Using interpolation techniques to determine the

Journal of Applied Geophysics 140 (2017) 154–167

Contents lists available at ScienceDirect

Journal of Applied Geophysics journal homepage: www.elsevier.com/locate/jappgeo

Using interpolation techniques to determine the optimal profile interval in ground-penetrating radar applications Refik Samet a,⁎, Ertuğ Çelik b, Serhat Tural a, Erkan Şengönül a, Merve Özkan a, Emre Damcı b a b

Computer Engineering Department, Ankara University, Ankara, Turkey Ankara Earth Science, Ankara, Turkey

a r t i c l e

i n f o

Article history: Received 24 April 2016 Received in revised form 12 March 2017 Accepted 7 April 2017 Available online 08 April 2017 Keywords: GPR synthetic data Profile interval Trace interval Mesh of grid Time slice Interpolation technique Visualization

a b s t r a c t Ground-penetrating radar (GPR) is a geophysical method that is seeing increasing use for near-surface underground research and applications. To achieve the required depth and accuracy for the GPR measurement of underground structures, the effects of certain data acquisition and interpolation parameters should be considered. These parameters include antenna frequency, sample length, profile interval, trace interval, sampling interval and resolution of the mesh of grid. For example, when the profile interval is large, underground structures may not be identified with sufficient accuracy. By contrast, selecting a narrower profile interval will increase the accuracy but will also increase the acquisition cost and processing time. The main objective of this study is to determine the optimal profile and trace intervals and the optimal mesh of grid by analyzing the interpolation-induced effects of different profile and trace intervals and different meshes of grid on the measured geometry of underground structures. Within the defined objective, an analysis procedure is proposed. This procedure determines the optimal profile and trace intervals to scan the search area by GPR at the data acquisition phase and the optimal mesh of grid to visualize the underground structures with high accuracy at the data processing phase. Proposed procedure was tested on the synthetic and real data. According to the main findings, the users are suggested to use the optimal profile interval 0.25 m and trace interval 0.04 m to acquire the data from the search area and the optimal mesh of grid (0.025 × 0.01) m2 to visualize the underground structures with high accuracy and with optimum acquisition cost and processing time. Obtained results showed that the determined optimal profile and trace intervals and mesh of grid exert positive effects about 5% for similarity and 21% for error when determining and visualizing the geometry of underground structures. © 2017 Elsevier B.V. All rights reserved.

1. Introduction The usage of ground-penetrating radar (GPR) in archeological (Böniger and Tronicke, 2010; Negri et al., 2008; Zhao et al., 2013, 2015), infrastructural (Alani et al., 2013; Ekes et al., 2014; Zhang et al., 2016) and other near-surface research and applications (Fu et al., 2014; Hirano et al., 2008; Monnier et al., 2011; Zhu et al., 2014) has been gradually increasing in recent years. The potential advantage of GPR is its non-invasive nature; GPR surveys are non-destructive and in theory faster, more economical and provide a better spatial resolution than conventional and invasive methods (Doolittle and Collins, 1995). To achieve the required accuracy in GPR studies, the properties of the environment, the data acquisition parameters and the data interpolation parameters are the main factors that must be considered. Users

Abbreviations: GPR, Ground Penetrating Radar; ERT, Electrical Resistivity Tomography; FDEM, Frequency-Domain Electromagnetics; 2D/3D, Two/Three Dimensions; RMSE, Root Mean Square Error; PI, Profile Interval; TI, Trace Interval. ⁎ Corresponding author. E-mail address: [email protected] (R. Samet).

http://dx.doi.org/10.1016/j.jappgeo.2017.04.003 0926-9851/© 2017 Elsevier B.V. All rights reserved.

cannot control the properties of the environment (properties of the underground structures of interest, dielectric permittivity, resistivity, etc.). Of course, if there is possibility, known techniques, like Electrical Resistivity Tomography (ERT), Frequency-Domain Electromagnetics (FDEM), etc., can be used to get information about the investigated environment and then to choose the proper geophysical method and then GPR parameters (Wang et al., 2015). But this is not always possible. However, the data acquisition parameters such as the antenna frequency, sample length, profile interval, trace interval (or step size) and sampling interval and the data interpolation parameters such as the type of used interpolation techniques, the resolution of mesh of grid, etc., which can be controlled and selected by users, also play an important role in the characterization of underground structures. Numerous studies have addressed the selection of the antenna frequency and sample length (Conyers, 2004; Dojack, 2012; Goodman et al., 2009; Grealy, 2006; Neubauer et al., 2002). Existing literature (Strange, 2003; Yi et al., 2016; Verdonck et al., 2015) indicates that no noticeable positive effects can be achieved by applying the interpolation techniques to data samples if there is no violation of the Nyquist sampling concept. So, investigation and selection of parameters such as the antenna frequency,

R. Samet et al. / Journal of Applied Geophysics 140 (2017) 154–167

sample length, sampling interval and the type of interpolation techniques are not objective of this paper. In other words, this paper investigates the effects of the data acquisition parameters, such as the interval between neighbor profiles and the interval between neighbor traces, and the data interpolation parameter such as the resolution of mesh on the geometry of underground structures. The profile interval is critical. The advantage of collecting data with a small profile interval is that doing so allows the geometry of underground structures to be visualized at high resolution. However, this benefit comes with the disadvantage of increasing the acquisition cost and data processing time. Determining the optimal profile interval requires establishing a suitable compromise between the required level of detail and the size of the search area. The search area should be divided into regular subareas according to the user defined profile interval to enable the high-resolution visualization of underground structures (Jol and Bristow, 2003). The choice of the profile interval is vital for the identification of underground structures. On the one hand, if the profile interval is larger than the size of an underground structure, then none of the profiles may intersect it. On the other hand, although collecting data with a narrow profile interval improves the resolution and, consequently, the accuracy with which the geometry of the underground structures is measured, using a narrow profile interval may be impossible because of rugged terrain, a limited available data acquisition and processing time, or other factors. Several previous experimental studies related to the acquired data profile interval in GPR have been conducted. Leckebusch (2003) proposed a standard profile interval of 0.25 m for 400–500 MHz antennas. Orlando (2007) determined that if a 1 m profile interval is used, the measured geometry of the underground structures will be inaccurate. He proposed a profile interval of 0.5 m (or less) for improved accuracy. Neubauer et al. (2002) tested profile intervals of 0.5 m, 1 m and 2 m for wall structures of 1.5 m in thickness. Because the data acquired using 1 m and 2 m profile intervals did not provide sufficient accuracy, he also recommended a profile interval of 0.5 m (or less). Pomfret (2006) determined that a 0.25 m profile interval provides better accuracy than a profile interval of 0.5 m. Another study showed that the profile interval may be suitably defined as one-fourth the width of the structure of interest (Bristow, 2009). As seen, the existing experimental studies discuss the intervals of profiles acquired in the search area in the data acquisition phase. Most of them propose the profile intervals of 0.25 m and 0.5 m to acquire the GPR data from search area. The trace interval is also critical. The trace interval is the distance between neighbor traces along a profile and is another vital parameter in GPR research (Jol and Bristow, 2003). The trace interval (or the distance on the surface by which the antenna are moved for each survey point) determines both horizontal and vertical resolutions, consequently, spatial resolution that can be imaged. Theoretically, the trace interval or spacing distance should not exceed the Nyquist sampling interval (Daniels, 1989, 2004). Manufacturers recommend different trace intervals for different antennas (Bristow, 2009). For instance, the maximum trace interval for a 100 MHz antenna may be 0.25 m. A narrower trace interval provides a higher vertical and horizontal resolution. Generally, the trace interval varies between 0.04 m and 0.1 m in land-based research and applications. The other critical parameter is mesh of grid. GPR data can be considered as a set of vertical and horizontal grids (see Appendix 1). The resolution of mesh of vertical grid (or radargram) and horizontal grid (or time slice) defines the accuracy of underground structures. As the mesh gets smaller, the accuracy increases. However the use of very small mesh will increase the data capacity and processing time but will not significantly improve the accuracy. Thus, the optimal mesh of grid must be determined. The horizontal grid and the time slice are two terminologies for the same element of GRP data structure (see Appendix 1). In followed sections the terminology of the time slice will be used. Time slice is an intersection of all profiles at certain time depth. In other words, the

155

elements of time slice are values of samples of all traces of all profiles at certain time depth. In this study, interpolation techniques will be applied to the acquired time slices to get the interpolated time slices with small meshes to increase the accuracy of visualization of underground structures. In existing literature there are a very few studies where the interpolation techniques have been applied to GPR data. Some of them are summarized here. Strange (2003) applied interpolation techniques to the samples along the time axis to increase the measurement precision. The results indicate that interpolating GPR traces along the time axis to increase resolution is inferior when compared with directly sampling the trace at a higher sampling rate. Safont et al. (2014) proposed the interpolation method named the expectation assuming an independent component analyzers mixture model (E-ICAMM) to recover the missing traces in GPR. Four statistical interpolation methods such as Kriging, Wiener, Splines and E-ICAMM were tested with experiments on simulated and real GPR data and the obtained results were compared. Results showed the superiority of E-ICAMM in comparison with the other three methods in the application of reconstructing incomplete traces. Yi et al. (2016) proposed the iterative interpolation method for GPR data to simplify the three dimensional GPR data acquisition and to recover the missing traces. This approach allows the reconstruction of the image from sparsely sampled data that violate the Nyquist criterion. The results showed that it is possible to reduce the data acquisition density in many GPR applications. The interpolation techniques were also used for solving the GPR clipping problem (Gulati and Ferguson, 2011; Jol, 2009) and for reconstruction the dense data before the velocity analysis (Yi et al., 2015). Booth et al. (2008) used a trace interpolation algorithm to upsample a pseudothree-dimensional grid. Verdonck et al. (2015) handled the question of how to determine the sample interval required taking full advantage of the spatial resolution capabilities of GPR without oversampling. As seen, existing studies used interpolation techniques for solving different specific problems related to GPR data reconstruction and processing. There are no studies related to the determining the optimal profile and trace intervals and the optimal mesh of grid of GPR data. The novelty of this paper can be defined as follows. This paper analyzes and evaluates the acquired data and interpolated data together and determines the optimal profile and trace intervals for acquired and interpolated data and therefore the optimal mesh of grid of GPR data. In other words, the main objective of this study is to determine the optimal profile interval, the optimal trace interval and the optimal mesh of grid by analyzing the interpolation-induced effects of different profile and trace intervals on the measured geometry of underground structures. Within the defined objective, an analysis procedure is proposed. This procedure determines the optimal profile and trace intervals to scan the search area by GPR at the data acquisition phase and the optimal mesh of grid to interpolate the acquired GPR data at the data processing phase for visualizing the underground structures with high accuracy. Proposed procedure was tested on the synthetic and real data and obtained results were evaluated. In scope of above defined objective, the coming topics will be presented in following order. First, an analysis procedure, to determine the acquired and interpolated optimal profile and trace intervals and therefore an optimal mesh of grid for visualizing the underground structures with high accuracy, will be proposed. Second, the proposed analysis procedure will be tested on synthetic data and obtained results will be evaluated. Next, the results of proposed analysis procedure will be applied to real data and results will be discussed. Finally, findings will be summarized. The terminologies will be defined in Appendix 1.

2. Analysis procedure The following procedure is proposed to determine the optimal profile and trace intervals to scan the search area by GPR at the data

156


of structure and surrounding environment, depth of upper and lower surfaces of the structure, etc. should be defined. These parameters are used by packet programs (for instance, GPRMax 2D/3D) to design the suitable models. 2.2. Obtaining the profiles with different intervals from designed model

Fig. 1. 3D view of the wall structure model used in this study.

acquisition phase and the optimal mesh of grid to visualize the underground structures with high accuracy at the data processing phase. 1) Designing the suitable model. 2) Obtaining the profiles with different intervals from designed model. 3) Producing the synthetic data corresponding to the obtained profiles. 4) Processing the synthetic data and extracting and visualizing the acquired data time slices (acquired horizontal grids). 5) Applying the different interpolation techniques with different meshes of grid to the acquired data time slices to build and visualize the interpolated data time slices (interpolated horizontal grids). 6) Comparing the slice obtained from the designed model with the corresponding acquired and interpolated data time slices. 7) Determining the optimal profile and trace intervals and the optimal mesh of grid. 2.1. Designing the suitable model The most widely used structures in Geophysics are mines, walls, pipes, etc. Generally, column and wall structures are investigated in archeological applications. Designed in scope of this study models were restricted to these structures. During the design of the models, the values of such parameters as the dimensions of search area, the dimensions of structure, the type of materials of structure, the type of surrounding environment, resistivity and dielectric coefficient of materials

Generally, high-frequency antennas are used to collect highresolution underground data from the near-surface region. By contrast, low-frequency antennas are used to collect data from deeper in the ground but at low resolution. Different antenna frequencies may be selected depending on the depth of the objects of interest. For instance, the use of 400 MHz antennas is recommended for the visualization of near-surface (1–3 m) objects, whereas the use of 250 MHz antennas is recommended for objects at depths of N3 m. The profiles can be obtained by scanning the search area by different profile intervals with different resolution, acquisition cost and data processing time. For example, the resolution, acquisition cost and data processing time of scanning the search area of (30 × 10) m2 with 0.5 m profile interval will be greater than with 1 m. Because in the first case 20 profiles and in the second case 10 profiles with 30 m length will be scanned. Packet programs such as MatGPR (Arkedani et al., 2014; Giannopoulos, 2005; Mahmoudzadeh et al., 2012) are used to simulate the antennas to scan the designed model for obtaining the profiles with different intervals. 2.3. Producing the synthetic data corresponding to the obtained profiles The synthetic data are produced on the base of profiles obtained in previous step. Packet programs such as MatGPR are used for producing the synthetic data. Finite difference algorithm is used to produce synthetic data in time domain with this software. The length of the synthetic data is defined by the length of profiles. 2.4. Processing the synthetic data and extracting and visualizing the acquired data time slices (acquired horizontal grids) One way to obtain visually useful maps to understand the plan distribution of reflection amplitudes within specific time intervals is the creation of horizontal grids - time slices (Conyers and Goodman, 1997). This data representation plays an important role in GPR investigations as it allows an easier correlation of the most important anomalies found in the area at the same depth, thus facilitating the interpretation. Time slice or horizontal grid consists of all sample values of all traces of all profiles measured at the same time depth (Fig. A-I in Appendix 1).

Fig. 2. 2D view of a profile (a) and the corresponding synthetic data obtained from the wall structure model (b).


157

Fig. 3. View of the model slice (a), the acquired data time slice (b) and the interpolated data time slice obtained by applying Cubic interpolation to the acquired data time slice using the mesh of grid ((PI / 10) × (TI / 4)) (c) for PI = 0.1 m and TI = 0.04 m.

The following data processing steps are applied to the 2D synthetic data: 1. Linear Gain (from +5 dB to +10 dB);

At the result of applying above listed steps, the acquired data time slices will be built. The MatGPR packet program is used for extracting and visualizing the acquired data time slices.

2. Band Pass Filters (HP 100 MHz and LP 800 MHz); 3. Linear Gain (from 0 dB to +10 dB); 4. Time Migration.

2.5. Applying the different interpolation techniques with different meshes of grid to the acquired data time slices to build and visualize the interpolated data time slices (interpolated horizontal grids)

As seen, Linear Gain is applied twice. In the first step, it is used to emphasize the weak signals. Gain process can yield noise which should be removed by appropriate filtering. In the third step, it is used to recover signal-noise ratio lost due to filtering which is done to remove noise. Band Pass Filters suppress the weak signals from the data at outrange of selected frequencies. Time Migration is used for removing the hyperbolas by collecting them to its apex and carries the reflections to their aspect position in order to reconstruct the geometrically correct radar reflectivity distribution of the surface. In order to calculate the time/depth slice, following procedure is applied. First, the processed 2D synthetic data are placed into a 3D cube. Then the maximum amplitude value is found in the cube. Finally, the time/depth slice corresponding to the maximum amplitude value is extracted from the cube. Each horizontal cut of underground structure gives users the corresponding time slice (Fig. A-I in Appendix 1).

After the acquired data time slices were extracted, they are interpolated and gridded on a regular mesh (Conyers and Goodman, 1997). Then, the interpolated data time slices are visualized to determine the geometry of underground structures. There are three possible methods of visualizing time slices. In the first method, the amplitude values (positive and negative) are directly visualized. The second method involves the visualization of the absolute values of the amplitudes. The third method is to visualize the squared amplitude values (Tamba, 2012; Nuzzo et al., 2002). In this study, the first method is used. According to this method the acquired amplitude values (positive and negative) are used to visualize the time slices. In order to visualize the positive and negative values the normalization was applied. Minimum negative value and maximum positive value of amplitudes were normalized to 0 and 1, accordingly.

Fig. 4. View of the model slice (a), the acquired data time slice (b) and the interpolated data time slice obtained by applying Cubic interpolation to the acquired data time slice using mesh of grid ((PI / 10) × (TI / 4)) (c) for PI = 0.25 m and TI = 0.04 m.

158


Fig. 5. View of the model slice (a), the acquired data time slice (b) and the interpolated data time slice obtained by applying Cubic interpolation to the acquired data time slice using mesh of grid ((PI / 10) × (TI / 4)) (c) for PI = 0.5 m and TI = 0.04 m.

The geometries of underground structures of interest can be visualized more explicitly by applying interpolation techniques to the acquired data time slices or by increasing the resolution of mesh for horizontal grid. If the interpolation technique and the mesh of grid are properly chosen, at the result of interpolation, the resolution and accuracy of the visualization will be increased but simultaneously the required data capacity and processing time will also be increased. These effects should be considered when performing such interpolations. The interpolation techniques are used to obtain the interpolated horizontal grids/amplitude maps/data time slices in GPR research. In other words, the acquired data time slices are interpolated to create interpolated data time slices. There are 3 commonly used interpolation techniques: the Cubic, Cubic Spline and Linear (Maeland, 1988; McKinley and Levine, 1998; Meijering and Unser, 2003; Samet and Tural, 2010; Samet et al., 2015a, 2015b). Each of these techniques has certain advantages and disadvantages. For instance, the Cubic and Cubic Spline provide high accuracy and smooth interpolation, but they require more processing time. Linear requires less processing time, but its accuracy is lower for non-linear functions. They are used in this study to produce the interpolated data time slices with different mesh of grid. There are two reasons why Cubic, Cubic Spline and Linear are selected. First, they are widely used and there are easily accessible implementations of these techniques as libraries. Second, professional

software such as GPRSoft, GPRSlice, and GPRVis, which were used during research and applications of this study, include these interpolation techniques. 2.6. Comparing the slice obtained from the designed model with the corresponding acquired and interpolated data time slices The comparison process is performed using two metrics: the Pearson Correlation Coefficient (r) and the Root Mean Square Error (RMSE) (Benesty et al., 2009; Levinson, 1947; Wang et al., 2004). The r is used to determine the similarity between two matrices and calculated using the following formula. r X;Y ¼

covðX; Y Þ ; σXσY

ð1Þ

where, X and Y are matrices; cov(X, Y) is the covariance of the two matrices; σX and σY are the standard deviations of corresponding matrices. The value of r varies between −1 and 1. A value that is close to −1 or 1 means that the similarity between the two matrices is strong. In this study; X is a slice obtained from the designed model at time depth of z and Y is an acquired data time slice extracted from the synthetic data, or an interpolated data time slice at time depth of z.

Table 1 The values of metrics for comparison between the model slice, the acquired data time slice and the interpolated data time slice for a profile interval of 0.1 m. Experiment

Data time slice

Interpolation technique Cubic

Cubic Spline

Linear

Comparison metric (similarity (r) and error (RMSE))

1 2 3 4 5 6 7 8 9 10 11 12

Name

Notation

r

RMSE

r

RMSE

r

RMSE

Acquired data time slice⁎

PI × TI (PI / 2) × TI (PI / 5) × TI (PI / 10) × TI PI × (TI / 2) PI × (TI / 4) (PI / 2) × (TI / 2) (PI / 2) × (TI / 4) (PI / 5) × (TI / 2) (PI / 5) × (TI / 4) (PI / 10) × (TI / 2) (PI / 10) × (TI / 4)

0.9505 0.9660 0.9680 0.9703 0.9555 0.9556 0.9712 0.9713 0.9732 0.9733 0.9755 0.9756

0.1282 0.1089 0.1059 0.1024 0.1220 0.1219 0.1014 0.1012 0.0982 0.0980 0.0943 0.0941

0.9505 0.9654 0.9674 0.9696 0.9558 0.9558 0.9709 0.9709 0.9729 0.9729 0.9751 0.9751

0.1282 0.1094 0.1066 0.1032 0.1217 0.1216 0.1016 0.1014 0.0984 0.0983 0.0947 0.0945

0.9505 0.9664 0.9692 0.9704 0.9449 0.9550 0.9710 0.9710 0.9731 0.9732 0.9751 0.9751

0.1282 0.1089 0.1050 0.1032 0.1230 0.1228 0.1027 0.1025 0.0998 0.0996 0.0966 0.0963

Interpolated data time slice (Mesh of grid)

⁎ For acquired data time slice PI = 0.1 m and TI = 0.04 m.


159


Data time slice


Cubic Spline

Linear


1 2 3 4 5 6 7 8 9 10 11 12 13

Name

Notation

r

RMSE

r

RMSE

r

RMSE

Acquired data time slice⁎ Interpolated data time slice (Mesh of grid)

PI × TI (PI / 2) × TI (PI / 5) × TI (PI / 10) × TI PI × (TI / 2) PI × (TI / 4) (PI / 2) × (TI / 2) (PI / 2) × (TI / 4) (PI / 5) × (TI / 2) (PI / 5) × (TI / 4) (PI / 10) × (TI / 2) (PI / 10) × (TI / 4) or (0.025 × 0.01) m (0.01 × 0.01) m

0.9186 0.9485 0.9478 0.9495 0.9240 0.9228 0.9543 0.9528 0.9536 0.9521 0.9554 0.9606 0.9610

0.1607 0.1302 0.1306 0.1285 0.1554 0.1567 0.1233 0.1252 0.1230 0.1256 0.1213 0.1273 0.1275

0.9186 0.9468 0.9461 0.9477 0.9242 0.9230 0.9528 0.9514 0.9521 0.9506 0.9537 0.9532 0.9534

0.1607 0.1318 0.1323 0.1302 0.1553 0.1565 0.1247 0.1265 0.1252 0.1270 0.1230 0.1237 0.1234

0.9186 0.9492 0.9486 0.9501 0.9235 0.9222 0.9545 0.9530 0.9540 0.9523 0.9555 0.9547 0.9548

0.1607 0.1304 0.1312 0.1294 0.1559 0.1573 0.1242 0.1263 0.1250 0.1271 0.1231 0.1242 0.1240


The RMSE is a metric that is used to find the error between the slice obtained from the designed model and the acquired data time slice, or the interpolated data time slice at time depth of z. The formula for the RMSE is given below. sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n ∑i¼1 ðX i −Y i Þ2 ; RMSE ¼ n

ð2Þ

where, Xi and Yi are ith (i = 1,2,…,n)) element of corresponding data. Generally, RMSE is calculated as the standard deviation of the difference between the predicted data and the real data. The value of the RMSE varies between 0 and 1. A value that is close to 0 means that the predicted and real data are identical. The significance of r and RMSE can be described as follows. By approaching to the values −1 or 1 for r and the value 0 for RMSE, the geometry of underground structure is becoming clearer and approaching to the real structure. The original values of the amplitudes in designed model are in the range of 0–1. In order to perform correct comparison of the results, acquired and interpolated amplitude values are also normalized in 0–1 range before calculation of r and RMSE.

2.7. Determining the optimal profile and trace intervals and the optimal mesh of grid Applying the interpolation techniques to acquired data time slices results in smaller mesh of grid or increases the resolution of mesh of grid. The use of very small mesh will increase the data capacity and processing time but will not significantly improve the similarity and error. Thus, the optimal profile and trace intervals and the optimal mesh of grid must be determined. To this end, first, by analyzing the comparison results with maximal value of r and minimal value of RMSE the optimal mesh of grid is determined. Second, the profile interval and trace interval of acquired data time slice corresponding to optimal mesh of grid will be determined as optimal.

3. Application of the proposed analysis procedure to the synthetic data 3.1. Model design In scope of this study three models were designed. In this section, the detailed results for only one model are given. Summary results for all models are given in Appendix II.


Data time slice


Cubic Spline

Linear


1 2 3 4 5 6 7 8 9 10 11 12 13

Name

Notation

r

RMSE

r

RMSE

r

RMSE

Acquired data time slice⁎ Interpolated data time slice (Mesh of grid)

PI × TI (PI / 2) × TI (PI / 5) × TI (PI / 10) × TI PI × (TI / 2) PI × (TI / 4) (PI / 2) × (TI / 2) (PI / 2) × (TI / 4) (PI / 5) × (TI / 2) (PI / 5) × (TI / 4) (PI / 10) × (TI / 2) (PI / 10) × (TI / 4) (PI = 0.01) × (TI = 0.01) m2

0.9146 0.9147 0.9268 0.9261 0.9202 0.9187 0.9303 0.9298 0.9293 0.9299 0.9312 0.9313 0.9313

0.1636 0.1630 0.1528 0.1539 0.1583 0.1598 0.1488 0.1494 0.1505 0.1511 0.1491 0.1480 0.1509

0.9146 0.9087 0.9179 0.9167 0.9204 0.9189 0.9230 0.9216 0.9207 0.9199 0.9215 0.9202 0.9200

0.1636 0.1695 0.1618 0.1634 0.1582 0.1596 0.1564 0.1576 0.1593 0.1600 0.1592 0.1602 0.1609

0.9146 0.9159 0.9261 0.9254 0.9197 0.9180 0.9289 0.9273 0.9283 0.9278 0.9300 0.9285 0.9285

0.1636 0.1637 0.1546 0.1554 0.1589 0.1604 0.1519 0.1534 0.1526 0.1531 0.1513 0.1527 0.1530


160


Table 4 Best results of similarity from Table 1, Table 2 and Table 3. Table #

Experiment #

PI and TI

Mesh of grid

r

Improvementa Δr

RMSE

Improvementb ΔRMSE

1

12

(PI / 10) × (TI / 4)

0.9756

0.0251 (2.6%)

0.0941

0.0341 (26.6%)

2

12

(PI / 10) × (TI / 4)

0.9606

0.0420 (4.5%)

0.1273

0.0334 (20.8%)

3

12

PI = 0.1 m TI = 0.04 m PI = 0.25 m TI = 0.04 m PI = 0.5 m TI = 0.04 m

(PI / 10) × (TI / 4)

0.9313

0.0167 (1.8%)

0.1480

0.0156 (9.5%)

a b

Δr = r((PI / 10) × (TI / 4)) − r(PI × TI). ΔRMSE = RMSE(PI × TI) − RMSE((PI / 10) × (TI / 4)).

The wall structure model used in this study was designed to lie within the search area of (4 × 4) m2. A 3D view of the designed model is provided below (Fig. 1). A wall structure with dimensions of (2 × 2) m2 is included in this model. The object (wall structure) is made of concrete, and the surrounding environment is soil. Based on the resistivity and dielectric coefficient of concrete, the corresponding object parameters were defined as 100 Ω m and 6 F/m, respectively. Similarly, the resistivity and dielectric coefficient of the surrounding environment were defined as 1000 Ω mand 3 F/m, respectively, based on the corresponding parameters for soil. The depths of the upper and lower surfaces of the object were defined to be 0.7 m and 1.2 m, respectively. 3.2. Obtaining the profiles with different intervals from designed model MatGPR was used to simulate the 400 MHz antennas to scan the designed model. To obtain the profiles, the model described above was scanned along parallel lines. Three sets of the profiles with the different profile intervals (PI) of 0.1 m, 0.25 m, and 0.5 m and with the same trace interval (TI) of 0.04 m were obtained from designed model. The profile orientations with respect to the considered model are illustrated in Fig. 1. The direction of the profiles was defined along the Y axis, and the profile length is 4 m, thus the first and last profiles were defined to lie at x = 0 m and x = 4 m, respectively. As seen from Fig. 1, every part of the wall model would be intersected at least once for each profile interval. In other words, the wall structure would be visualized in approximately the same manner in accordance with the data obtained using the different profile intervals. As an example, 2D view of a Profile #28 obtained from the designed model is shown in Fig. 2(a). The depth of all profiles is 2 m and the length/distance of all profiles is 4 m. 3.3. Producing the synthetic data corresponding to the profiles obtained from the designed model MatGPR was used to generate the synthetic data. As an example, 2D view of the synthetic data for Profile #28 shown in Fig. 2(a) is given in Fig. 2(b). Three sets of the synthetic data corresponding to the three sets of profiles obtained in previous step were produced. The length of the synthetic data is 4 m. The upper and bottom parts of the object are at the 8.24 ns and 16.57 ns in time domain, accordingly (Fig. 2(b)). In order to express the reflections and the synthetic data with enough range the time window was calculated as 20.69 ns (Fig. 2(b)).

The acquired data time slices at 8.24 ns are visualized in Fig. 3(b) (for PI = 0.1 m and TI = 0.04 m), Fig. 4(b) (for PI = 0.25 m and TI = 0.04 m), and Fig. 5(b) (for PI = 0.5 m and TI = 0.04 m). 3.5. Applying the different interpolation techniques with different meshes of grid to the acquired data time slices to build and visualize the interpolated data time slices The notation for mesh of grid ((PI / K) × (TI / L)), where K N 1 and L N 1 are integers, indicates that 2D interpolation (in both the profile and trace directions) is performed on the acquired data time slice for which K = 1 and L = 1. For example, ((PI / 2) × (TI / 2)) for PI = 0.1 m and TI = 0.04 m or (0.05 × 0.02) m2 means that interpolated profiles were estimated at 0.05 m intervals and interpolated traces were estimated at 0.02 m intervals. Each acquired data time slice obtained from the three sets of acquired synthetic data was interpolated using Cubic, Cubic Spline and Linear interpolation techniques and different meshes defined as the combinations of profile intervals of PI, PI/2, PI/5, PI/10 and trace intervals of TI, TI/2, TI/4. The interpolated data time slices at 8.24 ns using Cubic and mesh of ((PI / 10) × (TI / 4)) are visualized in Fig. 3(c) (for PI = 0.1 m and TI = 0.04 m), Fig. 4(c) (for PI = 0.25 m and TI = 0.04 m), and Fig. 5(c) (for PI = 0.5 m and TI = 0.04 m). 3.6. Comparing the model slice with the acquired and interpolated data time slices Following comparison procedure was applied. First, each acquired data time slice obtained in Section 3.4 was compared with the corresponding slice obtained directly from the model using r and RMSE. Second, each interpolated data time slice obtained in Section 3.5 was also compared with the corresponding slice obtained from the model using r and RMSE. Comparison results for different PI and TI will be presented below in separate subsections. 3.6.1. Comparison results for PI = 0.1 m and TI = 0.04 m Visualizations of the model slice obtained from the model, the acquired data time slice at 8.24 ns without interpolation obtained using the synthetic data of acquired profiles with 0.1 m interval and the interpolated data time slice at 8.24 ns obtained by applying Cubic

3.4. Processing the synthetic data and extracting and visualizing the acquired data time slices The steps defined in Section 2.4 were applied to the three sets of the 2D synthetic data corresponding to the three sets of profiles with the different PI of 0.1 m, 0.25 m, and 0.5 m and with the same TI of 0.04 m. At the result of processing the 2D synthetic data, the acquired data time slices were extracted and visualized. The first time/depth slice was recorded at the depth of 8.24 ns in 3D cube where the amplitude value was maximal approximately for all profile intervals (Fig. 2(b)).

Fig. 6. Object layout plan in the test area.


161

using different interpolation techniques with different mesh of grid for a profile interval of 0.1 m are given in the lines 2–12 of Table 1. As seen from Table 1, on the one hand, the similarity and error between the model slice (Fig. 3(a)) and the acquired data time slice (Fig. 3(b)) obtained in the Experiment 1 are characterized by values of r = 0.9505 (this value is minimal in the columns for r) and RMSE = 0.1282 (this value is maximal in the columns for RMSE) for all interpolation techniques. On the other hand, the similarity and error between the model slice (Fig. 3(a)) and the interpolated data time slice (Fig. 3(c)) obtained in the Experiment 12 are characterized by values of r = 0.9756 (this value is maximal in the columns for r) and RMSE = 0.0941 (this value is minimal in the columns for RMSE) for Cubic interpolation technique. As seen, due to Cubic interpolation with mesh (PI / 10) × (TI / 4) for PI = 0.1 m and TI = 0.04 m the similarity was increased from 0.9505 to 0.9756 (or 2.6%) and error was decreased from 0.1282 to 0.0941 (or 26.6%). So, positive influence of the results is about 3% for similarity and 27% for error.

Fig. 7. Profiles direction.

interpolation to the acquired data time slice using the mesh of grid ((PI / 10) × (TI / 4)) for PI = 0.1 m and TI = 0.04 m are shown in Fig. 3. In the wall structure model, there are no sections with a thickness of b0.1 m; as a result, the model could be visualized with high accuracy in the resulting time slices. The values of metrics for comparison of the model slice with the acquired data time slice and with the interpolated data time slice for a profile interval of 0.1 m are given in Table 1. The comparison results between the model slice (Fig. 3(a)) and the acquired data time slice without interpolation (Fig. 3(b)) obtained using acquired profiles with 0.1 m interval are given in the line 1 of Table 1. Also the comparison results between the model slice (Fig. 3(a)) and the interpolated data time slices (Fig. 3(c)) obtained by

3.6.2. Comparison results for PI = 0.25 m and TI = 0.04 m Visualizations of the model slice obtained from the model, the acquired data time slice at 8.24 ns without interpolation obtained using the synthetic data of acquired profiles with 0.25 m interval and the interpolated data time slice at 8.24 ns obtained by applying Cubic interpolation to the acquired data time slice using the mesh of grid ((PI/10) × (TI/4)) for PI = 0.25 m and TI = 0.04 m are shown in Fig. 4. As seen from Fig. 4(b), visualization of the acquired data time slice generated on the base of produced synthetic data is perceived as model slice with high accuracy. This means that the wall structure was properly scanned in the synthetic data generated using a 0.25 m profile interval. Corners and wall thicknesses are almost in natural sizes. The values of metrics for comparison of the model slice with the acquired data time slice and with the interpolated data time slice for a profile interval of 0.25 m are given in Table 2.

Fig. 8. (a) Schema of the measured profiles; (b) the total penetration depth is divided into 30 equal time slices from the surface of soil.

162


The comparison results between the model slice (Fig. 4(a)) and the acquired data time slice without interpolation (Fig. 4(b)) obtained using acquired profiles with a 0.25 m interval are given in the line 1 of Table 2. Also the comparison results between the model slice (Fig. 4(a)) and the interpolated data time slices (Fig. 4(c)) obtained by using different interpolation techniques with different mesh of grid for a profile interval of 0.25 m are given in the lines 2–12 of Table 2. As seen from Table 2, on the one hand, the similarity and error between the wall slice from the model (Fig. 4(a)) and the acquired data time slice (Fig. 4(b)) obtained in the Experiment 1 are characterized by values of r = 0.9186 (this value is minimal in the columns for r) and RMSE = 0.1607 (this value is maximal in the columns for RMSE) for all interpolation techniques. On the other hand, the similarity and error between the model slice (Fig. 4(a)) and the interpolated data time slice (Fig. 4(c)) obtained in the Experiment 12 are characterized by values of r = 0.9606 and RMSE = 0.1273 for Cubic interpolation technique. As seen, due to Cubic interpolation with mesh (PI/10) × (TI/4) for PI = 0.25 m and TI = 0.04 m the similarity was increased

from 0.9186 to 0.9606 (or 4.5%). Also, error was decreased from 0.1607 to 0.1273 (or 20.8%). So, positive influence of the results is about 5% for similarity and 21% for error. As seen, the best result was obtained using mesh of grid (PI / 10) × (TI / 4) for PI = 0.25 m and TI = 0.04 m or (0.025 × 0.01) m2 (the line 12 in Table 2). In order to evaluate the effect of very small profile and trace intervals or very small mesh of grid, extra experiment using smaller mesh of grid (0.01 × 0.01) m2 was performed and the results were presented in the line 13 of Table 2. As seen, the value of similarity (r = 0.9606) between the model slice and the interpolated data time slice for mesh of grid (0.025 × 0.01) m2 is nearly identical to the value of similarity (r = 0.9610) for mesh of grid (0.01 × 0.01) m2. The same discussion can be done for RMSE. Based on these results, the following conclusion can be drawn: selecting profile intervals and trace intervals smaller than mesh of grid ((PI / 10) × (TI / 4)) or (0.025 × 0.01) m2 will increase the processing time but will not significantly improve the similarity and error. In order to approve this conclusion the processing time and similarity for mesh (0.025 × 0.01) m2 are compared with the

Fig. 9. 3D and 2D data visualization results with GPRSlice: (a) interpolation result for mesh of grid ((PI / 5) × (TI / 2)); (b) interpolation result for mesh of grid ((PI / 10) × (TI / 4)) for PI = 0.25 m and TI = 0.04 m.


processing time and similarity for mesh (0.01 × 0.01) m2. Suppose that processing time for any mesh is t. Mesh (0.025 × 0.01) m2 can be divided into 2.5 smaller meshes (0.01 × 0.01) m2. On the one hand if mesh (0.025 × 0.01) m2 is processed as one mesh then processing time will be t. On the other hand, if mesh (0.025 × 0.01) m2 is processed as 2.5 smaller meshes (0.01 × 0.01) m2 then processing time will be 2.5*t. So, processing time of the same area will be increased 2.5 times. While the similarity will increase by 0.0004 (Δ = 0.9610–9606 = 0.0004) or 0.04%. So, increase rate of similarity is negligibly small. As a result, an interpolation scheme of mesh of grid (PI / 10 × TI / 4) is regarded as optimal.

3.6.3. Comparison results for PI = 0.5 m and TI = 0.04 m Visualizations of the model slice obtained from the model, the acquired data time slice at 8.24 ns without interpolation obtained using the synthetic data of acquired profiles with 0.5 m interval and the interpolated data time slice at 8.24 ns obtained by applying Cubic interpolation to the acquired data time slice using the mesh of grid ((PI / 10) × (TI / 4)) for PI = 0.5 m and TI = 0.04 m are shown in Fig. 5. With this profile interval, the structure appears to be fully scanned, but the vertical wall in Fig. 5(b) is observed to be thicker than in model. Therefore, the structure was not scanned accurately using this profile interval. Only 2 profiles intersected the underground structure in the range of 1–2 m along the X axis. This caused the visualization of this part of the structure in the time slice (Fig. 5(b)) to be thicker than its true size as seen in the model slice (Fig. 5(a)). Such a scenario will lead to errors in the interpretation of an underground structure. The values of metrics for comparison of the model slice with the acquired data time slice and with the interpolated data time slice for a profile interval of 0.5 m are given in Table 3. The comparison results between the model slice (Fig. 5(a)) and the acquired data time slice without interpolation (Fig. 5(b)) obtained using acquired profiles with a 0.5 m interval are given in the line 1 of Table 3. Also the comparison results between the model slice (Fig. 5(a)) and the interpolated data time slices (Fig. 5(c)) obtained by

163

using different interpolation techniques with different mesh of grid for a profile interval of 0.5 m are given in the lines 2–12 of Table 3. As seen from Table 3, on the one hand, the similarity and error between the model slice (Fig. 5(a)) and the acquired data time slice (Fig. 5(b)) obtained in the Experiment 1 are characterized by values of r = 0.9146 (this value is minimal in the columns for r) and RMSE = 0.1636 (this value is maximal in the columns for RMSE) for all interpolation techniques. On the other hand, the similarity and error between the model slice (Fig. 5(a)) and the interpolated data time slice (Fig. 5(c)) obtained in the Experiment 12 are characterized by values of r = 0.9313 and RMSE = 0.1480 for Cubic interpolation technique. As seen, due to Cubic interpolation with mesh (PI / 10) × (TI / 4) for PI = 0.5 m and TI = 0.04 m the similarity was increased from 0.9146 to 0.9313 (or 1.8%). Also, error was decreased from 0.1636 to 0.1480 (or 9.5%). So, positive influence of the results is about 2% for similarity and 10% for error.

3.7. Determining the optimal profile and trace intervals and the optimal mesh of grid The best results of similarity (r) selected from Table 1, Table 2 and Table 3 are listed in Table 4. On the one hand, according to the maximum value of similarity r = 0.9756, (PI / 10) × (TI / 4) is selected as optimal mesh of grid, PI = 0.1 m is selected as optimal profile interval and TI = 0.04 m is selected as optimal trace interval. On the other hand, according to the maximum improvement of similarity about 4.5%, (PI / 10) × (TI / 4) is also selected as optimal mesh of grid, PI = 0.25 m is selected as optimal profile interval and TI = 0.04 m is selected as optimal trace interval. As seen, according to both maximum value of similarity and maximum improvement of similarity, (PI / 10) × (TI / 4) was selected as optimal mesh of grid and TI = 0.04 m was selected as optimal trace interval. However, the final optimal profile interval from PI = 0.1 m and PI = 0.25 m will be determined on the base of following discussion.

Fig. 10. Data visualization results: (a) 3D view of underground structure; (b) 2D view of time slice.

164


Table 1 shows that the values of similarity and error between the model slice and the acquired data time slice for 0.1 m profile interval were calculated as 0.9505 (for the r) and 0.1282 (for the RMSE) (Experiment #1 in Table 1). On the one hand, when the same model was scanned with 0.25 m profile interval and Cubic interpolation technique with mesh of grid ((PI / 10) × (TI / 4)) was applied to the acquired data time slice, superior similarity of 0.9606 and error of 0.1213 were achieved (Experiments #12 in Table 2). It means that the mesh of grid ((PI / 10) × (TI / 4)) for 0.25 m profile interval gives better result than acquired data time slice (PI × TI) for 0.1 m profile interval. Considering the size of the search area, acquisition cost, and processing time scanning the search area using 0.25 m profile interval will save time while preserving the ability to detect underground structures with high accuracy. So, at the result of evaluation of 0.1 m and 0.25 m profile intervals, 0.25 m is determined as optimal profile interval. So, this paper suggests users to use the optimal profile interval of 0.25 m and the optimal trace interval of 0.04 m to acquire data in search area by GPR at data acquisition phase and the optimal mesh of grid

(0.025 × 0.01) m2 to visualize the underground structures with the highest accuracy at the data processing phase.

4. Application of the proposed analysis procedure to real data In this section, the results of applying the proposed analysis procedure to real data are presented. The real data acquired from a test area specifically designed and created within the scope of TUBITAK 1505 Project #5130012 were used. As mentioned in Introduction section, many researchers suggest the 0.25 m and 0.5 m profile intervals as sufficient for archeological research and applications. As studied and mentioned in Section 3, the 0.1 m and 0.25 m were also determined as an optimal profile intervals. So, the findings of this study have also been approved by existing works. Below, the optimal profile interval of 0.25 m, the optimal trace interval of 0.04 m and the optimal mesh of grid ((PI / 10) × (TI / 4)) were used to analyze real data.

Fig. 11. 3D and 2D data visualization results with GPRVis: a) Cubic interpolation result for mesh of grid. ((PI / 10) × (TI / 4)); b) linear interpolation result for mesh of grid ((PI / 10) × (TI / 4)) for PI = 0.25 m and TI = 0.04 m.


4.1. Real model The test area is located on the Golbasi Campus of Ankara University. The layout plan for the objects embedded in the test area is illustrated in Fig. 6. A real model of the wall structure represented by the object number 2a in Fig. 6 is shown below (Fig. 7). The wall structure, which is shaped like a square stone room, has the following dimensions: – – – – –

Width: 2 m, Length: 2 m, Thickness: 0.60 m, Embedded depth of the base: 1.20 m, Embedded depth of the top edge: 0.70 m.

4.2. Obtaining the profiles with 0.25 m profile and 0.04 m trace intervals from real model Data were acquired along 20 parallel profiles in the search area (Fig. 8(a)). The profile length was approximately 5 m. The distance between the profiles was 0.25 m. A monostatic shielded 400 MHz antenna was used for data acquisition. Data were recorded with 9 ns signal offset and in 90 ns scan range. The data were recorded using a trigger wheel sensor operating in “distance” mode. The trace interval of the recorded data was 0.04 m. An overlay on the photograph of the embedded wall, indicating the direction along profiles in which the data were recorded, is shown in Fig. 7. 4.3. Processing the obtained profile data Obtained profile data were read and process with professional software. First, marker alignment and direction editing operations were applied to the acquired data. The remaining data processing operations were then performed as follows: a) b) c) d) e) f)

DC Shift; Static Correction; Linear Gain; Band-Pass Filter; Background Removal; Resampling.

DC Shift is applied to each trace in order to move trace offsets by subtracting the value of each sample in trace from average of trace values (Cassidy, 2009). Static correction is performed to remove effects of directional waves from data. Background removal suppresses horizontal effects which are caused by system noise, electromagnetic interference and surface reflections and emphasizes hyperbolic and dipping signals that indicate a point of anomaly (Cassidy, 2009; Conyers, 2004). It should be applied carefully where horizontal events expected due to subsurface structures, because it can also suppress the signals which are coming from the subsurface structures. Purpose of resampling is emphasizing the reflections which are coming from objects and it also reduces the amplitude of the random reflection signals. Explanations for Linear gain and Band-pass filter are given in Section 2.4. 4.4. Obtaining and visualizing the time slice (horizontal grid) by interpolation GPRSlice, GPRSoft and GPRVis were used to visualize the real data of wall structure.

165

4.4.1. Data visualization with GPRSlice Time slice is a view of bird's eye of the total penetration depth of the scan area about its starting point (0, 0) in directions of X and Y of data in any desired depth (z). In this study, after data processing, the total penetration depth is divided into 30 equal time slices from the surface of soil (Fig. 8(b)). The data has 90 ns record length and signal has 9 ns length. User needs to sample at least 3 points of the signal length with 3 ns interval. Thus, 30 equal time slices can be got by dividing 90 ns with 3 ns. The depth time slices (look at a1–a30 in Fig. 8(b)), recorded as in *.grd format, were interpolated according to two different mesh of grid ((PI / 5) × (TI / 2)) and ((PI / 10) × (TI / 4)) using the Cubic interpolation technique, and the differences between the results were examined. The results of interpolating data recorded using PI = 0.25 m profile interval and TI = 0.04 m trace interval are shown in Fig. 9. 4.4.2. Data visualization with GPRSoft Unfortunately, GPRSoft does not allow users to select the interpolation techniques, parameters and their values. All of them are defined by default. Visualization results of wall structure on GPRSoft are shown in Fig. 10. As seen from Fig. 10, wall perception is successful, but there is deformation on wall edges. Also, the actual ratio of wall structure is a bit deformed. Thus, there is no possibility to select the parameters of interpolation in GPRSoft. Interpolation is performed by default. Default parameters are not known. There is also no possibility to select the profile interval and trace interval during visualization process in GPRSoft. 4.4.3. Data visualization with GPRVis GPRVis is new GPR software developed in scope of TUBITAK 1505 Project No 5130012. The same visualization procedure described in Section 4.4.1 was implemented on GPRVis and final results are shown in Fig. 11. There are a lot of interpolation options in GPRVis. Suitable interpolation techniques such as Cubic, Linear, Cubic Spline, etc. and the required values for PI and TI can be selected. The best results were obtained on GPRVis using Cubic and Linear interpolation techniques with mesh of grid ((PI / 10) × (TI / 4)) for PI = 0.25 m and TI = 0.04 m. Short comparison of the used software is given below. GPRSlice has more smooth visualization ability but the interpolation options are few. Starting point (0, 0) is set by default, it cannot be preferred. As seen from Fig. 9, corners of wall are extremely rounded. The actual shape of the wall is perceived as deformed shape. GPRSoft provides less smoothing and there are no interpolation options. Color pallets are very limited (there are only four pallets). There is no ISO surface feature. It is easy to use. Starting point (0, 0) is set by default, it cannot be preferred. It is very difficult to determine the original aspect ratio of the wall structure observed in the image in Fig. 10. The user tries to set the ratio of the wall structure manually. GPRVis has normal smoothing feature but interpolation options are very rich and color pallets are unlimited. Starting point (0, 0) can be selected by users. ISO Surface feature can be applied for selected data intervals. As seen in Fig. 11, corner perception of the result is very successful. 5. Conclusions In GPR studies, the data acquisition parameters such as the profile and trace intervals and data processing parameter such as mesh of grid, which can be controlled by users, play a vital role in the identification of underground structures. When the optimal values of these parameters are used, the accuracy or smoothness of the measured geometry of the underground structures increases. This study sought to determine the optimal profile and trace intervals to acquire GPR data from search area and the optimal mesh of grid to process acquired GPR data by analyzing the interpolation-induced effects of different

166

R. Samet et al. / Journal of Applied Geophysics 140 (2017) 154–167 Trace 1

Trace 2

Samples

Trace M

X

Profile Interval

1

X

2

Profile N

Trace Length

Profile 2 Profile 1

X

K

Trace Interval

(a)

(b)

Acquired Vertical Grid (Acquired Radargram)

(c) Acquired Horizontal Grid (Acquired Time Slice)

1 2 3 4

Acquired Profiles

Acquired Traces

(d)

Acquired Samples

(e)

(f)

Interpolated Vertical Grid (Interpolated Radargram)

Interpolated Horizontal Grid (InterpolatedTime Slice)

1 2 3 4 Interpolated Profiles Interpolated Traces

(g)

(h)

Interpolated Samples

(i)

Fig. A-I. GPR Data Structure: (a) Profiles; (b) Traces; (c) Samples; (d) Acquired Vertical Grid (Acquired Radargram) for M = 7 and K = 4; (e) Acquired GPR Data; (f) Acquired Horizontal Grid (Acquired Data Time Slice) for N = 4 and M = 7; (g) Interpolated Vertical Grid (Interpolated Radargram) for M = 7 and K = 4; (h) Interpolated GPR Data; (i) Interpolated Horizontal Grid (Interpolated Data Time Slice) for N = 4 and M = 7.

profile and trace intervals on the measured geometry of underground structures. In the considered context, an analysis procedure, to determine the optimal profile and trace intervals and an optimal mesh of grid for visualizing the underground structures with high accuracy has been proposed. The proposed analysis procedure has been tested on synthetic and real data and obtained results have been evaluated. Thus, 0.25 m and 0.04 m have been determined as the optimal profile and trace intervals, respectively, and ((PI / 10) × (TI / 4)) has been determined as optimal mesh of grid. So, this paper has suggested users to use the 0.25 m profile interval and 0.04 m trace interval to acquire data in search area by GPR at data acquisition phase and the mesh of grid (0.025 × 0.01) m2 to visualize the underground structures with the highest accuracy at the data processing phase. Obtained results regarding optimal profile interval are supported by existing studies where 0.25 m is also proposed as optimal profile interval. The obtained results have proved that an optimal mesh of grid exerts positive effects about 5% for similarity and 21% for error when determining and visualizing the geometry of underground structures. By investigating the optimal interpolation technique this rate can be improved.

Future research topics include the optimization of the interpolation techniques and an analysis of the effects of the instantaneous amplitude values on the time-slice resolution. Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.jappgeo.2017.04.003. Acknowledgments This work was funded by The Scientific and Technological Research Council of Turkey - TÜBİTAK under grant 5130012. Appendix 1. Definitions of main terminologies GPR data structure includes following elements: 1) Profiles; 2) Traces; 3) Samples; 4) Vertical grids (radargrams) and 5) Horizontal grids (time slices). GPR data consists of N acquired profiles (Fig. A-I(a)), each acquired profile consists of M acquired traces (Fig. A-I(b)), and each acquired trace consists of K acquired samples (Fig. A-I(c)). In addition, acquired GPR data (Fig. A-I(e)) can be considered as N acquired vertical grids (acquired radargrams) (Fig. A-I(d)) and K acquired


horizontal grids (acquired data time slices) (Fig. A-I(f)). Finally, interpolated GPR data (Fig. A-I(h)) can be considered as a set of interpolated vertical grids (interpolated radargrams) (Fig. A-I(g)) and a set of interpolated horizontal grids (interpolated data time slices) (Fig. A-I(i)). Profile interval (Fig. A-I (a)), trace interval and trace length (Fig. A-I (b)), sample interval (Fig. A-I (c)) are main parameters of GPR data structure elements. Profile interval is a distance between two acquired neighbor profiles scanned by GPR in search area. Profile interval and profile numbers (N) are defined by users depending on applications. Trace interval is a distance between two acquired neighbor traces scanned by GPR in search area. Trace interval is defined by scan rate of GPR. Scan rate is a number of traces per second produced by GPR and can be selected by users. Total number of traces (M) is defined by search area of applications. Trace length is a number of samples (K) which is defined by used GPR. Sample interval is a time between two acquired neighbor samples scanned by GPR in search area. Sample interval is defined as ratio of scan range and samples per scan of GPR. Acquired data time slice is an intersection of all acquired vertical grids at certain time depth. The elements of acquired data time slice are values of samples of all acquired traces of all acquired profiles at certain time depth. Interpolated data time slice is an intersection of all acquired and interpolated vertical grids at certain time depth. The elements of interpolated data time slice are values of samples of all acquired and interpolated traces of all acquired and interpolated profiles at certain time depth. References Alani, A.M., Aboutalebi, N., Kılıc, G., 2013. Application of ground penetrating radar (GPR) in bridge deck monitoring and assessment. J. Appl. Geophys. 97, 45–54. Arkedani, M.R., Neyt, X., Benedetto, D., Slob, E., Wesemael, B., Bogaert, P., Craeye, C., Lambot, S., 2014. Soil moisture variability effect on GPR data. 15th International Conference on Ground Penetrating Radar, Brussels, Belgium, pp. 214–217. Benesty, J., Chen, J., Huang, Y., Cohen, I., 2009. Pearson correlation coefficient. In: Benesty, J., Chen, J., Huang, Y., Cohen, I. (Eds.), Noise Reduction in Speech Processing. Springer Verlag, Berlin, pp. 37–40. Böniger, U., Tronicke, J., 2010. Improving the interpretability of 3D GPR data using targetspecific attributes: application to tomb detection. J. Appl. Geophys. 37, 360–367. Booth, A.D., Linford, N.T., Clark, R.A., Murray, T., 2008. Three-dimensional, multi offset ground-penetrating radar imaging of archaeological targets. Archaeol. Prospect. 15, 93–112. Bristow, C.S., 2009. Ground penetrating radar in aeolian dune sands. In: Jol, H.M. (Ed.), Ground Penetrating Radar: Theory and Applications. Elsevier, Amsterdam, pp. 273–298. Cassidy, Nigel J., 2009. Ground penetrating radar data processing, modelling and analysis. In: Jol, Harry M. (Ed.), Ground Penetrating Radar: Theory and Applications. Elsevier, Amsterdam, pp. 141–176. Conyers, L.B., 2004. Ground-Penetrating Radar for Archaeology. third ed. AltaMira Press, Lanham, UK (422 pp.). Conyers, L.B., Goodman, D., 1997. Ground-Penetrating Radar: An Introduction for Archaeologists. AltaMira, Walnut Creek, California. Daniels, J.J., 1989. Fundamentals of Ground Penetrating Radar, Proceedings of the Symposium on the Application of Geophysics to Engineering an Environmental Problems, SAGEEP 89, Golden, Colorado. pp. 62–142. Daniels, D.J., 2004. Ground Penetrating Radar 2nd Edition, the Institution of Electrical Engineers, London, United Kingdom. Dojack, L., 2012. Data collection parameters. In: Dojack, L. (Ed.), Ground Penetrating Radar Theory, Data Collection, Processing, and Interpretation: A Guide for Archaeologists, the University of British Columbia, pp. 11–15. Doolittle, J.A., Collins, M.E., 1995. Geomechanics abstract site investigation and field observation structural and geotechnical mapping: use of soil information to determine application of ground penetrating radar. J. Appl. Geophys. 33 (1–3), 101–108. Ekes, C., Takacs, P., Neducza, B., 2014. Condition assessment of critical infrastructure with GPR. The 15th International Conference on Ground Penetrating Radar, Brussels, Belgium, pp. 430–434. Fu, L., Liu, S., Liu, L., 2014. Internal structure characterization of living tree trunk crosssection using GPR: Numerical examples and field data analysis. The 15th International Conference on Ground Penetrating Radar, Brussels, Belgium, pp. 155–160. Giannopoulos, A., 2005. Modelling ground penetrating radar by GprMax. Constr. Build. Mater. 19, 755–762. Goodman, D., Piro, S., Nishimura, Y., Schneider, K., Hongo, H., Higashi, N., Steinberg, J., Damiata, B., 2009. GPR archaeometry. In: Jol, H.M. (Ed.), Ground Penetrating Radar: Theory and Applications. Elsevier, Amsterdam, pp. 479–508.

167

Grealy, M., 2006. Resolution of ground-penetrating radar reflections at differing frequencies. Archaeol. Prospect. 13, 142–146. Gulati, A., Ferguson, R.J., 2011. Accurate Declipping Hybrid Algorithm for Ground Penetrating Radar Data. CSPG CSEG CWLS Convention. Hirano, Y., Dannoura, M., Aono, K., Igarashi, T., Ishii, M., Yamase, K., Makita, N., Kanazawa, Y., 2008. Limiting factors in the detection of tree roots using ground-penetrating radar. Plant Soil 319, 15–24. Jol, H.M., 2009. Ground Penetrating Radar: Theory and Application. Elseiver Science (ISBN: 978-0444533487). Jol, H.M., Bristow, C.S., 2003. GPR in sediments: advice on data collection, basic processing and interpretation, a good practice guide. In: Bristow, C.S., Jol, H.M. (Eds.), Ground Penetrating Radar in Sediments. Geological Society Special Publication 211. Geological Society, London, pp. 9–27. Leckebusch, J., 2003. Ground-penetrating radar: a modern three-dimensional prospection method. Archaeol. Prospect. 10, 213–240. Levinson, N., 1947. The Wiener RMS (root mean square) error criterion in filter design and prediction. In: Nohel, J.A., Sattinger, D.H. (Eds.), Selected Papers of Norman Levinson vol. 2. MIT Press, pp. 163–180. Maeland, E., 1988. On the comparison of interpolation methods. IEEE Trans. Med. Imaging 7, 213–217. Mahmoudzadeh, M.R., Frances, A.P., Lubczynski, M., Lambot, S., 2012. Using ground penetrating radar to investigate the water table depth in weathered granites — Sardon case study, Spain. J. Appl. Geophys. 79 (2012), 17–26. McKinley, S., Levine, M., 1998. Cubic spline interpolation. College of the Redwoods Vol. 45 pp. 1049–1060. Meijering, E., Unser, M., 2003. A note on cubic convolution interpolation. IEEE Trans. Image Process. 12, 477–479. Monnier, S., Camerlynck, C., Rejiba, F., Kinnard, C., Feuillet, T., Dhemaied, A., 2011. Structure and genesis of Thabor rock glacier (Northern French Alps) determined from morphological and ground penetrating radar surveys. Geomorphology 134, 269–279. Negri, S., Leucci, G., Mazzone, F., 2008. High resolution 3D ERT to help GPR data interpretation for researching archeological items in a geologically complex subsurface. J. Appl. Geophys. 65, 111–120. Neubauer, W., Eder-Hinterleitner, A., Seren, S., Melichar, P., 2002. Georadar in the Roman civil town Carnuntum, Austria: an approach for archaeological interpretation of GPR data. Archaeol. Prospect. 9, 135–156. Nuzzo, L., Leucci, G., Negri, S., Carrozzo, M.T., Quarta, T., 2002. Application of 3D visualization techniques in the analysis of GPR data for archaeology. Ann. Geophys. 45 (2), 321–337. Orlando, L., 2007. Georadar data collection, anomaly shape and archaeological interpretation — a case study from Central Italy. Archaeol. Prospect. 14, 213–225. Pomfret, J., 2006. Ground-penetrating radar profile spacing and orientation for subsurface resolution of linear features. Archaeol. Prospect. 13, 151–152. Safont, G., Salazar, A., Rodriguez, A., Vergara, L., 2014. On recovering missing ground penetrating radar traces by statistical interpolation methods. Remote Sens. 6, 7546–7565. Samet, R., Tural, S., 2010. Web based real-time meteorological data analysis and mapping information system. WSEAS Trans. Inf. Sci. Appl. 9, 1115–1125. Samet, R., Çelik, E., Şengönül, E., Tural, S., Özkan, M., 2015a. Interpolation approach to search hidden result in GPR data. The 5th International Conference on Control and Optimization with Industrial Applications, Baku, Azerbaijan, pp. 422–425. Samet, R., Çelik, E., Tural, S., Şengönül, E., 2015b. A new multi-purpose easy and quick GPR data processing and visualization software. XIVth International Conference – Geoinformatics: Theoretical and Applied Aspects, Kiev, Ukraine, pp. 1–5. Strange, A.D., 2003. Analysis of time interpolation for enhanced resolution GPR data. 7th International Workshop on Advanced Ground Penetrating Radar IEEE Transactions, pp. 1–5. Tamba, R., 2012. Testing the use of geostatistics to improve data visualization. Case study on GPR survey of Tarragona's Cathedral. Archaeol. Prospect. 19, 167–178. Verdonck, L., Taelman, D., Vermeulen, F., Docter, R., 2015. The impact of spatial sampling and migration on the interpretation of complex archaeological ground-penetrating radar data. Archaeol. Prospect. 22, 91–103. Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P., 2004. Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13, 600–612. Wang, T., Chen, C., Tong, L., Chang, P., Chen, Y., Dong, T., Liu, H., Lin, C., Yang, K., Ho, C., Cheng, S., 2015. Applying FDEM, ERT and GPR at a site with soil contamination: a case study. J. Appl. Geophys. 121, 21–30. Yi, L., Takahashi, K., Sato, M., 2015. Estimation of vertical velocity profile by multistatic GPR Yakumo. Geoscience and Remote Sensing Symposium (IGARSS), pp. 1060–1063. Yi, L., Takahashi, K., Sato, M., 2016. A fast iterative interpolation method in f-k domain for 3-D irregularly sampled GPR data. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 9 (1), 9–17. Zhang, P., Guo, X., Muhammat, N., Wang, X., 2016. Research on probing and predicting the diameter of an underground pipeline by GPR during an operation period. Tunn. Undergr. Space Technol. 58, 99–108. Zhao, W., Forte, E., Pipan, M., Tian, G., 2013. Ground penetrating radar (GPR) attribute analysis for archeological prospection. J. Appl. Geophys. 97, 107–117. Zhao, W., Tian, G., Forte, E., Pipan, M., Wang, Y., Li, X., Shi, Z., Liu, H., 2015. Advances in GPR data acquisition and analysis for archeology. Geophys. J. Int. 202, 62–71. Zhu, S., Huang, C., Su, Y., Lu, M., 2014. Tree roots detection based on circular survey using GPR. The 15th International Conference on Ground Penetrating Radar, Brussels, Belgium, pp. 135–139.