A high-resolution weak signal reconstruction method for electromagnetic wave modeling and reverse time migration of ground-penetrating radar data Qihua Li1,2(*), Xiaofeng Jia1,2 and Daoyuan Sun1,2, 1. Laboratory of Seismology and Physics of Earth’s Interior, School of Earth and Space Sciences, University of Science and Technology of China, Hefei 230026, China; 2. National Geophysical Observatory at Mengcheng, University of Science and Technology of China, Anhui, China. Summary Staining algorithm (SA) was proposed to extract waves that pass through the target area and image the target area with the extracted wave to obtain a higher image quality. In this study, we proposed an approach to reconstruct weak signals for electromagnetic (EM) wave modeling and established the correspondence between subsurface target structures and the reconstructed wavefield. When using the reconstructed partial wavefield in the reverse time migration (RTM) of ground-penetrating radar (GPR) data, we can mute non-target information from the conventional RTM image and keep target related structures. Numerical experiments show that our method is able to extract low-energy waves under lossy layers. Furthermore, the constructed electromagnetic wavefield is actually a subset of the real electromagnetic wavefield. We applied this method to target-oriented imaging and obtained high-quality images of target structures in lossy media. Introduction Ground penetrating radar has been developed in theory, technique, and range of applications rapidly over the past few decades. GPR was applied to a variety of fields such as the study of subsurface contamination, archaeology, geotechnical engineering, and glaciology (Benson, 1995; Plewes and Hubbard, 2001; Jol, 2008). Reverse time migration (Baysal et al., 1983; Chang and McMechan, 1987) is a wave-propagation-based process that focuses reflections and diffractions and yields image of the subsurface area. Due to the similarity between the Electromagnetic wave and the seismic wave in kinematics and dynamics, RTM has been successfully implemented in processing GPR data to obtain the true depths and shapes of internal structures (Fisher et al., 1992; Leuschen and Plumb, 2001; Liu et al., 2014). However, the presence of electromagnetic wave attenuation distorts the phase and amplitude of the signal, and therefore degrades the image quality (Zhu et al., 2016). Attenuation in the ground can be highly variable and has a significant effect on the depth of penetration. Additionally, the conventional RTM generates noises and artifacts due to the limited acquisition system, overburden complexity, and the reflector dip angle (Xie et al., 2006). Staining algorithm (SA) (Chen and Jia, 2014; Li and Jia, 2017) is a processing technique to improves the image

quality of poorly imaged areas, which has been successfully applied to the seismic migration. Similar to fate mapping in developmental biology (Dale and Slack, 1987; Ginhoux et al., 2010) which traces target cells and their progeny at later stages of development, SA traces and extracts those waves that pass through target structures. The extracted wavefield is called the stained wavefield. When the wavefront reaches the ‘stained’ target structure, it will be automatically labeled and traced in subsequent propagation as well as its reflection and transmission. Thus, the stained wavefield is a subset of the real wavefield, and it includes only responses relevant to the stained structure or area. When a stained wavefield is used in RTM, non-target information, including both signals and noise, is muted from the migration results, while the low-energy target related information remains; therefore, the image quality of the target structures is improved. In this study, we proposed an approach to reconstruct weak signals for electromagnetic wave modeling and RTM of GPR data. The real and the constructed EM wavefields are linked up by regarding the real wavefield at a marked area as the boundary condition for the reconstructed wavefield. The amplitude and the waveform of this local EM wavefield are consistent with those of the real EM wavefield. We used our method to reconstruct the weak signals under lossy media. Using the real and the local EM wavefields in the RTM of GPR data, we obtained a conventional RTM image and an exclusive image of the target area. Our method improves the image quality of target area by muting non-target information from the image instead of enhancing the energy of target structure directly. Theory Our method is based on the transverse magnetic (TM) Maxwell equations (Irving and Knight, 2006), which are given by

, (1)

, (2)

, (3)

where and are the magnetic-field components in x- and z-direction, respectively; is the electric-field component in the y-direction; , and denote the dielectric permittivity, magnetic permeability, and electrical conductivity parameters, respectively. Variables with

© 2017 SEG SEG International Exposition and 87th Annual Meeting

Page 1091

Dow

nloa

ded

11/2

8/17

to 2

11.8

6.15

8.81

. Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

A high-resolution weak signal reconstruction method for RTM of GPR data

overbar denote the regular real EM wavefield. The local EM wavefield is constructed by

, (4)

, (5)

, (6)

, (7)

D1, 0, , (8)

where variables with tilde denote the reconstructed EM wavefield. labels the marked area and is set to be 1 at the marked area and 0 otherwise. Equations 7 and 8 actually define the boundary condition for equations 4-6. Stratton (1941) gives the solution to EM wave as

∯ ∗ ∗ , (9)

where G is the Green’s function and is the electromagnetic field. When the marked area is a boundary with a proper

thickness, can be accurately determined by equation 8.

Equation 9 allows reconstructing the wavefield on one side

of closed boundary with the given and on

boundary . Figure 1 shows the workflow chart for applying the wavefield construction method to RTM of GPR data. As the workflow chart shows, solving simultaneous equations 1-3 and simultaneous equations 4-8, we can obtain two forward-propagating wavefields and , respectively. Backward-propagating the observed data, we can obtain the backward-propagating wavefield , which is the y-direction component of the electric field in our problem. Zero-lag cross-correlation imaging condition (Claerbout, 1971) is used for imaging, given by

, , , , , , (10) and

, , , , , , (11) where is the maximum recording time, , denotes the conventional RTM image, and , denotes the migration image generated by the reconstructed forward-propagating source wavefield. Numerical Examples Several numerical experiments were conducted to show the application of the wavefield construction method in EM wave modeling and RTM of GPR data. The staggered finite-difference method in the time-space domain is used in the following examples. To absorb waves at the edges of the modeling grid, perfectly matched layer (PML) absorbing boundaries is used.

Figure 2 shows snapshots of component of the constructed and the real EM wavefields in homogeneous media of which 1.0, 12 and 0.6 / . The source pulse is the normalized first derivative of a Blackman-Harris window function (Chen et al., 1997) with a dominant frequency of 300Mhz. Waves passing through the red line in figure 2b will be extracted. This method generates extra backward-propagating wavefield. Since the propagation direction of the backward-propagating wavefield in the constructed wavefield is always contrary to that of the forward-propagating wavefield, the backward-propagating wavefield can be filtered by the propagation direction. Poynting vector is used to determine the propagation direction to filter the backward-propagating wave in our work. Poynting vector gives the direction of EM wavefield propagation as . (12)

Figure 1. The workflow chart for applying the wavefield construction method to GPR data RTM. is the maximum time step and is the backward-propagating receiver wavefield. The reconstructed wavefield after filtering shown in figure 2b is the wavefield passing through the red line. The reconstructed and the real wavefields have the same phase and amplitude. Wavefields along the blue lines in figure 2 are displayed in figure 3. The difference between the real and stained wavefield along line 1 is two orders of magnitude smaller than the real wavefield and exists above the marked area. The real and the reconstructed wavefields are identical below the marked area, i.e. depth larger than 4.0m in this case. After the backward-propagating wavefield is filtered out, the reconstructed partial wavefield is actually a subset of the real EM wavefield. When a small area is marked, we can obtain wavefield related to specific area or structure.

© 2017 SEG SEG International Exposition and 87th Annual Meeting

Page 1092

Dow

nloa

ded

11/2

8/17

to 2

11.8

6.15

8.81

. Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

A high-resolution weak signal reconstruction method for RTM of GPR data

We considered a high conductivity water-filled layer model. The relative magnetic permeability is 1.0 . The dielectric permittivity and conductivity models are shown in figure 4. The gird size is 1001 501 and the grid interval is 0.016m. Strong radar wave attenuation occurs in the water-filled reservoir prevents from reflecting at deeper reflector, especially for the reflector located around 8.0 , 6.0 , since the high conductivity layer over it is particularly thick. We are going to trace and extract the waves that pass through the area as the solid white line in figure 4a labels. The source is the normalized first derivative of a Blackman-Harris window function with a dominant frequency of 300Mhz located at distance 0.08m on the surface. 1001 receivers on the surface at a depth of 0.016m is used to record the E component.

Figure 2. Snapshots of the real and the reconstructed EM wavefields. The star marks the source point. (a) The real EM wavefield. (b) The reconstructed EM wavefield.

Figure 3. The wavefields and the differences between the real and the reconstructed wavefields along the blue lines in figure 2. Figure 5 shows the snapshots of the real and the reconstructed wavefields at time 67.2 and 107.2 . 67.2 is the time shortly after the down-going wave reaches the marked area. At this stage of propagation, the reflection from the marked area, as red arrows in figure 5 indicate, can be clearly identified from both snapshots of the real and the reconstructed wavefields. Note that the reflection in the reconstructed wavefield has the same phase with the real wavefield, while the amplitudes of the two reflections are not exactly matched. Generally, this amplitude difference is much smaller than the amplitude difference between high and low attenuation loss. Snapshots at 107.2 show that the traced wave is close to the ground

surface, as the red arrows indicated. The black arrows indicate the reflection from the rest part of this deep reflector. At this stage of propagation, the energy of the traced wave is much weaker than the reflection from rest part of this deep reflector due to longer propagation distance in the high conductivity layer. Figure 6 shows the components of the real and the reconstructed wavefields recorded on the surface. In figures 5 and 6, the red arrows indicate the reflection from target reflector; the black arrows indicate the reflection from the rest part of this deep reflector; the yellow arrows indicate the diffraction introduced by the endpoints of the marked line. The snapshots in figure 5 and the recorded data in figure 6 both show that our method is able to extract target related wavefield, even if its amplitude is much smaller than the others’. The reflection as the black arrows indicate in figure 5 and 6a are not reconstructed in the data shown in figure 6b. The signals as the yellow arrows indicate in figure 6b are diffractions from endpoints of the marked line and their arriving time and amplitude are different from those of the reflections as the black arrows indicate. 21 synthetic shot gathers are used in imaging. The first source is located at distance 0.0m and the last source is located at distance 16.0m . The source interval is 0.8m . Each shot gather contains 1001 traces with a trace interval of 0.016m. The totally recording length is 300.0ns and the sampling rate is 0.04ns . The waves passing through the location as the dashed white line labels in figure4a are used in RTM of GPR data. Figure 7 shows the conventional RTM image and the image obtained by the wavefield construction method . In the conventional RTM image, the electromagnetic impendence interfaces in the red box in figure 7a are poorly imaged due to higher attenuation, while electromagnetic impendence interfaces in the black boxes are well imaged because of lower attenuation. In the image obtained by the wavefield construction method, since the extracted target related wavefield is used in the imaging condition, non-target structures are muted from the image and target related information remains. The more complex the subsurface media is, the more unrelated information will be muted. Therefore, the improvement by the wavefield construction method is more significant in complex media. The backward-propagating wavefield generates a footprint and the shape and location of this artifact are the same with the marked area. Since the shape and location of the footprint change when the marked area changes, the footprint is easy to identify. The workflow chart shows two forward-propagations and one backward-propagation. Double forward-propagations require extra memory and computational time for this

Distance (m)

Dep

th (m

)

0 2 4 6 8 10 12 14 160

2

4

6

8

−5 0 5 10 15x 10

−3

Distance (m)

Dep

th (m

)

0 2 4 6 8 10 12 14 160

2

4

6

8

−5 0 5 10 15x 10

−3

(a) (b)

line 1

line 2

*line 1

line 2

0 2 4 6 8−0.02

−0.01

0

0.01

0.02

0.03

Depth(m)

Am

plitu

de

0 2 4 6 8−1

0

1 x 10−4

Depth(m)

Am

plitu

de d

iffer

ence

0 5 10 15−0.02

−0.01

0

0.01

0.02

0.03

Depth(m)

Am

plitu

de

0 5 10 15

−0.5

0

0.5

x 10−10

Depth(m)

Am

plitu

de d

iffer

ence

line1 line2

Amplitude difference Amplitude difference

real wavefieldreconstructed wavefield

real wavefieldreconstructed wavefield

© 2017 SEG SEG International Exposition and 87th Annual Meeting

Page 1093

Dow

nloa

ded

11/2

8/17

to 2

11.8

6.15

8.81

. Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

A high-resolution weak signal reconstruction method for RTM of GPR data

method. Therefore, the computational time of applying the wavefield construction method to the RTM of GPR data is less than twice computational time of the conventional RTM of GPR data.

Figure 4. Relative permittivity and conductivity of a four-layered lossy medium. The dashed and solid lines are two marked areas.

Figure 5. The snapshots of the real and the reconstructed wavefields at time 67.2 and 107.2 . The star marks the source location. The snapshots on the top are the real wavefields and those on the bottom are the reconstructed partial wavefields. Conclusions In this study, we proposed an approach to extract target-related wavefield in the modeling of EM wave, and we employed this novel method in the RTM of GPR data. The method is used to extract low-energy waves from the electromagnetic impendence interfaces under lossy media. The waveform and the amplitude of the forward-propagating wavefield in the extracted wavefield are the same with those of the real wavefield. The extracted wavefield is regarded as

the forward-propagating source wavefield in RTM to generate an image of the target structure, and therefore non-target information from the conventional RTM is muted and information of target area remains. In this way, our method improves image quality of target structure. Additionally, the improvement by the wavefield construction method is more significant in complex media. Furthermore, our method is potentially useful in attenuation compensation for RTM of the GPR data.

Figure 6. The components recorded on the surface. (a) The real wavefield. (b) The reconstructed partial wavefield.

Figure 7. (a) The conventional RTM image. (c) The image obtained by the wavefield construction method. Acknowledgements This study received support from the National Natural Science Foundation of China (41374006 & 41274117) and the Fundamental Research Funds for the Central Universities (WK2080000078).

Distance (m)

Dep

th (m

)

0 2 4 6 8 10 12 14 160

1

2

3

4

5

6

7

8

Distance (m)

Dep

th (m

)

0 2 4 6 8 10 12 14 16

0

1

2

3

4

5

6

7

8

(a)

(b)

σ=0.6mS/mσ=0.6mS/m

σ=10.0mS/mσ=10.0mS/m

σ=0.3mS/mσ=0.3mS/m

ε =12.0ε =12.0r

ε =8.0ε =8.0r

ε =11.0ε =11.0r

ε =2.0ε =2.0r

12345678

Dep

th (m

)

2 4 6 8 10 12 14 16Distance (m)

12345678

Dep

th (m

)

2 4 6 8 10 12 14 16Distance (m)

1234567

8

Dep

th (m

)

2 4 6 8 10 12 14 16Distance (m)

12345678

Dep

th (m

)

2 4 6 8 10 12 14 16Distance (m)

t=67.2ns t=107.2ns

* *

0

50

100

150

200

250

300

Tim

e (n

s)

0 5 10 15Distance (m)

0 2 4 x10-5

0

50

100

150

200

250

300

Tim

e (n

s)

0 5 10 15Distance (m)

0 1 x10-6

(a) (b)

012345678

Dep

th (m

)

0 2 4 6 8 10 12 14 16Distance (m)

012345678

Dep

th (m

)

0 2 4 6 8 10 12 14 16Distance (m)

(a)

(b)

© 2017 SEG SEG International Exposition and 87th Annual Meeting

Page 1094

Dow

nloa

ded

11/2

8/17

to 2

11.8

6.15

8.81

. Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

EDITED REFERENCES

Note: This reference list is a copyedited version of the reference list submitted by the author. Reference lists for the 2017

SEG Technical Program Expanded Abstracts have been copyedited so that references provided with the online

metadata for each paper will achieve a high degree of linking to cited sources that appear on the Web.

REFERENCES

Baysal, E., D. Kosloff, and J. Sherwood, 1983, Reverse time migration: Geophysics, 48, 1514–1524,

http://doi.org/10.1190/1.1441434.

Benson, A. K., 1995, Applications of ground penetrating radar in assessing some geological hazards:

examples of groundwater contamination, faults, cavities: Journal of Applied Geophysics, 33,

177–193, https://doi.org/10.1016/0926-9851(95)90040-3.

Chang, W. F., and G. A. McMechan, 1987, Elastic reverse-time migration: Geophysics, 52, 1365–1375,

https://doi.org/10.1190/1.1442249.

Chen, B., and X. Jia, 2014, Staining algorithm for seismic modeling and migration: Geophysics, 79, no. 4,

S121–S129, https://doi.org/10.1190/geo2013-0262.1.

Chen, Y. H., W. C. Chew, and M. L. Oristaglio, 1997, Application of perfectly matched layers to the

transient modeling of subsurface EM problems: Geophysics, 62, 1730–1736,

https://doi.org/10.1190/1.1444273.

Claerbout, J. F., 1971, Toward a unified theory of reflector mapping: Geophysics, 36, 467–481,

https://doi.org/10.1190/1.1440185.

Dale, L., and J. M. W. Slack, 1987, Fate map for the 32-cell stage of Xenopus laevis: Development, 99,

527–551.

Fisher, E., G. A. McMechan, A. P. Annan, and S. W. Cosway, 1992, Examples of reverse-time migration

of single-channel, ground-penetrating radar profiles: Geophysics, 57, 577–586,

https://doi.org/10.1190/1.1443271.

Ginhoux, F., M. Greter, M. Leboeuf, S. Nandi, P. See, S. Gokhan, M. F. Mehler, S. J. Conway, L. G. Ng,

E. R. Stanley, I. M. Samokhvalov, and M. Merad, 2010, Fate mapping analysis reveals that adult

microglia derive from primitive macrophages: Science, 330, 841–845,

https://doi.org/10.1126/science.1194637.

Irving, J., and R. Knight, 2006, Numerical modeling of ground-penetrating radar in 2-D using MATLAB:

Computers & Geosciences, 32, 1247–1258, https://doi.org/10.1016/j.cageo.2005.11.006.

Jol, H. M., 2008, Ground penetrating radar theory and applications: Elsevier.

Leuschen, C. J., and R. G. Plumb, 2001, A matched-filter-based reverse-time migration algorithm for

ground-penetrating radar data: IEEE Transactions on Geoscience and Remote Sensing, 39, 929–

936, https://doi.org/10.1109/36.921410.

Li, Q., and X. Jia, 2017, Generalized staining algorithm for seismic modeling and migration: Geophysics,

82, no. 1, T17–T26, https://doi.org/10.1190/geo2015-0652.1.

Liu, S., L. Lei, L. Fu, and J. Wu, 2014, Application of pre-stack reverse time migration based on FWI

velocity estimation to ground penetrating radar data: Journal of Applied Geophysics, 107, 1–7,

https://doi.org/10.1016/j.jappgeo.2014.05.008.

Plewes, L. A., and B. Hubbard, 2001, A review of the use of radio-echo sounding in glaciology: Progress

in Physical Geography, 25, 203–236, https://doi.org/10.1191/030913301668581943.

Stratton, J. A., 1941, Electromagnetic theory: McGraw-Hill Inc.

Xie, X. B., S. Jin, and R. S. Wu, 2006, Wave-equation based seismic illumination analysis: Geophysics,

71, no. 5, S169–S177, https://doi.org/10.1190/1.2227619.

Zhu, T., M. C. José, and A. B. B. Marco, 2016, Reverse time imaging of ground-penetrating radar and

SH-seismic data including the effects of wave loss: Geophysics, 81, no. 4, H21–H32,

https://doi.org/10.1190/geo2015-0397.1.

© 2017 SEG SEG International Exposition and 87th Annual Meeting

Page 1095

Dow

nloa

ded

11/2

8/17

to 2

11.8

6.15

8.81

. Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/