TY - JOUR
AU - Du,, Jun
AB - Abstract In this paper, we describe the application of wave-equation redatuming through downward and upward continuations of surface ground penetrating radar (GPR) data to image the target beneath a surface layer with geometric or material property heterogeneities. We first tested this technique with the use of a synthetic radar profile generated by the finite difference time domain method to show its effectiveness. We then applied it to the surface GPR data collected in several urban public transportation infrastructure sites including a project to use GPR to assess the quality of mortar consolidation behind a tunnel wall in the Xiangyin highway tunnel, Shanghai, China. The purpose of this redatuming processing is to enhance target images in later times of a GPR profile, by eliminating the contamination in the GPR profile caused by strong diffractive scattering from the steel rebars in the surface concrete slab or tunnel wall. The results for synthetic and observed GPR data show that the wave-equation redatuming technique is an effective way to eliminate unwanted diffraction signatures and ease GPR image interpretation for data collected at a site with a strongly heterogeneous surface layer. GPR, tunnel lining, wave-equation redatuming, downward and upward continuations, reinforced concrete, tunnels Introduction As a non-destructive testing technique, ground penetrating radar (GPR) is widely used at public transportation infrastructure construction and maintenance sites in urban environments for the purpose of quality control and structure condition assessment. Typical GPR applications include pavement condition assessment at both project and network levels for public highways, deterioration of bridge decks (Annan et al2002) and consolidation condition assessment behind tunnel linings (Xie et al2007). It is typical that many sites are covered by a surface layer with strong heterogeneities. This kind of layer has either an irregularly shaped interface in contact with deeper materials, a very heterogeneous material composition, or a combination of both. Road pavement over a rough ground surface is a perfect example of the first kind of heterogeneity, i.e., a surface layer of pavement with non-uniform thickness. Rebars and cemented aggregates in prefabricated reinforced concrete is a good example of the second kind, i.e., the heterogeneous material composition. Furthermore, the reinforced concrete with an uneven interface is an example of the surface layer with a combination of geometric and physical heterogeneities. One way to eliminate the adverse effects of the heterogeneous surface layer on image reconstruction of targets in deeper formations (or later times in a GPR profile) is shifting the reference datum from the original one (the surface on which the GPR data were taken) to an imaginary interface at greater depth (or later time in a GPR profile) to exclude the heterogeneous surface layer. This process is called downward continuation (Claerbout 2001). Once the effect of the surface layer can be modelled and separated, a more uniform layer can be virtually put back and the datum can be shifted back to the original one. This procedure is called upward continuation, and the whole process is called redatuming through downward and upward continuations (Claerbout 2001). In this paper we apply the redatuming scheme through downward and upward continuations based on the full wave equation (Berryhill 1979, 1984, 1986) to GPR data to suppress the surface layer effect and enhance the target images in later times of a GPR profile. The approach originated in seismic reflection studies in petroleum exploration and proved a very effective way to carry out the static correction for exploration sites with a rough topography or undulating interface between sediments and bedrock (Berryhill 1979, 1984, 1986). This kind of application deals with geometric heterogeneities, as characterized above. In this paper, we use the wave-equation redatuming method (Berryhill 1979), which uses the Kirchhoff integral formulation of the wave equation. The implementation of the wave-equation redatuming is essentially a precise and efficient computerized form of the Huygens principle. Unlike redatuming with static shifts, wave-equation redatuming removes the distortions caused by material interface irregularity in a manner consistent with wavefield propagation. This ensures that subsequent processing steps that assume hyperbolic form, or even more complicated trajectories consistent with wave propagation, can be accurately applied (Bevc 1997). The application of this approach to material property heterogeneities, however, has not been widely tested, and is the theme of this paper. The paper is organized as follows. First, we present the principle of wave-equation redatuming through two numerical examples: the model for the first example has a geometrically heterogeneous surface layer, similar to that originally proposed by Berryhill (1979); the model for the second example has material heterogeneities in a flat surface layer. We aim to validate the approach using models with a priori information about the subsurface. Second, we apply the synthetic data validated approach to real-world field GPR data obtained from several urban public transportation sites. The first one is from a highway bridge in Connecticut, USA. The second one is from an airport runway in Houston, Texas, USA and the last one is from the Xiangyin tunnel, a highway transportation tunnel crossing the Huangpu River in Shanghai, China. For all field examples, the purpose of the process is to suppress the influence of the heterogeneity caused by the steel bar in the surface layer (the reinforced concrete pavement for the first two cases and the tunnel wall segments in the second case) to obtain a better imaging result of deeper targets in later times of a GPR profile. Finally, we conclude that the wave-equation-based redatuming approach through downward and upward continuations is an effective way to eliminate the interference caused by the geometric and material property heterogeneity in the surface layer (e.g., a concrete slab). This process is capable of enhancing target recognition in deeper sub-grades in an engineering infrastructure. Wave-equation redatuming applied to synthetic models Reproduction of the original Berryhill model in the case of an electromagnetic wave The best way to validate the wave-equation redatuming algorithm is to reproduce the original example. First, we generated the model using the full wave simulation technique of FDTD (Liu and Arcone 2003, 2005) for the original Berryhill (1979) example. However, this model is for the electromagnetic wave case, but we keep the velocity ratio the same as the elastic wave case. The velocity model is shown as figure 1(a). The model contains a surface layer with an irregular bottom interface, and two linear reflectors in the sub-stratum: one horizontal and one with 16-degree dip to the right (figure 1(a)). The original synthetic record is shown in figure 1(b). It corresponds to the post-stacking case of the seismic reflection surveys and resembles Berryhill's original example. After the procedure of downward (figure 1(c)) and complete downward–upward continuations (figure 1(d)), it is clear that the effect of the irregular interface has been greatly eliminated, and the two linear reflectors were fundamentally recovered. This reproduction validated the algorithm that we will use to treat GPR data. Figure 1 Open in new tabDownload slide The original model (a) and the results of wave-equation redatuming (b)–(d) for the original Berryhill model (1979). The model contains a surface layer (in light blue) with an EM velocity 1.4 times slower than the substratum (dark red). The two linear reflectors have a velocity half of that in the substratum. After redatuming the two straight linear reflectors recover two linear lines (d). Figure 1 Open in new tabDownload slide The original model (a) and the results of wave-equation redatuming (b)–(d) for the original Berryhill model (1979). The model contains a surface layer (in light blue) with an EM velocity 1.4 times slower than the substratum (dark red). The two linear reflectors have a velocity half of that in the substratum. After redatuming the two straight linear reflectors recover two linear lines (d). Wave-equation redatuming applied to a piece of synthetic data Penetrating radar is often used to detect gaps and cracks between the engineered surface layer such as road pavement, tunnel lining, retaining walls, etc. Metal-fabric reinforced concrete is popular in the construction of such surface layers. This section deals with the application of wave-equation redatuming through downward–upward continuation to a set of synthetic GPR data generated on the model shown in figure 2(a). The concrete has a dielectric constant of 6 and electric conductivity of 0.005 S m-1. Below the concrete surface layer is the bedrock whose dielectric constant is 5 and electric conductivity is 0.0001 S m-1. Two gaps exist between the surface concrete layer and the bedrock, as shown in figure 2(a). The one on the left is air-filled and the one on the right is water-filled. The central frequency of the impulse source is 900 MHz and the source–receiver offset is 10 cm. Constant-offset reflection mode records are collected at 2 cm trace spacing. Strong reflections and diffractions from the rebars result in severe interference with the reflection scattering signatures from the two gaps, as seen in the original profile shown in figure 2(b). The reflection from the two gaps can hardly be identified due to the strong interference with the diffractions caused by the existence of the metal rebars in the concrete layer. Figure 2(c) shows exactly the same geometric setting, the only exception is that there are no rebars in the concrete slab. This time, the reflection from the gaps at about 4 ns can be easily identified with strong amplitude standout. We can also see a multiple for the left gap at around 6 ns and two multiples for the right gap at around 6 and 9 ns. The model and simulation techniques are discussed in detail by Liu et al (2007). Figure 2 Open in new tabDownload slide The results of wave-equation redatuming for the synthetic 900-MHz GPR data from the numerical modelling result (Liu et al2007) and the results after wave-equation redatuming. Figure 2 Open in new tabDownload slide The results of wave-equation redatuming for the synthetic 900-MHz GPR data from the numerical modelling result (Liu et al2007) and the results after wave-equation redatuming. Figure 2(d) shows the synthetic profile after the downward continuation and figure 2(e) shows the final redatuming result by completing the downward and upward continuation cycle. By comparing the GPR profile after redatuming (figure 2(e)) with the one without metal rebars in the concrete slab (figure 2(c)), it becomes obvious that the redatuming process makes the identification of the gaps and the multiple reflections from the GPR profile a much easier task. In the redatuming processed profile, the reflections from the gaps possess the same polarity as shown in the profile without rebars. Moreover, it has relatively fewer edge diffraction hyperbolas originated from the tips and edges of the gaps. Wave-equation redatuming applied to real field data A highway bridge refurbishment project in Connecticut, USA We now present the application of wave-equation redatuming to real GPR data sets. The first example deals with rebar diffraction suppression for GPR data collected using the 1 GHz antenna on a rebar reinforced bridge deck in Connecticut. Since the bridge deck is essentially a simple layered structure, no target in the sub-base of the concrete slab is expected. This first example is only for testing the algorithm to the real data to see the effectiveness. Figure 3(a) is a photo taken at the bridge where the refurbishment project was conducted. The thickness of the concrete slab is 30.5 cm. There are two layers of steel rebars in the concrete bridge deck, one layer is about 8.9 cm below the surface and the other is about 25.4 cm. Figure 3(b) shows the raw GPR profile with the dc component removed. Severe interference characterized by the obliquely conjugated ‘meshes’ can be seen in the entire time window. Figure 3(c) shows the data after downward continuation, and figure 3(d) shows the same profile after the complete redatuming process. Clearly, the redatuming process has essentially suppressed all the interference caused by the rebars in the surface layer; only horizontal strips are left and these are strong reflection multiples which can be suppressed by other data process techniques that we will not discuss here. This example gives us more confidence to use this process to deal with more complicated engineering structures as in the following examples. Figure 3 Open in new tabDownload slide (a) The reinforced bridge deck and (b)–(d) the results of wave-equation redatuming for the 1 GHz GPR survey over a highway bridge in Connecticut. Figure 3 Open in new tabDownload slide (a) The reinforced bridge deck and (b)–(d) the results of wave-equation redatuming for the 1 GHz GPR survey over a highway bridge in Connecticut. Locating a drain pipe at the edge of an airport runway in Houston, USA The purpose of this GPR survey was to locate the position of a 15.2 cm PVC drain pipe along the edge of a runway of an airport. The runway edge has a 38.1 cm thick slab of concrete, the outer 91.4 cm of which has rebar reinforcement that is 11.4 cm deep with 30.5 cm × 30.5 cm spacing between rebars. Twenty one GPR survey lines were collected on 15.2 cm line spacing. Along the survey line, data were collected every 1.3 cm with 512 samples spread over a 57 ns time window. Figure 4(a) shows the engineering sketch of a portion of the cross-section of the runway edge. The 15.2 cm PVC drain pipe lies in the deepest part of the drainage ditch. The drainage layer beneath the runway consists of coarse, unconsolidated aggregates (symbol 2 in figure 4(b)). Figure 4(b) shows one original GPR profile of those 21 GPR survey lines collected at this site. Four hyperbolas resulting from diffraction of the rebars in the concrete layer are clearly seen at about 2 ns two-way travel time in depth from the surface (about 12 cm in depth). The data also show the bottom of the concrete layer slightly dipping towards right. Figure 4(c) shows the profile after downward continuation, and figure 4(d) shows the profile after the complete cycle of redatuming with downward and upward continuations. With the wave-equation redatuming process to suppress the effect of the surface concrete slab, a few events in later times of the GPR profile show up more pronounced. First, at a horizontal distance of 1.7 m, the sudden interruption of the continuing coherent phase corresponding to the bottom of the concrete slab (about 16 ns) is clearly more visible. Second, the reflections from the 15.2 cm diameter PVC pipe at ∼26 ns become more pronounced. The slant interface between the drainage ditch and host formation on the right makes the events more complicated. Reflection events below 30 ns are mostly multiples of shallower events. Figure 4 Open in new tabDownload slide (a) The engineering sketch and (b)–(d) the results of wave-equation redatuming for the GPR survey for searching a 15.2 cm PVC pine beneath the edge of the runway of an airport in Houston, Texas. The numbered symbol in (a) stands for the following layers, respectively. 38.1 cm PCC pavement; 2: 15.2 cm drainage layer base course; 3: geotextile fabric; 20.3 cm compacted subbase; 5: 30.5 cm selected fill. Figure 4 Open in new tabDownload slide (a) The engineering sketch and (b)–(d) the results of wave-equation redatuming for the GPR survey for searching a 15.2 cm PVC pine beneath the edge of the runway of an airport in Houston, Texas. The numbered symbol in (a) stands for the following layers, respectively. 38.1 cm PCC pavement; 2: 15.2 cm drainage layer base course; 3: geotextile fabric; 20.3 cm compacted subbase; 5: 30.5 cm selected fill. Assessment of mortar consolidation quality behind tunnel walls in the Xiangyin tunnel, Shanghai, China Shanghai City has been under a rapid urban development in the last decade. One major improvement in the metropolitan public transportation system is the construction of a number of cross-river underwater highway tunnels to link the East Huangpujiang River District, which is experiencing the highest economic growth rate, to the city centre located west of the river. The Xiangyin tunnel is one of the major cross-river transportation projects. The tunnel is constructed by a geotechnical construction technique called shield tunnelling. Shield tunnelling permits fast, relatively safe construction work. It neither interferes with traffic above ground nor adversely affects nearby underground structures. The shield tunnelling technique employs a large, cylindrical-shaped tunnelling machine. The shield tunnelling machine excavates by rotation of an excavation face shield (steel shell) and a circular cutter head equipped with hard metal cutter bits (Koyama 1997). Pressurized slurry is injected into the excavation face to form a suitably viscous mixture. The cutter chamber, once filled with this mixture, enables stabilization of the excavation face. At the same time as excavation, segments of concrete block prefabricated elsewhere are assembled automatically inside the shield behind the work face to finish the tunnel. Dielectric permittivity of sediments and mortars In the shield tunnelling construction process, after the tunnel wall segments are positioned, backfill grouting mortar is injected into the gaps between the segments of concrete tunnel wall and the sediments through holes cast in the tunnel wall blocks. After proper consolidation, the grouting mortar provides further stability of the tunnel and seals the tunnel from water seepage. This is especially true for tunnels placed underneath an open water body such as rivers, lakes and sea straits. The uniformity in the coverage and quality of consolidation of the injected grouting mortar behind the prefabricated tunnel wall is a major concern for tunnel safety and can only be tested non-destructively. As one of the non-destructive testing (NDT) methods, GPR has been used in tunnel construction projects, other concrete structures and road pavements for quality assurance (QA) purposes (Annan et al2002, Liu and Guo 2003, Korhonen et al1997, Robert 1998, Yelf and Carse 2004). In order to design effective GPR surveys in the Shanghai highway tunnels, the dielectric permittivities of the sedimentary formations and grouting mortar were measured in a laboratory. Figure 5(a) shows the frequency dependence of the dielectric permittivity for the grouting mortar during the period of curing and figure 5(b) shows typical results for the sediment at the project site in Shanghai. In general, it is noteworthy that the permittivity of any earth material or engineered material is heavily dependent on water content at the time of data collection (Bungey et al1997, Liu and Guo 2003). Figure 5 Open in new tabDownload slide (a) The measured frequency dependence of the dielectric permittivity of the grouting mortar tested at the time of curing, and (b) the measured frequency dependence of the dielectric permittivity of the sediment samples acquired at the site (see Xie et al2007). Figure 5 Open in new tabDownload slide (a) The measured frequency dependence of the dielectric permittivity of the grouting mortar tested at the time of curing, and (b) the measured frequency dependence of the dielectric permittivity of the sediment samples acquired at the site (see Xie et al2007). The dielectric permittivity of the grouting mortar (mostly Portland cement) (figure 5(a)) dropped by 43% in 11 days during the early stage of the curing. The relative dielectric permittivity of the grouting mortar long after the curing period can still vary over a wide range from 5.4 (oven-dry condition) to 12.0 (saturated surface-dry (e.g., Bungey et al (1997)). Whenever possible, it is always advisable to use the in situ calibrated value rather than the typical value provided by the literature for dry concrete. We used a relative dielectric permittivity of 6.25 for the dry concrete, equivalent to an electromagnetic wave velocity of 0.12 m ns-1, which is a value calibrated by the known thickness of the tunnel wall. The electromagnetic parameters for all materials involved are listed in table 1. Table 1 Material properties used in redatuming by downward and upward continuations. Material Air Concrete Mortar Sediment εr 1 6.25 9 16 σ (S m-1) 0 0.001 0.005  0.005 Material Air Concrete Mortar Sediment εr 1 6.25 9 16 σ (S m-1) 0 0.001 0.005  0.005 Table 1 Material properties used in redatuming by downward and upward continuations. Material Air Concrete Mortar Sediment εr 1 6.25 9 16 σ (S m-1) 0 0.001 0.005  0.005 Material Air Concrete Mortar Sediment εr 1 6.25 9 16 σ (S m-1) 0 0.001 0.005  0.005 Field acquisition of GPR data in the Xiangyin tunnel A set of GPR data was collected in the Xiangyin tunnel on 14 July 2005 with the Senor & Software Noggin Plus system. The nominal central frequency of the antenna for this system is 250 MHz. GPR data were collected longitudinally along the axis of the tunnel, and transversely perpendicular to the tunnel axis on the floor of the tunnel at a number of locations in the Xiangyin tunnel. The wall of the Xiangyin tunnel was formed by prefabricated circular steel-bar reinforced concrete segments. Each tunnel segment is a 60° arc and six form a complete wall segment. The diameter of the Xiangyin tunnel is 11.58 m. The thickness of the prefabricated tunnel wall is 0.48 m and the width of each arc segment is 1.5 m. The diameter of the major rebars is 16–25 mm, and the diameter of the minor rebars is 10–13 mm. The spacing of the major rebar is 10–20 cm. The distance from the surface of the concrete wall segment to the centre of the major rebar is about 35–45 mm. There is an additional 8 cm thick concrete pavement to make the tunnel floor flat so that the total thickness varies from 0.48 to 0.56 m from the edge of the floor to the central axis of the tunnel on the floor. The grouting mortar is used to fill the gap between the prefabricated tunnel segments and the formation by a dual-fluid injection procedure through pre-cast holes in wall segments. The thickness of the mortar is 0.12 m but usually between 0.1 and 0.3 m. The Xiangyin tunnel was completed in early 2005 and the grouting mortar injection and consolidation was carried out at the time of completion. Therefore the mortar has cured for a half year before the GPR survey in July 2005. Figure 6(a) shows a longitudinal GPR reflection profile 134 m long (line 21) acquired in the Xiangyin tunnel. The total recording time is 48 ns for each trace. There are 2681 traces, with 1 trace per 0.05 m. The sampling interval is 0.4 ns. Figure 6(b) is an extraction of a portion (40–56 m) without any suspicious features and events from the long profile to show the details of the diffraction from the rebars in the concrete tunnel floor (the black dots inside the concrete tunnel floor layer). From the given thickness of the tunnel wall it is straightforward to calculate that the radar wave velocity is about 0.12 m ns-1, and the two-way travel time of the reflected wave from the wall-mortar interface is about 9.3 ns. Figure 6(a) barely shows that the horizontal phase continuity is broken into two major segments: one from 60 to 78 m and the other from 122 to 130 m. The reason is unknown; one possibility is an incomplete injection of the mortar between the tunnel wall and the host. The reflection multiples in later times are also interrupted, featuring much smaller amplitudes (figure 6(a)). Figure 6 Open in new tabDownload slide (a) A 134 m long longitudinal 250 MHz GPR reflection profile (line 21), and (b) the extraction of a portion between 40–56 m of line 21 acquired in the Xiangyin highway tunnel, Shanghai, China. Figure 6 Open in new tabDownload slide (a) A 134 m long longitudinal 250 MHz GPR reflection profile (line 21), and (b) the extraction of a portion between 40–56 m of line 21 acquired in the Xiangyin highway tunnel, Shanghai, China. Wave-equation redatuming for the profile of line 21 The results of applying wave-equation redatuming to GPR profile line 21 are shown in figure 7. The reference surface was shifted 0.56 m to the bottom of the tunnel wall by downward continuation (figure 7(b)). It is equivalent to 9.3 ns on the time axis. Next, by applying upward continuation back to the original tunnel surface, the effect of the tunnel wall was essentially eliminated, and the events in later times become more pronounced. The mortar layer (16–17 ns) appears to be relatively uniform. The two possible segments of imperfect mortar layer consolidation at the two locations (60–78 m and 122–130 m) on line 21 were emphasized by this treatment (figure 7(c)). Figure 7 Open in new tabDownload slide The results of redatuming for GPR profile line 21 acquired inside the Xiangyin tunnel. From top to bottom: (a) the original profile, (b) the profile after the downward continuation and (c) the profile after the downward–upward continuation. Figure 7 Open in new tabDownload slide The results of redatuming for GPR profile line 21 acquired inside the Xiangyin tunnel. From top to bottom: (a) the original profile, (b) the profile after the downward continuation and (c) the profile after the downward–upward continuation. Conclusions In this paper we presented the application of wave-equation redatuming through downward and upward continuations to several cases in public transportation engineering projects. The purpose is to enhance the targets in later times of a GPR profile for a more confident target characterization. Wave-equation redatuming by downward and upward continuations was applied to both synthetic and field GPR data to test the method's effectiveness. The examples of wave-equation redatuming presented in this paper demonstrate that this method is capable of suppressing the diffractions and interferences caused not only by the geometric heterogeneity, but also the material property heterogeneity in the surface layer. This approach is an effective and economical way to suppress and eliminate the strong reflections and diffractions from rebars in the surface concrete slab to highlight events in the later times of a GPR profile. Acknowledgments The authors are grateful to Robert Mehl (Sky Research) for his careful editing of the text for an early version of the manuscript. Sixin Liu (Jilin University, Changchun, China) provided the synthetic GPR profile presented in figure 2. Patrick Quist (Quist Radar, Houston, Texas) provided the GPR field data presented in figure 4. The data presented in figure 3 were collected in a research project sponsored by the Joint Highway Research Advisory Council (JHRAC) of the University of Connecticut and the Connecticut Department of Transportation (ConnDOT) through Project 00-2. References Annan P , Cosway S W , de Souza T . , 2002 Applications of GPR to map concrete to delineate embedded structural elements and defects , Proc. 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TI - Image enhancement with wave-equation redatuming: application to GPR data collected at public transportation sites
JF - Journal of Geophysics and Engineering
DO - 10.1088/1742-2132/4/2/003
DA - 2007-06-21
UR - https://www.deepdyve.com/lp/oxford-university-press/image-enhancement-with-wave-equation-redatuming-application-to-gpr-Wp7obV46SO
SP - 139
VL - 4
IS - 2
DP - DeepDyve
ER -