TY - JOUR
AU - Yao,, Weihua
AB - Abstract We introduce a new and potentially useful method for wave field inverse transformation and its application in transient electromagnetic method (TEM) 3D interpretation. The diffusive EM field is known to have a unique integral representation in terms of a fictitious wave field that satisfies a wave equation. The continuous imaging of TEM can be accomplished using the imaging methods in seismic interpretation after the diffusion equation is transformed into a fictitious wave equation. The interpretation method based on the imaging of a fictitious wave field could be used as a fast 3D inversion method. Moreover, the fictitious wave field possesses some wave field features making it possible for the application of a wave field interpretation method in TEM to improve the prospecting resolution. Wave field transformation is a key issue in the migration imaging of a fictitious wave field. The equation in the wave field transformation belongs to the first class Fredholm integration equation, which is a typical ill-posed equation. Additionally, TEM has a large dynamic time range, which also facilitates the weakness of this ill-posed problem. The wave field transformation is implemented by using pre-conditioned regularized conjugate gradient method. The continuous imaging of a fictitious wave field is implemented by using Kirchhoff integration. A synthetic aperture and deconvolution algorithm is also introduced to improve the interpretation resolution. We interpreted field data by the method proposed in this paper, and obtained a satisfying interpretation result. transient electromagnetic method, wavefield transformation, migration imaging, pre-conditioned regularized conjugate gradient method (PRCG), focusing synthetic aperture, pulse compression 1. Introduction The transient electromagnetic method (TEM) is widely used in complex geological exploration since it can provide much useful information and, for this reason, the emphasis about the TEM theory should be not only on the forward modeling but also on the inversion algorithm. A lot of geophysicists have been involved and much fruit has been reported, such as the 2D and 3D modeling (Adhidjaja and Hohmann et al1988, 1989, Hohmann et al1990) and 1D and 3D inversion (Pellerin and Hohmann 1990, Zhdanov et al2006, 2010, 2011). With the increasing demand of fine exploration in the engineering industry, the existing inversion algorithms of TEM cannot meet the practical requirements in a large number of geological surveys. The migration imaging for TEM data is another way to realize the TEM 3D interpretation. The transient electromagnetic field virtual wave equation migration is based on the wave field transforms. Kunetz (1972) first presented the transform formula from diffusion equation in TEM to the wave equation in seismic exploration. From then on, pseudo-seismic interpretation of TEM has become a hot topic. The transient electromagnetic (TEM) field fictitious wave equation migration is based on the wave field transform. The basic principles of wave field transform between diffusion equation and wave equation have been formulated in Lavrent’ev et al (1980), Lee et al (1987) and Lee et al (1989), Lee and Xie (1993), Lee et al (1994), and Das Kaushik et al (2002). Though TEM fictitious wave field migration imaging has important features in common with seismic migration (Li et al2005, 2010), there is a great difference between the TEM migration imaging and seismic migration imaging. The TEM wave field transform has been introduced in Li et al (2005) and Xue et al (2007). As we all know, it is the first kind Fredholm integral equation, and the inverse transformation, from diffusion field to wave field, is a typical ill-posed problem. Besides, the dynamic time range of transient electromagnetic sampling is so wide that it makes the ill-posed problem more serious. To solve the problem, in the paper by Lee et al (1989) singular value decomposition (SVD) was adopted to transform the TEM field to the quasi wave field, while Li (2005) and Xue et al (2007) proposed the regularization method to solve the problem. However, the question still remains ill-posed when the sampling channel number is greater than one hundred. Meanwhile, the regularized conjugate gradient (RCG) method is a useful way to solve the ill-posed problem. In this paper we proposed the pre-conditioned regularized conjugate gradient method (PRCG) to deal with this problem. The over relaxation pre-conditioned process effectively reduces the condition number of the coefficient matrix, while the regularized conjugate gradient method (RCG) helps run the inverse transformation of the wave field in full dynamic time range. The Kirchhoff migration imaging of a seismic-wave is a great success, while the direct Kirchhoff migration result of a fictitious wave, which was acquired by wave field transform, is not good. Zhdanov et al (1995), Zhdanov et al (1996) and Zhdanov and Portniaguine (1997) developed a different imaging algorithm, which was called the reverse-time migration and imaging method, that achieved good results from the experiments on single- and multi-electric anomalous-body models. Lee et al (1989) realized the subsurface migration imaging of MT data. Sasaki (1989) gave a good result of 2D geological-electrical structure with wavenumber domain MT data by PSPI method from seismic migration. Strack and Vozoff (1996) processed the LOTEM data with seismic interpretation techniques. Lee et al (2002, 2005) realized the electromagnetic travel-time tomography using an approximate wave field transform. These achievements make me trust that the TEM fictitious wave field migration could be better. With numerous model analysis, it is found that the fictitious wave field attenuates very quickly when propagating in dispersive earth. This causes the high-frequency signal to be absorbed very quickly. In order to solve the problem of absorption and broadening of the fictitious wave field, the impulse deconvolution method (Xue et al2011) has been adopted from seismic exploration and combined with minimum phase filtering to realize the impulse compression of the fictitious wave field. Synthetic aperture radar (SAR) is widely used in military observations, remote sensing, environmental assessment, resource exploration etc. Besides, it is able to obtain a higher resolution than real aperture radar because the amplitude and phase information from a series of radar measurements can be combined as if they were made simultaneously by a much larger instrument. As we all know, synthetic aperture technology in radar exploration can improve the resolution of targets. By suggesting it to TEM, it is possible to process the profile data using the correlation superposition, which is similar to radar data processing. In this paper, we present a new pseudo-seismic migration imaging method of TEM data. Figure 1 is the roadmap of TEM pseudo-seismic migration imaging method. We demonstrate that pre-conditioned regularized conjugate gradient method is an effective method for TEM wave field transformation. With synthetic aperture and impulse deconvolution processing, the TEM fictitious wave field Kirchhoff migration can give more detailed information of the underground structure. Figure 1. Open in new tabDownload slide Roadmap of the TEM virtual wave field Kirchhoff migration. With the PRCG method, we can obtain fictitious wave data from the TEM survey data. After the synthetic aperture and pulse compression processing, and with the velocity of the fictitious wave, we can realise the TEM virtual wave field migration imaging based on the Kirchhoff integral. Figure 1. Open in new tabDownload slide Roadmap of the TEM virtual wave field Kirchhoff migration. With the PRCG method, we can obtain fictitious wave data from the TEM survey data. After the synthetic aperture and pulse compression processing, and with the velocity of the fictitious wave, we can realise the TEM virtual wave field migration imaging based on the Kirchhoff integral. 2. Methodology 2.1. Theory of wave field transformation Based on the mathematic relationship between the wave equation pseudo-seismic wave field satisfied and the diffusion equation the electromagnetic field satisfied, the relationship between the pseudo-seismic wave field and the time domain transient electromagnetic response of the center loop source according to the Maxwell equations can be expressed as (Lee et al1989) hz(r,t)=12πt3∫0∞τe-τ2/4tU(r,τ)dτ1 where the dimension of variable τ is the square root of the time variable t, U(r,τ) is the pseudo-seismic wave field function with the wave speed 1/σμ0 ⁠, σ is the conductivity of the underground medium and hz(r,t) is the diffusion field of electromagnetic response in the time domain. This is the famous formula converting wave equation to the diffusion equation. All the components of the transient electromagnetic field satisfy the transform relationship. In this study we just take the vertical magnetic component as an example, and the transform relationship is shown as formula (1). It is the first kind Fredholm integral equation, and the inverse transform, from diffusion field to fictitious wave field, is a typical ill-posed problem. To solve the problem, the pre-conditioned regularized conjugate gradient (PRCG) method has been proposed. The discrete equation of equation (1) is shown as hz(r,t)=∑j=1nU(x,y,z,τj)a(ti,τj)wj2 where a(ti,τj)=1/2πti3τje−τj2/4ti is the kernel function. wj is the integral coefficient. Rewrite it to be matrix form AU=F3 where A=[aijwj]m×n, and it contains the integral coefficient wj ⁠, U=[Uj]n×1 is the fictitious wave field, and F=[hi]m×1 is the received signal of the underground response. The conjugate gradient method is an efficient solver for approximating the solution of linear equations, provided the coefficient matrix is symmetric positive definite (SPD) and a good precondition is obtainable when it is ill-conditioned. In order to ensure coefficient matrix symmetric positive definite, the equation (3) changes to be equation (4) ATAU=ATF.4 If coefficient matrix A is a full column rank matrix, ATA is symmetric positive definite. Fortunately, our matrix is a full column rank matrix, so the conjugate gradient method can be employed to solve equation (4). The operation from A to ATA may considerably improve the condition number of the coefficient matrix of equation (4), and it makes the ill-posed problem more serious. To deal with the problem, we present a class of the pre-conditioned regularized conjugate gradient (PRCG) method for solving the system of equation (4). In the PRCG method, the equation (4) is first reasonably shifting and contracting the spectrum of the coefficient matrix ATA with the regularized parameter, and its solution is then approximated successively by a sequence of regularized linear systems. At each step of iteration the regularized linear system itself is iterative solved by CG method. Moreover, the regularized linear system can be preconditioned by employing an SSOR pre-conditioner. We would like to reference the papers of Wang (2003) and Zhdanov and Tolstaya (2006) for the choice of the regularized parameter v ⁠. The basic idea of the method is as follows: given a starting vector x0 ⁠, suppose that we have got approximations x0,x1,x2,⋯xk to the solution x* of the equation (4), then the next approximation xk+1 to x* is obtained through solving equation (5). The PRCG method itself is an outer iteration and the CG its inner iteration. Finally, the TEM full-domain wave field transform could be realized M(v)−1A(v)x=M(v)−1(vxk+f)5 where A(v)=vI+ATA ⁠, M(v)−1 is the SSOR pre-conditioner, whose expression is M=1ω(2-ω)[(D+ωL)-1D-1(D+ωU) ︀]. D, L and U are the diagonal matrix, tril and upper triangular matrix, respectively, of the coefficient matrix A(v) ⁠. ω∈(0,2) is the relaxing factor. After the transient electromagnetic field transformed into the pseudo-seismic wave field, the waveform of the obtained fictitious wave field satisfies the wave equation and the wavelet has wave field propagation property. In order to explain the phenomenon, we give the fictitious wave field transformed from the TEM response of layered model with A, H, K and Q type. (A, H, K, Q are three-layer model names. The resistivity distribution of the A-type model is ρ1<ρ2<ρ3 ⁠. The resistivity distribution of the H-type model is ρ1>ρ2<ρ3 ⁠. The resistivity distribution of the K-type model is ρ1<ρ2>ρ3 ⁠. The resistivity distribution of the Q-type model is ρ1>ρ2>ρ3 ⁠. ρ1 ⁠, ρ2 ⁠, ρ3 is the resistivity of first layer, second layer, third layer, respectively.) Figure 2(a) is the decay curve and fictitious wave of the A-type model. In the left of figure 2(a) is the decay curve of the A-type model and the right of figure 2(a) is the wave convention result of the left picture. The function U′(τ) with the black line is the theory waveform of the A-type model, and the function U(τ) with the red line is the waveform acquired with wave transform method. T1 is the fictitious time, which corresponds with the first underground surface. T2 is the fictitious time too, which corresponds with the second underground surface. Figures 2(b)–(d) are the decay curve and fictitious wave of H, K, and Q, respectively. The labels in those pictures have the same meaning as in figure 2(a). Comparing the fictitious waveform with theory waveform of the geological-electrical model, it is found that the fictitious wave field attenuates very quickly when propagating in dispersive earth and this is similar to the earth filtering effect in a seismic survey. Figure 2. Open in new tabDownload slide (a) The decay curve and fictitious waveform of the A-type model. (b) The decay curve and fictitious waveform of the H-type model. (c) The decay curve and fictitious waveform of the K-type model. (d) The decay curve and fictitious waveform of the Q-type model. In the left of (a) is the decay curve of the A-type model and the right of (a) is the wave convention result of the left picture. U′(τ) with the black line is the theory waveform of the A-type model, and U(τ) with the red line is the waveform acquired with wave transform method. T1 is the fictitious time, which corresponds with the first underground surface. T2 is the fictitious time too, which corresponds with the second underground surface. (b) The decay curve of the H-type model and its wave convention result. (c) The decay curve of the K-type model and its wave convention result. (d) The decay curve of the Q-type model and its wave convention result. The U′(τ) ⁠, U(τ) ⁠, T1 and T2 of (b)–(d) have the same meaning as (a). Figure 2. Open in new tabDownload slide (a) The decay curve and fictitious waveform of the A-type model. (b) The decay curve and fictitious waveform of the H-type model. (c) The decay curve and fictitious waveform of the K-type model. (d) The decay curve and fictitious waveform of the Q-type model. In the left of (a) is the decay curve of the A-type model and the right of (a) is the wave convention result of the left picture. U′(τ) with the black line is the theory waveform of the A-type model, and U(τ) with the red line is the waveform acquired with wave transform method. T1 is the fictitious time, which corresponds with the first underground surface. T2 is the fictitious time too, which corresponds with the second underground surface. (b) The decay curve of the H-type model and its wave convention result. (c) The decay curve of the K-type model and its wave convention result. (d) The decay curve of the Q-type model and its wave convention result. The U′(τ) ⁠, U(τ) ⁠, T1 and T2 of (b)–(d) have the same meaning as (a). 2.2. Synthetic aperture algorithm of TEM The synthetic TEM aperture imaging is based on the idea of synthetic aperture radar that utilizes the relative motion between airborne aperture transmitter and the object, and makes equivalent small-sized antenna apertures to be a major transmitter via data processing to improve the resolution and to strengthen the penetration (Guo et al2012, Li et al2010). The algorithm of TEM wave field transformation creates the condition for TEM synthetic aperture imaging. Furthermore, both numerical results and model experiments show that the reflections from the same geological body at nearby points correlate well with each other. Based on these features mentioned above, we adopt the correlation superposition method for synthetic processing (Zhang and Xu 2006) and the synthetic process is shown in figure 2. The weighing functions are obtained based on the correlation coefficients of different positions. Firstly, we choose a central point i, and the value of fictitious wave field is U(ri,τj) ⁠, where ri is the station of point i and τj is the virtual time. Secondly, we designate the size of synthetic aperture, and choose the points from –N to N on the two sides of point i to correlate with the central point. The normalized cross-correlation coefficients are as follows: ρ(ri,τ)=∑j=1,nU(ri,τj)U(ri+k,τj-τ)[∑j=1nU2(ri,τj)∑j=1nU2(ri+k,τj)]12,6 where n is the number of tracks of each point. The cross-correlation coefficient ρik(ri,τ) shows the correlation of two wavelets. We change the corresponding shift factor τ and get the maximum correlation coefficient. The maximum coefficient corresponds to the best offset τB ⁠. Then we get 2N+1 maximum correlation coefficients ρikmax(ri,τkB) and the best offset τkB (k = -N, •••, N). We multiply the maximum correlation coefficient with its track and get the synthetic value as below U∼(ri,τj)=∑k=-NNρikmax(rik,τkB)U(ri+k,τj-τkB)j=1,2,⋯,n.7 The function U˜(ri,τj) is the synthetic aperture value of the centre point i at the time of τj ⁠. Finally, we can get the synthesized values of the central points by moving along the line point by point, which can eventually compose a synthesized profile. The processing mentioned above is the 1D synthetic aperture algorithm and it can be extended to 2D model. 2.3. Pulse compression technique for TEM fictitious wave processing After the wave field inverse transform, the fictitious wave could be described by the waveform equation mathematically. It also has some typical transmitting features as a wave function, such as reflection and refraction. When the fictitious wave is transmitting into the earth, a part of the energy of the electromagnetic wave transformed into heat and vanished since the earth is lossy. Therefore, the amplitude of the fictitious wave will decrease. Furthermore, the earth can be treated as a wave filter. The high frequency energy is absorbed quickly with the increase of detection depth, thus the low frequency wave plays a dominant role. The broadening effects in this process will reduce the resolution of the wave field. For the purpose of avoiding those problems aforementioned, we used a deconvolution method for the impulse compression to improve imaging quality. To illustrate this problem, we only used the simple minimum phase deconvolution method, which is commonly used in seismic interpretation. This method can be found in almost every classical seismic prospecting book. Consequently, we give the results directly without the derivation process. We take the double positive-crest model (Q-type model wave field transform result) as an example. Process the data of inverse transformation using the method discussed in this paper and the result is shown in figure 3. The pictures (a, b) (in figure 3) show the wave field image before deconvolution and after deconvolution respectively. In summary, the pulse compression method improved the resolution of the fictitious wave field efficiently. Figure 3. Open in new tabDownload slide Contrast before and after pulse compression processing with fictitious wave data. (a) The fictitious wave acquired with wave field transformation. (b) The result of fictitious wave after pulse compression processing. ‘s’ is seconds; τ is the fictitious time and its dimension is s ⁠. Figure 3. Open in new tabDownload slide Contrast before and after pulse compression processing with fictitious wave data. (a) The fictitious wave acquired with wave field transformation. (b) The result of fictitious wave after pulse compression processing. ‘s’ is seconds; τ is the fictitious time and its dimension is s ⁠. 2.4. Kirchhoff migration imaging The equations satisfying diffusion equation is transformed to equations satisfying wave equation after finishing waveform transformation of the TEM field; therefore, those mature migration imaging techniques in seismic interpretation could be used. Kirchhoff integration migration imaging is a commonly used algorithm in seismic migration imaging. In 1883, Kirchhoff proposed that if the displacement potential ϕ(x,y,z,t) and its derivative of a given wave from a closed surface Q which the source is located in are known and continuous, then the displacement potential ϕ at arbitrary measuring point M(x1,y1,z1) outside Q which is caused by the source could be calculated by the Kirchhoff integration equation φ(x1,y1,z1,t) ︀ ︀ ︀ ︀=-14π∯Q{ ︀[φ]∂∂n(1r)-1r[∂φ∂n]-1vr∂r∂n[∂φ∂t] ︀} ︀ ︀dQ ︀.8 By utilizing the synthetic aperture wave field value and adopting the Kirchhoff migration imaging (Li 2005,Guo et al2012) in seismic exploration, we have, based on the virtual wave equation, given the 3D imaging of an underground target. Because migration is the reversion of recording, it is possible that let the self-exciting and self-receiving upcoming wave be G(x,y,z0,t) ⁠, and it is the value on the ground surface excited by the second source g(x,y,z,t) in the underground surface. Their relationship is shown as equation (9). In practice, it is necessary to discrete the Kirchhoff integration for the discrete property of the data. Put the 3D boundary element method to use and we get the 3D migration imaging result at the specified migration distance g(x,y,z,t)=−14π∬Q0[∂∂n(1r)−1r∂∂n−1vr∂r∂n∂∂t]G(ξ,η,ζ0,t+rv)dQ0.9 3. Modelling analysis and case study 3.1. Modelling analysis We put a low resistivity target into a half space (shown in figure 4), and take it as a theory model to test the synthetic aperture algorithm. The resistivity of the half space is 50  Ω⋅m ⁠. The resistivity of the target is 5  Ω⋅m ⁠, the size is 40 m × 40  m × 50 m ⁠, and its buried depth is 100 m. The survey line and point stations are shown in figure 5. Figure 4. Open in new tabDownload slide Schematic diagram of the synthetic aperture process. i is the center point we chose, N is the synthetic aperture range, the rhombus is the position of the transmitter and receiver, and Δτ is the best shift. Figure 4. Open in new tabDownload slide Schematic diagram of the synthetic aperture process. i is the center point we chose, N is the synthetic aperture range, the rhombus is the position of the transmitter and receiver, and Δτ is the best shift. Figure 5. Open in new tabDownload slide Resistivity target into a half space and the surface line. The gray block in the figure is the underground target, its size is 40 m × 40 m × 50 m and the depth is 100 m. The loop configuration is in loop and there are five lines and eleven points in each line. The line space and point distance are both 20 m. Figure 5. Open in new tabDownload slide Resistivity target into a half space and the surface line. The gray block in the figure is the underground target, its size is 40 m × 40 m × 50 m and the depth is 100 m. The loop configuration is in loop and there are five lines and eleven points in each line. The line space and point distance are both 20 m. With the FDTD forward modelling algorithm (Sun et al2013), we acquire the response of those points, and transform them to the fictitious wave field. The fictitious wave field of the typical survey line is shown in figure 6(a). With the correlation superposition processing we give the synthetic results of the whole survey line. Comparing figures 6(b) with (a), the synthetic aperture algorithm strengthens the deeper weak abnormal signals, and it is good for detecting the boundary of the underground object. Then, with the Kirchhoff migration method we can obtain the imaging of the underground object based on the synthetic data. The result coincides well with the theory model (shown in figure 6(c)). Figure 6. Open in new tabDownload slide (a) Fictitious wave field result of the survey line 3. (b) Result of the synthetic process based on the fictitious wave field data. (c) Migration imaging based on the synthetic data. The positive pulse in red color is the peak of the fictitious wave in figure 4(a). It corersponds to the interface of the geo-electric model. Comparing figures 4(a) and (b), it is obvious that the synthetic process strengthens the signal and improves the S/N ratio. The yellow square is the position of the underground object in figure 4(c) and corresponds to the depth with the top and bottom surface of the object. Figure 6. Open in new tabDownload slide (a) Fictitious wave field result of the survey line 3. (b) Result of the synthetic process based on the fictitious wave field data. (c) Migration imaging based on the synthetic data. The positive pulse in red color is the peak of the fictitious wave in figure 4(a). It corersponds to the interface of the geo-electric model. Comparing figures 4(a) and (b), it is obvious that the synthetic process strengthens the signal and improves the S/N ratio. The yellow square is the position of the underground object in figure 4(c) and corresponds to the depth with the top and bottom surface of the object. 3.2. Case study We take a 3D data as an example, which was acquired in a coal mine with TEM, to verify the algorithm we proposed. The coal mine is located in Shanxi province, China. The geomorphology of the area is loess hilly (figure 7). Figure 7. Open in new tabDownload slide Photo showing the geomorphology of the field case area. Figure 7. Open in new tabDownload slide Photo showing the geomorphology of the field case area. The GDP-32II electrical workstation was used to survey field data with central loop equipment. The transmitter frequency was selected as 25 Hz, and the time range was from 0.087 to 8 ms. There are eleven lines and eleven points in each line. The line spacing and point spacing are both 20 m. Figure 8(a) is the 3D apparent resistivity section of the survey area. The apparent resistivity changes from tens to hundreds in the survey region. It just seems like an H-type model whose resistivity is higher in the shallow and deep areas than in the central area. Figure 8(b) is the section of the apparent resistivity for the contour of this typical section. In the shallow layer, the resistivity is high, reaching more than 100  Ω⋅m ⁠. Starting from about 120 m, the resistivity decreases rapidly, and reaches a minimum about 55  Ω⋅m at about 150 m. With a further increase of depth, the resistivity begins to increase slowly, and at 500 m the resistivity has returned to 100  Ω⋅m ⁠, the same as the shallow layer. Two electric interfaces can be vaguely interpreted from this figure. The first interface is at the depth of 110–130 m, however, it is not easy to determine the location of the second interface because its change is very slow, but it can be tentatively estimated to occur from approximately 250–350 m. Figure 8. Open in new tabDownload slide (a) 3D apparent resistivity section of the survey area. (b) Section of the apparent resistivity for the contour of line 1400 of the typical section. Figure 8. Open in new tabDownload slide (a) 3D apparent resistivity section of the survey area. (b) Section of the apparent resistivity for the contour of line 1400 of the typical section. Figure 9 shows the application of the synthetic aperture imaging processing to the typical section. The abscissa axis is the point number and the vertical axis is the virtual time. The figure shows the subsurface interfaces which are similar to a three-layer model. There are interfaces at the virtual time about 100ms and 400ms ⁠, respectively. Based on the data processed with the synthetic aperture algorithm, the 3D TEM imaging by continuation from surface to underground has been realized by introducing Kirchhoff integration (shown in figure 10). The imaging results show that the first interface is located at about 100 m, and the second interface is at about 160 m, between the two interfaces it is the low resistivity of being water-filled. In order to show the result clearly we give one more figure about the sections (shown in figure 11). Compared to the apparent resistivity section, this figure gives out more apparent layers. Though the anomalous zone is extended for the low resistivity of water, the imaging result is more helpful to detect the boundary of the water-filled object than the apparent resistivity section. It combines the two together, and we can get not only the underground structure but also the underground medium electrical distribution. Compared with the actual geological conditions, the results fit the geological structure well, which proves that migration imaging with synthetic aperture method is effective. Figure 9. Open in new tabDownload slide (a) Synthetic aperture imaging process to the typical section. (b) 3D display of the synthetic aperture imaging. The plus in panels (a) and (b) both correspond to the interface of the resistivity changing. Figure 9. Open in new tabDownload slide (a) Synthetic aperture imaging process to the typical section. (b) 3D display of the synthetic aperture imaging. The plus in panels (a) and (b) both correspond to the interface of the resistivity changing. Figure 10. Open in new tabDownload slide Kirchhoff migration imaging of the survey area. Figure 10. Open in new tabDownload slide Kirchhoff migration imaging of the survey area. Figure 11. Open in new tabDownload slide (a) Imaging without the water-filled zone. (b) Migration imaging displayed in a different direction. Figure 11. Open in new tabDownload slide (a) Imaging without the water-filled zone. (b) Migration imaging displayed in a different direction. 4. Conclusion TEM has been applied and developed in China for many years, but there are still many problems to be solved. In recent years, TEM pseudo-seismic migration imaging has been a significant research area. The algorithm of transient electromagnetic field transform realizes the conversion from the diffused transient field to the fictitious wave field, making transient electromagnetic pseudo-seismic imaging technology possible. The Kirchhoff migration imaging, mentioned above, is a helpful method to achieve the transient electromagnetic pseudo-seismic imaging. This article is based on past studies in wave field transform and develops further on this research. In order to further improve the imaging resolution, to extract more useful information from existing data, ideas were learnt from the theory of synthetic aperture in synthetic aperture radar. In particular, the idea that synthesis of many small loops into a large one in the transient electromagnetic method could be successful. In order to verify the effectiveness of this proposed method, we especially designed a block anomalous body model. After processing to models we found that the related synthesis could enhance useful signals, improve signal-to-noise ratio, and increase resolution. The practical use shows that the 3D TEM imaging by synthetic aperture continuation can image the 3D underground, and the resulting images match well with the actual geological structure. Both synthetic modeling and practical use show that 3D TEM imaging of the virtual wave field continuation has the ability to distinguish the underground resistivity distribution, and proves to be an effective method in 3D data interpretation. The synthetic aperture method can help improve the resolution of wave field. This means that the imaging by wave field continuation makes high-resolution TEM imaging possible. As an exploratory study, there is much further work that needs to be done. If this method can be further improved and applied, it will have far-reaching significance for high-resolution airborne TEM exploration. 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TI - Inverse transformation algorithm of transient electromagnetic field and its high-resolution continuous imaging interpretation method
JF - Journal of Geophysics and Engineering
DO - 10.1088/1742-2132/12/2/242
DA - 2015-04-01
UR - https://www.deepdyve.com/lp/oxford-university-press/inverse-transformation-algorithm-of-transient-electromagnetic-field-hCdv0UPmKT
SP - 242
VL - 12
IS - 2
DP - DeepDyve
ER -