In view of the above situation, we often have to study the chemical composition of rocks by means of mathematical simulation, so as to spy out the genetic information of chemical composition from the vast random interference. Therefore, the author designed the petrochemical genetic information method [1] to explore the genetic information contained in petrochemical components. The principle, calculation process and function curve meaning of this method have been discussed in another document [2]. Through an example, this paper focuses on solving the problem of fitting the parametric function curve of constant regular components for readers' reference.
1 Brief introduction of parameter calculation method
Under normal circumstances, with the decrease of temperature, the ratio of Si∶O in magma chamber magma increases, and the polymerization degree of silicon-oxygen tetrahedron groups is enhanced. Therefore, in the process of crystallization, silicate rock-forming minerals with island, chain, belt, layer and frame structure are sequentially precipitated from magma (table 1). The order of elements reflected in the chemical composition is as follows:
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Obviously, the chemical composition of intrusive rocks is a function of temperature, so we can explore the conditions such as formation temperature by studying the chemical composition of rocks.
Therefore, the author chooses Mg, Ca, K and Na, which are most sensitive to temperature change, as typomorphic indicator elements of genetic constants, and calculates them into three parameters (calculated by atomic number) as follows:
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Table 1 Summary of polymerization degree of siloxane tetrahedron and characteristics of metal cation ligands and minerals formed.
* According to A.л Yegrov,1962; * * Press гггггггггггггггггггггг, 1936.
Then, with the horizontal axis as m and the vertical axes as a and c, the calculated parameter values are drawn in the rectangular coordinate system with equal proportion, and the points A and C are connected respectively to form two parametric function curves of ma and mc. By analyzing these two curves, we can get genetic information such as magmatic genetic series, intrusion stage, in-situ crystallization differentiation, condensation rate and crystallization temperature gradient. The revelation of these information is very important for studying magmatism, diagenetic and metallogenic characteristics and distinguishing simple rock mass from composite rock mass.
2 curve fitting formula
In order to fit the constant regular component parameter function curve, the author determines the curve equation formula according to the measured curve shape type, which is proved to be effective by several examples and used as the empirical formula for curve fitting:
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① and ② represent 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 specific constants.
Because the above two curve equations can't be directly transformed into a linear function, A, B and C can be simply obtained by multiple regression, which is described as follows:
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(1) Change the curve function to a straight line function.
Therefore, the natural logarithm with E as the base on both sides of the equation:
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Let Y=lnyA, X 1=lnx, X2=X, B0=lnA, B 1 =-c, B2 =-b.
Therefore, the equation y = lnya = lna-clnx-bx can be rewritten as: Y=B0+B 1x 1+B2x2.
(2) According to the list of x, yA values:
Y=lnA, X 1=lAx, 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
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(4) A set of normal equations
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Solve the normal equations to get b 1, b2.
(5) Find B0
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(6) According to B0=lnA, find A=eB0.
(7) Since B2 =-b and B 1 =-c, it can be concluded that B =-B2 and C =-B 1. After finding a, b and c, you can determine the curve type in detail.
(8) Substitute the X value of each point into the specific curve formula, find the corresponding yA value, and connect the drawn yA points to get a fitting curve.
YC=C+Bx+Ax2 curve
(1) let B0=C, B 1=B, B2=A, X 1=X, X2=X2, then the equation:
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Can be rewritten as:
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(2) Find (1), (2), (3), (4), (5), (6) and (7) of the same curve algorithm.
(8) Step.
(3) The quadratic curve yC=C+Bx+Ax2 has a maximum value, and the x value of the maximum value can be obtained by derivation:
Settings:
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Then:
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(4) Substitute the X value of the maximum point into the equation yC=C+Bx+Ax2 to get the corresponding yC value, and draw on the coordinates and connect to get another fitting curve.
3 curve fitting example
Practice shows that due to the influence of random interference factors such as assimilation and contamination, hydrothermal alteration, the A and C values of rock mass formed in the same period often change to some extent (generally
3. 1 general situation of rock mass
The listed rock bodies are located in the middle of Kangdian axis, east of Zhuo Da fault of Anning River, controlled by the second-order north-south fault, and intruded into limestone and quartzite of Huili Group of Lower Proterozoic before Sinian.
Since 1752, copper-nickel alloy has been smelted from the ore of rock mass, which has a history of more than 200 years. During this period, a lot of production and scientific research work have been done on this rock mass. Up to 1972, this rock mass has always been considered as a typical intrusive in-situ crystalline differentiation simplex rock mass, which is divided into diorite gabbro, gabbro and peridotite, and the copper-nickel sulfide deposits contained in it are also considered as typical in-situ crystalline dissolution genetic deposits. Moreover, as a typical example of in-situ dissolution deposition, it is included in the teaching materials and related documents of universities and technical secondary schools. In the early 1970s, the supplementary exploration work of Chuanye 60 1 Team found that the ore-bearing peridotite facies was late intrusive rock, which was in intrusive contact with gabbro. After 1980, the author's observation and study show that diorite, gabbro and peridotite facies are all intrusive contact relations. Therefore, the rock mass is actually a composite rock mass formed by multi-stage intrusion (Figure 1).
Figure 1 Geological Profile of Copper-bearing Nickel Ore Body
3.2 Curve fitting
See Table 2 for simple chemical analysis results and calculation parameters of various lithofacies of rock mass.
Plot the parameter values of m, c and a in Table 2 in rectangular coordinate system according to the above method, and get two groups of function curves (ma 1, mc 1 and ma2, mc2), with a group of point numbers of 2, 3, 4, 5, 8, 9,10; The other group of dot numbers are 1, 6, 7,1,12, 13, 14, 15, 16 (.
Table 2 Constant Typomorphic Composition and Parameter Table of Copper-nickel Bearing Rock Mass
Fig. 2 image of constant regular composition parameter function of copper-nickel bearing rock mass
Now the obtained function curve is fitted with the above empirical formula, and the method steps are as follows:
A curve connected by points 2, 3, 4, 5, 8, 9, 10.
(1)ma 1 curve:
Let yA stand for a and x stand for m, then
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1) The natural logarithm with E as the base takes both sides of the equation:
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Let X 1=lnx, X2=X, Y=lnya, B0=lnA, B 1 =-c, B2 =-b, then
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2) List (Table 3) Calculate x, yA, y, X 1, X2, X2 1, X22, X 1X2, X 1y, X2y and their sum with the arithmetic average.
Table 3 Calculation Table of Copper-bearing Nickel Ore Body Curve
3) Find variance and mean square error:
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4) List the normal equations:
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Solve the equation:
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②-① 0.7534B2 = 0。 0 194.
rule
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5) Find B0:
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6) According to B0=lnA, find out a:
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7) Since B2 =-b and B 1 =-c, B=0.02575.
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8) specifically determine the curve type:
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9) Substitute different x values.
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Get the corresponding yA value (2 in Table 4), plot and connect the coordinate points, and get the theoretical curve of ma 1 (Figure 2).
(2)mc 1 curve:
Table 4 Calculation results of parameter function curve of copper-bearing nickel ore body
Let yC stand for C and X stand for M, then: yC=C+Bx+Ax2.
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 y0 = B0+b1x/kloc-.
2) Calculate yC, X, X 1=X, X2=X2, X2 1, X22, X 1X2, X 1yC, X2yC and their sum with the arithmetic average.
3) Find variance and mean variance:
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4) List the normal equations:
Table 5 Calculation table of yC=C+Bx+Ax2 curve of copper-nickel bearing rock mass
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Solve the equation:
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②-① Obtain:
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5) Find B0:
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6) Because B0=C, B 1=B, B2=A, therefore,
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7) specifically determine the curve type:
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8) Substitute different X values into yC = 33.07+0.7287-0.1149x2 to get the corresponding YC values (Table 4). Draw and connect the coordinate points to get the theoretical curve of mc 1
9) Find the maximum value:
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Curves connected by points 1, 6, 7, 1 1 ~ 16.
The fitting method of the curve connected with points 1, 6, 7,1~16 is the same as above, and will not be described here. The main calculation results are as follows:
(1)ma2 curve
Calculation data of x, yA, y, X 1, X2, X2 1, X22, X 1X2, X 1y, X2y, etc. Listed in Table 6.
Table 6 Calculation Table of Copper-bearing Nickel Ore Body Curve
(2)mc2 curve type
1)L 1 1=0.9958，L22=3320.28，l 12 = l 2 1 = 57.339 1，L 1y=-2. 106 1，L2y =- 122. 122
2)A= 15.9 159，B=0.04706，C=-0.5948
(3)yA curve type
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(4) See Figure 2 for the theoretical curve of Ma2 (curve ma2 curve).
(5)mc2 curve
The calculation results of 1)yC, x, X 1=X, X2=X2, X2 1, X22, X 1X2, X 1yC, X2yC, etc. are listed in Table 7.
2)L 1 1=3320.28，L22=49358889.77
L 12=L2 1=404675.66，L 1yC=- 1955.74
L2yC=-239 132.89
3)A=-0.006222，B=0. 1682，C=4 1.44
Table 7 Calculation table of yC=C+Bx+Ax2 curve of copper-nickel bearing rock mass
yC = 4 1.44+0. 1682 x-0.006222 x2
The theoretical curve is shown in Figure 2 (mc2 curve):
4) Maximum value:
X= 13.52
yC=42.57
4 image cause information analysis
(1) The constant typomorphic component parameters of rocks are distributed into two sets of function curves (ma, mc 1 and ma2, mc2 in Figure 2). This shows that the rock mass is a two-stage intrusive rock or a composite rock mass with two genetic series.
(2) The intermediate-basic diorite gabbro was invaded in the first stage, and gabbro was invaded in the second stage.
(3) 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.
(4) The rocks invaded in the second stage are discontinuous on the same slope, which further reveals that there are two intrusions in the second stage, one is gabbro and the other is peridotite.
(5) During the second intrusion, the second intrusion (or stage) opened the ultrabasic magma, which is essentially sulfide-rich slurry. This shows that in the same complex rock mass, the late intrusive rock mass has good ore-bearing property.
(6) The molten magma forming the composite rock mass is immiscible with the deep liquid, and the sulfide-rich slurry formed by the deep liquid differentiation of the molten magma in the main ore-rich system permeates into mineralization, which is not caused by in-situ crystallization and melting.
refer to
[1] Fu Debin, 19865438+
Fu debin, Cui, 1984, function image of constant typomorphic composition parameters of intrusive rocks and its genetic information, journal of geology.