(College of Resource Engineering, University of Science and Technology Beijing, Beijing 100083)

Guan Zhining

(Department of Geophysical Exploration, China Geo University, Beijing 100083)

Based on the analysis of previous inversion methods of gravity and magnetic interface, this paper puts forward a magnetization function fitting the distribution of crustal magnetization, and further puts forward a forward and backward iterative algorithm for inversion of Curie depth and magnetic stratum interface depth. This method overcomes the shortcomings of previous methods, saves time and has high inversion accuracy and accuracy. In the research work of the national "Climbing Plan -B" project to find large and super-large deposits, valuable achievements have been made in the geological research of the northern margin of North China Platform and the precious metal prospecting.

Magnetization function; High-precision stratum interface

1 magnetization function and magnetic layer interface model

Different researchers have put forward different hypotheses about the formation mechanism and distribution range of magnetic field sources in the crustal region. The current knowledge comes from lithospheric research and continental scientific drilling. According to the physical profile parameters of the deep crust and the Curie point data of magnetic minerals, we think that the rock magnetism changes with the depth, and becomes paramagnetic when the temperature is higher than the Curie point of magnetic minerals. At the same time, the magnetization of rocks varies with lithology and geological structure units in the lateral direction. This is the basic feature of crustal magnetization distribution. We propose a magnetization function, which can well fit the magnetic characteristics of this crustal rock, as shown in figure1a. The expression is:

Proceedings of the 30th International Geological Congress Volume 20 Geophysics

Where J(ξ, η, ζ) is a function of magnetization, n= 1 or 2, a(ξ, η), b(ξ, η) > 0, and c(ξ, η)≥0 is a variable that varies laterally with different magnetic geological tectonic units.

We use the magnetic stratigraphic model as shown in figure 1b to explain the regional magnetic anomalies. This is a magnetic layer model with fluctuating upper and lower interfaces. The medium above the upper interface of the model is weakly magnetic or nonmagnetic sedimentary rocks, and the rocks below the lower interface (Curie depth) become paramagnetic. There are vertical and horizontal magnetic differences described by magnetization function in the magnetic layer.

2 Iterative method for inversion of magnetic interface depth

Figure 1 Schematic diagram of magnetization function and magnetic stratum model

A—— Crustal structure, magnetization change and magnetization function; B magnetosphere model

In order to use aeromagnetic data to explain the deep geological structure and understand the changes of Curie depth and Archean top depth, we have studied all previous inversion methods in combination with the work of the national "Climbing Plan -B" project. The accuracy and precision of the inversion results are limited because of the low approximation of the crust magnetic hypothesis by traditional methods or the filtering of magnetic anomalies or depth values in the inversion process. Therefore, based on the above magnetization function and magnetospheric model, we study and propose a method of inverse magnetic interface depth by combining positive and negative iterations, which is abbreviated as MIDI in English. In order to save space, the forward calculation formula when n= 1, c(ξ, η) = 0 is given here.

Using the polarization field spectrum of the vertical component Z(x, y) of the plane magnetic field,

Proceedings of the 30th International Geological Congress Volume 20 Geophysics

Where Z()uv and F{} represent Fourier transform or frequency spectrum. J(ξ, η, ζ) is the magnetization of magnetic layer. H (zeta, η) = h+Δ h (zeta, η), and h (zeta, η) = h+η h (zeta, η), which are the depths of the upper and lower interfaces respectively. H, h is the average depth of the upper and lower interfaces. Δ h (zeta, η) and Δ h (zeta, η) are the fluctuation ranges of the upper and lower interfaces, respectively. R(x—ξ，y—η，ζ)=[(x—ζ)2+(y—η)2+ζ2]- 1/2 .f { R } = exp(-2πf)exp[-2πj(uξ+vη)]/f .

Using Taylor series expansion of exponential function, there are:

Proceedings of the 30th International Geological Congress Volume 20 Geophysics

We substitute the magnetization expression (1) into expression (2), and finally derive the magnetic field spectrum expression of the magnetic layer whose magnetism changes with the magnetization function and the upper and lower interfaces fluctuate as follows:

Proceedings of the 30th International Geological Congress Volume 20 Geophysics

The vertical component Z(x, y) of magnetic field can be obtained by actual measurement or Δ t (x, y) conversion.

According to the forward formula, if the depth of one interface is known, the depth change of another interface can be reversed. The part excluding the series term can be directly inverted, which is called direct inversion formula. Iterative inversion can be constructed by combining direct inversion formula with series term. When the difference between the interface depth value of the nth inversion and the depth value of the n- 1 inversion, or the difference between the spectrum values of two adjacent intermediate magnetic fields meets the accuracy requirements, the iterative calculation is terminated.

3 Accuracy of calculation method

Constant magnetization is a special case of MIDI in this paper. In this case, the MIDI method is consistent with the existing method. Under the condition of variable magnetization, the inversion calculation on the theoretical model shows that MIDI inversion can accurately and relatively save time to converge to the known theoretical truth value, whether it is continuous undulating interface, jumping undulating interface (especially the interface undulation caused by large cracks) or the form and amplitude of undulation, but the higher the accuracy of the inversion result, the longer the calculation iteration time. Fig. 2a is an example in which the iteration accuracy is required to reach 5% and then terminated. Iterate 355 times on a 486 microcomputer with 4M memory, which takes 22 minutes. It can be clearly seen from the figure that the inversion depth isoline (dashed line) is almost consistent with the theoretical model depth (solid line).

One of the characteristics of MIDI method is that there is no need to filter the area field value, and there is no need to filter the depth or field value in the inversion process, which may change the characteristics of the field source. Therefore, the inversion calculation speed is fast and the depth resolution ability is strong. The MIDI method is compared with Parker method [4, 10] by using the wavy interface shown in Figure 2b. Calculate the magnetic field value with the same magnetization, and then invert the interface depth fluctuation from the magnetic field. The inversion results are shown in Figures 2c and 2d, respectively. The calculation time of both methods is limited to 20 minutes. Obviously, MIDI method has strong depth resolution.

4 Discussion on average depth

The selection of average depth is always a difficult problem in gravity and magnetic interface inversion. In MIDI algorithm, when one interface is known, because the nonlinear change of magnetization is given in advance, the average depth of another interface to be inverted can be determined by inversion calculation and adjustment. An example of model calculation is shown in Figure 3. Given the average depth value of the upper interface h=2.0km, the depth fluctuation is the model shown in Figure 2b. The average depth of the lower interface H=5.0km, and the lower interface is horizontal. Calculate the magnetic field Z(x, y) of this magnetosphere model. Then, the lower interface is unchanged and the upper interface is reversed. When h takes different values, the mean value (Ria) of the inverted depth fluctuation amplitude δ h (x, y) is different. When the given value is greater than the true value of 2.0, Ria is negative; Ria is positive when the given value is less than the true value of 2.0. The closer the given H value is to the true value, the smaller the Ria is. When h takes the true value, Ria tends to zero (not zero due to calculation error). Ria has obvious directivity to the true value of H, so we can use Ria as an index to solve the average depth.

Figure 2 Accuracy test of theoretical model method

A— The solid line is the depth isoline of the given model, and the dashed line is the isoline of MIDI inversion result. The comparison results between MIDI method and Parker method are given. Example 2: b interface depth model; C-Parker inversion results; D-MIDI inversion results are the same as Parker's method. Depth unit: kilometers

Fig. 3 Adjustment and calculation of average interface depth

When the average depth is close to the true value, the average depth fluctuation (Ria) tends to zero.

5 inversion of Curie depth in Hohhot-Zhangjiakou area

The depth of the lower bound of the crust magnetosphere, that is, Curie depth, is determined by the temperature field of the crust and is an important index of the underground thermal state. This is of great significance to the study of deep geological structure, seismology and mineral prediction. We chose Hohhot-Zhangjiakou area with important deep structure and upper mineral value within 53200km2 to study the inversion of Curie depth distribution. Fig. 4a shows the distribution of Archean strata, magmatic rocks and intrusive basalts in this area. Archean and basalt have strong magnetism. Fig. 4b is an aeromagnetic anomaly map of this area.

Fig. 4 Archaean stratigraphic distribution map (a) and aeromagnetic anomaly map (b) in Hohhot-Zhangjiakou area.

Abnormal value unit: NTD

(1) According to the statistical results of rock and stratum magnetism in this area and related known stratum depth results, the magnetization change data of different depths are roughly obtained, and the magnetization function selected by genetic algorithm [5] is:

Proceedings of the 30th International Geological Congress Volume 20 Geophysics

(2) In order to extract the magnetic field information of Curie depth, regularization filtering (factor L=40Km) is used to eliminate the influence of shallow magnetic variation. The filtering result is considered as a comprehensive anomaly of Curie depth interface fluctuation and magnetic base top boundary fluctuation.

(3) According to the known stratum depth data and artificial seismic profile interpretation [7, 1 1, 13], the approximate depth of the fluctuation of the magnetic basement top interface in the whole area is obtained by interpolation from the known Archean stratum top interface (Ar) position. Its average depth is 3.2km west of 1 14 and 3.5km east of1/4. This depth distribution act as an interface on that magnetic layer.

(4) The Curie depth is adjusted to 33.0km by calculation. According to the intermediate result of the inversion iteration, the difference between the depth values before and after the iteration is 5% as the iteration termination condition, and the obtained inversion result is shown in Figure 5. It can be seen that the main bulge in Curie depth is consistent with the main deep fault structure in this area.

Fig. 5 Change map of residential depth in Hohhot-Zhangjiakou area.

Depth contour unit: km

6 Archean top inversion in Caijiaying area

Polymetallic minerals such as gold, lead and zinc in the northern margin of North China platform are generally closely related to the ups and downs of Archean strata (sometimes with Proterozoic strata), fault structures and magmatic activities (especially Yanshanian intrusive rocks). The Archaean strata are extremely thick and have strong magnetism compared with the overlying strata. Therefore, it has a good physical premise to study the top interface between concealed structures and Archean strata by using aeromagnetic anomalies. We chose the Caijiaying area in Zhangjiakou City, which is deepening and expanding the prospecting, with the scope of 26 1 12km2, and conducted research. Filter the aeromagnetic anomaly of1/200,000 to eliminate the shallow surface interference [12], and use the above Curie depth results to participate in the calculation. See Figure 6 for the results of Archean top depth fluctuation in Caijiaying area. The depth change is almost the same as the inversion result of Bouguer gravity anomaly genetic algorithm in some sections [5]. Combined with the geological structure, magmatic rock distribution and gravity anomaly in this area, we interpret the inversion results as follows.

(1) There are old strata uplift in the south of Caijiaying and Tuchengzi. Caijiaying mine is located in the uplift and depression around the old strata, and now Caijiaying mine is located in the secondary gentle section of the depression. This depression corresponds to an anomaly of relatively low gravity. Due to the low density of Yanshanian magmatic rocks in this area, there should be Yanshanian concealed rock masses in this depression. Rock deformation can be seen on the surface. Similarly, there are similar gentle areas in the south of Tuchengzi and the south of Zhangbei uplift. These two areas should be promising areas for searching for polymetallic deposits such as gold, lead and zinc.

(2) The Cenozoic basalt layer between Shangyi-Zhangbei-Tuchengzi and its northwest should be thin. This can be clearly explained from aeromagnetic maps and filtering results. The Archean uplift in the southwest of Tuchengzi should be under this basalt.

(3) There should be a deep fault between Shangyi and Kangbao (Figure 6). This can be clearly seen from aeromagnetic anomaly map and Archean zenith fluctuation inversion. The magnetic field characteristics on both sides of the fault are completely different from the Archean depth.

Under the support and guidance of Academician Liu Guangding of China Academy of Sciences, the professor gave great help to the geophysical interpretation in Caijiaying area. Teachers such as Professor Tan Chengze from the Paleomagnetism Laboratory of China Geo University, lecturer Yao Changli from the Institute of Geophysics of Chinese Academy of Sciences and associate researcher Hao gave great help to the research work. I would like to express my heartfelt thanks here.

Figure 6 Archean topographic map of Caijiaying area

The dotted line is an assumed deep fault, and the depth data unit is km.

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