1 INTRODUCTION

Transient electromagnetic method(TEM) is a commonly used geophysical method for measuring the secondary electromagnetic field excited by underground vortex current after switching off the transmitter current in the coil or grounded wire(Nabighian and Macnae, 1991; Jiang, 1998; Li, 2002; Niu, 2007) . At present, the popular measurement of TEM method is studying the time variation of the magnetic field(dB/dt) using the induced electromotive force(EMF) in the sensor coil. While tuning off the TX current, the primary EMF is induced in the RX coil, which is mixed with the secondary EMF induced by the underground targets. This phenomenon leads to the missing of early-time TEM data, so as to cause the blind zone during the investigation(Telford et al., 1990; Ji et al., 2006; Wang, 2010) . With the rapid development of railway, highway and urban infrastructure construction, it has become a requisite to carry out shallow geophysical prospecting in limited working space. Thus the TEM configuration has turned smaller and smaller, and the turn number of coils has become larger and larger(Meju et al., 2000; Lin, 2000; Ranieri et al., 2005; Xue, 2007; Yan et al., 2009) . However, it increases the mutual inductance between the TX and RX coils.

To reduce the primary EMF, the TX and RX coils of TEM system are often separated(McNeill, 1991) , but this method cannot eliminate the primary EMF completely. Smith and Balch(2000) , Ji et al.(2007) , Walker and Rudd(2009) proposed to compute the theoretical primary EMF and then subtract it from the measured EMF. However, due to the complexity and variability of the underground targets or configuration, there is always a discrepancy between the theoretical calculation and actual measurement. Kuzmin and Morrison(2011) , Chen(2012) adopted a bucking coil to cancel the primary EMF with the TX/RX/Bucking coils concentric and coplanar. This system was used a lot in airborne TEM surveys. But TX coil of this system is much larger than the RX coils, which makes underground primary field very complex.

Based on the theory that the primary EMF will be zero if the primary magnetic flux through the RX coil never changes with time, we proposed the opposing coils transient electromagnetic method(OCTEM) . In the method, a pair of currents with equal amplitudes and reverse directions is injected into a pair of physically same and coaxial coils, acting as dual opposing coils source; the RX coil is placed coaxially in the middle plane of the dual opposing coils, where the primary magnetic flux is zero all the time as equal and reverse magnetic flux is caused by the dual opposing currents.

We studied OCTEM theoretically and practically in this paper. The primary magnetic field in free space of the opposing coils source has been computed, indicating that it is possible to measure pure secondary EMF by using OCTEM, which has also been proved by field test. The secondary transient electric field has been computed and the results show that, compared to conventional TEM with single coil source, OCTEM has advantage in sensitivity and lateral resolution, which has also been verified by numerical modeling results. Field test of detecting shallow ditch water proves that OCTEM is useful for shallow surface detection.

2 METHOD AND THEORY

The geometry of OCTEM system is showed in Fig. 1, the upper TX⁽⁻⁾ coil and the lower TX⁽⁺⁾ coil are connected in series, they are physically same and coaxial coils, the RX coil is coaxially in the middle of them. The primary field, the secondary field, and the model response are computed as follows.

2.1 Primary Field of OCTEM

Primary field is the magnetic field of the source current. For OCTEM, it can be computed by superposition of the fields caused by TX⁽⁻⁾ and TX⁽⁺⁾ coil. In Fig. 2, suppose a horizontal coil with radius a, carrying current I, and centered at the origin of the cylindrical coordinates system(unit vector: uρ, uθ, u_z) . r, r' are corresponding radius vector of the observation point P(ρ, θ, z) and source point P'(ρ', θ', z') . In free space, according to Nabighian and Macnae(1991) , the vector potential of a finite source is

(1)

J(r') is the current density vector, G(r, r') is the Green function,

(2)

For the horizontally current coil,

(3)

Substitute Eq.(2) , Eq.(3) into Eq.(1) , and according to the derivation by Jackson(1998) , we get the vector potential

(4)

(5)

K(q) and E(q) are the first and second kind of complete elliptic integral respectively.

The magnetic field is computed by expression

(6)

So the magnetic components are

(7)

(8)

(9)

According to the above expressions, the primary field of OCTEM is easy to be calculated. The magnetic line vectors on the central cross plane are illustrated in Fig. 3. It is found that on the middle plane of the opposing coils where the RX coil is located, the vectors are horizontal, which means the primary magnetic flux in RX coil is zero all the time, so the primary EMF in RX coil will be zero and only secondary EMF will be measured.

2.2 Secondary Field of OCTEM in Homogeneous Half Space

By comparing the secondary field generated by opposing coil source of OCTEM with that generated by a single coil source of conventional TEM in homogeneous half space, we will see that OCTEM has advantage in lateral resolution. We just discuss the transient electric field or the induction current. The formulas are derived in frequency domain first, then transformed to time domain by Laplace transform.

Homogeneous half space can be seen as a two layer media(Fig. 4) , the upper layer is non-conducting air(conductivity σ₀ ≈ 0, permeability μ₀) , and the lower layer is conductive earth(conductivity σ₁, permeability μ₀) . For the coil of radius a, carrying a current Ie_iωt, above the uniform earth at height h, in cylindrical coordinate system, the magnetic vector potential has vertical component only, and has no relation with θ. It can be expressed as F₀ = F₀(ρ, z) u_z and F₁ = F₁(ρ, z) u_z respectively. F₀, F₁ is the scalar magnetic potential.

Here we have assumed the quasistatic case i.e. displacement currents are ignored.

So for a certain point in the air, the scalar magnetic potential can be written as(Nabighian, 1992)

(10)

In the formula

(11)

J₀ and J₁ are zero-order and first-order Bessel function respectively.

For a certain point underground, the scalar magnetic potential satisfies the equation

(12)

On the surface(z = 0) , boundary conditions is B_z0 = B_z1, H_ρ0 = H_ρ1. The permeability of the two layers are both μ₀, so H₀ = H₁ and F₀ = F₁. According to Nabighian(1992)

(13)

The electric field is computed by expression

(14)

So only tangential component exists

(15)

By Laplace transform, the underground transient electric field due to a current step I in the coil is

(16)

where

(18)

A convenient dimensionless form of Eq.(16) can be obtained by making the substitutions

(18)

(19)

(20)

For any reasonable σ₁, t, H, R, Z, the values of y₁, y₂ oscillate between positive and negative values and attenuate infinitely close to zero(Fig. 5) . So the infinite integral can be approximately calculated by finite numerical integration as follows.

(21)

We computed the numerical integration in MATLAB. Theoretically, the larger the m is, the smaller the Δ_x is, and the closer it is to the true integral values. Actual calculation shows that when m = 2, Δx = 0.01, the results can be accepted. Then, according to j_θ = σ₁εθ = Iε^*/a² and field superposition, the induction current density for single coil source and opposing coils source are both easily calculated. They are showed in Fig. 6. We find that, for opposing coils source, the current value is smaller than that of the single coil source, but the distribution range of the equivalent current is smaller, and the angle between the diffusion path of max(j_θ) and z axis is smaller(Fig. 7) . They prove that the OCTEM has enhanced lateral resolution as it uses opposing coils source.

2.3 Model Calculation

The numerical model of adjacent conductive thick-plates in free space was calculated using Maxwell software(Version 5.9.1) for opposing coils source system and conventional single coil source system. Model and parameters are showed in Fig. 8a. The spacing between two measurements is 2 m. The simulated TEM responses are showed in Fig. 8. The responses of opposing coils source are weaker but there are two peak responses corresponding to the top center of the plates, which means it distinguishes the two thick plates very well. While the responses of single coil source show a total TEM response of the two thick plates, which are not able to clearly identify the two plates. It indicates that the opposing coils source system has advantages in lateral resolution to detect shallow small targets.

3 FIELD TEST

An OCTEM system prototype as shown in Fig. 9 has been made to carry out the field test. The TX⁽⁻⁾ coil and the TX⁽⁺⁾ coil are 1.24 m in diameter and 10 turns. Vertical distance between them is 0.3 m. The RX coil is 0.5 m in diameter and 100 turns. The tests were carried out in the Lugu park of Changsha, Hunan province, China. The TX waveform is showed in Fig. 10. The transmitting frequency is 25 Hz. The current is 8 A, and the turnoff time is 50 μs. Measurement was taken after the current was completely shut off.

3.1 Pure Secondary Field Measurement Test

In the test, the middle plane of the opposing coils source where the primary magnetic flux was zero was set as z = 0 plane, and the RX coil was moved along z axis from down(z > 0) to up(z < 0) . The measured EMFs normalized by transmitting current(ε/I) were showed in Fig. 11. We have found that, in early times before t=90 μs, the further the RX coil to z = 0 plane is, the larger the measured value is, indicating it includes more primary EMF. When the RX coil is almost on z = 0 plane, the measured values are the smallest, which means almost pure secondary EMFs were measured.

3.2 Shallow Water Detection Test

There is a water ditch in the Lugu park, which is 1.8 m wide. And a stretch of it is buried underground 0.4 m deep. Tests were taken to detect the buried ditch water, using the OCTEM with opposing coils source and conventional TEM with single coil source respectively on the ground. The measuring profile is across the water ditch. Data point separation is 0.5 m, and the point x = 5 m was right above the middle point of the water ditch. The TEM responses of both sources were showed in Fig. 12. It shows that both systems have abnormal response corresponding to the ditch water. However, for single coil source, measured signal overflows at time t = 1.6 μs, 9.6 μs, and 30.4 μs(present as a horizontal line in the figure) , and at time t = 98 μs, it distorts because of the response of the primary EMF. While for opposing coils source, measured signal has no overflow and distortion, and the relative abnormal response is weaker at early times and strengthened gradually. It agrees with the theory.

4 CONCLUSIONf

OCTEM eliminates the primary EMF by constructing a receiver plane where the primary magnetic flux is zero, so that almost pure secondary EMF will be measured. It helps to improve the accuracy of the signal and narrow the blind zone of detection. Although the opposing coils source used by OCTEM provides weaker primary field than conventional single coil, in return it energizes a more concentrated induced underground current, which increases the lateral resolution of the method. Moreover, OCTEM adopts small TX and RX coils, which are easy to manufacture and con-venient for detection in limited space, and also has high consistency for all measuring points.