Profiling the Rough Surface by Migration

258 IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 6, NO. 2, APRIL 2009

Profiling the Rough Surface by MigrationXuan Feng, Motoyuki Sato, Senior Member, IEEE, Cai Liu, and Yan Zhang

Abstract—It is often advantageous to estimate the ground sur-face topography from radar returns. However, the popularmethod, searching for the brightest pixel in the ground-penetrating radar profile, cannot achieve accurate surface topog-raphy in the sharp variable surface case because of the effectsof diffraction waves. In this letter, we propose a method to solvethe problem and improve the accuracy of surface topography.A migration technique is introduced to refocus the diffractionwaves before searching for the brightest pixel. Experimental datahave been used to display the effects of diffraction waves and testthe method. The result shows that the method can dramaticallyestimate accurate surface topography even in the sharp variablesurface area.

Index Terms—Ground-penetrating radar (GPR), migration,rough surfaces, topography.

I. INTRODUCTION

I T IS OFTEN advantageous to acquire ground-penetratingradar (GPR) measurements from antennas that are offset

from the air–ground interface by a nonnegligible distance,either because the ground surface is rough or because mea-surements must be collected remotely [1], for example, thedetection of buried landmines. In this case, the GPR antenna(s)must be elevated above the ground surface [2]. This requirementresults in heavy surface clutter, particularly when the ground isrough [2]–[4].

For low-contrast targets, for example, a plastic landmineburied under a flat dry sandy soil, the signal-to-clutter ratio isbelow −10 dB [5] and even much lower for a rough ground [2].Consequently, the low contrast in electromagnetic propertiesof the buried objects and their surrounding soil means thatsignals from objects in the near-surface area can be corrupted orobscured by the ground surface clutter [2]. Several authors haveexplored how spatial interface variations affect the detectabilityof subsurface targets [1], [6], [7]. Thus, the estimation of theground surface topography is therefore needed to compensatesurface height variations [1] and for the removal of roughsurface scattering effects [8], a task particularly crucial for

Manuscript received July 24, 2008; revised October 12, 2008, December 1,2008, and December 16, 2008. First published January 27, 2009; currentversion published April 17, 2009. This work was supported in part by theNational Natural Science Foundation of China under Grant 40704020, by theJilin Provincial Science and Technology Department under Grant 20070123,and by the 973 Program under Grant 2009CB219301.

X. Feng and C. Liu are with the College of Geo-Exploration Science andTechnology, Jilin University, Changchun 130026, China (e-mail: [email protected]).

M. Sato is with the Center for Northeast Asia Studies, Tohoku University,Sendai 980-8576, Japan (e-mail: [email protected]).

Y. Zhang is with the College of Earth Sciences, Jilin University, Changchun130061, China (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/LGRS.2008.2011922

detecting and imaging shallow low-contrast subsurface objectswith sizes of a few centimeters, such as nonmetallic antiper-sonnel landmines [2], which are most commonly buried justbeneath a rough ground surface [9].

In many instances, it is simple enough to merely measurethe profile with a range-finding sensor, since the ground surfaceis exposed and accessible. It is preferable, instead, to arrive atan automatic topographical estimate based on the radar returnsalready available without the aid of additional equipment [1]. Inmost cases, by far, the brightest reflector visible in GPR imagesis the air–ground surface itself, unless some methods have beenemployed intentionally to remove it. This naturally gives rise toa method, searching for the brightest pixel in the GPR profile,by which the surface profile may be estimated.

The method of searching directly for the brightest pixel cangenerally estimate precise surface topography in the planarair–ground interface or slow variable surface case. However, inthe sharp variable surface case, the method cannot accuratelyestimate the surface topography because of the diffractionwaves. The incorrect estimation of the surface topography willaffect the compensation of the surface height variations and thesuppression of the surface clutters.

To improve the accuracy of surface topography estimation,this letter proposes that migration technique is used to processGPR data before searching the brightest pixel in the GPRprofile. The migration technique has been much developedin acoustic, seismic, and geophysical engineering and wasoriginally developed in 2-D form by Hagedoorn [10]. Morerecent developments employ wave equation methods such asKirchhoff migration, finite-difference migration, and frequencywavenumber migration [11]–[13]. It moves reflectors into theirtrue positions and collapses diffractions [13], thereby delineat-ing precise features such as air–ground interface.

The rest of this letter is organized as follows. The method-ology is discussed in Section II. An application of the newmethod to experimental data is shown in Section III. A briefcomparison between the two methods and conclusions are givenin Section IV.

II. METHODOLOGY

A. Diffraction Waves Decreasing the Accuracy of Topography

A review of the forward scattering models is helpful inunderstanding the method proposed here. Christian Huygens’principle is that each point on the wave front at time t isconsidered to be a secondary source of a small spherical (3-D)or circular (2-D) wave front called a Huygens’ wavelet [14].Huygens’ principle can also be adapted to consider the responseof a continuous reflector as the superposition of the responses ofa huge number of point diffractors or scatter points [13], [14].

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FENG et al.: PROFILING THE ROUGH SURFACE BY MIGRATION 259

Fig. 1. (b) GPR down-range profile from (a) a planar reflector.

At the ends of the reflector, as shown in Fig. 1, the diffractionhyperbolas remain because of the sharp discontinuities [13].

Therefore, in the sharp variable surface case, the diffractionwaves appear at the points where surface varies sharply. Themethod of surface topography estimation, directly searchingfor the brightest pixel in the GPR profile, cannot distinguishdiffractions from reflections and cannot identify all the brightestscatterers visible in the GPR images as the air–ground interface.However, the estimated interface caused by diffraction wavesdoes not physically exist. The false interface decreases theaccuracy of the surface topography estimation.

B. Migration Collapsing Diffractions

For GPR measurements recorded in TE mode in a perfectlyresistive medium, the electric field variation can be describedby a scalar wave propagation equation, and it is mathemati-cally similar to the acoustic wave equation [15]. The integralsolution of the scalar wave equation gives the output wavefield Pout(x0, y0, z0) at the location of the diffractor (x0, y0, z0)from the zero-offset wave field Pin(x, y, t), which is measuredat the plane (z = 0) [16], [17]. The solution is the foundation ofKirchhoff migration. Considering only far-field term, we writethe migration integral in discrete form [13]

Pout(x0, y0, z0) =ΔxΔy

4π

∑

A

cos θ

vr

∂

∂tPin(x, y, t) (1)

where Δx and Δy are inline and crossline trace spacings, t isdefined by r/v, and the surface area A is the aperture ofthe observation made by GPR. r = [(x − x0)2 + (y − y0)2 +z20 ]1/2, which is the distance between the output points and

measurement point (the location of T/R) (x, y, z = 0), and θ isthe angle between the direction of propagation and the verticalaxis [13]. Because most GPR measurements perform in thenear fields, the adoption of only far-field equation will importerror in the reconstructed wave field. However, the error will

not destroy the purpose of collecting diffraction wave. Exceptthe factors in front of Pin(x, y, t), the equation will become thediffraction summation migration that can successfully refocusscattered signals [13]. The migration technique has been in usefor almost five decades in seismic reflection survey and candepress the effects of diffractions, because it can refocus thescattered signals and collapses diffractions.

C. Processing Procedure for Accurate Surface Topography

The migration algorithm was applied by the followingstages:

1) normal moveout (NMO);2) migration;3) searching for the brightest pixel.The procedure proposed here is based on the common

nonzero-offset GPR data. The processing of NMO is neededbefore the processing of migration, because the migration tech-nique proposed here is based on zero-offset data. However,generally, the transmitter and receiver are separated in the GPRsystem. Therefore, for the measurement data, nonzero-offsetdata, such as NMO [13], which is a popular method in seismicdata processing, are used. Otherwise, when we calibrate thesearched topography, we need to consider the separation dis-tance between the transmitter and receiver. After migration, wecan achieve the accurate surface topography through searchingfor the brightest pixel in the GPR profile.

III. APPLICATION TO EXPERIMENT DATA

A. GPR System and Experiment Description

Based on the transmit antenna, receive antenna, scanningplatform, and vector network analyzer, we constructed astepped-frequency (SF) GPR system shown in Fig. 2. Parallelantipodal Vivaldi antennas are employed in this system. Twomiddle antennas are used in the experiment. One is used totransmit the signal, while the other is used to receive it. Itis a single copolarimetric GPR system. Vivaldi antenna is akind of microstrip antenna, which possesses a wide-bandwidthfrequency range [18]. Sato et al. [19] described the characteris-tics of the Vivaldi antenna designed by ourselves. The antennaworks effectively in the frequency range between 2 and 10 GHz[19], which is a 10-dB bandwidth. The frequency sweep rangeused in the experiment is from 500 MHz to 8 GHz. Therefore,the effective bandwidth in the experiment is from 2 to 8 GHz,and the down-range resolution is about 2.5 cm calculated by theequation of down-range resolution

Δx =c

2B0√

εr(2)

where εr is one in the air, B0 is the signal baseband bandwidth,and Δx represents the down-range resolution. The system isa downward-looking GPR system and radiates the generatedsignal by the transmit antenna toward the ground. Part ofthe signal is scattered at the ground surface, while the restpenetrates into the ground. The signal scattered from the groundis used to estimate the ground surface topography. As a broad


Fig. 2. SF GPR measurement system setup. (a) Scene. (b) DisassembleVivaldi antenna array. (c) Schematic diagram.

Fig. 3. Sand model including sharp variable surface marked by arrow.

range of frequencies is transmitted, the antenna footprint variedand the phased distortion needs to be corrected [20].

We built a special sand model, shown in Fig. 3, that includesa sharp variable surface area indicated by an arrow. The height

Fig. 4. GPR profile across the sand model shown in Fig. 3. (a) GPR profilebefore migration. (b) GPR profile after migration.

of the sand model is about 7 cm, and both of the length and thewidth are about 40 cm. Then, the SF GPR system conducteda 2-D scan (or C-scan) above the experiment area coveringthe sand model and acquired 3-D GPR data. It is about 10 cmof the elevation distance of the Vivaldi antenna relative to theground surface. The number of frequency sampling points was401. The interval between two adjacent GPR spatial samplingpoints was 1 cm in both inline and crossline directions. Thescanning range in both the crossline and inline directions was70 cm. Therefore, the raw data matrix is a 71 × 71 × 401matrix.

B. Data Processing

A preprocessing procedure is needed to prepare data forthe processing of surface topography estimation, because thedata acquired by the SF GPR system are in the frequencydomain. First, direct antenna coupling components, which can

FENG et al.: PROFILING THE ROUGH SURFACE BY MIGRATION 261

Fig. 5. Ground surface topography of the sand model shown in Fig. 3estimated from the migrated GPR data.

be acquired prior to a measurement pointing the antennas tothe air space, were subtracted from the measured data. Then, adigital bandpass filter and inverse fast Fourier transform wereapplied to construct nonzero-offset data in time domain.

After the processing of NMO, the calibration for the sepa-ration of transmitter and receiver, we achieved the zero-offsetGPR data in time domain. The zero-time point is located atthe bottom of the Vivaldi antenna. In the measurement, allzero-time points construct a zero-time plane, which is thereference plane for profiling the ground surface. Fig. 4(a) showsa GPR profile that crosses the sand model, including a sharpvariable surface area. In the GPR profile, the diffraction waves,indicated by the arrow, remain at the sharp variable surface area,indicated by the arrow shown in Fig. 3. If we directly search forthe brightest pixel in the GPR profile to estimate the surfacetopography, we will make the error at the sharp variable sur-face area.

After the processing of migration, we achieved the migratedGPR data in spatial domain. Fig. 4(b) shows a migrated GPRprofile that crosses the exactly same section as in Fig. 4(a). Inthe GPR profile, the diffraction waves, shown in Fig. 4(a), havecollapsed. Thus, the effects of diffraction waves are depressed.Finally, we searched for the brightest pixel based on the mi-grated GPR data and estimated the ground surface topography(see Fig. 5).

IV. DISCUSSION AND CONCLUSION

To clearly view the effects of diffraction waves, signalsacquired at three different locations were shown in Fig. 6. Com-paring signals before migration and after migration, we clearlyfind the diffraction wave indicated by the arrow in Fig. 6(b) atthe location x = 0.16 (m). After migration, the diffraction wavewas suppressed. In addition, we searched the brightest pixel inthe two kinds of GPR profiles to estimate the surface height,and results are shown in Fig. 7. Diffraction waves producea false slow variable surface area, while migrated GPR datashow the true sharp variable surface area at the same location.

Fig. 6. Signals before migration and after migration located at (a) x =0.04 (m), (b) x = 0.16 (m), and (c) x = 0.3 (m). Diffraction wave wasindicated by the arrow in (b).

Fig. 7. Surface height estimation, indicated by a dash line from the GPRprofile before migration shown in Fig. 4(a) and indicated by a solid line fromthe migrated GPR profile shown in Fig. 4(b).


Through the experiment, the effects of the diffraction waves tothe estimation of surface topography were clearly displayed.By introducing the migration technique into the estimationprocessing procedure, we have obtained the accurate groundsurface topography.

For using the estimation method, we have to note thatzero-offset GPR data should be prepared before the migra-tion processing we proposed here. However, there is anothermigration technique, called prestack migration [12], that canprocess the nonzero-offset data directly and achieves a littlebetter result, but it may consume much computation time.

There is a static value between the altitude and the topogra-phy value estimated by searching for the brightest pixel. Theshift value is composed of the absolute altitude of our zero planand the distance between the brightest pixel and the first arrival(or first break) of the wavelet signature. A processing technique,so-called deconvolution [13], can compress the wavelet anddecrease the distance between the brightest pixel and the firstarrival of the wavelet.

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Profiling the Rough Surface by Migration