Pre-stack migration applied to GPR for landmine detection

Transcription

1 INSTITUTE OF PHYSICS PUBLISHING Inverse Problems (4) S99 S115 INVERSE PROBLEMS PII: S (4)78795-X Pre-stack migration applied to GPR for landmine detection Xuan Feng 1, and Motoyuki Sato 1 1 Center for Northeast Asian Studies, Tohoku University, Sendai, Japan College of GeoExploration Science and Technology, Jilin University, 136 Changchun, People s Republic of China sato@cneas.tohoku.ac.jp Received 4 April 4, in final form 3 August 4 Published 8 November 4 Online at stacks.iop.org/ip//s99 doi:1.188/ //6/s7 Abstract Detection of buried landmines by ground penetrating radar (GPR) normally suffers from very strong clutter that will decrease the image quality in GPR data. Problems are also encountered when imaging steeply dipping landmines by GPR. To solve these problems, we have developed a steppedfrequency continuous-wave array antenna ground penetrating radar system, called SAR-GPR, that can acquire common middle point multi-offset data. As an approximate solution to the general wavefield inversion problem, migration algorithms were used to refocus the scattered landmine information to improve signal clutter ratio and re-construct the landmine image. Also, pre-stack migration was found to efficiently deal with the steeply dipping landmine problem. Before migration processing, subtracting antenna coupling was used. The SAR-GPR system was tested under two conditions. The first condition is designed to simulate inhomogeneous soil under rough ground conditions and the second condition is to simulate steeply dipping buried landmine. Very strong clutter in the GPR data was exhibited in the first condition. After prestack migration, strong clutter was efficiently suppressed and a high quality landmine image was re-constructed in both experiments. (Some figures in this article are in colour only in the electronic version.) 1. Introduction The human suffering caused by antipersonnel (AP) landmines that remain active from past conflicts has received considerable public exposure in the last few years. Large numbers of landmines are found in more than 6 countries worldwide. Although research on detecting buried landmines was initiated as early as the Second World War, the search for mines is still a quite difficult task because of the complex nature of the problem and the high degree of /4/699+17$3. 4 IOP Publishing Ltd Printed in the UK S99

2 S1 X Feng and M Sato detection efficiency required. Hence great effort has been expended over the past several years to develop sensors to detect landmines. Detection of minimum-metal landmines by conventional metal detectors is a difficult and challenging task. Ground penetrating radar (GPR) can be an effective subsurface imaging tool for landmine detection, because it can detect both metal and nonmetal objects based on the dielectric properties. However, the detection of buried landmines by GPR normally suffers from very strong clutter that will decrease the signal clutter ratio and degrade the image of the landmine in GPR data. Clutter is characterized as signal components that are not directly correlated with primary scattering from mine objects. Detection problems also arise when steeply obliquely buried landmines are imaged by GPR, due to the different reflecting wavefield of the dipping reflecting boundary of the mine. The technique of migration is now commonly used to process GPR data, and has been in use for almost five decades in seismic reflection surveys [6]. Migration can improve the signal clutter ratio through the refocusing of the scattered signals. Conventional post-stack migration processing is based on the zero-offset dataset. The operations mainly consist of two steps. Firstly, normal moveout (NMO) correction and stacking are used to process a multi-offset dataset to form a stacked dataset. Then post-stack migration is used to process the stacked dataset. Here the key assumption is that the stacked dataset, which is generated by NMO and stacking, is a zero-offset dataset, which is the base for post-stack migration. When the medium is simple, for example homogeneous soil and flat ground surface, and flat reflection interface, the assumption is tenable. But when the media is complex or the reflection interface is steeply oblique, the assumption is broken and conventional processing will meet some problems. The pre-stack migration on multi-offset data does not need NMO correction and stacking, thus it should provide better results in a complex situation. Also pre-stack migration can efficiently deal with steeply dipping objects []. Because common middle point (CMP) techniques have been used in conjunction with GPR [4, 5, 13, 16] with good results, we developed a steppedfrequency continuous-wave array antenna ground penetrating radar system, called SAR-GPR, to gather CMP data. This paper focuses on applying pre-stack migration to the SAR-GPR system for improving the quality of reconstructed landmine images and demonstrating the dramatic results via experiment.. SAR-GPR system Based on the vector network analyser (HP8758E), position controller, coaxial switch and transmitting receiving antenna array, we developed the stepped-frequency continuous-wave array antenna (the SAR-GPR) system [14]. To employ the CMP technique, we developed an antenna array, shown in figure 1, which is constructed of 1 antipodal Vivaldi antennas. These antennas are used to form five pairs of transmitting receiving antennas. In each pair of antennas, one is used to transmit the signal while the other receives. Separation between the antennas is 3 cm. Depending on the antenna array, we can acquire CMP multi-offset data directly. The antipodal Vivaldi antenna was chosen because it is a wide frequency range antenna [9, 18] and can easily be used to construct an antenna array due to its flat shape. A coaxial switch is used to connect the vector network analyser to the transmitting receiving antenna array, because while the antenna array has five transmitter and receiver antennas, the vector network analyser has only one transmitting port and one receiving port. A position controller is used to move the antenna array in two dimensions (the X and Y directions) with precision.

3 Pre-stack migration applied to GPR for landmine detection S Tx Rx Figure 1. Transmitting receiving antenna array of SAR-GPR. 3. Application of pre-stack migration Leparoux [1] indicated that because it is possible to describe electromagnetic wave propagation with the scalar wave propagation equation that is mathematically similar to the acoustic wave equation, it should be possible to adapt the seismic migration concept to radar data since both the direct and inverse problems are based on this equation. From the scalar wave equation, the famous Kirchhoff diffraction integral will be derived through Green s theorem. Trorey [17], Hilterman [7, 8], and Berryhill [, 3] make extensive use of the Kirchhoff integral in forward modelling studies of diffraction [15]. To study the diffraction behaviour due to a landmine, a landmine model was buried in homogeneous gravel soil, under a flat ground surface. We acquired data through 1-D scan above the landmine model. Figure shows the stacked section of the experiment. We found that the diffraction hyperbolas, which are due to sharp discontinuities at both ends of the landmine in figure, stand out. The migration processing is necessary to focus and re-construct the landmine image. Also, because the migration processing will sum the amplitudes along the hyperbolic trajectory, the signal will be enhanced and the signal clutter ratio will be improved. The reflection energy from the interfaces can be considered as the superposition of the scattered energy from a large number of closely spaced points on the interfaces. The reflection amplitude at each point is taken as proportional to the reflection coefficient of the interface at this point. This sampled subsurface model is called a scatter point model, as illustrated in figures 3 and 4, which forms the basis of the Kirchhoff migration method. In addition, the points that may not locate at any recognizable interface can be considered as scatter points with zero or very small reflection amplitudes [11]. Kirchhoff migration [15] is based on the computation of the travel-time surface over which energy from a subsurface point is scattered. Input samples on the travel-time surface are summed, according to the Kirchhoff diffraction integral, directly to an output migrated sample [1]. Schneider [15] and Berryhill [3] are excellent references for the mathematical treatment of the Kirchhoff migration method. The intergral solution of the scalar wave equation gives the output wave field P out (x out, y out, z, t) at a subsurface scatter point (x out, y out, z) from the

4 S1 X Feng and M Sato.5 Time(ns) Ground surface diffraction hyperbolas diffraction hyperbolas x(m).5.3 Figure. Stacked section of 1-D measurement for detection of landmine model buried in gravel soil under flat ground surface. y (x out, y out ) input point (x in, y in ) t θ r r x Diffraction hyperbolas Scatter point ( x out, y out, z ) v z Figure 3. Geometry for Kirchhoff migration based on zero-offset dataset. zero-offset wave field P in (x in, y in, z =, t), which is measured at the surface (z = ). The integral solution used in migration is given by P out (x out, y out, z, t) = 1 [ cos θ P π r in (x in, y in, z =, t + r ) v + cos θ vr ( t P in x in, y in, z =, t + v) r ] dx dy, (1)

5 Pre-stack migration applied to GPR for landmine detection S13 (a) y S n h n h 1 h n ( ) out y out x, SP S 1 α h 1 CMP ( x, y ) in in h 1 R 1 R n t sn t s1 x t R1 t Rn z ( x y z), Scatter point, out out (b) y h n h 1 h 1 S n S 1 CMP R 1 R n ( ) out y out x, SP ( x, y ) in in h n t sn t s1 t R1 x t Rn z ( x, y z) out out, Scatter point Figure 4. Geometry for Kirchhoff pre-stack migration based on multi-offset dataset with source S and receiver R. α is the angle between the x-coordinate and antenna array. (a) Arbitrary α and (b) α =. where v is the root-mean-square (rms) velocity at the scatter point (x out, y out, z) and r = [(x in x out ) + (y in y out ) + z ] 1/, which is the distance between the input point (x in, y in ) and scatter point (x out, y out, z), as illustrated in figure 3. Cos θ is the obliquity factor or directivity factor, which describes the angle dependence of amplitudes and is given by the cosine of the angle between the direction of propagation and the vertical axis z, shown in figure 3. 1/vr is the spherical spreading factor. The time derivative of the measured wave field yields a 9 phase shift and adjustment of the amplitude spectrum. In equation (1) the first term, the nearfield term, is proportional to (1/r ), therefore, its contribution is negligible as compared to the second term, which is proportional to (1/r). The first term usually is dropped in practical implementation of the integral. It is the second term, the far-field term, that is used in migration. The complete migrated dataset is obtained by performing the integration and setting t = for each output location [19]. So, the migration integral based on zero-offset wave field is given by P out (x out, y out, z) = 1 [ ( cos θ π vr t P in x in, y in, r )] dx dy. () v

6 S14 X Feng and M Sato In equations (1) and (), the diffraction hyperbola is given by r/v, which is the travel time of wave propagation. For multi-offset common middle point (CMP) dataset, the total travel time is modified by adding the source to scatter point time t S and the scatter point to receiver time t R to give t SR = t S + t R. (3) From the geometry of figure 4(a), and defining that the location of CMP is (x in, y in ), the location of transmitter antenna S is (x in h cos α, y in + h sin α) and of the receiver antenna R is (x in + h cos α, y in h sin α). Here, h is half the source receiver offset and α is the angle between the x-coordinate and antenna array. So, equation (3) can be expanded to given the double square root (DSR) equation, [ z + (x in h cos α x out ) + (y in + h sin α y out ) ] 1/ t SR = v [ z + (x in + h cos α x out ) + (y in h sin α y out ) ] 1/ +, (4) v where (x out, y out, z) is the position of the scatter point. Generally, we set the antenna array along the x-coordinate direction. At this situation, the angle α =, as illustrated in figure 4(b). Substituting α = into equation (4), we obtain: [ z + (x in h x out ) + (y in y out ) ] 1/ t SR = v [ z + (x in + h x out ) + (y in y out ) ] 1/ +. (5) v The pre-stack migration integral based on CMP multi-offset wave field is given through the modification of equation (): P out (x out, y out, z) = 1 [ ] cos θ π vr t P in(x in, y in, h, t SR ) dx dy dh. (6) A form of aliasing is possible in migration. Consider the conversion of a trace s(t) to a depth trace s(z) with a desired depth sample interval of z. The time to depth conversion will effectively extract samples from s(t) at the interval t eff = n z/v. This is a form of re-sampling. If t eff > tthen aliasing will occur as the depth trace is constructed. If f max is the maximum signal frequency in s(t), then the sampling theorem assures that s(t) can be re-sampled to t 1/(f max ) without loss of signal. Therefore, the depth sample interval should not be chosen arbitrarily but t eff should be chosen to ensure that signal is preserved. This leads to the condition z v/4f max [1]. 4. Experiment The target was a model of a landmine, type 7 model, shown in figure 5. The type 7 antipersonnel mine has low metal content and is difficult to locate using metal detectors under most field conditions. Its height is 4 mm and diameter is 78 mm. Its relative dielectric constant is about 3.. The measured data were acquired over a sandbox in D scanning mode. The scanning procedure consisted of moving the transmitting receiving antenna array in the horizontal direction (i.e., the X and Y directions) by increments of 1. cm. So, the dataset

7 Pre-stack migration applied to GPR for landmine detection S15 Figure 5. Type 7 landmine model. x y Figure 6. Case I: a landmine model was buried in inhomogenous soil under rough ground condition. acquired by the SAR-GPR system is 4D P (x, y, h, f ) stepped frequency CMP multi-offset data. Experiments were carried out to validate the technique in two cases. Since strong clutter is the serious problem in landmine detection by GPR, we used a mixture of large gravel and small crushed rocks, shown in figure 6, in order to simulate inhomogeneous soil under rough ground conditions in case I. Figure 7 displays the dataset acquired by a single pair of transmitter and receiver antennas (called common offset) with 3 cm separation. Figure 7(a) shows the vertical slice, figure 7(b) shows the horizontal slice and figure 7(c) shows the 3D image. In the figure, we can find very strong clutter that obscures the image of landmine and makes it difficult to distinguish the landmine image. In case II, we obliquely buried the landmine model in small crushed rocks, shown in figure 8, under the flat ground surface for the simulation of a steeply dipping landmine. Figure 9 displays the common-offset dataset acquired in this situation. Figure 9(a) shows the oblique slice and figure 9(b) shows the 3D slice image. In the figure, although the ground surface is flat and clutter is very slight we cannot find the landmine image in the position where the landmine model was buried. 5. Data processing The dataset acquired by SAR-GPR in experiments should be preprocessed before migration. Preprocessing of the data includes subtracting antenna coupling, bandpass filtering, inverse

8 S16 X Feng and M Sato (a) x1-4 1 (b).4 x X(m). Time(ns) Y(m) X(m) (c) T(ns) X(cm) Y(cm) 4 Figure 7. Common-offset dataset of case I: (a) vertical slice, (b) horizontal slice and (c) 3D image. y x Figure 8. Case II: a steeply dipping landmine model was buried in homogeneous soil under flat ground conditions.

9 Pre-stack migration applied to GPR for landmine detection S17 (a).649 T(ns) Y(m).31.4 X(m) (b).649 T(ns) Y(m) X(m) Figure 9. Common-offset dataset of case II: (a) oblique slice and (b) 3D slice image. discrete Fourier transform (IFFT), trace balancing and velocity analysis. Figure 1 illustrates the flowchart of data processing. A band pass filter and inverse discrete Fourier transform (IFFT) are used to transform the signal from the frequency domain to the time domain. Considering the effect of antenna coupling shown in figure 11(a), we measure it by pointing the antennas upward without any target. Comparing the antenna coupling and the signal before

10 S18 X Feng and M Sato Input subtracting antenna coupling Bandpass filtering IFFT Trace balancing velocity analysis v Pre-stack migration Output Figure 1. Flowchart of data processing. subtracting antenna coupling shown in figure 11(b), we can find that relatively large fluctuations of antenna coupling might mask a signal of interest. So we subtract the antenna coupling in the frequency domain before band pass filtering, leaving just the signal shown in figure 11(c). After IFFT, we get the dataset P(x, y, h, t). Figure 1(a) displays traces of a CMP gather P(h, t) at a measurement point (x, y). Here, t is the time and h is half the transmitter receiver offset. From figure 1(a), we find that the energy of the trace becomes weak along the h-axis in CMP gather, because the travel distance becomes long. To balance the energy of traces, a weighting factor was multiplied: P in (x, y, h j, t i ) = P(x, y, h j, t i )W i,j, i = 1,..., M, j = 1,..., N, (7) where P in (x, y, h j, t i ) is the dataset after trace balancing and P(x, y, h j, t i ) is the dataset before trace balancing. M is the number of sampling points each trace gathers and N is the number of traces each CMP gathers. In our experiments, N is 5 in the measurement dataset acquired by SAR-GPR. W i,j is the weighting factor. To obtain the weighting factor, the average amplitude of each trace is calculated first: Q j = 1 M P(x, y, hj, t i ), (8) M i=1 and then the average amplitude of all traces each CMP gathers is calculated: Q = 1 N Q j. (9) N J=1 Then, the weighting factor W i,j is defined by W i,j = Q Q j. (1) Equation (7) should be used for every measurement point (x, y) to obtain the dataset after trace balancing. Figure 1(b) displays the result after applying trace balancing to the traces shown in figure 1(a). From the figure, we can find that the amplitudes were adjusted.

11 Pre-stack migration applied to GPR for landmine detection S19 (a) x Amplitude Time(ns).5 3 (b) x Amplitude Time(ns).5 3 x 1 3 (c) Amplitude Time(ns) Figure 11. Single signal: (a) antenna coupling, (b) before subtracting antenna coupling and (c) after subtracting antenna coupling.

12 S11 X Feng and M Sato (a) Trace h(cm) Time(ns).5 3 (b) Trace h(cm) Time(ns).5 3 Figure 1. Traces of a CMP gather: (a) before trace balancing and (b) after trace balancing. From equation (6), we find that the velocity parameter is needed for migration. Rootmean-square (rms) velocities can be estimated by the velocity spectrum method, which is based on the cross-correlation of the traces in a CMP gather and not on the lateral continuity of the stacked events [19]. Several studies have successfully adapted this type of velocity analysis and dynamic correction to radar data for stratified media [4, 5, 1]. To estimate the velocity, one CMP gather P(h j, t i ) was chosen from the dataset P in (x, y, h j, t i ) obtained by trace balancing at a measurement point (x, y). A stacked amplitude is defined as [19] N ( S i,k = P in hj, t ), (11) j=1 where t is the two-way time lying along the trial stacking hyperbola: ( ) 1/ t = ti + h j v, k = 1,..., NK. (1) k

13 Pre-stack migration applied to GPR for landmine detection S Time[ns] Velocity[m/ns] Figure 13. Velocity spectrum. Because the propagation velocity of an electromagnetic wave is smaller than.3 m ns 1, v NK is generally defined as.3 m ns 1. The expression for the unnormalized cross-correlation sum within a time gate is given by C i,k = 1 L [ Si,k N ] Pin (h j, t), (13) i=1 j=1 where L is the length of the time gate. Figure 13 displays the cross-correlation sum C i,k on a plane of velocity v k versus two-way time t i, which is called the velocity spectrum. From the velocity spectrum, ( we can) pick up the rms velocity by the peak value of the contour. Lastly, P in x, y, hj, t i obtained by trace balancing and the rms velocity acquired by velocity analysis were substituted into pre-stack migration equation (6). Pre-stack migration creates one output migrated trace by summing energy from all input traces within the migration aperture. The migrated dataset is shown in figures 14 and Discussion Figure 14 displays the pre-stack migrated dataset of case I where an horizontal landmine model was buried in inhomogeneous soil under rough ground conditions. Figure 14(a) shows

14 S11 X Feng and M Sato (a) Depth(m) (b) X(m) X(m) Y(m) (c) Z(cm) Y(cm) 8 34 X(cm) Figure 14. Migrated CMP multi-offset dataset of case I: (a) vertical slice, (b) horizontal slice and (c) 3D image.

15 Pre-stack migration applied to GPR for landmine detection S113 (a).64 Z(m) Y(m).4.31 X(m) (b).64 Z(m) Y(m) X(m) Figure 15. Migrated CMP multi-offset dataset of case II: (a) oblique slice and (b) 3D slice image.

16 S114 X Feng and M Sato the vertical slice, figure 14(b) shows the horizontal slice and figure 14(c) shows the 3D image. Comparing the common-offset data shown in figure 7 and migrated CMP multi-offset dataset shown in figure 14, one can see a dramatic improvement in the migrated CMP multi-offset dataset. The signal clutter ratio was improved and the reconstructed image is much better. Figure 15 displays the pre-stack migrated dataset of case II where a steeply dipping landmine model was buried in homogeneous soil under flat ground conditions. Figure 15(a) shows the oblique slice and figure 15(b) shows the 3D slice image. From the figure, we can find that the reconstructed landmine model image is clearly visible after pre-stack migration processing. 7. Conclusion Rough ground conditions and inhomogeneous soil can produce strong clutter in GPR data. The strong clutter will decrease the signal clutter ratio and degrade the image quality of any detected landmines in GPR data. We have shown that diffraction hyperbolas can be found in GPR data, which are due to sharp discontinuities at both ends of the landmine. Along the diffraction hyperbolas, migration processing can refocus the diffraction information to enhance the signal and improve the signal clutter ratio. By migration processing techniques, we can improve the signal clutter ratio and re-construct a high quality image of a landmine. Landmines buried at steeply oblique angles present special difficulties in detection, even when the overlying ground surface is flat and clutter is very slight. Pre-stack migration can also efficaciously deal with the problem and re-construct the image of a steeply dipping landmine based on CMP multi-offset data acquired by the SAR-GPR system. Acknowledgments This work was supported by JST (Japan Science and Technology Corporation) and JSPS Grant-in Aid for Scientific Research (S) References [1] Bancroft J C, Geiger H D and Margrave G F 1998 The equivalent offset method of prestack time migration Geophysics [] Berryhill J R 1977 Diffraction response for nonzero separation of source and receiver Geophysics [3] Berryhill J R 1979 Wave-equation datuming Geophysics [4] Fisher E, McMechan G A and Annan A P 199 Acquisition and processing of wide-aperture ground-penetrating radar data Geophysics [5] Greaves P J, Lesmes D P, Lee J M and Toksoz M N 1996 Velocity variations and water content estimated from multi-offset, ground-penetrating radar Geophysics [6] Hermance J F 1 Ground-penetrating radar: postmigration stacking of n-fold common midpoint profile data Geophysics [7] Hilterman F J 197 Three-dimensional seismic modeling Geophysics [8] Hilterman F J 1975 Amplitudes of seismic waves a quick look Geophysics [9] Langley J, Hall P and Newham P 1993 Novel ultrawide-bandwidth Vivaldi antenna and low crosspolarisation Electron. Lett [1] Leparoux D, Gibert D and Côte P 1 Adaptation of prestack migration to multi-offset ground-penetrating radar (GPR) data Geophys. Prospecting [11] Li X and Bancroft J 1998 The natural relation between prestack time migration and residual statics analysis CREWES Res. Rep [1] Margrave G F 1 Numerical Methods of Exploration Seismology with Algorithms in Matlab (Calgary: Department of Geology and Geophysics, The University of Calgary) pp

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