The Transient Electromagnetic Response of UXO in Complex Three-Dimensional Terrain

In practical exploration, the complex and diverse topographic effects are important for the processing and interpretation of EM exploration data. The interpretation of the electromagnetic data results in large errors when the influence of topographical factors is simply ignored. At present, the study of TEM is mainly based on the ideal situation of flat terrain, and the study of topographic effect is less. However, topographic relief is inevitable in practical exploration. In this article, the correctness of the time-domain 3-D forward evolution based on the finite-element method (FEM) is verified by comparing the numerical results with those of the homogeneous full-space and half-space analytical solutions and the lumped high conductor model. In this article, 3-D numerical simulations of time-domain transient electromagnetic methods are calculated based on the FEM. Several exploration scenarios for complex terrain were constructed under the transmitting loop source, and the effect of terrain size and filling medium changes on the electromagnetic response was analyzed. The parameters of the topographic effect, earth resistivity, surface resistivity, and target conductivity are analyzed from the z-component of the magnetic field, apparent resistivity, and time-domain numerical solution, and the relative error distribution results in the whole observation period are shown. The results show that the influence of topographic effects on the electromagnetic response is concentrated in the early part of the time domain, with puddles of the same size having a higher influence on the electromagnetic response than raised soils and hollows. In practical exploration, puddles should be avoided where possible, whereas small-sized topographic reliefs and hollows have a negligible effect on the electromagnetic response.

The Transient Electromagnetic Response of UXO in Complex Three-Dimensional Terrain Taoming Lu , Huotao Gao , Shengjie Lv , Wang Yao , Yunkun Yang , Bin Zhang , and Yanjie Xiang Abstract-In practical exploration, the complex and diverse topographic effects are important for the processing and interpretation of EM exploration data.The interpretation of the electromagnetic data results in large errors when the influence of topographical factors is simply ignored.At present, the study of TEM is mainly based on the ideal situation of flat terrain, and the study of topographic effect is less.However, topographic relief is inevitable in practical exploration.In this article, the correctness of the timedomain 3-D forward evolution based on the finite-element method (FEM) is verified by comparing the numerical results with those of the homogeneous full-space and half-space analytical solutions and the lumped high conductor model.In this article, 3-D numerical simulations of time-domain transient electromagnetic methods are calculated based on the FEM.Several exploration scenarios for complex terrain were constructed under the transmitting loop source, and the effect of terrain size and filling medium changes on the electromagnetic response was analyzed.The parameters of the topographic effect, earth resistivity, surface resistivity, and target conductivity are analyzed from the z-component of the magnetic field, apparent resistivity, and time-domain numerical solution, and the relative error distribution results in the whole observation period are shown.The results show that the influence of topographic effects on the electromagnetic response is concentrated in the early part of the time domain, with puddles of the same size having a higher influence on the electromagnetic response than raised soils and hollows.In practical exploration, puddles should be avoided where possible, whereas small-sized topographic reliefs and hollows have a negligible effect on the electromagnetic response.

I. INTRODUCTION
T HE transient electromagnetic is an important detection method that has been developed rapidly in the field of geophysics in recent years [1], [2], [3].It has the characteristics of large detection depth, high sensitivity, convenience, and low cost, and is widely adopted in metal, petroleum, mineral, coal, Taoming Lu, Huotao Gao, Wang Yao, and Yunkun Yang are with the Electronic Information School, Wuhan University, Wuhan 430072, China (e-mail: 15516590571@163.com;gaoght863@163.com;yaowang070907@qq.com;yangyk16@whu.edu.cn).
Digital Object Identifier 10.1109/JSTARS.2023.3332451geothermal, and groundwater detection.However, in reality, field exploration conditions are usually complex and variable.
The quality of the data can be influenced by a variety of factors such as terrain conditions, human disturbance, and environmental factors, and particularly the impact of terrain on the detection data cannot be ignored.Most of the current processing and interpretation of transient electromagnetic exploration data is predicated on the ideal situation of flat terrain [4].In China, there are numerous mountains, plateaus, and hills, and these areas of complex terrain cover approximately half of the total land area, with ideally flat terrain rarely existing.The effects of complex terrain are easily misinterpreted into the subsurface target body when flat terrain data is applied directly for calculation and processing, in areas of complex terrain where exploration work conditions are implemented.This will make large errors in the interpretation of the data and result in the electromagnetic response of the real target body in the subsurface being obscured.
With the constant development of computational and electromagnetic exploration techniques, it has emerged as an important research instrument to investigate the effects of complex terrain on electromagnetic data by applying numerical simulation methods.The utilization of numerical simulation methods will not only reduce exploration costs and waste of collected data but will also simplify complex terrain problems in near-realistic exploration conditions.Therefore, the investigation of numerical forward simulations of transient electromagnetic systems under complex terrain conditions is an important guide to both practical exploration and data interpretation.Air-borne transient detection systems, vehicle-borne transient detection systems, and portable transient electromagnetic mine detectors have been designed based on the convenience, speed, and low false alarm rate of the transient electromagnetic method [5], [6].The frequency-domain airborne electromagnetic (AEM) response of several typical terrains, such as slopes, ridges, and valleys, has been performed by Liu and Becker [7] employing the boundary element method.The authors in [8] and [9] implemented a 3-D numerical simulation of the frequency-domain AEM utilizing a staggered mesh-based finite-element method (FEM) and simulated the AEM response under simple topographic conditions.The authors in [10], [11], and [12] successfully simulated the forward modeling of a small-range 3-D geological body by using finite differences.In 2-D modeling, the authors in [4], [13], [14], and [15] used a finite element (FE) program to correct the effects of terrain.Nam et al. [16] used the edge FEM to calculate the response of 3-D terrain to magnetotelluric.Ansari et al. [17] used a variety of software to build the real geological body, tetrahedral partition and realized the forward modeling of the geoelectric model.Franke et al. [14] proposed an adaptive unstructured triangular mesh FEM, which can effectively simulate 2-D structure models.This method has been successfully applied to terrain surfaces containing arbitrary geometric shapes.
In particular, 2-D simulations were mainly calculated, with fewer 3-D simulation results considering complex terrain conditions, and the impact of the entire terrain was rarely assessed over the entire observation time period [13].At present, the transient electromagnetic response in undulating terrain can be simulated by a variety of numerical methods, including the integral equation (IE) method [12], [18], [19], finite difference method (FDM) [10], [13], [20], [21] [10], finite volume method and FEM [22], [23], [24].However, there are difficulties in solving Green's function for complex terrain conditions with the IE method.The FDM is simple to implement but cannot be discretized into an unstructured grid.It is difficult to obtain numerical simulations with high-order accuracy using the finite volume method.The FEM has become the most widely adopted method for solving 3-D orthogonal problems in electromagnetism because of its ability to be discretized into unstructured meshes, its flexibility in local mesh optimization, and its applicability to complex geoelectric models.
Most of the numerical simulations result in the use of a large loop source (with a loop side length of several hundred meters) while frequently ignoring the deformation.This kind of model usually combines Maxwell's equations and boundary conditions to solve for the electromagnetic field distribution in a geometrical model of the dielectric by the vector FEM imposed on the source by complex terrain conditions.The portable exploration system is more practical than the large loop line source exploration system since it not only reduces manual set-up but also enables exploration in a variety of complex terrain conditions.In this article, the ground transient electromagnetic response with topography is calculated based on the FEM based on a portable emission source.However, considering the simulation scenario of complete and complex terrain, it will be difficult to separate the coupling between terrain and multiple parameters such as emission source and receiving source.This will require the establishment of a large number of simulation scenarios to explore the influence of a single parameter change on the electromagnetic response.In this article, only small terrain exploration scenarios such as puddles, voids, and ridges that may be encountered on the surface of the plain are considered to explore the numerical results of electromagnetic response under different terrain parameters.In this article, the accuracy and precision of 3-D forward modeling based on the vector FEM are verified by using a full-space analytic solution and numerical solution of the high conductor model as a reference.The depressions of different sizes are constructed under the emission loop source, and the depressions are filled with air and rain, respectively, to simulate the actual holes and puddles in the exploration.The ridges of different sizes were constructed to simulate the soil-raised areas in the actual exploration.We show the relative error distribution results for different terrain conditions over the entire observation period compared with the next step response of a homogenous half-space model.The effect of the variation of the electrical parameters of the terrain on the transient electromagnetic response is shown.The electromagnetic response rules under complex terrain conditions are analyzed and summarized in detail.

II. 3-D FORWARD THEORY
The 3-D numerical simulation of electromagnetic exploration by the FEM requires modules that include geometric modeling, mesh discretization, and solving systems of partial differential equations.However, these modules have already been applied in mature applications, and repeating the investigation will take a lot of effort and time, and it is difficult to obtain breakthrough progress.In many numerical simulation software and opensource libraries based on the FEM, COMSOL 6.0 is widely applied as a multiphysics simulation software in many fields including electromagnetic, mechanics, acoustics, and chemical engineering.Therefore, a 3-D peak and valley model was created with the assistance of the COMSOL for numerical simulation and analysis of the electromagnetic response characteristics of both models.This provides guidance in the design of exploration systems and reliable theoretical support in practical exploration work.
In this article, the numerical simulation of the electromagnetic characteristics of the electric and magnetic field (MF) in the steady state, transient, and frequency domains is carried out with the ac/dc module in COMSOL.The module combines Maxwell's equations and boundary conditions to solve the electromagnetic field distribution within the dielectric of the geometric model by the vector FEM.Low-frequency electromagnetic sources are usually adopted in transient electromagnetic exploration, and the effect of displacement currents can generally be neglected, considering the quasi-static mode with the following Maxwell's equations: where H is the MF strength, E is the electric field strength, B is the magnetic induction intensity, D is the electric displacement vector, J e is the applied field source current density, σ is the ground model conductivity, ρ v is the body free charge density, and t is time.We redefine the electric field and MF by introducing the potential function to solve the system of time-domain equations where A is the vector magnetic potential and ϕ is the scalar potential function.Combining ( 2) with ( 1) and appending the current continuity equation to obtain the system of equations in Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
the time domain where μ o is the magnetic permeability in a vacuum.The following system of frequency-domain equations can be derived from the condition e iwt : where ω = 2πf is the angular frequency and f is the frequency.We solve ( 3) and ( 4) with the Dirichlet boundary conditions as follows: where ξ is the outer boundary of the computational region and n is the outer boundary unit normal vector.The geometric model in the calculation region is discretized by the vector FEM to form the corresponding system of numerical model equations.
The numerical solution of A at the grid cell is then solved by either the direct method or the iterative method.
Transient electromagnetic exploration is a method for solving the electromagnetic response characteristics of a target body in the time domain.Therefore, we directly select the transient study and calculate the time step through the backward difference equation.

III. 3-D FORWARD MODELING VERIFICATION
In this section, the numerical simulation process of the transient electromagnetic response (geometric modeling, grid discretization, time step, etc.) will be explored through the MF physics field in the COMSOL ac/dc module.The reliability of the computational process is verified by the analytical solution as well as the available literature to ensure the validity of the numerical simulation and subsequent analysis of the transient electromagnetic response, so that reasonable modeling parameters can be obtained.Magnetic dipole source detection is a relatively common device for working with transient electromagnetic fields.Assuming a sphere of conductivity σ, radius a, and central burial depth h located directly below the circular emission loop, the expression for the transient electromagnetic field for the coincident-loop TEM device is given as follows: where R is the radius of the circular transmitter loop and L/ √ pi for the square transmitter loop.τ is the time constant, which gives the expression for the sphere: τ = μ 0 σa 2 /π 2 .Next, we verify the validity of the 3-D forward numerical simulation of the transient electromagnetic method with (6).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 emission loop is 0.5 m, the current magnitude is 5 A, and the number of turns is 30.The use of lower frequencies and natural Dirichlet boundaries in the EM method requires a large enough geometric region to avoid edge truncation effects.
The infinite element domain is added to the periphery of the geometric region to improve the accuracy and efficiency of the calculation.The infinite elementary domain can be specified with central coordinates and the geometric region stretched along a specific coordinate axis, which serves to approximate an infinite domain and effectively avoid edge truncation effects.The emission current is set to the lower step current waveform, and the electromagnetic response of any waveform of current can be obtained by convolving the lower step response with the real current waveform.In this model, the excitation current is turned ON and OFF for about 10 ms and 40 μs, respectively.The excitation field turn-ON duration was determined empirically, whereas the turn-OFF time was derived from [25] and [26].The target body is located directly below the circular transmitting coil with the parameters σ = 1.12e7S/m, a = 0.032 m, h = 0.4 m, and τ = 0.00146s.Fig. 1 illustrates the COMSOL numerical and analytical solutions for the transient electromagnetic response for coincidentloop devices in homogenous full space.The curves are essentially identical for the late conditions at t >> τ , which can be seen in Fig. 2. The error in the numerical simulation for the late conditions is approximately 5%, indicating that it is feasible to carry out the transient electromagnetic method forward numerical simulation utilizing COMSOL.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.
Next, the reliability of the electromagnetic exploration method in 3-D modeling and simulation is further verified by including a 3-D geoelectric model of a massive subsurface anomaly.In this model, a highly conductive anomaly with an electrical conductivity of 2 S/m is buried in a 3-D homogeneous The size of the rectangular transmitting loop is 100 × 100 m and the current is set to 1 A. The geoelectric model was first implemented by Newman et al. [10] in 3-D forward of the electromagnetic method using the IE method, and detailed geometrical parameters can be obtained from.We compared the COMSOL numerical solution to the IE for the frequency-domain MF response of a geoelectric model with a block conductor.As shown in Fig. 2(a), the numerical solution calculated by COM-SOL agrees well with the IE solution.We then compared the COMSOL numerical solution, the IE solution, the time-domain finite difference solution (FDTD), and the FE solution for the time-domain MF response of a geodesic model containing a block conductor.Li et al. [27] adopted the FEM for numerical calculations by first calculating the frequency-domain response and then using the cosine transform to obtain the time-domain numerical results.This method of frequency-time transformation is an indirect calculation method.The COMSOL numerical results in this section are also calculated by simulation with FEM.However, the time-domain solution is obtained in time steps, which is a direct method.The electromagnetic response is solved directly in the time domain by discretizing the time in a differential format.As shown in Fig. 2(b), the numerical solution of this modeling agrees well with the IE solution and the FE solution in the range 10 −4 -10 −3 and is slightly larger than the FDTD result in the range 10 −3 -10 −2 .It is worth noting that the IE solutions, time-domain finite difference results, and FE solutions were taken directly from the papers of these researchers and are less accurate than the numerical solutions of the original calculations.Therefore, we have not provided the relative error to these numerical results.

A. Effect of Terrain Change on Electromagnetic Response Characteristics
Unexploded ordnances (UXOs) are mainly made of metal and have a very low resistivity compared to geological layers.However, the resistivity of geological layers is dependent on the structure and properties of the soil.The electrical conductivity of soil varies with its resistivity.The moisture content of the soil and the inclusion of sand and gravel can affect the resistivity.Table I gives reference values for soil resistivity under different conditions (soil depth less than 10 m).Table II shows the electrical conductivity and relative permeability of the main materials in this article.The areas where unexploded bombs exist are usually remote areas, shallow beaches, and test ranges in complex environments, which puts forward strict requirements for the environmental adaptability of detection systems.Moreover, UXOs are buried at very shallow depths, usually about 0-2 m below the surface.In this section, the soil environment where the UXO exists is loess, and its resistivity is set at 100 Ω•m.The main material of the UXO is cast iron (σ = 0.15e7 S/m), and the maximum buried depth is 2 m.Several typical terrains were selected for numerical simulations to investigate the effect of terrain relief on the transient electromagnetic response.We constructed depression regions of different sizes by means of Bessel functions (shown in Fig. 3).The depressed regions were filled with air and rainwater dielectric.The shutdown response of the homogeneous half-space model (without terrain) was used as a reference to investigate the effect of air and rain depression areas on the electromagnetic response respectively.Fig. 3 shows a schematic diagram of the depression region model and the grid discretization.The geologic resistivity of this model is 100 Ω•m, the air conductivity is 10 −6 S/m, and the relative permeability and relative dielectric constant are set as 1.However, considering the restrictions on the portability of coil diameter, mass, and power, the transmit coil diameter and enamel wire cross-sectional area were selected to be 1 m and 1.5 mm 2 , respectively.Thus, the winding type can be determined with the number of winding turns N = 30 and the coil height h = 7cm given.In this model, the input current is  depression regions were grid-encrypted to balance efficiency and computational accuracy, and the layers near the ground were also locally grid-encrypted (shown in Fig. 3).The depth variation parameters of the depressed region were 0.1, 0.3, and 0.5 m, where the conductivity of rainwater was 0.2 S/m.The time-domain response is calculated in the range 10 −6 -10 −2 s, with 50 time points per ten times the frequency in the logarithmic domain.In model calculations, depressed regions of the same geometry (e.g., 0.5 m deep) should be on the same grid profile, regardless of whether the filling material is air, rain, or geological bodies.In the calculation of relative errors, the same grid is preserved to avoid numerical errors caused by different grid profiles.
Most previous studies have shown that the Bz component of the electromagnetic response is the most conducive to generating images [28].The images it generates are not only related to the geometric structure of the target but also easy to interpret the data.Therefore, we showed the relative error results for the MF response Bz and the homogeneous half-space model from −4 to 4 m.The detection system starts from x = −4 m, moves along the measurement line (Position is x1,0,1), and conducts detection at a distance of 25 cm.Finally, the Bz component of MF response is selected for plotting.The relative error profiles of the timedomain numerical solutions with respect to the homogenous half space in the presence of 0.1-, 0.3-, and 0.5-m air hollows are given in Fig. 4.
The horizontal coordinate is the measured line response and the vertical coordinate is time.It is worth noting that the increase in hollow depth is accompanied by an increase in relative error to around 0.04%.It can be seen in Fig. 4 that a larger area of influence appears around 10 −6 s compared to the homogeneous half-space terrain.The relative error and area of effect increase as the depth of the depression region becomes greater.The results of this error distribution are mainly related to the propagation characteristics of the primary field.After the magnetic coupling source emits a downward step current, a broadband excitation is formed and the induced eddy currents in the subsurface dielectric are excited.In the early period, the high-frequency resonance component of the frequency spectrum dominated.The high frequencies have a skinning effect, resulting in eddy currents being concentrated mainly near the surface layer of the dielectric.The high-frequency component is absorbed by the dielectric as time increases.The low-frequency component begins to dominate and it excites very strong eddy currents in the geological body.The secondary field generated by this induced eddy current was received by the receiving source at a later time.However, the generated eddy currents also disappear quickly due to the presence of heat losses.The distance between the secondary field and the receiver point increases as the depth of the depression becomes greater, therefore the relative error gradually increases.The early response mainly reflects geological information at the surface, with time the influence of the surface topography diminishes and information from the deep subsurface medium was demonstrated.Moreover, the magnitude of the influence is also related to the distance from the receiver point.It can be seen from Fig. 4 that the areas of larger error formation are concentrated within a certain time period, with the relative error increasing the further the surface of the depression terrain is from the reception point.The overall error level increases with increasing distance from the depression surface, and yet the greater resistivity of the geological body generates eddies that disappear in a very rapid time.In the actual exploration, when there are depressions less than 0.5 m on the plain surface, the error effect of the hollow topography on the electromagnetic response is basically negligible.Fig. 5 shows the relative error results for the time-domain numerical solutions for 0.1, 0.3, and 0.5 m depressed regions filled with rainwater with respect to a homogeneous half space.The relative error results increase for the same depression regions compared to Fig. 4. The distribution of the relative error results is mainly concentrated in the early part of the receiving source, which is generally consistent with the distribution pattern in Fig. 4. The maximum relative error increases to about 1.40% with increasing depth.The region with the highest relative error is not only time dependent but also related to the depth of depression.The electrical conductivity of rainwater is greater than that of the geological body, and greater induced vortices are excited, compared to the depressed regions filled with air.Thus, the secondary fields received are also more intensified.The effect of rain on the transient electromagnetic response is also greater than that of air for the same size of depression region.
Fig. 6 shows the results of the relative error distribution of the time-domain numerical solutions for topography at different heights of the bulge with respect to a homogenous half-space model.The regions with large relative errors are concentrated in the early time periods.The higher the raised area and the closer the receiving source is to the ridge topography, the greater the relative error.The overall level of error increases as the height of the ridge continues to increase.The maximum relative error area is gradually shifted to a more concentrated area due to the influence of height.The main effect of this error distribution is related to the penetration characteristics of the electromagnetic signal.The higher frequency electromagnetic signals penetrate at shallower distances and cause induced eddy currents in the shallow subsurface medium, where the secondary fields generated by the eddy currents are acquired at an earlier time.The earlier the reception time, the higher the frequency component contained.The frequency components of the electromagnetic signals causing induced eddy currents differ when the ridge topography is at different heights, thus the relative error is not only height-dependent but also time-dependent.As shown in Fig. 6, there are slight changes in both time and distance in the electromagnetic response of the ridge compared to Fig. 4. The ridge topography corresponds to an increased part of the dielectric region compared to the homogeneous half space, increasing the induced vortices and generating a stronger secondary field.This makes the relative error areas more concentrated compared to Fig. 4. The valley terrain provides a reduced time and distance response.The valley topography is a reduced part of the dielectric region compared to the homogeneous half space, and the lack of induced eddy currents in this part makes the secondary field smaller than in the homogeneous half space.In this section, different sizes of terrain are set up, and it can be found that these sizes of terrain have less impact on the electromagnetic response.In actual exploration, terrain much smaller than the size of this section exists on the plain surface and the effect of terrain on the electromagnetic response can be largely ignored.

B. Electromagnetic Response of Target Bodies in Complex Terrain
In complex terrain conditions, the maximum relative error caused by topography is 1.40% (shown in Figs.4-6).The global apparent resistivity curve is calculated to get a more intuitive understanding of the effect of topographic effect.We have chosen a condition of 0.5 m for both depression depth and ridge height to form a complex terrain and use the numerical solution of a homogeneous half-space model as a reference.The effect of complex terrain on the electromagnetic response of the target body is explored through ridges and valleys which are filled with air and rain, respectively.It should be noted that compared with homogenous half-space modeling, the MF response errors caused by 0.5-m depression and ridge regions are smaller and are concentrated in the early time period.The relative error of the central area under the most severe rain conditions is only 1.40%, and the error of the late period is basically below 0.10%.For the multichannel plots of MF Bz components, it is difficult to distinguish the effects of complex terrain in the range of H depth = 0.5 m.Therefore, this section does not provide the distribution of MF response multichannel results under complex terrain conditions.
The target body is an artillery shell of diameter (D = 82 mm), the main component of which is cast iron.The material characteristic parameters of unexploded bombs are all taken from Table II.The UXO was retrieved from the material store after being certified safe by the authorities and the geometric parameters were measured by hand.The geometric parameters of the unexploded bomb are modeled in CAD-2018 and imported into COMSOL 6.0.
The numerical solution for the apparent resistivity of the transient electromagnetic response without topography is displayed in Fig. 7.The parameter Settings of the numerical calculation model in this section are consistent with those in the previous section.The maximum depth of the geometric center of the target body from the surface of the terrain is 1 m (shown in Fig. 3).The apparent resistivity showed low resistance anomalies in the early stage.The conductivity of the target body σ = 0.15e7 S/m and the numerical calculation results of apparent resistivity are shown in Fig. 7(b).The presence of a low-resistance abnormality at a late stage is evident in the apparent resistivity as time continues to increase.The apparent resistivity for valley topography conditions is shown in Fig. 8.The apparent resistivity of the   valley topography conditions is essentially identical compared to Fig. 7(a).The apparent resistivity of the anomalies in the valley topography conditions is essentially the same compared to Fig. 7(b).It is noteworthy that the apparent resistivity maximum is greater than presented in Fig. 7(b).The effect of complex terrain on apparent resistivity is almost negligible, which can be seen in Figs.7-10.The numerical solution for the apparent resistivity also remains consistent with the results of the previous section.The apparent resistivity is greatest for rainfall conditions, followed by peaks and least for valleys, with respect to the homogenous half-space numerical solution for conditions without topography.The distribution patterns in Figs.8-10 are generally consistent and it is difficult to distinguish the impact of topography, compared to that provided in Fig. 7, which does not contain topography.In practical exploration, the effect of topography on the electromagnetic response is negligible for complex terrain sizes smaller than those in this section.

A. Topographic Surface Resistivity Variation
In complex terrain conditions, the main consideration in this article is the undulation of the terrain surface.The maximum dimensions of ridge height and valley depth were limited to 0.5 m in the context of the actual exploration environment.From previous studies, it can be found that complex terrain with a size of about 0.5 m still has a small effect on the electromagnetic response compared to models without terrain.However, in practical exploration, the electrical parameters of terrain are often affected by geological characteristics and the natural environment.The natural environment of weathering, erosion and rainfall can cause variation in the resistivity of the terrain surface.Therefore, this section explores the effect of geological surface resistivity variations on the electromagnetic response through a homogeneous half-space model.This section shows the normalized time-domain response of the Z-component of the MF at the center point of the emitted loop source.Fig. 11 illustrates the time-domain numerical solution at the center point of the receiving source for different conditions.The electromagnetic response of the Z-component of the MF is observed by varying the resistivity of the geological surface and its thickness respectively.The homogenous earth resistivity is set to 100 Ω•m.The electromagnetic response changes and the curves gradually coincide when resistivity keeps increasing to 100 Ω•m.The initial value error of the MF response decreases with the increase of the resistivity.The smaller the resistivity the greater the conductivity the greater the induced eddy currents and the stronger the secondary fields they generate.The amplitude of the MF response is not only related to the thickness of the geological surface layer but also to the resistivity.The changes in the topographic surface mainly affect the electromagnetic response over a certain time period and are associated with the early response.The variation in MF response occurs mainly  in the early response from 1 * 10 −6 -5.5 * 10 −6 .The deeper geological information is shown with increasing time, which is consistent with the conclusions of the previous section.The topographic effect is mainly related to the characteristics of the ground surface, and the effect of the low-resistance surface layer is much greater than that of the high-resistance surface layer.

B. Effect of Terrain Resistivity Changes on Transient Electromagnetic Response
The time-domain solutions of the electromagnetic response for terrain conditions loess, clay, rock, and sand are shown to further investigate the effect of terrain resistivity on the transient electromagnetic response.We adopted homogeneous half space for modeling, the earth soil is loess, and the UXO material is cast iron as a reference, and the numerical simulation results are shown in Fig. 12.The numerical results of Fig. 12(a) (without target) show that the variation of terrain resistivity has a significant effect on the transient electromagnetic response.The initial amplitude and decay rate of induced voltage induced by terrain are both affected by terrain resistivity.Fig. 12(b) (target) shows the electromagnetic response results under different terrain resistivity and full-space models respectively.Meanwhile, the background of the full-space model is air, and the conductivity is 1E-6 S/m.Throughout the decay process, the terrain resistivity has a significant effect on the initial amplitude of the induced voltage compared to full space modeling.The smaller the topographic resistivity, the larger the initial amplitude of the induced voltage.Therefore, the induced voltage can be roughly divided into early and late responses throughout the decay process.The early response is mainly determined by the resistivity of the terrain, and the late response is determined by the target.The resistivity of the terrain has a significant effect on the TEM response, and the TEM response varies greatly between resistivity conditions for the same terrain.In the actual exploration, it is far from enough to interpret the terrain through resistivity characterization and geological landform.It is necessary to process and interpret the data in relation to the actual geological data.

C. Effects of Changes in Conductivity on the Electromagnetic Response of Target Bodies (Including Complex Terrain)
The resistivity distribution is largely consistent as can be seen from the results of the exploration in the previous section, and it is difficult to distinguish the effect of topography on the electromagnetic response of the target body.This section calculates the time-domain solution model containing the target body and complex terrain.The effect of complex terrain conditions on the electromagnetic response of the target body and a comparison with a homogeneous half-space model (without topography).The main material of the target body is cast iron and the material properties are taken from Table II.Fig. 13(a) shows that the Z-component response of the target body is basically the same under various terrain conditions.The effect of topographic effects is small and can be ignored for exploration data containing topographic effects under conditions where the target body produces a strong secondary field.The Z-component electromagnetic response of the main constituent materials of the target body under homogeneous half-space modeling is shown in Fig. 13(b).The initial amplitude and decay rate of Z-component-induced voltage are affected not only by the electrical conductivity but also by the relative permeability.The lower the conductivity of the target, the higher the initial amplitude of the induced voltage and the faster the decay rate.The higher the conductivity of the target, the lower the initial amplitude of the induced voltage and the slower the decay rate.However, the relative permeability also affects the initial value of the induced voltage and the decay rate (shown in Fig. 13(b).Therefore, the detailed material characteristics of the target will help to improve the accuracy of exploration.

VI. CONCLUSION
In this article, a transient electromagnetic detection method was adopted.With the sensing equipment 1m from the ground surface, we constructed a variety of exploration scenarios below the transmitter loop.The holes, puddles, and soil bulges commonly encountered in plain terrain are simulated by FEM.The effects of terrain size, terrain electrical parameters, and target material parameters on the transient electromagnetic response are analyzed and summarized in detail.The topographic effect has a certain influence on TEM response, and the relative error is mainly concentrated in the early period, and gradually decreases with time.
1) The effect of puddles on the electromagnetic response is higher than that of hollows and raised soils for the same size.In actual exploration, the sensor trajectory should avoid large puddles as much as possible, whereas terrain smaller than the puddles, hollows, and ridges described in this article can be ignored.
2) The ridge topography of the same geometric size has a greater influence on the electromagnetic response than the valley topography.The effect of valley topography on the electromagnetic response is to reduce the secondary field response in the early time periods, whereas ridge topography is the opposite.The effect of topographic effect on electromagnetic response is mainly manifested in the early time period, and the effect in the late time period is very small.3) With the decrease in geometric size, the degree of terrain influence gradually decreases, and the electromagnetic response is mainly concentrated in the early period.The area affected by the electromagnetic response is basically the same as the width of the terrain.The effects of terrain effect, electrical parameters of terrain, and material parameters of the target on electromagnetic response were investigated from the MFs, apparent resistivity, and induced voltage, respectively.The effects of the electrical parameters of the terrain and the material parameters of the target on the electromagnetic response cannot be ignored.The terrain resistivity has a greater influence on the initial amplitude of the induced voltage at the target compared to the homogenous full space model; the smaller the terrain resistivity the greater the initial amplitude of the induced voltage.However, the initial amplitude of the induced voltage is also influenced by the conductivity and relative permeability of the target body.Therefore, detailed electrical parameters of the target body are provided to help improve the accuracy of the numerical simulation of the induced voltage.In this article, a large number of models were used to analyze the influence of various factors on TEM response, and the rules were summarized, which provided important guidance for the identification of terrain effects and later data processing.
Taoming Lu received the master's degree in communication engineering from Central China Normal University, Wuhan, China, in 2021.He is currently working toward the doctorate degree in communication and information systems with Wuhan University, Wuhan, China.
His current research interests include transient electromagnetic response in complex terrains.
Huotao Gao received the M.S. degree in radio physics and the Ph.D. degree in electromagnetic field and microwave technology from Wuhan University, Wuhan, China, in 1998 and 2001, respectively.
He is currently a Professor with the School of Electronic Information, Wuhan University.He authored or coauthored more than 90 articles.He holds seven Chinese patents.His research interests include antenna theory and design, the art and science of optical rectifying antennas, radio wave propagation and scattering, radar detection, and signal processing.
Shengjie Lv received the master's degree in broadcasting and transmission from the Communication University of China, Beijing, China, in 2010.
His research interests include radio transmission technology.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

Fig. 1 .
Fig. 1.Comparison of analytical solutions and simulation results.

Fig. 2 .
Fig. 2. Magnetic field responses for a 3-D conductive body embedded in a homogenous half-space.(a) Frequency domain.(b) Time domain.
5 A and the distance from the ground to the transmitting coil is 1 m.The entire calculation region was a 40 m × 40 m × 40 m cube, surrounded by a 5-m-thick infinite element domain.The emission loop and

Fig. 4 .
Fig. 4. Relative error distribution of TEM responses for models with and without the air hole.(a) Air hole: H depth = 0.1 m.(b) Air hole: H depth = 0.3 m.(c) Air hole: H depth = 0.5 m.

Fig. 5 .
Fig. 5. Relative error distribution of TEM responses for models with and without the water hole.(a) Water hole: H depth = 0.1 m.(b) Water hole: H depth = 0.3 m.(c) Water hole: H depth = 0.5 m.

Fig. 6 .
Fig. 6.Relative error distribution of TEM responses for models with and without the soil bulge.(a) Soil bulge: H depth = 0.1 m.(b) Soil bulge: H depth = 0.3 m.(c) Soil bulge: H depth = 0.5 m.

Fig. 13 .
Fig. 13.(a) Time-domain numerical solution of terrain effects on target body response when H depth = 0.5 m and ρ earth = 100 Ω•m.(b) TEM responses at the central receiving point for models with UXO (without topography) at different material properties.