3.1 Magnetic Effect of a 3D Mass in a Forward Method
One of the essential measures in magnetometry is the magnetic susceptibility of the rocks. The magnetism observed in each rock consists of inductive and residual components. In the inversion, one of the calculations required is forward modeling (Doulati Ardejani et al., 2011; Moradzadeh et al., 2005; Moradzadeh et al., 2021). The magnetization depends on the contrast of the magnetic susceptibility of the mass with surrounding rocks for an inductive magnetic field (Hosseini et al., 2013; Hosseini et al., 2014). When the susceptibility contrast is minimal, the magnetization is proportional to the magnetic susceptibility contrast and equal to its product in the inductive magnetic field. In practice, under the earth surface, following Fig. 3, it is divided into tiny prisms, and the cell is given a constant value of the magnetic susceptibility contrast, and the magnetic field obtained from them is calculated (Tsokas & Papazachos, 1992; Utsugi, 2019).
prism extending from the depths za to zb, first should calculated Equation 3 for a prism with a depth of za and magnetization M, then for a prism with a depth of zb and magnetization –M. By coding in MATLAB using equation 3, the anomaly of the total magnetic field caused by a prism can be calculated at a viewpoint (Diethart-Jauk & Gegenhuber, 2018; Hubbert, 1948; Lelièvre & Oldenburg, 2006; Stocco et al., 2009).
3.2 Modeling of Artificial Magnetic Data
In Fig. 4, the magnetic field of a cube-shaped 2D block is calculated using the MATLAB function and equation 3 for slopes 0, 30, 60, and 90 degrees. The angle of inclination varies sharply for different slopes, and for slopes 0 and 90 degrees, the diagram's meeting point of the angle of inclination with the x-axes (x = 0) is close to the edges of the 2D model (Mallick & Sharma, 1997; Stocco et al., 2009).
Fig. 5 shows the magnetic anomaly on a square prism. This model is a cube with geometric and physical parameters located at a depth of 2 km (Agocs, 1951; Loke & Barker, 1996; Zhou et al., 2015). The remaining cubic density is 1000 kg/m3, and its length, width, and thickness are 2 km. The MATLAB function calculates the magnetic anomalies caused by this model, two for loops, and a definition of a Surveying grid with dimensions of 20 km × 20 km and with 50 m × 50 m at the base level (z = 0). The anomalies of the total magnetic field are calculated by MATLAB function, taking into account the 60-degree inclination angle and the deviation angle of 0 ° for the earth's magnetic field, the magnetization vector, and the magnitude of magnetization 1 A / m. The position of maximum points and the shape of this signal can be used to identify the regular fountain's boundaries and estimate its depth. In Fig. 5, another processing that can significantly help detect abnormalities is analytic signal processing. This process amplifies the anomaly edges and displays the magnetic bipolar as outstanding anomalies used to model the Surveyed data.
3.3 Survey Grid Design
Due to the extent of the area and the mineralization debris and tectonic conditions that are the main mineralization factors in each region, the Survey grid was first selected in the form of profiles of 20 m and Survey points at a distance of 10 m. Given the evidence and the structural appearance of the mineral mass, the eastern - western data mining direction was selected to discontinue the mineralization of the exploration area. While the survey, according to the range of magnetic field changes during the measurement and according to the priorities in the area, the distance between the Survey profiles was reduced up to 10 m, and the distance between the stations reduced up to 5 m. In total, with the performed design, there are 1000 reading measurement points, which this exploration network covers an area of approximately 21 hectares. In Fig. 6, the Survey grid is shown for the first zone. The magnetometer used in this survey is GEM made in Canada. The sensitivity of this device is up to one-tenth nanotesla, and it is equipped with DGPS. The earth's magnetic field changes with latitude, longitude, and time are calculated by the complete empirical computational equations known as the International Geomagnetic Reference Fields (IGRFs). This information is very useful in obtaining actual field values and regional corrections. Due to time changes in this data, IGRF needs to be updated every few years. Therefore, it is necessary to change when air or land Survey within a few months or years. The magnetic field parameters in the study area are obtained using the coordinates of a point in the region of the IGRF system, as shown in Table 1.
Table 1. Parameters of the geomagnetic field in the studied area
Declination (D)
|
Inclination (I)
|
Total Intensity (F)
|
4.52º
|
53.25º
|
47390 (nT)
|
The geomagnetic field is equal to a magnetic dipole field with a 1025×8 electromagnetic unit located in the earth's center. The magnetic field intensity measurement unit in the surveys is nanotesla (nT). The magnetic anomalies found on the earth's surface can cause changes in magnetic field intensity up to a few hundred nanoteslas.
The topographic map of the exploration area can be seen in Fig. 7 that after the preparation of magnetic data and modeling them, drilling sites can be proposed on the map, which is one of the goals of the present geophysical study.
3.4 Data Preparation and Processing
Generally, in the magnetometric analyses, after the corrections on the Survey data, which are known as raw data, the map of the intensity of the entire magnetic field in the vertical axis direction is first provided. In the map of the entire magnetic field intensity, magnetic anomalies appear in solid and weak poles.
Magnetic flow around the earth is affected by magnetic gradient angles and magnetic field deviation angles. These two parameters affect the intensity of the total field. The amount of this effect changes with the change of latitude and longitude. Also, the two parameters make the magnetic anomaly precisely not be placed on its causative agent. Therefore, it is necessary to reduce pole correction for areas that are not exactly on the pole (like Iran). IGRF is used for this, and this amount is reduced from the Surveyed data. It means that by doing this, it is thought that the Surveys are taken in pole; as a result, the anomalies are exactly on its causative factors. Another critical factor affecting the intensity of the earth's magnetic field is residual magnetism in the presence of rocks. The residual magnetism hurts this correction. The residual magnetism in rocks sometimes causes excessive kurtosis of anomalies or, conversely, a very slight decrease in anomalies. Suppose this correction in the region does not cause excessive data kurtosis or excessive deformation of anomalies. In that case, this map will be used as a base for other processes, such as upward continuation and field derivative methods. Otherwise, the map of the magnitude of the total magnetic field will be used in the direction of the vertical component as the base map. Another processing that can significantly help detect anomalies is analytical signal processing. This process amplifies the anomaly edges and displays the magnetic dipoles as outstanding ones.
3.5 Modeling Magnetic Data and their Interpretation
After preparing the data and making the required files, magnetic field intensity maps and different processing maps were prepared by data networking through appropriate cells. The Surveyed field data are networked using the least-squares method and according to their frequency to minimize the minimums and maximums to prepare maps.
As seen in Figs. 8 and 9, there are four distinct anomalies in this map, with two western anomalies very superficial and insignificant, but in the east of the first zone, there are two notable anomalies. From these two eastern anomalies, southern anomalies appear as a complete dipole with a more significant negative pole, and its very high-intensity variations indicate its proximity to the data acquisition surface. However, only the positive pole has been recorded from the north anomaly, and its negative pole is likely to be seen in the north direction if data acquisition is continued. This anomaly has a relatively more significant but less intense extent and is probably related to high-depth mineralization. Of course, another possibility is the presence of magnetic rocks like gabbro-diorite, etc., with little magnetization and sometimes appear as false anomalies. However, the task of this anomaly must be determined by exploratory excavation.
Magnetic flow around the earth is affected by magnetic gradient angles and magnetic field deviation angles. These two parameters affect the intensity of the total field. The amount of this effect changes with the latitude and longitude changes. Also, the two parameters make the magnetic anomaly precisely not to be placed on the causative agent. Therefore, it is necessary to reduce-to-pole correction for areas that are not exactly on the pole (like Iran). As the anomalies must be transferred to the actual location, the reduction-to-pole filter was applied to the initial data, which it is significant in Fig. 10. Due to the application of this filter, anomalies have somewhat shifted to the north
Another processing that can significantly help detect abnormalities is analytical signal processing. This process amplifies the anomalous edges and displays the magnetic dipoles as outstanding ones.
Fig. 11 shows the analytical signal map of zone one. In this map, the horizontal extension of mineralization is determined and limited. The proposed drilling points of zone one will be determined according to this map.
In Fig. 12, upward continuation filter maps 5 to 40 m of zone one are shown. As the maps show, the western anomalies are very trivial, and they have been almost eliminated in upward continuation 10 m. However, the eastern anomalies continue to depths of 30 to 40 m. Therefore, the final depth of the southern mineralization in the eastern part of the first zone, due to the changes in the intensity and shape of the anomaly, is expected to be at most 15 m.
Euler's method was not used for the eastern part (zero tailing depth) due to outcrops in this part. Of course, it should be noted that the low-intensity northeast anomaly extends to depths of more than 40 m, and it extends to the north. Thus, the tailing thickness of this part seems to be more than 10 m.
3.6 2D and 3D Inverse Modeling
The interpretation of magnetometric data in the Baba Ali iron ore deposit range was performed to identify the status of anomalies. The magnetometric method can identify the area effectively at the beginning of the work, given the relatively low exploratory costs. By performing modeling and interpretation of anomalies and integrating geological information and existing information, valuable and applicable results will be obtained to drill structures. In Fig. 13, the magnetic intensity map of the range is shown.
For further identification and interpretation of anomalies and structural conditions of the area, it is necessary to deduct the area's anomaly effects from the Bouguer anomalies using proper methods to obtain the remaining anomalies and to be used for exploratory purposes. First, using the second-order surface process filter, the region effects seen in Fig. 14 are plotted. Afterwards, by removing the regional effects from the magnetic intensity anomaly, the remaining map (Fig. 15) used for modeling is obtained.
Modeling should be done to determine geometric parameters (such as depth, shape, structure, etc.) and physical parameters (density, etc.) and interpret residual magnetic anomalies. Regarding the separation of the anomalies made by the anomaly separation filters, the best answer is the residual magnetic anomaly of the second-order surface process. For this purpose, according to Fig. 16, profiles are drawn perpendicular to the region's anomaly spread.
A polygon was plotted on each anomaly as the first assumption, according to Fig. 17. As the interpretation of the magnetic anomaly and the separation is given, it can be seen how the density of these anomalies will be about each other.
In all modelings, the background density is considered to be 3.5 g/cm3. Therefore, 3D modeling is performed on all profiles of the map at the same time. In this modeling, the background and polygon gravity is assumed to be 2.67 and 2.2 mGal, respectively. By using Fig. 17, a polygon is plotted on each anomaly in the remaining map of the second-order surface process, and its answer is calculated with a 3D forward modeling. After considering the modeling error, it was found out that this error is greater than the target Root Mean Square error (RMS = 2). Therefore, parametric inverse modeling is used to confirm the curve of the answer model and the measured value curve of gravity data and reduce the error. After several repetitions, the error modeling operation was reduced to RMS = 1.94, which is acceptable to the target error. As a result, 3D modeling by Fig. 20 has been able to reconstruct the properties of the productive resources of anomalies correctly.
In Figs. 18 and 19, the modeling results are shown for anomalies A and B. In this modeling, the graphs of the residual anomaly and the graph of the model showed an excellent conformation two-dimensionally (Table 2).
Table 2. 3D modeling results for four anomalies