Simulation Analysis Based on COMSOL Helicopter Time-domain Aeromagnetic Method

This paper takes the time-domain aeromagnetic system as the research object and uses the finite element software COMSOL Multiphysics 6.0 to establish the three-dimensional system model. By comparing the COMSOL Multiphysics forward simulation solution with the one-dimensional numerical solution, it verifies that the COMSOL software meets the simulation accuracy requirements of the three-dimensional time-domain aeromagnetic method, and focuses on the analysis of the transient response at different flight altitudes is also analyzed. Based on the analysis of this paper, a set of aeromagnetic parameters with high detection capability is determined for engineering practice, and a test of the system is completed.


Introduction
Airborne Electromagnetic Method (AEM) is a geophysical exploration technology method based on the principle of electromagnetic induction.The method is based on the premise of the difference in electrical and magnetic properties of different underground ore bodies and identifies rare underground materials based on the received data signals, which can quickly achieve the detection of mineral resources over a large area [1].
Airborne AEM systems have been around since 1948 and until 2000 they were dominated by two types of systems installed on two very different types of platforms: fixed-wing AEM time domain systems and HFEM systems.To combine the high transmitting power of fixed-wing systems for deep penetration with the slower speeds and altitudes of HFEM systems for higher spatial resolution or more rugged terrain surveys, research began on helicopter airborne systems [2], where time-domain AEM had a greater depth of detection and a wider range of applications compared to frequency-domain AEM.Therefore, the research and development of time-domain aeromagnetic simulation methods are of great importance for the optimization of aeromagnetic system parameters and the processing and interpretation of measurement data [3].For time-domain airborne EM problems in complex media, including rugged terrain and geological layers, differently shaped target objects, etc., where the target objects often represent local bodies with different structures with anomalous conductivity [4], it is necessary to construct effective 3D models for computation.Multiphysics 6.0 is to build a 3D system model, which improves 3D visualization and thus provides theoretical support for later exploration.

Principle of operation of time-domain aeromagnetic systems
The Helicopter-borne Transient Electromagnetic (HTEM) system consists of a transmitting subsystem, a receiving subsystem, and a data interpretation subsystem.The transmitting device is a metal coil in which a current excitation is applied.The receiving device consists of a receiving coil, which is used to shield the primary field signal [5], and a compensation coil, which is used to collect the secondary field signal.The principle is shown in Figure 1.

Time domain airborne electromagnetic orthorectification theory
The HTEM 1D orthorectified formulation starts from a system of Maxwell equations in the frequency domain and the derivation of the non-flush Helmholtz equation in the active region.Swidinsky and Nabighian [6] deduced the frequency-domain response of the vertical magnetic dipole at a Position (x, y, z) in a uniform half-space to the magnetic field equation: Where h is the height of the emitting source; m is the emitted magnetic moment; R is the distance from the observation point to the magnetic dipole;  is the integration variable; TE r is the reflection coefficient of the electromagnetic field TE mode in the geodetic medium; 0 J is the zero-order Bessel function.
When the observation point is located at the center of the circle of the emission return, i.e., R a  and 0 r  , the equation for the vertical component of the magnetic field of this "central return" arrangement is: The signal measured by the aerial transient electromagnetic method is the induced voltage of the receiving coil: where S is the area enclosed by the receiving coil, and dB dt is the derivative of the magnetic field component perpendicular to the receiving coil concerning time.

COMSOL multiphysics model building
The system can be solved by selecting the magnetic field application mode in the physical field AC/DC module and using the time domain transient step for the calculation.

Geometric construction and parameter setting
The creation of a finite element model is directly related to the speed and accuracy of the simulation.When 3D simulations in uniform full space are done, we consider using a spherical domain and two planes and the work plane function, for splitting out the upper air region and the two lower ground regions, where the ground and air boundary conditions do not need to be set manually and can be automatically coupled within the system to meet the boundary conditions [7].Since COMSOL cannot include a single conductor by setting boundary conditions in the time domain, the anomalous body must be of finite size.The overall model is shown in Figure 2.

Establishment of field sources and boundary conditions
The secondary induction field is excited by adding a step-change and opposite-direction current excitation to the transmitting and compensating coils.Due to the nature of electromagnetic wave propagation and the need for infinite boundary conditions in aerial electromagnetic sounding, an infinite domain is added to the model [8].

Meshing and solver selection
For the simulations in this paper, user-defined mesh dissections were mainly used as the model is highly non-linear.To obtain more accurate results, significant refinement of the anomalies and coils is required.Refinement of the grid within the anomaly requires making at least a few elements within each diffusion distance and corner refinement at the corners of the anomaly to reduce the cell size scale factor.For an infinite domain, a grid subdivision of the entire infinite domain is completed by scanning different paths.
COMSOL built-in solver is divided into the iterative solver and direct solver.Due to the difference of several orders of magnitude in the material conductivity of this model, there will be approximately ill-conditioned problems [9].Direct solvers have better robustness compared to iterative solvers, therefore direct solvers are chosen.

Post-processing
In the two-dimensional plotting group, the horizontal and vertical cross-sections of different parameters can be studied by selecting the two-dimensional cross-sections in the data, which allows a very intuitive observation of the electromagnetic response characteristics of different parameters at different times and depths [10].

Accuracy verification
To check the correctness of the COMSOL finite element simulation model, a homogeneous full-space model with a resistivity of 100 in the lower half-space and air in the upper half-space is constructed in this paper, which is treated as a five-layer homogeneous half-space model with a resistivity of 100 in the first four layers of 200 m thickness for the verification of the 1D algorithm, and the transmitting and receiving coils are horizontal co-center devices located at ground level.A step excitation current of 300 A is applied to the transmitting coil, the transmitting coil has 4 turns and a radius of 12 m, and the receiving coil has an area of 1 m 2 .The simulated solution of the model is compared with the numerical solution to find out the relative error, as shown in Figure 3 and Figure 4 below.In all four models, the induced electromotive force gradually decreases as the altitude of the flight increases.In the early channel, as the electromagnetic wave has just entered the surface, its energy is stronger and the induced electric potential is more affected by the flight altitude.When entering the late channel, due to the absorption and attenuation effect of the underground medium, the energy of the electromagnetic wave is weakened and the induced electric potential is little affected by the flight altitude.From the above analysis of the orthorectified results, in the actual exploration, we keep other conditions constant.To obtain a stronger induced electric potential, one should fly as low as possible.

Experimental validation and results
In engineering practice, the actual coil structure needs to be machined and designed.Given the excessive processing difficulties of aluminum alloy bending, the coils are unified in a square dodecagonal scheme instead of a toroidal scheme, where the transmitting coil has a radius of 12 m and 3 turns, the compensating coil has a radius of 4 m and 1 turn, the receiving coil has a radius of 2 m and 200 turns, and the three coils are placed horizontally and co-centrally.Lay a square abnormal body with a side length of 200 m and a number of turns of 4 on the ground, and use a sling to fix the coil part on the helicopter for flight testing, as shown in Figure 10:

Figure 1 .
Figure 1.Time domain aeromagnetic operating principle

Figure 2 .
Figure 2. Model diagram of a time-domain airborne electromagnetic detection system

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between the simulated and numerical solutions shows that it is feasible to use COMSOL Multiphysics for the numerical simulation of the forward evolution of the time-domain aeromagnetic method.This paper provides basic modeling ideas and operational techniques based on the COMSOL Multiphysics time-domain aero-transient electromagnetic method.Combined with model examples, the transient response of the anomalies of interest at different flight altitudes is obtained, and its rich postprocessing capabilities make the results intuitive and visual, providing a good orthorectification environment for staff.EPATS-2023 Journal of Physics: Conference Series 2636 (2023) 012033 IOP Publishing doi:10.1088/1742-6596/2636/1/012033Based on the transient response results of COMSOL Multiphysics at different flight altitudes and integrated with actual flight experiments, the validity of the COMSOL Multiphysics orthorectified model was determined, providing theoretical support for future field exploration.

Table 1 .
The parameter settings of the geoelectric model are shown in Table1below.Geoelectric model parameters 1 5