Source shape impact on controlled source EM surveys

Journal of Applied Geophysics 171 (2019) 103858

Contents lists available at ScienceDirect

Journal of Applied Geophysics journal homepage: www.elsevier.com/locate/jappgeo

Source shape impact on controlled source EM surveys Zikun Zhou, Aihua Weng, Xueqiu Wang ⁎, Zonglin Zou, Yu Tang, Tianqi Wang College of Geo-Exploration Sciences and Technology, Jilin University, Changchun, Jilin 130026, China

a r t i c l e

i n f o

Article history: Received 17 May 2019 Received in revised form 16 September 2019 Accepted 16 September 2019 Available online 09 October 2019 Keywords: CSEM Grounded-line source Source shape EM exploration Impedance

a b s t r a c t Impact of the shape of grounded-line sources on the frequency domain response observed in the controlled source electromagnetic (CSEM) method has not been addressed thoroughly. In this paper, we use the electromagnetic (EM) fields from a half space as examples to discuss the impact of shape. The EM fields from current dipoles along a curved source are summarized. To illustrate the impact, the ratios of the fields from a curved line source to that of a straight line source with the same current are computed. Numerical results show that the impact of source shape on EM fields occurs mainly from a few hertz to higher frequencies. In our examples, shape deformation causes about 7% variation in the real part, and up to a relative error of ~22.5% in the imaginary part at middle frequencies. However, for the derived impedance, the impact can be ignored. Spatially, in the coaxial zone, the impact of source curvature can also be ignored; but in the equatorial zone near the source, the impact needs to be considered. In our examples, the maximal distance between a curved source and the corresponding straight line source is about 1/4 of the spacing between two current poles, more curved than usually seen in field work. Therefore, our results indicate that we do not need to care about source shape when working in a far zone or with source curvature smaller than that of the sources here. There are two possible ways to lessen the shape impact. One is to lay out grounded line source in a Z shape, but a more complete way is by using impedance derived from orthogonal electrical and magnetic fields to present observed data. © 2019 Published by Elsevier B.V.

1. Introduction The controlled-source audio-frequency magnetotelluric method (CSAMT) was invented by Goldstein and Strantway (1975), and further developed by Zonge and Hughes (1988), Tang and He (2005), and Di and Wang (2008). A thorough review of the CSAMT method can be found in Zonge and Hughes (1988). Meanwhile, advances in moving from theory to application can be seen in the three-dimensional inversion of controlled source EM (CSEM) method (Avdeev, 2005; Alumbaugh and Newman, 1997; Weng et al., 2012; Egbert and Kelbert, 2012; Kelbert et al., 2014; Lin et al., 2018). This progress makes CSAMT a great tool in handling interpretation. CSEM is a method that considers the configuration between sources and receivers, surveyed in quasi-grid mode, and not only inverses parameters, such as impedance, apparent resistivity and phase, but also electrical and magnetic fields. Hereafter, CSEM denotes the controlled source EM method in the frequency domain. With respect to work efficiency, EM survey areas could extend to the whole region around the source irrespective of near or far zone from controlled source. For example, in the time domain, unlike the longoffset transient EM method (Strack, 1992), a short-offset transient EM method (Xue et al., 2013) has been developed to work in the near ⁎ Corresponding author. E-mail address: [email protected] (X. Wang).

https://doi.org/10.1016/j.jappgeo.2019.103858 0926-9851/© 2019 Published by Elsevier B.V.

zone; or in the frequency domain, instead of traditional far-field configuration (Zonge and Hughes, 1988), a method called wide-field EM method has been proposed (He, 2010). However, in near zone survey mode, the relatively short distance from an observatory to a transmitter makes the approximation of a controlled source of finite length by a dipole no longer accurate. A special case occurs when a grounded line source of up to thousands of meters is used to counter-balance the spatial attenuation of EM fields, while retaining high signal-noise ratio (e.g., Constable and Srnka, 2007; Ziolkowski et al., 2007). As to grounded sources of finite length, the effect on the response from these sources, has been recognized and discussed by Kaufman and Keller (1983). Additionally, when the receiver-transmitter spacing is not large enough, the field structure is different from that of the far field, leading to the so-called source effect (Zonge and Hughes, 1988). Li and Piao (1993a, 1993b) have proposed a scheme to correct this effect. Zhou et al. (2011) discussed the response superposition from dipoles and the equivalence between the circular loop and inscribed polygon. Recently, to overcome the incompleteness of the correction by Li and Piao (1993a, 1993b), three-dimension inversion allowing for source length has been developed (Liu, 2013; Weng et al., 2017). Meanwhile, the curvature of line sources may also affect the EM response. This kind of consideration has mainly been taken in timedomain EM methods. Shi et al. (2009) had to find an expression of the induced voltage from a large rectangular loop at any point to derive an apparent resistivity that is not subject to edge effects. Xue et al.

2

Z. Zhou et al. / Journal of Applied Geophysics 171 (2019) 103858

(2011) found that in short-offset zones, the error from the assumption of magnetic dipole and electric dipole cannot be completely compensated by the surface or line integral over a loop source. Li and Huang (2018) found that source curvature affects the transient responses much stronger in equatorial zones than in coaxial zones. As for frequency domain responses, we should keep in mind that they are complex, containing real and imaginary parts, and that the transient EM signal is an integral of frequency domain electromagnetic responses (Kaufman and Keller, 1983). Moreover, a transient signal is more sensitive to the imaginary part of the frequency response (Mitsuhata et al., 2001). Therefore, results regarding the impact of shape on a transient signal may not adequately extend to the frequency domain response. For example, after analyzing the deviation caused by the altitude of a dipole source in an ocean EM method, Liu et al. (2012) found that a 12° emission dipole tilt could result in up to 20% error at short offset. Streich and Becken (2011) found a ~10% variation in inline electrical fields due to wired source deformation in marine EM exploration. These studies indicate that the impact of source shape is lower in the frequency domain than in the time domain. Therefore, a thorough consideration of source shape impact on complex fields observed in the CSEM method is needed, especially for threedimensional surverys. In this paper, we will take Ex (parallel to the source) and Hy, as well as their derived impedance Zxy, over a half space as examples to discuss the effect of source shape in the frequency domain. Since a uniform half space is the first-order approximation of complex earth, the obtained results naturally extend to the real earth. First, we describe the computation method of the EM field in the frequency domain from a grounded line of arbitrary shape. Then, the impact of source shape on the frequency responses from the sources of different shapes is discussed. After that, the pattern of the spatial distribution of the impact is summarized, and conclusions presented. 2. Method 2.1. EM fields from a dipole A short-grounded line, if its length is much shorter than its distance to an observation point, can be considered as an electric dipole. In the coordinate system in Fig. 1, the expressions of the EM field from a horizontal electric dipole on uniform half space refers to Nabighian (1987). For completeness, when the harmonic factor is

Fig. 1. The coordinate system used to calculate the electromagnetic fields from a current dipole over the ground. The moment of the dipole is Ids, and its direction is in the positive x-axis. The equatorial zone is the area around the y axis (in horizontal lines); the coaxial zone is around the x axis (vertical lines).

e-iωt, we rewrite them as follows: Ex ¼


 Ids 3x2 −ikρ −2 þ ð ikρ þ 1 Þe þ ρ2 2πσρ3

ð1Þ

Ey ¼

6xyε 4πρ5

ð2Þ

Hx ¼


            Ids xy ikρ ikρ ikρ ikρ ikρ ikρ K −I K −8I K1 ikρ I 0 1 1 0 1 4π ρ2 2 2 2 2 2 2

ð3Þ   Ids x2 6I K þ ikρ ð I −K Þ þ ½ ikρ ð I −K Þ−8I K  Hy ¼ − 1 1 1 0 0 1 1 1 ρ2 4πρ2

ð4Þ

and Hz ¼ −

Idsy h 2 2πk ρ5

 i 2 3− 3 þ 3ikρ−k ρ2 e−ikρ

ð5Þ

Here, I indicates the current strength; ds represents the length of electric dipole; σ denotes the conductivity of uniform half space; ρ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2 þ y2 (with x and y being the coordinates of the observing point); and k represents the complex wave number. μ and ε are the vacuum magnetic permeability and dielectric constants. I0, I1, K0 and K1 are the modified Bessel functions of zeroth and first orders. For a straight grounded wire of finite length, the fields could be calculated by integrating the dipole field in eqs. (1)–(5) along the source trace. By dividing the straight line into small enough subsegments, we get the discrete format of the path integral. Then each segment can be considered as a dipole (Li et al., 2016). In our calculation, the division will continue until the relative error of the fields from adjacent divisions is less than the pre-defined precision 10−10. 2.2. Fields from grounded finite line In practical applications, unmovable obstacles make it difficult to lay out current lines in a straight line, and the configuration is more like that shown in Fig. 2. This curved wire starts from point A, passes through each point Ai until the end at point B. Each sub-line segment AiBi is almost straight. To facilitate computation, we construct a global coordinate system, in which the x-axis passes through A and B; origin O is at their middle point, the y-axis is perpendicular to the x-axis through O, and the zaxis points out of the paper in accordance with the right-hand rule.

Fig. 2. Schematic diagram showing the calculation of the EM field at point P from a curved source AB in current direction A → B. The EM fields Ei’, Hi’ from a straight sub-wire AiBi at P is firstly estimated in the local coordinate system x'o'y’; Ei’, Hi’ is then reversely rotated to the global coordinate system xoy to get Ei and Hi and then added to the fields from the other straight sub-wire to obtain the total E and H.

Z. Zhou et al. / Journal of Applied Geophysics 171 (2019) 103858

3

Fig. 3. Schematic diagram of the typical wire shapes used as examples.

As the fields (E'i, H'i) at point P from a single straight grounded sub-line can be calculated, the total fields (E, H) from a curved wire can then be obtained by adding all the fields from these single subsources, that is:

½E; H  ¼

N X ½E i ; H i 

ð6Þ

i¼1

Here, N is the number of straight segments. Since the corner of a curved source is important in the field calculation, the wire should be laid out as straight as possible, with all the coordinates of the inflection points on the wire being identified.

Once E and H have been obtained, the impedance apparent resistivity ρxy and phase φxy can be calculated after Boschetto and Hohmann (1991). ρxy ¼

  1  Ex 2 ωμ H y 

  Ex φxy ¼ arg Hy

ð7Þ

ð8Þ

2.3. Coordinate transformation To calculate the EM fields at point P from sub-source AiBi, we shift and rotate the coordinates of point P from the global coordinate system

Fig. 4. Source shape impact on Ex in the equatorial zone. (a) and (b) are its real and imaginary parts. (c) and (d) are the relative changes in real and imaginary parts from different sources.

4

Z. Zhou et al. / Journal of Applied Geophysics 171 (2019) 103858

Fig. 5. Source shape impact on Ex in the coaxial zone. (a) and (b) are its real and imaginary parts.

Fig. 6. Source shape impact on Hx in the equatorial zone. (a) and (b) are its real and imaginary parts. (c) and (d) are the relative changes in real and imaginary parts from different sources.

Z. Zhou et al. / Journal of Applied Geophysics 171 (2019) 103858

5

Fig. 7. Hy in the coaxial zone from different sources. (a) real part; (b) imaginary part.

(xOy) to the local system containing (x'Oi'y’). Assuming that in the local system, the middle point of AiBi is set as the origin O’i, and the angle made by the line AiBi and x-axis is θi, then the coordinate of point P in the local coordinate system can be estimated by.   x0 ¼ x−xO0i  cosθi þ y−yO0i sinθi   y0 ¼ y−yO0i  cosθi − x−xO0i sinθi

2.4. Field vector rotation Upon obtaining the EM fields in the local coordinate system from each segment, they can be stacked component by component after a field vector inverse rotation from the local coordinate system to the global coordinate system. Using the electrical fields from a curved source on the ground as an example, we have:

ð9Þ Ex ¼

N  X 0 0 Ex;i cosθi −Ey;i sinθi i¼1

Using the local coordinates of P, and the length of AiBi, the EM fields from source AiBi at P in the local coordinate system can be estimated after eqs. (1)–(5) and denoted as E'i and H'i.

N  X 0 0 Ex;i sinθi þ Ey;i cosθi Ey ¼

ð10Þ

i¼1

Fig. 8. Frequency response of impedance phase (a) and apparent resistivity (b) in the equatorial region from different sources. For these two parameters, the impact of source shape is negligible, so the curves from different sources overlap each other.

6

Z. Zhou et al. / Journal of Applied Geophysics 171 (2019) 103858

3. Impacts on sounding curves Considering the actual CSAMT operation where scalar EM field measurements are often used (Zonge et al., 1985), in the following discussions we will take Ex, Hy, ρxy and φxy as examples to illustrate source impact, and focus on the impact at two typical measuring points; one in the equatorial region, and the other in the coaxial region. 3.1. Typical source shapes Typical shapes of curved sources in the field are displayed in Fig. 3, where all the sources are 2 km long over the ground. The earth is a uniform half space of resistivity 1000 Ω·m. The ‘Straight’ source is a grounded straight line of length 2 km, and its EM fields are used as a standard to assess the impact of source curvature. The ‘Triangle’ source is bent at its midpoint, and this isosceles triangle has a height of 577 m. The ‘Half-triangle’ source is a combination of a triangle and straight line, joined at the mid point of the wire. The final

source shape is ‘Serration’, which arches toward the second and the fourth quarters with a tooth height of 577 m. The isosceles triangle's height (577 m) is intended to represent the extreme of a realistic source curvature. 3.2. Electric field Ex The frequency responses of Ex are presented in Fig. 4. Fig. 4a shows that in the equatorial region, the real part of Ex is affected by the shape of the source. Fig. 4c indicates that the impact on the response from the triangle source is the largest (causing a ~5.5% relative variation), followed by the half-triangle source (about 2.5% variation). However, the response from the serration source almost overlaps with that of the straight line, implying that at this observation point serration shape does not affect the real part of Ex. Fig. 4b shows that the imaginary parts of Ex from different sources are affected by the sources only at middle frequencies around 10 Hz. This impact can be most clearly seen in Fig. 4d. We can see that the

Fig. 9. Spatial variation the EM fields from the triangle source, frequency is 32 Hz. (a) Re(Etriangle )/Re(Estraight ); (b) Im(Etriangle )/Im(Estraight ), (c) Re(Htriangle )/Re(Hstraight ) and (d) Im(Htriangle )/ x x x x y y y Im(Hstraight ). Blank shades in (a), (b), (c) and (d) roughly mark very low-amplitude regions in which Ex is almost zero and could not be measured accurately. y

Z. Zhou et al. / Journal of Applied Geophysics 171 (2019) 103858

relative changes increase with frequency, that the impact from the serration source can be omitted, while the half-triangle source and triangle source affect the responses gradually and severely, respectfully. Here we only show the results from 10−3 to 32 Hz, because Ex at this point approaches zero and becomes numerically unstable, and the relative errors at higher frequencies are not reliable. In the coaxial region, both the real component and imaginary component of E x from these different sources are almost the same (as shown in Fig. 5). Therefore, in the coaxial region, we can ignore the shape of the source, and simply consider it a straight line. Because the transient response can be considered as an integration of frequency domain responses, the above impacts we computed are consistent with previous work (Li and Huang, 2018). However, as the integration will accumulate the relatively small impacts in the frequency domain, the responses in the time domain will exaggerate these errors and result in larger source shape impact, especially when Ex(t) is considered (Li and Huang, 2018). At this point, we can say source

7

shape has more impact on the transient EM method than on frequency domain CSEM. 3.3. Magnetic field Hy The source shape impact on magnetic fields are shown in Figs. 6 and 7. Fig. 6 shows that source shape affects the real part of Hy in the equatorial region, with a maximum relative change b7%. In comparison with Fig. 4c, the impact feature is same as the real part of Ex. In the frequency range from a few to several tens of Hz, the imaginary part of Hy alternates its sign from positive to negative (or vice versa), leading to a relative change of about 20% around zero. In this sense, if we measure the transient magnetic field, the source effect can lead to an accumulated larger error in the equatorial region. However, similar to Ex in the coaxial zone (Fig. 5), there is no obvious impact on the magnetic field in the coaxial region (Fig. 7). In both cases of Ex and Hy, towards the lower frequencies all the fields from different sources approach that of a straight line source,

Fig. 10. Spatial variation the EM fields from the half-triangle source, frequency is 32 (a) Re(Ehalf-triangle )/Re(Estraight ); (b) Im(Ehalf-triangle )/Im(Estraight ), (c) Re(Hhalf-triangle )/Re(Hstraight ) and x x x x y y (d) Im(Hhalf-triangle )/Im(Hstraight ). y y

8

Z. Zhou et al. / Journal of Applied Geophysics 171 (2019) 103858

and the impact of source shape vanishes. This suggests that at this limit the fields become static, and only the positions of A and B control the EM fields (Streich and Becken, 2011). On the contrary, at high frequency the screening effect will decrease both the real and imaginary parts of the total field, resulting in the electrical and magnetic fields becoming zero, irrespective of whichever source is used (Kaufman and Keller, 1983). 3.4. Apparent resistivity and phase Since in the coaxial region, E x and H y are weakly affected by source shape in the far zone (Fig. 5, 7), a natural deduction is that the impedance apparent resistivity ρxy and the phase φxy will not reflect the impact of source shape. Therefore, if we use impedance as an interpretation parameter in the coaxial zone, the source effect can be ignored. Consequently, we need only be concerned about the impact in the equatorial region, and the corresponding sounding curves are displayed in Fig. 8. However, the figure shows that the impact of source shape on impedance response is not seen, even though

Ex and Hy in Fig. 4 and 6 are affected by source shape. A plausible explanation is that the ratio of Ex with respect to Hy offsets the source shape impact, and defining this parameter in CSAMT could eliminate the source effect on controlled source EM observations (Goldstein and Strantway, 1975). In addition, from Fig. 8 we can see that the phase response at high frequency is about 45°, approaching the phase of MT over half space. Towards lower frequencies, the phase becomes 0°, an indicator of static EM fields; and at the frequencies overlapping the CSAMT frequency band, there is a transition increasing gradually from 0° to 45°. This phase variation reminds us that the impedance from a controlled source at low frequency is different from that of a natural source, implying that simply using the MT inversion scheme to convert the impedance apparent resistivity and phase from a controlled source into resistivity is not valid at middle to low frequencies. Nevertheless, this feature reveals that when source curvature effect cannot be ignored, instead of E or H, we can use impedance as an inversion parameter, this also being the parameter of the best inversion resolution (Weng et al., 2015).

Fig. 11. Spatial variation the EM fields from the serration source, frequency is 32 Hz. (a) Re(Exhalf-triangle)/Re(Exstraight); (b) Im(Exhalf-triangle)/Im(Exstraight), (c) Re(Hyhalftriangle)/Re(Hystraight) and (d) Im(Hyhalf-triangle)/Im(Hystraight).

Z. Zhou et al. / Journal of Applied Geophysics 171 (2019) 103858

9

4. Impact in plain view

5. Conclusions

Chen et al. (2015) found that the transient responses are more affected by source shape in the near zone than in the far zone. In combination with the results above, it is clear that source shape impact differs from point to point. So, what is the spatial distribution of the impact? Here, we still take the Ex and Hy on the ground as examples. The discussion above indicates the impact occurs mainly in middle frequencies, so in the following context we discuss the fields at 32 Hz. For comparison, the field from a straight line will be used to normalize the fields from other kinds of sources. Because Ex is almost zero in the diagonal zones of the coordinate system in Fig. 1 (Zonge and Hughes, 1988), we will only discuss the fields in the remaining regions.

In this paper, taking half space as an example, we have computed the electric and magnetic fields in the frequency domain from groundedline sources with different shapes to address the impact of source shape. The EM fields from a horizontal electric dipole are added to simulate the fields from a grounded-line source of finite length. We analyzed the relative change of the electric and magnetic fields from irregular sources in comparison to that generated by a grounded straight line. We found that the impact of source shape is more significant in the equatorial region than in the coaxial region. Source shape impacts mainly electrical fields, and the imaginary part is much more seriously affected than the real part. The magnetic fields seem to be less affected by source shape. The impact of source shape on impedance can be ignored. As in our example, the deformation of a curved source is about 1/4 of its length, and more curved than usually seen in the field. Therefore, if working in a far zone, we need not care about source shape. If the source must be laid out in a curved shape, the Z shape is the best one to use. To lessen the shape effect on observation, we can also measure Ex and its orthogonal magnetic field Hy and transform them into impedance and phase. In this case, we can apply the theory of the CSEM method (instead of CSAMT) to interpret the results.

4.1. Triangle source The normalized Ex of the triangle source is displayed in Fig. 9a, and b. From the figures we find that: 1) the impact of source shape is mainly on the imaginary part of Ex, with a relative change up to ~20% in the equatorial zone; on the real part, the impact is b10%; 2) in the coaxial region, (whether in the far or near zone), the impact is b5%; 3) the impact in the co-curved direction makes the field stronger, while in the anti-curved side, the impact decreases Re(Ex) by ~5% and Im(Ex) by ~20%. Fig. 9c and d show the impact from source shape on Hy. The pattern of this impact is almost the same as that on Ex in Fig. 9a and b. As source shape impact is more significant in the imaginary part than in the real part, and recalling that transient EM signals are more relevant to the imaginary part of frequency responses, the induced voltage or electrical field in the time domain will carry more source shape information, particularly when the measurement is in the near zone (Xue et al., 2013). Consequently, in the time domain method, source shape needs to be considered.

4.2. Half-triangle source The distributions of the impact on the EM fields from a half-triangle curved source are displayed in Fig. 10. Comparing with the triangle source, this source is asymmetrical. The influence pattern in Fig. 10 reveals this characteristic. For example, the contours of the ratio deforms in the triangle side; and even the curved part shrinks to half of the straight line, the impact could be as high as up to ~15% in the imaginary part. However, in most regions around the source, the impact on the real part is only about ~1–5% (usually less than measuring error).

4.3. Serration source Although the serration shaped source is the most complicated source in Fig. 3, its impact on EM fields is the least, as shown in Fig. 11. From the figure, we can see that whether in the equatorial zone, or in the coaxial zone, the impact is usually less 2% on the real part and the imaginary part of the complex field. The largest influence occurs in the imaginary part of Ex at the far zone, but beyond the optimal surveying region in CSAMT (Zonge and Hughes, 1988). Therefore, for this kind of source, we do not need to consider the source shape during signal measuring or data inversion. Comparing the impacts from the source shapes of straight line, triangle, half-triangle and serration, we find that the triangle source has the largest influence, followed by the half-triangle source, and that the serration source can be considered as a straight-line source. Therefore, in field work where obstacles or tough terrain cannot be avoided, the grounded line should be laid out in a Z shape. Otherwise, we need to take into account both the length of the source as well as its shape impact in CSEM data inversion.

Declaration of Competing Interest We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted. References Alumbaugh, D.L., Newman, G.A., 1997. Three-dimensional massively parallel EM inversion-II. Analysis of a crosswell EM experiment. Geophys. J. Int. 128 (2), 355–363. Avdeev, D.B., 2005. Three-dimensional EM modelling and inversion from theory to application. Surv. Geophys. 26 (6), 767–799. Boschetto, N.B., Hohmann, G.W., 1991. Controlled-source audio-frequency magnetotelluric responses of three-dimensional bodies. Geophysics 56 (2), 255–264. Chen, W.Y., et al., 2015. Analysis on the influence from the shape of electric source TEM transmitter. Prog. Geophys. 30 (1) (in Chinese). (0126-013). Constable, S., Srnka, L.J., 2007. An introduction to marine controlled-source EM methods for hydrocarbon exploration. Geophysics 72, WA3–WA12. Di, Q.Y., Wang, R., 2008. Controllable Source Audio Magnetotellurics. (in Chinese). Science Press, Beijing. Egbert, G.D., Kelbert, A., 2012. Computational recipes for EM inverse problems. Geophys. J. Int. 189 (1), 251–267. Goldstein, M.A., Strantway, D.W., 1975. Audio-frequency magnetotellurics with a grounded electric dipole sources. Geophysics 40 (4), 669–683. He, J.S., 2010. Wide field EM sounding methods. J. Central South University (Science and Technology) 41 (3), 1065–1072 (in Chinese). Kaufman, A.A., Keller, G.V., 1983. Frequency and transient soundings. Elsevier, New York. Kelbert, A., et al., 2014. Modem: a modular system for inversion of EM geophysical data. Comput. Geosci. 66 (66), 40–53. Li, Z.H., Huang, Q.H., 2018. 1D forward modeling and inversion algorithm for grounded galvanic source TEM sounding with an arbitrary horizontal wire. Prog. Geophys. 33 (4), 1515–1525 (in Chinese). Li, J.S., Piao, H.R., 1993a. On the calculation and application of the apparent resistivity of transient EM sounding by electric dipole. Geophys.Geochem. Exp.Technol. (2), 108–116 (in Chinese). Li, J.S., Piao, H.R., 1993b. Research and correction of non-dipole influence of transmitter AB and receiver in near-zone TDEM. J.Changchun University of Earth Sci. (2), 191–196 (in Chinese). Li, Z.H., et al., 2016. A general 1D forward modelling and inversion algorithm from TEM sounding with an arbitrary horizontal loop. Pure Appl. Geophys. 173 (8), 2869–2883. Lin, C.H., et al., 2018. The effects of 3D topography on controlled-source audio-frequency magnetotelluric responses. Geophysics 83 (2), WB97–WB108. Liu, Y.H., 2013. Three-dimensional frequency-domain airborne EM modeling and inversion in anisotropic media. (in Chinese). Post Doctorial Report. Jilin University, Changchun. Liu, Y.H., et al., 2012. Attitude effect for marine CSEM system. Chinese. J. Geophys. 55 (8), 2757–2768 (in Chinese). Mitsuhata, Y., et al., 2001. The Fourier transform of controlled-source time domain EM data by smooth spectrum inversion. Geophys. J. Int. 144 (1), 123–135. Nabighian, M.N., 1987. Electromagnetic Methods in Applied Geophysics. Vol.1. SEG, Tulsa, Oklahoma.

10

Z. Zhou et al. / Journal of Applied Geophysics 171 (2019) 103858

Shi, X.X., et al., 2009. Improvement for interpretation of central loop transient EM method. Chinese J. Geophys 52 (7), 1931–1936 (in Chinese). Strack, K.M., 1992. Exploration with Deep Transient EMs. Elsevier. Streich, R., Becken, M., 2011. EM fields generated by finite-length wire sources: Comparison with point dipole solutions. Geophys. Prospect. 59 (2), 361–374. Tang, J.T., He, J.S., 2005. Controlled Source Audio Frequency Em Method And Applications. (in Chinese). University Press, Changsha: Central South. Weng, A.H., et al., 2012. Three-dimensional controlled source EM inversion using nonlinear conjugate gradients. Chinese. J. Geophys. 55 (10), 3506–3515 (in Chinese). Weng, A.H., et al., 2015. Selection of parameter types in controlled source EM method. Chin. J. Geophys. 58 (2), 697–708 (in Chinese). Weng, A.H., et al., 2017. 1D inversion for controlled source EM sounding using limited memory Quasi-Newton method. J. Jilin Univ. (Earth Sci. Ed.) 47 (2), 597–605 (in Chinese).

Xue, G.Q., et al., 2011. Theoretical study on the error caused by dipole hypothesis of largeloop TEM response. Chin. J. Geophys. 54 (9), 2389–2396 (in Chinese). Xue, G.Q., et al., 2013. Short-offset TEM technique with a grounded wire source for deep sounding. Chin. J. Geophys. 56 (1), 255–261 (in Chinese). Zhou, N.N., et al., 2011. Response of large-loop TEM based on approximation of electric dipole. Coal. Geol.Exp. (4), 49–54 (in Chinese). Ziolkowski, A., et al., 2007. Multitransient EM demonstration survey in France. Geophysics 72, F197–F209. Zonge, K.L., Hughes, L.J., 1988. Controlled source audio-frequency magnetotellurics // Nabighian M N ed EM Methods in applied geophysics. Soc.Exp.Geophys. 2, 713–809. Zonge, K.L., et al., 1985. Controlled-source audio-frequency magnetotelluric measurements. In: Vozoff, K. (Ed.), Magnetotelhuic Methods: Geophysics Reprint Series, no. 5, Society of Exploration Geophysicists, pp. 749–763.