Estimation of the maximum detection depth of artificial ferromagnetic objects in the thickness of a semiconducting medium..
SHCHERBAKOV Grigory Nikolaevich, professor, doctor of technical sciences
ANTSELEVICH Mikhail Aleksandrovich, doctor of technical sciences
UDINTSEV Dmitry Nikolaevich, candidate of technical sciences
ASSESSMENT OF THE MAXIMUM DEPTH OF DETECTION OF FERROMAGNETIC OBJECTS OF ARTIFICIAL ORIGIN IN THE THICKNESS OF A SEMICONDUCTING MEDIUM
To detect local field inhomogeneities in non-ferromagnetic covering media (earth, water, snow, etc.) caused by ferromagnetic objects of artificial origin, the most widely used magnetically sensitive devices are ferroprobe gradiometers or magnetometers [1 5]. A similar task arises when searching for steel oil and gas pipelines, sunken equipment, small arms, firearms and bladed weapons, unexploded aerial bombs and artillery shells, most anti-tank, anti-landing and anti-personnel mines. These objects either have their own magnetic field or distort the uniform field of the Earth, and in both cases the magnitude of the magnetic field in the zone of the sensitive element – the ferroprobe changes its magnitude and direction. This is a sign of the presence of a ferromagnetic object. In relation to the sought object, these devices are passive, that is, they do not have any effect on the object.
The electromotive force (emf) at the output of the sensitive system of the gradiometer [2] is proportional to the difference in the values of the magnetic field strength at two points in space (Fig. 1), located at a distance lfrom each other (gradiometer base). The main parameter of a magnetometer is its sensitivity. Sensitivity is measured by the magnitude of magnetic induction or magnetic field strength that the device is capable of registering. Another equally important characteristic is the resolution, which determines the minimum difference in magnetic field parameters that can be registered by the device. Modern magnetometers have a resolution from 0.01 nT to 1 nT, depending on the operating principle and the class of problems being solved [1, 2, 6].
Fig. 1. Detection of small-sized ferromagnetic inhomogeneities of artificial origin in non-ferromagnetic covering media using fluxgate gradiometers
In [3], a dependence is given that allows one to approximately determine the detection range of a search object approximated by a ferromagnetic sphere using a flux-gate gradiometer:
,(1)
where
is the radius of the ferromagnetic sphere, m;
– magnetic constant, 1.257×10-6 H/m;
– the Earth's constant magnetic field strength, A/m;
– the gradiometer sensitivity by field, T/m.
This formula has satisfactory accuracy for practice, despite a number of accepted assumptions and limitations:
- the value of the magnetic permeability of the search object is not taken into account
as significantly exceeding the magnetic permeability of the external covering medium 
; - the relative magnetic permeability of the external covering medium is taken to be equal to 1;
- the distance between the ferroprobes (base length) l is not taken into account.
Thus, formula (1) is not applicable for a comprehensive assessment of the influence of the magnetic properties of the search object and the covering medium, the length of the magnetometer base on the maximum detection range.
The sequence of deriving the dependence, taking into account, in addition to the factors taken into account in (1), the magnetic properties of the search object, the sheltering medium and the length of the magnetometer base, is given below.
The strength of the external disturbed magnetic field is described by the expression [7]:
(2)
where 
– the strength of the external undisturbed magnetic field, in our case equal to the strength of the Earth's constant magnetic field , A/m;
r – the distance from the center of the ferromagnetic sphere to the observation point.
Considering the equality, in the vast majority of cases, of the magnetic permeabilities of the medium in which the measuring instrument is located (air, water) and the covering medium (soil, water, snow, etc.):
, (3)
interface conditions:
, (4)
can be represented as:
. (5)
The intensity of the external disturbed magnetic field in the center of the lower ferroprobe:
, (6)
where 
is the maximum detection depth of the search object approximated by a ferromagnetic sphere by the ferroprobe gradiometer.
The strength of the external disturbed magnetic field in the center of the upper ferroprobe:
, (7)
The difference between the strengths of the external disturbed magnetic field in the centers of the magnetometer ferroprobes:
, (8)
The maximum depth of object detection corresponds to the condition:
, (9)
The analysis showed satisfactory convergence of the results of theoretical calculations using formula (8) and the conducted full-scale experimental studies to assess the maximum detection depth of ferromagnetic spheres of various radii (photo 1) by the device for determining the location of ferromagnets OGF-L type 83 015 (photo 2, Fig. 2).
Photo 1. Ferromagnetic spheres used in experimental studies
Photo 2. Device for determining the location of OGF-L ferromagnets type 83 015
Fig. 2. Results of theoretical calculations using formulas (1) 1, (8) – 2 and conducted full-scale experimental studies using OGF-L type 83 015 – 3
Fig. 3 shows the dependences of the maximum detection depth of a ferromagnetic sphere by a differential magnetometer with a magnetic field strength resolution of 0.01 A/m on its radius. Dependences of the required base length l differential magnetometer for detecting a ferromagnetic sphere of radius
at a depth of 10 m with different resolution of the device for magnetic field strength are shown in Fig. 4.
From these dependencies (Fig. 3, 4) it is evident that the relative magnetic permeability of the search object is more 
= 10, at 
=1, can be considered as significantly exceeding the magnetic permeability of the medium. The error in determining the maximum depth of the search object in this case is no more than 8%. The length of the magnetometer base has the most significant effect on the search depth. This is explained by the fact that the measurement in these devices is relative, and increasing the base length allows one of the sensitive elements to be removed from the search object to the zone of least disturbance.
In Fig. 5 shows the dependence of the maximum detection range of 
a ferromagnetic sphere of different radii differential magnetometer with a magnetic field strength resolution of 0.01 A/m from the distance between the ferroprobes l. Analysis of this graph suggests that the appropriate maximum length of the magnetometer base for a given resolution depends on the size of the search object.
Dependence of the maximum detection depth ferromagnetic sphere ( = 100) on the length of the base l and the resolution of the differential magnetometer for magnetic field strength, presented in Fig. 6, shows that a significant increase in the search depth is possible with an increase in the resolution of the device.
Fig. 3. Dependences of the maximum detection depth of a ferromagnetic sphere ( = 100) by a differential magnetometer with a magnetic field strength resolution of 0.01 A/m on its radius
Fig. 4. Dependence of the required base length l of a differential magnetometer for detecting a ferromagnetic sphere of radius at a depth of 10 m with a resolution of the device for magnetic field strength: 1 – 0.01 A/m; 2 0.001 A/m; 3 – 0.0001 A/m
Fig. 5. Maximum detection depth of a ferromagnetic sphere ( = 100) depending on its radius and the distance between the ferroprobes l of the differential magnetometer with a magnetic field strength resolution of 0.01 A/m
a)
b)
Fig. 6. Dependence of the maximum detection depth of a ferromagnetic sphere ( = 100) on the base length l and the resolution of the differential magnetometer for the magnetic field strength at the sphere radius: = 0.5 m (a); = 0.1 m (b)
Thus, dependence (8) allows:
1. To estimate the maximum detection depth of search objects with given geometric dimensions by existing magnetometers.
2. Justify the characteristics of the developed magnetometers depending on the required (specified) depth of occurrence (search) and geometric dimensions of the objects.
3. Determine the magnetic permeability of objects with known geometric dimensions and distance to the object.
Analysis of dependence (8) and graphs (Fig. 3 – 6) allows us to draw the following conclusions:
1. The influence of the relative magnetic permeability of search objects with a value of more than 10 on the detection depth is insignificant.
2. The appropriate length of the base depends on and should be consistent with the expected dimensions of the search object. An appropriate length of the base is one that exceeds the geometric dimensions of the search object by 1.5 to 2 times. A decrease in length leads to a significant decrease in the search depth, an increase to an insignificant increase.
3. The maximum detection depth of typical small-sized search objects (small arms and bladed weapons, most engineering anti-tank, anti-landing and anti-personnel mines) by modern magnetometers does not exceed 3 m.
References:
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3. Shcherbakov G.N. Detection of objects in concealing environments. For forensics, archeology, construction and counterterrorism. Moscow: Arbat-Inform, 1998.
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