The Electromagnetic Characteristics of UXO Using the Electromagnetic Method

doi:10.21203/rs.3.rs-4352508/v1

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The Electromagnetic Characteristics of UXO Using the Electromagnetic Method

https://doi.org/10.21203/rs.3.rs-4352508/v1

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In the process of UXO removal, effective detection is crucial for the clearance of UXO. This paper investigates the method of TEM to detect UXO, the design optimization of magnetic coupling source and the electromagnetic response characteristics of UXO with different attitudes and depths. The numerical results show that the designed and optimized single-transmitter multiple-receiver TEM detection can not only provide fast localization, but also greatly reduce data processing and improve detection efficiency. Based on the finite element modeling, the electromagnetic response of the target is analyzed in detail with the variation law of position and attitude by combining the information of the fast localization. The field experimental results show that the variation trends of the numerical simulation results of the time-domain electromagnetic response under different attitudes are basically consistent with the measured results. The measuring line response enables the fast localization of suspicious sites by marking them. The planar response establishes the spindle location information. The detection depth has a strong influence on the initial amplitude of the time domain response, while the inclination angle determines the symmetry characteristics of the planar response. This will provide a basis for the design and optimization of the TEM detection system.

UXO

Transient Electromagnetic Method

Electromagnetic Response

Finite-Element Method

Unexploded ordnance (UXO) refers to all types of explosive ordnance (unexploded or abandoned) that remain in an area after the end of armed conflict and military exercises. These include artillery shells, grenades, mines, mortar shells, rockets, missiles, and other munitions. These weapons can explode decades after they are deployed or abandoned, posing a lethal and unstable risk. Especially in the post-war region, hundreds of accidental bombings occur every year, causing tens of thousands of casualties and seriously endangering the personal safety of local residents. The detection of UXO has attracted a lot of attention from researchers in recent years. They have developed a number of geophysical methods to detect UXOs, including: magnetic detection, ground-penetrating radar, electromagnetic detection, joint method detection, etc¹. Magnetic detection (MD) is carried out by local geomagnetic field anomalies caused by magnetic unexploded ordnance. Moreover, the best detection performance cannot be achieved due to the detection of a single target material and unsatisfactory detection results (high false alarm rate)². Ground-penetrating radar (GPR) is used to detect targets by producing different scattering effects of electromagnetic waves on different media layers³. However, tiny targets on the ground may make the measurement results inaccurate, and the anti-interference performance is extremely poor⁴. Electromagnetic detection (ED) method is to detect the target by generating varying electromagnetic excitation characteristics. It has a large detection range, low false alarm rate, high discrimination ability of the target body, and is not affected by the environment in which the object is located⁵. The main mechanism of its detection is based on the principle of electromagnetic induction, which can be divided into two types of time-domain and frequency-domain electromagnetic methods (T- and F- EM)⁶. Frequency domain electromagnetic detection systems: The target bodies at different depths are detected by excitation coils emitting electromagnetic signals with one or more frequencies, including Geophex's GEM-2, GEM-3 and GEM-5. The frequency domain electromagnetic method is adopted by most mine detection devices, owing to its advantages such as fast detection speed, stable and reliable performance, and easily achieves different depth detection. The frequency domain electromagnetic method has been widely applied in detection devices, MIL-D1 and Minex 2FD being typical representative devices. However, there are many types of unexploded ordnance such as artillery shells and grenades with different volumes, and time domain EM is still the main detection method. Time-domain electromagnetic detection system: The primary field is emitted to the underground with a transmitting coil, and the secondary field generated by the target body is received during the shutdown of the primary field with time. Then, the electromagnetic characteristics and spatial pattern distribution of the target body can be identified⁷. Compared with other detection methods, TEM can not only acquire a wealth of subsurface information, but also quickly locate target bodies and other shapes of metals.

Moreover, TEM only explores the secondary field response generated by the target body, which greatly simplifies the effects brought by the primary field and can further reduce the false alarm rate and improve the detection performance. TEM is a more widespread exploration method, with a sensitive response to metal and magnetic objects. There have been many examples of using ground and airborne TEM devices to detect subsurface target bodies, and some detection results have been obtained. Chen et al. investigated a special time-domain electromagnetic system and utilized it for effective detection of unexploded ordnance⁸. Li et al. showed the detection and identification of small target bodies near the surface by placing the transmitting and receiving coils in a staggered time domain electromagnetic system⁹. Qu et al. designed a handheld time domain electromagnetic system to obtain the response characteristics and horizontal position of the target body¹⁰. Li adopted the vector finite element method for numerical simulation of transient electromagnetic fields in the central return line, etc¹¹. It is well known that there are many types of unexploded ordnance, the size of the volume varies, and the actual environment in which they are located is complicated and variable. Although, MD, GPR and ED play a very important role in the UXO detection and identification procedure. However, there is still a lot of space to improve the portability, miniaturization, fast positioning and real-time display of the test results of the device.

In this paper, we first investigate the transient electromagnetic response modeling of UXO by comparing the results of the analytical solution of a sphere with the finite element modeling response of the same shape. After determining a reasonable finite element modeling (FEM) procedure, we extended the finite element modeling to the complex geometry of the actual UXO shape. The magnetic coupling source detection type and structural parameters are explored in detail. The central-loop TEM device is used to detect UXO, not only can have the best coupling with the detected geological object, but also not easily affected by the surrounding geology, and has a high discrimination ability. Next, we employ a single-transmission, multiple-receiver sensing device, which can attain fast localization of UXO by measuring the line response. On the basis of the positioning information, the variation law of target body response with parameters of target body position, attitude and depth is analyzed in detail. The field experimental results show that the variation trends of the numerical simulation results of the time-domain electromagnetic response under different attitudes are basically consistent with the measured results. The detection depth has a great influence on the initial amplitude of the time-domain response, while the inclination angle determines the symmetric characteristics of the planar response. Therefore, the three-component transient electromagnetic response of the axisymmetric target body can obtain information about position, inclination and depth. Moreover, the measurement method of TEM is simple and fast compared to frequency domain electromagnetic methods and greatly reduces the influence of background fields. The exploration instrument fabricated by the TEM has the advantages in small size, light weight, low power consumption and high efficiency, and is less restricted by the terrain and more suitable for areas with lush vegetation and variable terrain.

Analysis of Transient Electromagnetic Response Theory

The use of magnetic dipole source detection is a more common type of transient electromagnetic field-work device. Assuming that the sphere with conductivity σ, radius a and center burial depth h is located directly below the circular transmitting coil, the expression of the transient electromagnetic response:

(a) Central-loop TEM device

$$V(t)=3{\pi ^{ - 1}}\frac{{{\mu _0}}}{\tau }\frac{{I{a^3}{R^2}{r^2}}}{{{{({R^2}+{h^2})}^{{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-0pt} 2}}}{{({r^2}+{h^2})}^{{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-0pt} 2}}}}}\sum\limits_{{k=1}}^{\infty } {exp(-{k^2}t/\tau )}$$

where R is the radius of the circular transmitter loop and ${L \mathord{\left/ {\vphantom {L {\sqrt \pi }}} \right. \kern-0pt} {\sqrt \pi }}$ for the square transmitter loop. The current of the transmitting loop is I. ${\mu _0}$is the permeability in a vacuum. r is the radius of the receiving loop. t is the time to receive the secondary field after the primary field is shut off. $\tau$ is the time constant, which gives the expression for the sphere:$\tau ={{{\mu _0}\sigma {\text{a}^2}} \mathord{\left/ {\vphantom {{{\mu _0}\sigma {\text{a}^2}} {{\pi ^2}}}} \right. \kern-0pt} {{\pi ^2}}}$.

(b) Coincident-loop TEM device

$$V(t)=3{\pi ^{ - 1}}{\mu _0}\frac{{I{R^4}{a^3}}}{{{{({R^2}+{h^2})}^3}\tau }}\sum\limits_{{k=1}}^{\infty } {exp(-{k^2}t/\tau )}$$

The equations given above are applicable in the late conditions of $t>>\tau$. In the case of satisfying the late condition, $V(t) \propto {1 \mathord{\left/ {\vphantom {1 \tau }} \right. \kern-0pt} \tau } \cdot exp(-t/\tau )$decays according to an exponential law. The rate of decay of the late response is influenced by the time constant $\tau$. More importantly, the decay rate is determined by both the conductivity and the shape of the target body.

COMSOL MULTIPHYSICS is a large-scale advanced numerical simulation software based on the finite element method (FEM). The software simulates various actual exploration methods, including hydrological exploration, electrical and magnetic exploration, acoustic exploration, etc. Numerical simulation allows prediction and analysis of the possible conditions and results of the exploration, thus providing a more accurate picture of the specific distribution of the target in the subsurface region. The results obtained by numerical simulation are applied to take solution measures in advance, which will save a lot of labor and material resources. In this paper, we mainly use the MF (magnetic field) application mode of its AC/DC module for the numerical simulation of transient electromagnetic fields in 2D or 3D models. The time-domain transients are used in the 2D or 3D models, and the observation time range is mainly concentrated within 10ms. Magnetic Field Interface (MF) Solves Ampere's law for magnetic vector potentials. Magnets, motors, transformers, induction-based NDT and eddy current generation are typical applications of this physical field interface. Electromagnetic exploration methods commonly adopt electromagnetic signals at low frequencies. Therefore, the system of Maxwell's equations can be simplified as follows under quasi-static (no displacement currents are considered conditions:

$$\nabla \times {\rm H}={\varvec{J}}={{\varvec{J}}_e}+\sigma {\varvec{E}},\nabla \times {\varvec{E}}= - \frac{{\partial {\varvec{B}}}}{{\partial t}},\nabla \times {\varvec{D}}={\rho _v} and \nabla \times {\varvec{B}}=0$$

Where, Electric field intensity E, Conductivity of the geoelectric model$\sigma$, Electric displacement vector D, Magnetic field intensity H, Magnetic flux density B, the total conduction current density J, Current density of applied field source J_e, Electric charge density${\rho _v}$.

Take the divergence of both sides of the first equation in Eq. (3). The current continuity equation can be calculated:

$$\nabla \cdot {\varvec{J}}=0$$

In order to simplify the process of solving for the electromagnetic response, a bit-function is introduced to describe the electric and magnetic fields according to Eq. (3):

$$B=\nabla \times {\varvec{A}},{\varvec{E}}= - \nabla \varphi - \frac{{\partial {\varvec{A}}}}{{\partial t}}$$

Where, A ($T \cdot m$) is vector magnetic potential and$\varphi$ is scalar potential function. The governing equation in the time domain is obtained by taking the bit-function into Eqs. (3) and (4):

$$\nabla \times \nabla \times {\varvec{A}}+\mu \sigma \frac{{\partial {\varvec{A}}}}{{\partial t}}+\mu \sigma \nabla \varphi =\mu {{\varvec{J}}_e}$$

$$\nabla \cdot (\sigma \frac{{\partial {\varvec{A}}}}{{\partial t}})+\nabla \cdot (\sigma \nabla \varphi )=\nabla \cdot {{\varvec{J}}_e}$$

Where, µ is the permeability. In this paper, vacuum permeability µ₀ is selected. When the current on the coil is specified as I_coil, the coil applies an external current density along the wire direction, which can be calculated from Equation ${{\varvec{J}}_e}=\frac{{N{I_{coil}}}}{{{A_s}}}$, where N is the number of turns specified and A_s is the total cross-sectional area of the coil domain. The natural Dirichlet boundary conditions are adopted in order to solve Eqs. (6) and (7):

$${({\varvec{n}} \times {\varvec{A}})_\varGamma }=0$$

$${\varphi _{_{\varGamma }}}=0$$

Where, $\varGamma$is the outer boundary of the calculation region, and n is the unit normal vector of the outer boundary. In the calculation of electromagnetic field, A and $\varphi$ in Eq. (5) are not unique. Therefore, some canonical conditions need to be applied in order to obtain unique solutions for A and$\varphi$. Meanwhile, in combination with the coupling relationship between A and $\varphi$ in Eqs. (8) and (9), $\varphi$ is chosen to be 0 and only A is retained. This not only ensures the uniqueness of the results, but also further simplifies the problem to be solved. Here,${\varvec{B}}=\nabla \times {\varvec{A}},{\varvec{E}}=-{{\partial {\varvec{A}}} \mathord{\left/ {\vphantom {{\partial {\varvec{A}}} {\partial t}}} \right. \kern-0pt} {\partial t}}$and Eq. (3) are combined to solve A. The governing equation in the time domain:

$$\nabla \times \nabla \times {\varvec{A}}+\mu \sigma \frac{{\partial {\varvec{A}}}}{{\partial \text{t}}}=\mu {{\varvec{J}}_\text{e}}$$

In the numerical simulation of the time domain, Eq. (10) is used as the governing equation. The model equations in the computational region are discretized by the vector finite element method, using weak formulation. This will form corresponding numerical model equations to solve the approximate solution of vector magnetic potential A at each grid element. The magnetic induction intensity B and its first derivative${{d{\varvec{B}}} \mathord{\left/ {\vphantom {{d{\varvec{B}}} {dt}}} \right. \kern-0pt} {dt}}$with respect to time are usually selected as the observation result of the time domain electromagnetic method, where${\varvec{B}}=\nabla \times {\varvec{A}}$. In this paper, the numerical solution of electromagnetic response is obtained directly in time domain. The transient study is applied to the physical field of the magnetic field in the AC/DC module in COMSOL, and the time stepping method is selected for the backward difference method.

In this paper, the central loop TEM device is used in order to produce a higher coupling between the detection device and the measured target and to obtain a better resolution of the received signal. The measurement device in which the geometric centers of the transmitting and receiving coils co-coincide is called a central loop TEM device. The size of the excitation signal transmitting coil of this detection device is equal to or larger than the signal receiving coils. Conversely, it causes the detection device to produce extremely lower matching power and efficiency. According to the theory proposed by Spies, the penetration depth H_depth depends on the peak magnetic moment M of the emitted current, the ground resistivity ρ₁ and the minimum resolvable level $\eta$ in the case of the homogeneous-ground¹².

$${{\varvec{H}}_{depth}}=0.55{(\frac{{{\varvec{M}}{\rho _1}}}{\eta })^{{1 \mathord{\left/ {\vphantom {1 5}} \right. \kern-0pt} 5}}}$$

According to the mentioned equation, it can be found that the detection depth can be improved by increasing the transmitting magnetic moment M or decreasing $\eta$. The minimum discriminable level$\eta$ that can be received by the receiver coil is normally composed of internal sensor noise, ambient noise, and other electromagnetic interference. The internal noise of the sensor is the only factor that determines the maximum penetration depth of the system. In practical exploration, the detection error caused by the sensor's internal noise V_ns should not exceed 2% (V_ns $\leqslant$$0.02\eta$) of the minimum resolvable level. Assuming the ground resistivity ${\rho _1}=100\Omega \cdot \text{m}$ in the half-space modeling¹³, the penetration depth H_depth with the sensor internal noise V_ns and the transmitting current magnetic moment M can be calculated as shown in Fig. 1.

From Fig. 1, it can be seen that the magnetic moment M corresponds to the y-axis setting of 5–50$\text{A} \cdot {\text{m}^2}$, V_ns corresponds to the x-axis setting of 1-100nV/m², and the penetration depth curves correspond to the range of 10-40m. The minimum distinguishable level that can be recognized when the effective area of the receiver coil is normalized is 0.5uV/m² (V_ns=10nV/m²), corresponding to a penetration depth of 15-25m, which is far greater than the penetration depth in shallow layers. From the above discussion we can set V_ns=10nV/m² as the target value for sensor design and optimization¹³. The simulated electromagnetic response of the finite element method was further validated in purpose of determining other parameters of the transmitting coil. The coil current off time is not greater than 20us and the coil current density is not greater than 5A/mm² as the design and optimization objectives of the transmitter, depending on the existing transient electromagnetic penetration model. The transmitter coil and receiver coil wire diameter are selected for 1mm diameter copper wire, which is a very common wire in the market.

The current shutdown is achieved by adopting a constant-voltage clamp technique, during which the emission current falls linearly to zero and the shutdown time can be calculated¹³.

$${t_{off}}=\frac{{{L_T}{I_T}}}{{{V_{dss}}}}$$

Where, L_T and I_T are the inductance and input current of the transmit coil, respectively, and V_dss is the clamp voltage of the transmit coil, which is controlled by the transmitter. For air-core firing coils, when the firing coil diameter D is much larger than its cross-sectional parameter h, the inductance of the firing coil can be calculated by the following Eq. 1:

$${L_T}=\frac{{{\mu _0}R{N^2}}}{4}[ln(\frac{{16R}}{h})-1.75]$$

Where, h is the transmitting coil cross-sectional parameter. The number of turns can be determined to be 30 in accordance with Fig. 1(a) and (b) with a switch-off time of not more than 20us and a clamp voltage setting of 200V. Therefore, the radius of the transmitting coil can be determined to be 0.26m for a magnetic moment 30Am² at the minimum resolution level.

The UXO for the simulation modeling derives from projectiles recovered from the site that have been tested safely by professional authorities. The retrieved unexploded ordnance is measured by hand and modeled with Auto CAD-2018, then imported into COMSOL. The sphere and circular transmitting coil have a better symmetry, and the 2D axial-symmetry of AC/DC module in COMSOL is chosen for modeling, which can reduce the calculation and the simulation time. The analytical and finite element solutions were verified by calculating the spheres created under the identical conditions, owing to the fact that the analytical equations for other 3D conducting bodies could not be given accurately. The variation of the decay curves of the analytic solution of the secondary induction potential and the numerical solution of the secondary induction field in the homogeneous full space is shown in Fig. 2. The simulation model was set up as a homogeneous full-space geoelectric model. The air conductivity is 1E-6 S/m, the relative permeability and relative permittivity are both set to 1, the radius of the circular transmitter loop is 0.26m, the current magnitude is 5A and the number of turns is 30. The target body is located directly below the circular transmitting coil with the parameters σ = 1.12e7 S/m, a = 0.032m and h = 0.4m respectively. The analytical and numerical solutions calculated by Eq. (1) are selected for comparison to verify the reliability of the simulations under the identical conditions. The analysis of the numerical solution compared with the theoretical solution shows that the curve patterns have been basically consistent. The induced voltage arising from the secondary field was chosen as a standard of measurement because it is a key parameter that can be used to discriminate the target body during its excitation by the primary field under the ground. The induced voltages are calculated in COMSOL and will be used for comparison and analysis shown in the subsequent diagram. When the receiving point is positioned at the center of the transmitting coil, the analytical solution for the central point of a circular loop with equal area can be utilized to verify its numerical accuracy. In the subsequent data processing, we normalize the induced voltage and convert it to ${{V(t)} \mathord{\left/ {\vphantom {{V(t)} q}} \right. \kern-0pt} q}$. Where, q is the effective area of the receiving coil and I is the transmitting current.

Figure 2 shows the variation trend of the induced voltage received by the receiving coil with time, and the curve is plotted on the logarithmic coordinate. The curves are essentially the identical for the late conditions at$\text{t}>>\tau$which can be seen from the Fig. 2. The error in the numerical simulation for the late conditions is approximately 4%, indicating that it is feasible to carry out the transient electromagnetic method forward numerical simulation utilizing COMSOL MULTIPHYSICS software. Moreover, the numerical solution is larger than the analytical solution in the early response, indicating that more target body characteristics can be obtained by the numerical solution and the signal-to-noise ratio of the signal can be greatly improved.

Numerical Solution Modeling

In the COMSOL modeling space, each model is centered on a$25 \times 25 \times 25{m^3}$cube, which represents the geologic layer. This "ground" block is located below another block of $25 \times 25 \times 25{m^3}$, which includes the height of the air and probe sensors, where z = 0 represents the earth surface. The set-up of each cubic block has followed the equation relationship shown in (4) and (6), and the relative permeability of each part is 1. The rest of the boundary conditions are selected by default. A very critical factor in finite element calculations is determining the size of the discretized mesh. The mesh discretization in finite elements is the partitioning of the geometric model into simple small units by the idea of discretization. In COMSOL, the geometric model can be partitioned into tetrahedral mesh cells, with every domain consisting of tetrahedral cells. However, the size of the partitioned mesh cells varies between domains. The basis for this is that, considering the depth, attitude, and location of the UXO model, the distribution of the response of buried ferrous material to magnetic fields is different across the ground. The coils on the ground need to receive the secondary fields generated by the UXO, and the magnetic field variations in the upper half of the ground block are of more interest to us compared to the lower half. Therefore, smaller cell meshes are used for dissection near the ground surface and in the UXO region, while larger mesh dissections are applied to regions further from the ground surface. A significant consideration is that in COMSOL numerical simulations, the precision of the solution of a geometric model is related to the quality of the cell mesh. A better cell mesh quality provides a more accurate numerical resolution, but at the cost of longer time and a higher computer configuration. We have optimized the mesh size of our geometric models through computer configuration while ensuring that the modeling produces correct and reliable results when compared to the analytical solution¹⁴. In order to take into account both efficiency and calculation accuracy, grid encryption is carried out at the transmitting loop and receiving point, and local grid encryption is also carried out near the surface and target body. We used the above meshing scheme to perform the grid dissection of the modelling region and obtained an average grid cell mass of 0.75 and a minimum grid cell mass of 0.2, where the optimal grid cell mass is 1. The Degrees of Freedom (DOF) within the entire model is 979266. The DOF is related to the number of nodes, the computational points that define the shape of each finite element. The average cell mass of the encrypted local grids of the target body, the transmitting source, the receiving point and the part near the ground surface is 0.95 and the minimum cell mass is 0.8. We perform mesh convergence tests on the forward model discussed in this paper. We have simulated the grid thickness of the air domain and the ground block away from the ground surface and found that the grid size has a negligible effect on the aspect of the secondary induction field, and there is no significant difference in the induced voltage from the fine-grid to the coarse-grid. The numerical simulation results are compared with the analytical solutions, and the results are basically consistent. Therefore, we have chosen to simulate a mesh grid that does not affect the accuracy of the induced voltage calculation and run as stably as the computer configuration permits.

Figure 3(a) shows a schematic of the meshing of the 82mm shell and other geometric regions in COMSOL modelling. The geometric center of gravity of the UXO is used as the parameter for its location and the depth of burial of the UXO is 0.5m in the modelling. Figure 3(b) shows the spatial coordinate system used in COMSOL modeling and the height of the sensor from the soil surface, respectively. The resistivity of the soil is${\rho _1}=100\Omega \cdot m$. In Fig. 3(b), θ is the angle between the main axis of the axisymmetric target body (red dashed arrow) and the z-axis, and $\varphi$ is the angle between the projection of the main axis in the xoy-plane and the x-axis.

Numerical Solution Analysis

The In the modeling, air conductivity air σ = 1E -6 S/m, soil resistivity${\rho _1}=100\Omega \cdot m$, the material of the UXO is iron, and its conductivity is σ = 1.12e7 S/m. The parameters of the sensor and the buried depth of the UXO are consistent with Fig. 3. We investigated the influence of the attitude of UXO on the time-domain response by modeling UXO at different angles. The time-domain three-component response at the receiver point of the homogeneous half-space model was calculated in the observed time range. Figure 4 shows the time domain response of the 82 mm mortar projectile (length 31.6 cm and diameter 82 mm) for three components (Vx,Vy,Vz) and the target body response for inclination angles $\theta$ of ${0^ \circ },{30^ \circ },{60^ \circ }$ and ${90^ \circ }$, respectively. Although the decay trend of the three-component time domain response is almost identical, the amplitude of the induced voltage response for Vx and Vy is much smaller than that of the induced voltage response for Vz. The UXO has an axisymmetric properties with a similar structure in the x and y directions, and it can be found that Vx and Vy almost coincide. The difference between the decay curves of A and B at the late stage is mainly caused by the asymmetric distribution of fins in the tail of the unexploded ordnance. Therefore, only its two component induced voltages need to be known to obtain the target properties.

It can be seen from the Fig. 4(a) that the long axis Vz of the induced voltage response is much larger than the short axis Vx (or Vy), and that Vz decays more slowly than Vx (or Vy) and takes longer to decay. The time-domain Z-component response at receiver 0 for the UXO model is calculated separately for different deflection angles θ in Fig. 4(b). In the Z-component response of different inclination angles, the initial amplitude of the attenuation signal increases slightly with the increase of the angle (θ), but the overall trend is basically the same. The long axis response of the target is not only greater than the short axis response, but also the attenuation rate is slow. When θ = 0°, the long axis is excited by the primary field and produces a strong secondary field response, which decays at a slower rate. As shown in Fig. 4 (b), the late decay rate of the target body Z-component response accelerates as the target body deflection angle increases. The initial amplitude and decay rate of the electromagnetic response of the target body is related to the inclination of the target body. The effect of the long and short axes on the time domain decay signal is mainly in the decay rate as the inclination of the target body varies. The time domain attenuation signal provides a simple identification of the electromagnetic properties of the target body.

In order to investigate the time-domain electromagnetic response characteristics of the 82 mm UXO calculated by the 3D forward model, field experiments and analyses were carried out. Meanwhile, the UXO was placed vertically in a deep pit (head down tail up). Head down, tail up is the typical attitude of UXO in soil. The target body was placed and backfilled with soil as shown in Fig. 5. We chose a low EMI environment for the field tests, where the distances to high voltage lines and roads were more than 1km and 10m respectively. The sensor is placed horizontally on the ground, the distance between each measuring point is 0.5m and the length of each measuring line is 4m (As shown in Fig. 5). The transmitting and receiving coils are 1m *1m square coincident loop devices with an excitation emission frequency of 75Hz. The target body was buried at a depth of 1m, and a single measuring point was selected for fixed-point detection. The transient electromagnetic sensor is placed directly above the target, and each measuring point is detected four times to eliminate random errors. Finally, we superimposed and averaged the four detection results to obtain the time-domain electromagnetic response curve as shown in Fig. 6.

The results of the measured time-domain electromagnetic response of the 82mm unexploded ordnance in the field are shown in Fig. 6. It is easy to find that the three-dimensional forward numerical simulation results are basically consistent with the trend of the measured results. In this section, the reliability of the finite element 3D forward geoelectric simulation proposed in this paper is verified by comparing the numerical simulation results of UXO in different attitudes with the measured data. Next, we perform the subsequent transient electromagnetic response characterization by adopting the experimentally verified and reliable 3D geoelectric forward model.

The time domain decay signal can be a simple identification of the detection target electromagnetic characteristics, the exploration of further identification of the target also need to contain more information amount of line and plane response ^15,16. The measurement line response of the target is the series of transient electromagnetic responses obtained by moving the detection system along a fixed line with a specified step size (shown in Fig. 7). As shown in Fig. 3(c), the center of the UXO as the origin of the coordinate system, the target body projection and the x-axis angle φ = 0, the target body long axis in the xoz-plane. The detection target position can be expressed in coordinates and the inclination angle with z-axis is θ. The probe system moves along the line of measurement in the x-axis direction, and more target characteristics can be obtained by calculating the time domain response of both Vx and Vz components. The target body measurement line response can be obtained when the detection system moves to $({x_0},0,0)$as shown in Fig. 7.

As shown in Fig. 7, three mortar shells were placed at different attitudes at $h \geqslant 0.5m$ directly below the measurement line. For the purpose of achieves lightweight and high localization capability while requiring sufficient detection data for subsequent inversions, we designed and proposed one-transmission, three-receiver sensor. The sensor contains three receivers all in the same straight line, located at the center of the transmitting coil at Receiver 0, Receiver 1 at a distance of -D and Receiver 2 at a distance of D (where, D = 0.52m is the diameter of the transmitting coil). The probe system in the − 5–5m measuring line direction with 20cm as the distance, a total of 51 points measured, to get the target body inclination and depth of the line response results for $( - {30^ \circ }, - 0.5m)$,$({45^ \circ }, - 0.5m)$ and $({0^ \circ }, - 0.8m)$ respectively. The detection results for t = 0.1ms and t = 1ms under the z-component response of the receiver coils R1 and R2 are shown in Fig. 7. As shown in Fig. 7, the target bodies in different attitudes are precisely located by receivers 1 and 2. There are many intersection points in the measured line response results of receivers 1 and 2, however, we choose the intersection point of the curve at the site of the maximum decline in receiver 1 results and the site of the maximum rise in receiver 2 as the localization point of the target body. The signal received by the receiver continues to increase as the sensor moves closer and closer to the pre-embedded target body, and continues to decrease as it moves away from the target body. The intersection of receivers 1 and 2 provides precise positioning information of the pre-built target body.

We can mark suspicious locations with the continuous data- sampling mode of the sensing system. The continuous acquisition mode is often used for data acquisition in field exploration. This exploration mode not only improves the work efficiency, but also can obtain enough sampling point data. Fixed-point sampling model will be utilized for further identification of the target body once these positions are marked. The fixed-point sampling model provides additional target body information, including attitude, depth, and category identification. More information on the inclination of the target body is shown in Fig. 8(a) and (b). Figure 8(a) and (b) show the measured line response for UXOs with inclinations θ = 0°, 30°,60° and 90° respectively, where the UXOs are buried at a depth of 0.5m and are located in the center of the line. As shown in Fig. 8, the x-component measurement line responses are all point-symmetric, with the response amplitude at the center point being 0. The Z-component responses are axisymmetric, with the maximum response amplitude at the axis of symmetry. As the inclination angle increases from 0° to 90°, the magnitude of both the x- and z-components change significantly, which allows good discrimination of the inclination information of the target body. The response amplitudes in Fig. 9 all decay rapidly with increasing time. The early signal amplitude is hundreds or even thousands of times that of the late signal, so the use of an effective early response can greatly improve the signal-to-noise ratio, and thus improve the detection depth (As shown in Fig. 9).

The measured line response results for 82 mm mortar rounds with a depth of 0.5-2.5m and a target body inclination of $\theta ={0^ \circ }$ are calculated in Fig. 10(a) and (b). Figure 10(a) and (b) show the normalized x-component response and z-component response of the target body, respectively. The response amplitude decreases rapidly when the depth of the target body increases, whether it is the x-component measurement line response or the z-component measurement line response. The response amplitude decreases by about 50% for each 0.5m depth from 0.5m to 2.5m depth. The tendency of the response results will not vary significantly with increasing depth for either the x-component response or the z-component response. The magnitude of the electromagnetic response of the unexploded bomb decreases rapidly with increasing depth, and the x and z component response trends are almost invariable. Therefore, the desire to double the depth of detection requires a tens of times increase in the peak magnetic moment of the system and a reduction in the system noise level.

The 2D plane response of the target body is calculated as further identification of the target body attitude parameter variations^16,17. After the position of the target body is localized, monostatic measurements are applied to calculate the component response at different attitudes. The x-component response and the horizontal component response are calculated in Fig. 11 and Fig. 13 when phi = 0°,30°,60°,theta = 0°,30°and 60°, respectively. The horizontal component response is calculated by combining the x-component and y-component responses. The target body is located at -0.5m and the plane responds to a square with a side length of 3m. As shown in Fig. 11, when θ = 0°, the x-component response has axisymmetric characteristics and the magnitude is symmetric about the y-axis, where the y-axis position is the target body position. The x-component response is not varied with φ when θ = 0°, as shown in Fig. 11 (a), (d) and (g), and always has the symmetry axis at the location of the target body center. As shown in Fig. 11(b), (c) or (e), (f) or (h), (i), the entire x-component response is shifted to the right and the symmetry is broken as θ continues to increase. More importantly, the maximum and minimum values are equal. The corresponding amplitude of the target body reaches a maximum when θ and phi = 0°, and the response amplitude decreases as the inclination angle increases. Moreover, the values of the maximum and minimum values are not the same. The pattern allows a rough identification of the attitude distribution of the underground target body.

As shown in Fig. 12, when theta = 0°, the y-component response moves upward as phi increases. However, it has always been symmetric about x-axis. At the same time, the y- component response has different values for the maximum and minimum values. At phi = 0°, the amplitude of the y- component response decreases as theta increases and the overall distribution shifts to the right. The y-component response is essentially similar to the x-component response, with a good symmetry in the target body x (or y)-component response for either theta = 0 or phi = 0. Furthermore, the values of the magnitude of the maximum and minimum values can also identify the attitude of the unexploded ordnance. The maximum value always corresponds to the direction of the head of the unexploded ordnance.

The horizontal component response of the target body at different attitudes is calculated in Fig. 13, where the target body is located at -0.5m. The three rows of the horizontal component response represent theta = 0°,30° and 60°, and the three columns represent phi = 0°,30° and 60°, respectively. As shown in Fig. 13, the horizontal component response amplitude has circular symmetry when $\theta$ and $\varphi ={0^ \circ }$. The position of the target body is its center of symmetry, and the horizontal component response has a minimal value point above the target body. The horizontal component response at the location of the target body is the smallest, and the outward response amplitude increases first and then decreases. The horizontal component response has great and small values on both sides of the long axis position of the target body when θ = 30° and 60°. The target body horizontal component response varies with phi when theta > 0°. The minimum of the horizontal component shifts to the right and the maximum to the left, varying with θ. The response continues to be distributed in circular symmetry after moving away from the target body. The horizontal component of the target body is minimum at θ and phi = 60°, and maintains a short axis symmetric distribution around the target body. As theta increases, the horizontal response moves to the right and the amplitude decreases. The axisymmetric characteristic is gradually broken, and the extreme value on the right side hardly varies corresponding to the tail of the shell, and the extreme value on the left side first decreases and then increases corresponding to the head of the shell when θ increases from 0° to 60°. It can be seen that the center of the line connecting the maximum and minimum of the horizontal component is the location of the long axis of the target body. The rotation angle of the target body can be determined from the symmetry axis of the horizontal response component of the target body. It can be seen that the horizontal component of the planar response contains both the target body inclination information and the position characteristics.

As shown in Fig. 14, the z-component response of the target body is much higher in magnitude than the x-component response, the y-component response and the horizontal component response. When theta = 0°, the z-component response decreases as phi increases and the overall distribution is always symmetric about the y-axis. When theta = 0°, there is always circular symmetry with the position of the target body, and the z-component response is greatest at the location of the target body, decreasing in amplitude outwards. The maximum value of the z-component response of the target body follows the changes in theta and phi. The amplitude of the z-component response of the target body is much larger than the horizontal component response, which is beneficial for improving the signal-to-noise ratio. However, the z-component response identifies the attitude of the target body to a much lesser extent than the horizontal component response. Therefore, a three-component receiver coil needs to be designed to improve the detection performance of the system while obtaining the z-component and horizontal component.

Summarize

We investigated the electromagnetic response model of unexploded ordnance by COMSOL MULTIPHYSICS based on the finite element method. The results of the theoretical response of a solid nonmagnetic iron sphere and the response of a finite element model of the identical geometry are first compared. After establishing confidence in the finite element procedure, we extended the finite element modelling to the complex geometry of real UXO. Next, we adopted a homogeneous half-space for modelling the 3D geological body in order to make the UXO buried in a more realistic geographical environment. The design of the magnetic coupling source and the related parameters are derived and analyzed in detail. The electromagnetic response characteristics of UXO with transient electromagnetic excitation are explored. We conclude that the attitude and position of the target body cannot be identified by the time-domain response of the z-component in the single-transmitter-single-receiver sensor operation mode. The transient EM sensing system of single-transmitter and triple-receiver was established, which can not only realize the rapid localization of the target body, but also obtain richer EM response data to realize the inversion. The multiple attitudes and depths of the target body are investigated in detail through the line and plane responses. The combination of line and plane response provides multi-attitude information about the target body including the principal axis deflection angle and depth of the UXO. The x component is symmetric about x = 0 at θ = 0° in the measured line response. The amplitude of the x-component response on the left side of the symmetry axis is greater than that on the right side indicates θ > 0° and conversely, θ < 0°. Extremely large and small values arise in the two-dimensional plane response, as θ and $\varphi$ vary. This is related to the shape of the front and rear ends of the UXO. The direction of the main axis of the UXO can be determined by connecting the maximum and minimum values. Reasonable geoelectric modelling combined with field experiments can not only improve the exploration efficiency but also provide assistance for the selection of instrument parameters and data interpretation. The numerical results show that optimized three-component receiver coils placed at suitable locations can greatly improve the detection efficiency and provide a reference for the preparation of sensing systems.

Data availability statement

All data generated or analyzed during this study are included in this published article [and its supplementary information files].

Author contributions

T.L.: design, simulation, analysis of data, writing original draft. H. G.: conceptualization, methodology, review manuscript. L.C., G.C. and M.Z.: provides the original experimental data and some thoughts. B.Z. and R.X.: conducted the final review of the paper. All authors reviewed the manuscript.

Competing interests

The authors declare no competing interests.

Additional information

Correspondence and requests for materials should be addressed to H.G.

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Liu, H. et al. Active Detection of Small UXO-Like Targets through Measuring Electromagnetic Responses with a Magneto-Inductive Sensor Array. IEEE Sens J 21, 23558–23567 (2021).
Lhomme, N., Pasion, L. R., Billings, S. D. & Oldenburg, D. W. Inversion of frequency domain data collected in a magnetic setting for the detection of UXO. in Detection and Sensing of Mines, Explosive Objects, and Obscured Targets XIII vol. 6953 69531I (SPIE, 2008).
O’Neill, K., Haider, S. A., Geimer, S. D. & Paulsen, K. D. Effects of the ground surface on polarimetric features of broadband radar scattering from subsurface metallic objects. IEEE Transactions on Geoscience and Remote Sensing 39, 1556–1565 (2001).
Schneidhofer, P. et al. Geoarchaeological evaluation of ground penetrating radar and magnetometry surveys at the Iron Age burial mound Rom in Norway. Archaeol Prospect 24, 425–443 (2017).
Beard, L. P. et al. Field tests of an experimental helicopter time-domain electromagnetic system for unexploded ordnance detection. GEOPHYSICS 69, 664–673 (2004).
Song, L. P., Oldenburg, D. W., Pasion, L. R., Billings, S. D. & Beran, L. Temporal orthogonal projection inversion for EMI sensing of UXO. IEEE Transactions on Geoscience and Remote Sensing 53, 1061–1072 (2015).
Yin, C., Qi, Y. & Liu, Y. 3D time-domain airborne EM modeling for an arbitrarily anisotropic earth. J Appl Geophy 131, 163–178 (2016).
Chen, S., Zhang, S., Luan, X. & Liu, Z. Improved Differential Evolution Algorithm for Multi-Target Response Inversion Detected by a Portable Transient Electromagnetic Sensor. IEEE Access 8, 208107–208119 (2020).
Li, J. H., Zhu, Z. Q., Liu, S. C. & Zeng, S. H. 3D numerical simulation for the transient electromagnetic field excited by the central loop based on the vector finite-element method. Journal of Geophysics and Engineering 8, 560–567 (2011).
Zhu, X., Shu, Y., Luo, C., Huo, F. & Zhu, W. Transient Electromagnetic Voltage Imaging of Dense UXO-Like Targets Based on Improved Mathematical Morphology. IEEE Access 8, 150341–150349 (2020).
Queralt, P., Jones, A. G. & Ledo, J. Electromagnetic imaging of a complex ore body: 3D forward modeling, sensitivity tests, and down-mine measurements. Geophysics 72, (2007).
Spies, B. R. Depth of Investigation in Electromagnetic Sounding Methods. GEOPHYSICS vol. 54 (1989).
Chen, S. et al. An improved high-sensitivity airborne transient electromagnetic sensor for deep penetration. Sensors (Switzerland) 17, (2017).
Churchill, K. M., Link, C. & Youmans, C. C. A comparison of the finite-element method and analytical method for modeling unexploded ordnance using magnetometry. IEEE Transactions on Geoscience and Remote Sensing 50, 2720–2732 (2012).
Liu, Y. & Yin, C. 3D anisotropic modeling for airborne EM systems using finite-difference method. J Appl Geophy 109, 186–194 (2014).
Wang, L., Zhang, S., Chen, S. & Jiang, H. Fast localization of underground targets by magnetic gradient tensor and gaussian-newton algorithm with a portable transient electromagnetic system. IEEE Access 9, 148469–148478 (2021).
Wigh, M. D., Hansen, T. M. & Døssing, A. Synthetic case study: Discrimination of unexploded ordnance (UXO) and non-UXO sources with varying remanent magnetization strength using magnetic data. Geophys J Int 228, 773–791 (2022).

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The Electromagnetic Characteristics of UXO Using the Electromagnetic Method

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