 5.3m M/CMax ratio
The ratio of mM/CMax can reveal the temperature gradient information of magma cooling. When the ratio is small (when the value of mM is small and the value of CMax is large), it shows that calcium, which is involved in the composition of plagioclase, is dominant in magma for a long time, and the magma cools slowly and the temperature gradient is small. When the ratio is large, it shows that alkali metals dominate the magma, and the magma cools quickly and the temperature gradient is large. When the proportion is moderate, it is a common normal situation, and the temperature gradient at this time is normal. The ratio of mM/CMax usually varies from 0. 1 to 1.
5.4 Genetic information provided by the position of the image in the coordinates
Author in аеерсман [10], ап. лнхач.
(1) early high temperature (>: 1500 ~ 1600℃) Fe-Mg magma containing platinum and chromium;
(2) intermediate temperature (900 ~ 1500℃) calc-iron magma containing titanium and nickel;
(3) Late hypothermia (
According to the average chemical composition of magmatic rocks in China (thomas lee et al., 1963) [12], the positions of the above three kinds of magma on the function image are shown in Figure 2. Information about the genesis, composition and mineralization characteristics of the studied rocks can be obtained from Figure 2. But this problem is still immature and needs further exploration.
Fig. 2 The average composition parameter function curve and magma classification image of magmatic rocks in China.
To sum up, the image of constant canonical component parameter function curve of intrusive rocks can reveal a series of important genetic information problems such as homology, genetic series, intrusion period, crystallization differentiation, condensation rate and diagenetic temperature gradient of molten magma.
Six examples
The constant canonical component parameters and their function images of more than ten kinds of nickel-bearing basic-ultrabasic rocks at home and abroad have been studied. The revealed genetic information not only enables the author to discover the hidden intrusive contact relationship, but also greatly promotes the study on the genesis of magmatic copper-nickel sulfide deposits. Taking a basic-ultrabasic rock mass of a copper-nickel sulfide deposit discovered for the first time and studied in detail in China as an example, the research method and its effect are briefly described.
The rock mass in the list has mined copper and nickel ore from 1752. During the period of 1939 ~ 1947, Ruan Weizhou and Guo successively did geological work in the mining area. Since the founding of New China, many geologists have done a lot of in-depth research on the geological genesis of this deposit since 1954, and published some works [13 ~ 16]. It is almost agreed that the basic-ultrabasic rocks are the cause of an intrusion and in-situ crystallization differentiation, and the copper-nickel sulfide deposits contained in them belong to the typical magma in-situ crystallization and melting in China.
Obviously, whether the deposit is a magma in-situ crystallization melting deposit depends on whether the ore-bearing rock mass is a single intrusive rock mass or a multi-stage intrusive composite rock mass.
Based on the supplementary exploration work of Chuanye 60 1 Team, the constant typomorphic composition parameters of rock mass and their function images are studied. The results show that the ore-bearing complex rock mass invaded by two rock systems and ultrabasic peridotite facies invaded in the later stage belong to deep ore-forming slurry infiltration, not crystalline molten deposits formed by in-situ crystallization differentiation. According to the method described in this paper, as follows.
(1) According to the table in the appendix 1 of the document [1], the weight percentages of MgO, CaO, Na2O and K2O in the intrusive body are converted into atomic numbers. By the way, the specific copper-nickel mineralization has no effect on the suggested parameters of magnesium, calcium and alkalinity, so it is unnecessary to consider them.
(2) Calculate the parameters of M, A and C, and the accuracy is 0. 1. The calculation results are listed in table 1.
Table 1 calculation result
* In the table,1~ 5,8 ~10 is diorite-gabbro; 6 ~ 7 are gabbro; 1 1 ~ 16 is ore-bearing peridotite.
(3) Put points on the plane rectangular coordinate system with equal scale, and connect the points to form a parametric curve function image (Figure 3). Two pairs of curves can be seen from Figure 3. The points of a pair of curves are 2, 3, 4, 5, 8, 9, 10. The dot numbers of the other pair of curves are 1, 6, 7,1,12, 13, 14, 15 and 16.
Fig. 3 image of parameter function curve of constant typomorphic components of nickel-bearing basic-ultrabasic rocks.
(4) The function curve obtained by empirical equation fitting. Due to the limitation of space, the specific operation steps are omitted.
(5) Analyze the genetic information revealed by the function curve image (Figure 3): ① There are two pairs of curves (ma 1, mc 1 and ma2, mc2) in the fitting function curve image of rock constant regular component parameters, which indicates that the rock mass is a composite rock mass formed by two-stage intrusion of magma, rather than a simple rock mass. ② Combined with petrological research, it is further recognized that the first stage intruded into intermediate-basic diorite gabbro, and the second stage intruded into ultrabasic rock-bearing peridotite. It should be pointed out that the latter function curve shows discontinuous characteristics on the same slope, indicating that the magma invaded in the second stage has two intrusions or two stages. ③ The ultrabasic lithofacies invaded for the second time in the second intrusion period is rich in copper-nickel sulfide, which indicates that the lithofacies formed in the middle and late intrusion period of the same complex rock mass has good ore-bearing property. ④ The mM/CMax values of the first and second intrusive lithofacies are 0.7 1 and 0.32, respectively, indicating that they are formed in different temperature gradients, and the former crystallizes slower than the latter. ⑤ The magma that formed the complex rock mass experienced deep liquid stratification and differentiation. The main ore-rich bodies are formed by the infiltration of sulfide-rich slurry formed by deep liquid differentiation of molten slurry, rather than by in-situ crystallization and melting.
In the process of writing this article, I received the careful guidance of Wang Hengsheng and the enthusiastic help of Yu, Sui Hongwei and Du Youshi, and I am deeply grateful.
refer to
[ 1] Четвериков С Д.Руководство к петрохимическим пересчетам.госгеолхиздат, 1956
[2] Заварицкий А Н.В ведение в петрохимию изверженных горных пород.изд.АН СССР, 1950
Wang Hengsheng, Bai Wenji. Chemical calculation and graphic method of basic rocks and ultrabasic rocks. Journal of Geology,1975 (1): 77 ~ 91.
Wu liren Metallogenic specificity of basic and ultrabasic rocks in China. Geological science, 1963 (1), 29 ~ 4 1.
[5] niggli p. Swiss oil company. Vierteljahreschrift der Naturfoschenden Gesellschaft in Zurich, 19 19, (64), Heft 1 ~ 2.
[6] Бетехтин А Г.Академик А.Н.Заварицкий иэбранные труды.изд.АН СССР. 1956,с: 2 1 1 ~ 232.
[7] Кузнецов Е А.О способах пересчета и изображения химического состава магматических горных пород.Вестникмосковского университета, 1947 ( 3)
[8] Mathematics Department of Jilin University. Mathematical analysis. Beijing: People's Education Press, 1978.
Fu debin. Discussion on the genesis of Cu-Ni sulfide deposit in 40 1 mining area 1 rock mass. Geology of Jilin,1982 (4):1~16
[10] Department of Geology, Nanjing University. Geochemistry. Beijing: Science Press, 1962: 2 12.
[ 1 1] Лихачев А П.О природе магматических месторождений.сов.геол. 1963,( 5)
[12] Average chemical composition of China magmatic rocks such as thomas lee. Journal of Geology, 1963, (3)
[13] A sulfide-bearing peridotite from Sichuan. Geological society of china bulletin. 1936 ( 4) : 3 ~4
[14] Duan Guolian et al. Geology of disseminated copper-nickel sulfide deposits in western Sichuan. Geological Monthly, 1958, (9)
[15] Zhang Yunxiang. Discussion on metallogenic regularity of Limahe copper-nickel deposit. Geological Monthly, 1958, (6)
Zhang Qinglin. Genesis of Cu-Ni sulfide deposits. Geological Review, 1958, (6): 448 ~ 450.
Function diagram of common typomorphic components of intrusive rocks and its genetic information
abstract
Magma is a complex multiphase ionic electronic liquid, which is mainly composed of semi-isomorphic groups of SiO _ 4 and oxides of positive metal ions in coordination polyhedron [MEOX] 2x-N.
After magma intrusion, the ratio of silicon to oxygen increased (from 0. Twenty-five to zero. 5) As the temperature drops. Therefore, the semi-crystalline state of SiO _ 4 is different under different temperature conditions; Silica with different axes attracts different metal cations to form minerals with different structures and compositions, which are separated in turn.
With the decrease of temperature, the chemical components are precipitated in the following order: Mg → Fe → Ca → Na → K. The author thinks that temperature (t) is the derivative constant of time (t) in the formation of intrusive rocks. The change of magma composition (c) is controlled by time (t). The author has come to the conclusion that temperature (t) is a function of time (t); Component c is a function of temperature t. There is a complex functional relationship between c and t (i.e. T = h (t), C = g (T), C = f[h (t)]). The above functional relationship is the theoretical basis for studying the source of rock components.
According to the geochemical characteristics, thermodynamics and petrochemistry of rock-forming elements. The common typomorphic components (Mg, Ca, K +Na) which are most sensitive to temperature are selected as indicator elements for studying genetic information. Then, the atomic number parameters of magnesium (m), calcium (c) and alkali (a) are calculated according to the following formula:
Selected works of Fu Debin's geological papers
The calculated parameters are plotted on the coordinates with the abscissa m and the ordinate a and c; At the same time, a and c are connected with m respectively, forming two curves of ma and mc. The function diagram is obtained from the empirical curve equation:. By analyzing the discontinuity and continuity of the parametric function diagram, the position of Cmax and the ratio of mM/Cmax are determined. Information about genetic relationship, genetic series, invasion stage, crystallization differentiation, cooling ratio, formation temperature and gradient can be obtained. These data are very important for studying magmatic diagenesis and the genesis of orthomagmatic deposits.