A New Algorithm for More Accurate Estimation of …...A New Algorithm for More Accurate Estimation...

A New Algorithm for More Accurate Estimation of Wave Propagation Velocity by Common-Offset Survey Method

Janet F.C. SHAM, Wallace W.L. LAI*

Department of Land Surveying and Geo-informatics, The Hong Kong Polytechnic University,

Hong Kong

Phone: +852 3400-8960; Fax:; email: [email protected]

Abstract

This paper presents a new algorithm to estimate electromagnetic (EM) wave propagation

velocity (v) with high-frequency 2GHz ground penetrating radar (GPR)’s shielded antenna. The

data collection makes use common offset method with particular consideration of antenna’s

separation distances and its corresponding triangulation geometry. This method calculates the

distribution of discrete velocities at each point oblique to the embedded target object, analogous

to the similar yet ambiguous curve fitting process of hyperbolas in most software. Validation test

in air and a steel bar in concrete media were conducted and the results were satisfactory.

Comparison with the tradition hyperbola geometry method was conducted and the results show

that error on velocity analysis is significantly reduced by the proposed method. Based on the

result, works on next stage will be about differentiation of velocity variations in concrete as a

result of water seepage and leakage.

Keywords: ground penetrating radar (GPR), velocity analysis

1. Introduction Object identification and mapping in concrete has been the focus of GPR community working on

concrete structures in past decade. With the advent of electronics and signal processing

techniques, this task is much easier and more accurate results have been produced. The next

stage of work will be about characterization of long term concrete serviceability which means

corrosion, cracks, spalling and delaminations. On one hand, mechanical wave is the best

candidate to measure mechanical properties while electromagnetic wave works best for

aforementioned parameters of concrete serviceability, in which the root cause is water seepage. It

is an enduring and complex issue for the residents and also the Hong Kong government. In

Singapore, which has similar weather condition and environment as Hong Kong, [1] revealed

that water seepage is the most significant building maintenance problems in high-rise buildings.

It causes corrosion and eventually induces cracks and delamination in reinforced concrete

structures. Besides, it is also a threat to hygiene. Water seepage causes damp environment which

enhances the development of defects [2]. Therefore, it is crucial to develop more accurate

moisture mapping technique which helps to locate the source and extent of water seepage.

Amongst non-metallic materials, water is the single most influential factor affecting radar wave’s

traveling velocity and reflection strength, and absorbing high-frequency portion in spectral

content [3-11]. Therefore, presence of water seepage/leakage can be found by investigating the

International Symposium Non-Destructive Testing in Civil Engineering (NDT-CE)

September 15 - 17, 2015, Berlin, Germany

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change of wave propagation velocity. However, as mentioned in HKIS [12], the major problem

on using GPR technique for water seepage measurement is data interpretation. Skilled operator is

required for better and more accurate data interpretation. This paper proposed a new developed

mathematical algorithm and software which allow more accurate estimation of EM wave

propagation velocity from GPR by adding suitable constraints and calculates the distribution of

discrete velocities at each point oblique to the embedded target object. In this paper, we

attempted to measure GPR wave velocity traveling in concrete, and validate our result in air and

concrete.

2. Principle of Velocity Analysis In ground penetrating radar survey, there is a rule of thumb relating velocity to dielectric

constant (ε’) for rough estimation of velocity [13]:

士噺算√資 Equation 1

where v is the EM wave propagation velocity, c is the propagation velocity in free space

(3x108m/s) and ε is the dielectric constant of the material which the EM wave propagate. The

condition for applying the above equation is dielectric constant of the material (where the EM

wave propagate) is known. Dielectric constant of the material can be estimated by applying time-

domain reflectometry (TDR). However, access of taking sample from the interested region for

TDR examination is always difficult and challenging.

2.1. Depth to the known reflector method

Another more reliable method for estimating velocity of the EM wave propagation from GPR is

when depth of the object (i.e. reflector) is known. This method is called ‘depth to the known

reflector method’ which bases on a general relationship of the time taken for a travelled distance:

士噺匝拶嗣 Equation 2

where D is the depth of the reflected object and t is the two-way travel time of the signal

reflected from the object which can be obtained directly by GPR. This is a simple method to

estimate the EM wave propagation velocity. However, the main problem of this method is that

the depth of the inspected object is unknown. Therefore, velocity estimation by depth to known

reflector method is not always applicable. Besides, only a single wave velocity can be obtained.

Detection of a rounded object by GPR renders the reflected signal as a hyperbola due to a certain

beam width affected by antenna design, frequency and material properties. While the only signal

for calculating the wave velocity make use of the fastest time (which is the peak of the reflected

hyperbola signal), the reflection events of the hyperbola tails are not used. Therefore, the

following hyperbolic geometry method is normally used for determining discrete velocities using

every point of the hyperbola in GPR commercial software.

2.2. Hyperbolic geometry method

In this paper, shield antenna is used i.e. transmitter and receiver are shielded with a fixed

separation. It is called common-offset survey method. Therefore, velocity sounding method



cannot be applied and the following velocity estimation method – hyperbolic geometry is used.

The general equation for hyperbolic geometry is shown as below: 懸噺 2捲紐建掴態伐建待態 Equation 3

Where to refers to the two-way travel time of EM wave transmitted to the target and reflected

back and received by the receiver when the shielded antenna is located normal to the target. On

the other hand, tx refers to the two-way travel time of the EM wave transmitted to the target and

reflected back and received by the receiver when the shield antenna is located position x, oblique

to the target. This method is only valid when the reflector is round-shaped. Both velocity

sounding and hyperbolic geometry can be used to estimate EM wave propagation velocity from

GPR without the information of dielectric constant and depth of the object. Therefore, they are

widely applied in the commercial software which make use of hyperbolic geometry method as

curve fitting for estimating velocity of EM wave propagation as shown below (from Software

Reflexw):

Figure 1: Sample of velocity estimation by curve-fitting method

However, it is biased by human judgment and become very subjective. As shown in Figure 1, it

is only based on curve-fitting the bands of colors (as a result of polarity) by the reflections. The

velocity estimation may not be consistent and hence significant deviations may be induced when

different analysts are handling the data. There is no systematic guideline on this hyperbola fit.

Besides, Equation 3 assumes that the subsurface object is a point reflector. However, this

assumption does not hold in real case, e.g. in reinforced concrete wall with small concrete cover.

The effect of size of the reinforcement becomes very significant because the size and cover are in

comparable magnitude. Moreover, the equation does not take into account the effect of antenna

separation which changes the triangulation geometry of wave emission and reflection. This

causes significant error when the targeted object is located at a shallow level where the size of

the targeted object is comparable to the antenna separation.

3. Formulation and implementation In each signal received by the GPR antenna, it records the whole waveform (A-scan) with

amplitude at discrete time. The location of reflector is recognized by locating the time at which

stronger (either positive or negative polarity) reflective amplitude is recognized. This time of

stronger signal can be converted to the estimated distance between the reflector and antenna if

velocity is known. In this study, shielded antenna with common separation of transmitter and

receiver is used i.e. transmitter and receiver are enclosed within one casing. The basic geometry



of signal travel with the antenna (enclosed with transmitter and receiver) is represented in the

following figure:

Figure 2: Schematic diagram of the geometry of common-offset survey by shielded antenna

By referring to the above figure, the equation of geometric analysis for velocity estimation based

on hyperbola reflection obtained by common-offset survey (using shielded antenna) on

subsurface round-shaped target is shown below:

For any ‘x’,

懸岫捲岻噺経態髪経戴建掴 Equation 4

経態噺俵峪岫経墜髪堅岻伐岫経墜髪堅岻堅紐岫経墜髪堅岻態髪捲態崋態髪峪峭捲伐堅抜捲紐岫経墜髪堅岻態髪捲態嶌伐稽崋態

Equation 5

経戴噺俵峪岫経墜髪堅岻伐岫経墜髪堅岻堅紐岫経墜髪堅岻態髪捲態崋態髪峪峭捲伐堅抜捲紐岫経墜髪堅岻態髪捲態嶌髪稽崋態

Equation 6

Substitute Equation 5 and Equation 6 into Equation 4

懸岫捲岻噺俵峪岫経墜髪堅岻伐岫経墜髪堅岻堅紐岫経墜髪堅岻態髪捲態崋態髪峪峭捲伐堅抜捲紐岫経墜髪堅岻態髪捲態嶌伐稽崋態髪俵峪岫経墜髪堅岻伐岫経墜髪堅岻堅紐岫経墜髪堅岻態髪捲態崋態髪峪峭捲伐堅抜捲紐岫経墜髪堅岻態髪捲態嶌髪稽崋態建掴

Equation 7



The above velocity equation (Equation 7) allows calculation of the wave velocity of discrete

travelling time of signal reflected from the embedded object. This modified equation is

especially designed for GPR survey on rounded object by common-offset method. Better than

the “depth to the known reflector method”, instead of giving single value for wave velocity on a

reflected hyperbola (based on the fastest reflection time at the peak of the hyperbola), it gives

discrete velocity values which consider the signals of the whole hyperbola (i.e. including the tail

region of the hyperbola). In the equation, it requires the input of ‘Do’ as the depth of the object,

radius of the object ‘r’, ‘x’ the horizontal distance of the antenna from any oblique relative to the

normal position of the target; ‘tx’ the two way travel time of the reflection from the

transmitting/receiving antennae to the target at any distance ‘x’ and ‘B’ the antenna separation.

The new developed equation concerns many parameters and hence the discrete velocities derived

by the new equation are very similar to the wave velocity obtained by the tradition depth to the

known reflector method. The new algorithm was used to build up a velocity analysis program

and validated the steel bar reflections from two media: (1) air and (2) concrete wall.

4. Development of New GPR Velocity Analysis (GPR-VA) Program As mentioned before, another problem for unreliable velocity estimation by various software in

the market is that they rely on human judgment for curve-fitting the bands of colors by the

reflections. In order to minimize the human interference on examining the velocity analysis

process, a statistical method for GPR velocity analysis (GPR-VA) has been developed by using a

virtual programming platform - LabVIEW. The mathematical algorithm developed in the

previous session is applied in the GPR-VA program. This program enables calculation of

distribution of discrete velocities at each point oblique to the embedded target. The interface of

the developed program is shown below at Figure 3. It includes figures of selected (A) A-scan,

(B) radargram (B-scan) generated by combining all A-scans captured when moving the antenna

horizontally., (C) distance-time curve of the selected hyperbola signal and also (D) the

corresponding discrete velocities at each point of the hyperbola. The only human judgment is to

identify the region of interest (ROI), after specifying the ROI, the program will select only the

relevant points to form the hyperbola signal (graph (C) in Figure 3). At this stage, the program is

compatible to file format in either 16bit or 32bit.

Figure 3: Interface of GPR-VA program build up by LabVIEW Instrument.

(B)

(A)

(C)

(D)



According to the assumption of velocity analysis in both the traditional Equation 3 and the

developed equation (Equation 7), the velocities along the whole hyperbola signal should have the

same velocity. However, sometimes the calculated velocities can be quite fluctuate, therefore,

statistical method (i.e. setting standard deviation (SD) limit) is applied to regulate the amount of

discrete velocity for velocity analysis. The program will stop selecting the velocities along the

hyperbola signal when the SD of the batch of selected velocities exceeds the designated SD set

before analysis. It shows that by restricting the required SD, the program can automatically select

the most suitable data set and avoid erroneous data for velocity analysis. The proposed statistical

method enables automatic calculation of more reliable wave velocity of GPR survey.

5. Validation of Velocity Analysis

5.1. Validation test in AIR

In order to validate the results obtained by the modified velocity analysis equation and GPR-VA

program, hyperbola signal was collected by transmitting and receiving reflected signal of a

reinforcement bar through a unique medium, i.e. air. Y25 steel bar is used as the target. The

experimental setup is shown in the following photographs:

Figure 4: Experimental setup of the calibration process

The above figures show the experimental setup of the calibration process. A frame was built for

holding a steel bar. The steel bar was placed at different levels apart from the GPR antennae:

2GHz antennas was used for the calibration. The media for the travelling of GPR wave is air, in

which the travelling velocity of EM wave is known as 0.2998m/ns. The speed of EM wave in air

is a constant because air is a non-dispersion media for EM wave propagation, and will not be

affected by the frequency of antenna used for the experiment, angle, distance of the target etc.

Therefore, it is the most suitable and stable media to be used to calibrate the proposed method for

estimating wave velocity by GPR. The following table shows the mean wave velocity calculated

by the proposed VA method and the hyperbola geometry method. The selected data are all

collected with set standard deviation of less than 0.03 and data larger than 0.29979m/ns are

treated as invalid and hence disregarded in calculating mean wave velocity.

Table 1: Wave velocity obtained by the proposed method and by the hyperbola geometry method

Reference velocity (m/ns)

Depth of Steel

Bar (m)

Proposed VA method Hyperbola geometry method Mean Wave

Velocity

Standard Deviation

% error with respect to the

reference

Mean Wave Velocity (m/ns)

Standard deviation


reference velocity

Y25 Steel bar 2G GPR Antenna



(m/ns) velocity 0.29979 0.2 0.288 0.004 -5% 0.282 0.016 -6%

0.29979 0.3 0.287 0.003 -4% 0.280 0.017 -7%

0.29979 0.4 0.288 0.002 -4% 0.280 0.015 -7%

0.29979 0.5 0.289 0.003 -4% 0.266 0.023 -11%

The following figures show the discrete velocity data of the reflected hyperbola by different

methods:

0.200

0.220

0.240

0.260

0.280

0.300

0.320

-80 -60 -40 -20 0 20 40 60 80

Velocity Analysis (Air with 200mm object depth)

New method (Equation 7) Speed of Light Hyperbola (Equation 3)

Apex of hyperbola

0.200

0.220

0.240

0.260

0.280

0.300

0.320

-80 -60 -40 -20 0 20 40 60 80


New method (Equation 7) Speed of Light Hyperbola (Equation 3)

Apex of hyperbola

0.200

0.220

0.240

0.260

0.280

0.300

0.320

-80 -60 -40 -20 0 20 40 60 80 100


New method (Equation 7) Hyperbola (Equation 3) Speed of Light

Apex of hyperbola

Vel

ocity

(m

/ns)

V

eloc

ity (

m/n

s)

Vel

ocity

(m

/ns)

Position

Position



Figure 5: Velocity analysis of the reflected hyperbola signals with different object depth in air by different methods.

As shown in

Figure 5, the calculated discrete velocities using the developed equation (Equation 7) are quite

constant when comparing to those velocities calculated by hyperbola geometry method

(Equation 3). According to Table 1, the standard deviation of the new VA equation is only

ranging from 0.002-0.004 while it is 0.015-0.023 by hyperbola geometry method. Also, it shows

that all data points by the proposed method are included under the two constraints (1) standard

deviation <0.03 and (2) calculated velocity <0.3m/ns while most of the data points derived by

hyperbola geometry method were lost. Besides, when considering the average percentage error,

the table shows that it is only -4% to -5% by new method while it is up to ranging from -6% to -

11% in hyperbola geometry method.

5.2. Validation test on Concrete

After validation in air, another validation test was done on a concrete wall as shown in the

following Figure 6:

0.220

0.230

0.240

0.250

0.260

0.270

0.280

0.290

0.300

0.310

-80 -60 -40 -20 0 20 40 60 80


New method (Equation 7) Speed of light Hyperbola (Equation 3)

Apex of hyperbola

0.220

0.230

0.240

0.250

0.260

0.270

0.280

0.290

0.300

0.310

-80 -60 -40 -20 0 20 40 60 80


New method (Equation 7) Speed of light Hyperbola (Equation 3)

Apex of hyperbola

Vel

ocity

(m

/ns)



Figure 6: Concrete wall for validation test.

Similar to the validation process in air, the selected data were collected with set standard

deviation of less than 0.03 except that the reference velocity was calculated by “depth to the

known reflector method”. The following table shows the mean wave velocity calculated by the

proposed method and the hyperbola geometry method:

Table 2: Wave velocity obtained in concrete by the proposed method and by the hyperbola

geometry method Reference

velocity (m/ns)

Proposed VA method Hyperbola geometry method Mean Wave

Velocity (m/ns)

Standard Deviation


reference velocity

Mean Wave Velocity (m/ns)

Standard deviation


reference velocity

0.106 0.106 0.003 5% 0.140 0.022 38%

Figure 7: Velocity analysis of the reflected hyperbola signals in concrete by different methods.

The above result shows that the new algorithm also gives a very satisfactory result in concrete. It

is very close to the estimation made by “depth to known reflector” method. According to

Table 2, the standard deviation of the new velocity analysis equation is only 0.003 while it is

0.022 by hyperbola geometry method. The percentage error of using the proposed method in

0.050

0.100

0.150

0.200

0.250

-25 -20 -15 -10 -5 0 5 10 15 20 25

Velocity Analysis (concrete with a steel bar with 50mm cover depth)

New method (Equation 7) Depth to known reflector Hyperbola (Equation 3)

Apex of hyperbola

50m

m c

over

Vel

ocity

(m

/ns)



concrete is only 5% while it is up to 38% error with respect to the “depth to the known reflector

method”. The error obtained by the hyperbola geometry method is still quite large even though

constraints were added for data selection.

6. Discussion and Conclusion

In conclusion, this paper proposed a new alogorithm and program for more accurate and

consistant velocity analysis for GPR survey with common-offset survey method. Several

highlights are listed as below:

1. A new equation was formulated by concerning parameters such as antenna seperation, depth

and size of the embedded object which are neglected in commercial software.

2. By applying the proposed method, discrete velocities can be obtained for better investigation

of variation of material properties since more data points can be used.

3. New program is build up in a virtual programming platform LabVIEW by applying the

developed equation.

4. Statistical method i.e. considering standard deviation among the calculated velocities of the

reflected hyperbola signal as a quality check of data, is proposed. This constraint can largely

reduce the error induced by human interference during signal post-processing.

5. Validation test of the proposed method and program have been tested in two environment (1)

air and (2) concrete wall. Satisfactory results were obtained by using the new method in

which only -4% to -5% percentage error with standard deviation of 0.002-0.004 in air while

only -1% to 5% percentage error with standard deviation of 0.001-0.005 in concrete are

observed.

References

[1] M. Y. L. Chew and N. DeSilva, "Maintainability problems of wet area in high-rise residential

buildings in Singapore," Building Research and Information, vol. 31, pp. 60-69, 2003.

[2] M. Y. L. Chew and W., Building Facades : A Guide to Common Defects in Tropical Climates. Singapore ; Hong Kong: Singapore ; Hong Kong : World Scientific, c1998, 1998.

[3] J. Hugenschmidt and R. Loser, "Detection of chlorides and moisture in concrete structures

with ground penetrating radar," Materials and Structures, vol. 41, pp. 785-792, 2008.

[4] J. A. Huisman, S. S. Hubbard, J. D. Redman and A. P. Annan, "Measuring Soil Water

Content with Ground Penetrating Radar: A Review," Vadose Zone Journal, vol. 2, pp. 476-491,

2003.

[5] W. L. Lai, W. F. Tsang, H. Fang and D. Xiao, "Experimental determination of bulk dielectric

properties and porosity of porous asphalt and soils using GPR and a cyclic moisture variation

technique," Geophysics, vol. 71, pp. K93-K102, 2006.

[6] G. Klysz and J. -. Balayssac, "Determination of volumetric water content of concrete using

ground-penetrating radar," Cement and Concrete Research, vol. 37, pp. 1164-1171, 2007.

[7] W. L. Lai, T. Kind and H. Wiggenhauser, "A Study of Concrete Hydration and Dielectric

Relaxation Mechanism Using Ground Penetrating Radar and Short-Time Fourier Transform,"

EURASIP Journal on Advances in Signal Processing, pp. 1-14, 2010.



[8] W. L. Lai, T. Kind and H. Wiggenhauser, "Frequency-dependent dispersion of high-

frequency ground penetrating radar wave in concrete," NDT&E International, vol. 44, pp. 267-

273, 2011.

[9] W. L. Lai, T. Kind and H. Wiggenhauser, "Using ground penetrating radar and time-

frequency analysis to characterize construction materials," NDT&E International, vol. 44, pp.

111-120, 2011.

[10] W. L. Lai, S. C. Kou and C. S. Poon, "Unsaturated zone characterization in soil through

transient wetting and drying using GPR joint time-frequency analysis and grayscale images,"

Journal of Hydrology, vol. 452-453, pp. 1-13, 2012.

[11] W. L. Lai, T. Kind, S. Kruschwitz, J. Wostmann and H. Wiggenhauser, "Spectral absorption

of spatial and temporal ground penetrating radar signals by water in construction material,"

NDT&E International, (Paper Accepted), 2014.

[12] Hong Kong Institute of Surveyors Building,Surveying Division, Professional Guide to Water Seepage Investigation, Diagnosis, Testing & Reporting in Residential Buildings. Hong

Kong: Hong Kong : Hong Kong Institute of Surveyors, 2014, 2014.

[13] c. a. Balanis, Advanced Engineering Electromagnetics. New York: John Wiley & Sons,

1989.



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