Elsevier

Journal of Applied Geophysics

Attenuation analysis of real GPR wavelets: The equivalent amplitude spectrum (EAS)

Abstract

Absorption of a Ground Penetrating Radar (GPR) pulse is a frequency dependent attenuation mechanism which causes a spectral shift on the dominant frequency of GPR data. Both energy variation of GPR amplitude spectrum and spectral shift were used for the estimation of Quality Factor ( Q *) and subsequently the characterization of the subsurface material properties. The variation of the amplitude spectrum energy has been studied by Spectral Ratio (SR) method and the frequency shift by the estimation of the Frequency Centroid Shift (FCS) or the Frequency Peak Shift (FPS) methods. The FPS method is more automatic, less robust. This work aims to increase the robustness of the FPS method by fitting a part of the amplitude spectrum of GPR data with Ricker, Gaussian, Sigmoid–Gaussian or Ricker–Gaussian functions. These functions fit different parts of the spectrum of a GPR reference wavelet and the Equivalent Amplitude Spectrum (EAS) is selected, reproducing Q* values used in forward Q* modeling analysis. Then, only the peak frequencies and the time differences between the reference wavelet and the subsequent reflected wavelets are used to estimate Q*. As long as the EAS is estimated, it is used for Q* evaluation in all the GPR section, under the assumption that the selected reference wavelet is representative. De-phasing and constant phase shift, for obtaining symmetrical wavelets, proved useful in the sufficiency of the horizons picking. Synthetic, experimental and real GPR data were examined in order to demonstrate the effectiveness of the proposed methodology.

Introduction

Absorption of Electromagnetic (EM) waves is a frequency dependent attenuation mechanism. Higher frequency harmonics of Ground Penetrating Radar (GPR) pulses attenuate rapidly with distance causing the reduction of resolution with depth (Annan, 1996, Bano, 1996) and a spectral shift of GPR data dominant frequency. This frequency dependent attenuation phenomenon can provide information for the subsurface, by evaluating the attenuation or the quality factor of GPR targets. Turner and Siggins (1994) proposed an approximation of the frequency dependent component of GPR attenuation using a frequency independent quality factor (Q*). There are several available methods for the estimation of Q* by analyzing the spectral variation of GPR records.

Both total energy variation of GPR amplitude spectrum and spectral shift were used for the characterization of the subsurface material properties. The variation of the amplitude spectrum energy has been studied by spectral ratio (SR) methods (e.g. Harbi and McMechan, 2012) and the frequency shift by the estimation of the Frequency Centroid (FCS) or the Frequency Peak Shift (FPS) (Liu et al., 1998, Quan and Harris, 1997, Bradford, 2007). Q* estimation using surface GPR data also includes the scattering attenuation which means that the estimated attenuation factor is really an apparent value (Bradford, 2007). However, it provides valuable subsurface information such as lateral variations of subgrade layers in road construction.

According to Turner and Siggins (1994) Q, used in seismics and Q* factors differ only on the total amplitude variation. Thus, simulation procedures, designed for the Q factor, can be used for the study of the Q* factor as well. de Castro Nunes et al. (2011) studied the estimation of Q on zero-offset synthetic seismic data. They ranked the spectral variation frequency analysis methods in terms of automation from simple to complex in sequence FPS, FCS and SR, while in terms of robustness when applied on noisy data, in the reverse order. Cheng and Margrave (2012) used a wavelet fitting method on surface seismic reflection data which is similar to SR method and computes a matching filter in time domain, in an effort to increase robustness. The main advantage of SR methods is that they are independent from the source spectrum. However, SR and FCS methods' complexity and robustness lie on the choice of an effective bandwidth of both the reference and the studied wavelet's amplitude spectra (Haase and Stewart, 2003). Another drawback of these two methods when dealing with real data is that GPR wavelets overlap each other.

On the other hand, the FPS is characterized by a high degree of automation, especially when cumulative Q* (or Q) estimation is utilized (Bradford, 2007, Zhang and Ulrych, 2002). This requires the study of the reference amplitude spectrum and only the peak frequency values of the subsequent events. Robustness of the FPS method depends on the estimation of time difference between the reference wavelet and the subsequent events as well as the frequency peak shift.

The problem of the peak frequency value accuracy mainly depends on the signal-to noise-ratio (SNR) and the sample interval in frequency domain. Assuming that the estimation of peak frequency of GPR wavelets is accurate using the Fast Fourier Transform (FFT), then the sample interval in frequency domain can be sufficiently enhanced by sinc-interpolation (zero-padding in time domain). For relatively low SNR and/or overlapping wavelets, the multi-taper method for spectrum smoothing can be used (Thomson, 1982, Cheng and Margrave, 2012). However, clear wavelets, with high SNR and no overlapping, are preferred when dealing with spectral analysis, as only the sinc-interpolation does not add information to the data. The evaluation of time difference between reference wavelet and a reflected event is another crucial aspect and certainly requires high SNR data. Bandpass filtering may enhance the efficiency of this procedure and deconvolution may aid in calculating the time differences between reflectivity series (Economou and Vafidis, 2011, Economou, 2015). Regarding the reference wavelet spectrum, the Ricker wavelet and the Gaussian distributions have been widely used by many researchers to fit the amplitude spectra of real GPR data (Liu et al., 1998, Quan and Harris, 1997, Bradford, 2007). Quan and Harris (1997) proposed trying to model GPR signal using boxcar and triangular shaped amplitude spectra.

The main problem of real GPR wavelets is that their amplitude spectra are rarely symmetrical, with respect to a vertical axis passing through their maxima and they are not Ricker spectra (Zhang and Ulrych, 2002). In an effort to increase the robustness of the FPS method for GPR data, several real GPR wavelets from devices of different manufacturers propagating in different media were used as reference wavelets. The Ricker, Gaussian, Ricker–Gaussian or Sigmoid–Gaussian (Stancik and Brauns, 2008) functions are fitted through the corresponding pass band of the reference wavelet. Since the real wavelet spectrum is replaced by a known analytical function, only the peak frequencies and the time differences between the reference wavelet and the subsequent reflected wavelets are used to estimate Q*. The sufficiency of the proposed approach in this work is demonstrated using synthetic, experimental and field data. A list of all abbreviations and symbols used is given in Table 1.

Section snippets

Relating Q* to the frequency peak shift

According to the linearization of the attenuation by Turner and Siggins (1994), the attenuation of an EM wave, α, is related with Q* as (Bano, 2004): a f ≈ a 0 + πf μ 0 ε ′ Q * where α 0 is the initial value of attenuation (α), ε′ is the real part of the complex dielectric permittivity at frequency f and μ0 is the magnetic permeability. Turner and Siggins (1994) showed that Q* is a generalization of Q, which means that when a 0 is equal to zero in Eq. (1), then Q*   = Q. By studying only the change in a pulse

Examples using synthetic and real GPR wavelets

In order to study the performance of the proposed methodology, a synthetic trace was created by convolving a reflectivity series with a 900   MHz Ricker wavelet (Fig. 2a). Time interval and record length was set to 0.1   ns and 30   ns, respectively. The same trace was subjected to non-stationary convolution, as applied in seismics (Q   =   30, Margrave, 1998) (Fig. 2b). The first 15   ns of the trace correspond to the reference wavelet while the rest 15   ns of the same trace resemble its reflection wavelet

The water box

The example presented here is similar to the one performed by Turner and Siggins (1994). In this experiment, a metal plate was placed in a plastic tank with dimensions W   ×   L   ×   H   =   0.9   ×   1.6   ×   0.6   m filled with water. Turner and Siggins (1994) used the Debye approximation and calculated a Q* value of 14 for water. They confirmed the same Q* value from real measurements with a 900   MHz antenna. The current experiment was implemented by placing the GPR device above the water surface. A clear reflection from

Field data

Non-destructive characterization of road subgrade layers is of great importance regarding the safety and the maintenance of road networks. Road maintenance is a costly issue, which leads to the need of research for cost–benefit assessments (Benedetto and Pensa, 2007, Patriarca et al., 2013). GPR proved to be a useful tool for non-destructive road inspection and condition monitoring (Loizos and Plati, 2007). Patriarca (2013) and Patriarca et al. (2013) studied the influence of clay on the

Discussion

The real GPR wavelets amplitude spectrum is rarely Gaussian or Ricker. In an effort to make the peak frequency attenuation analysis method more robust, a methodology is developed which fits a user defined function through part of the amplitude spectrum of a reference wavelet. This method can be automated and is useful in the most GPR applications where a large number of data is acquired. From the analysis of several real GPR wavelets, it has been observed that the Ricker function provides a

Conclusions

In this work, a methodology to enhance the robustness of attenuation analysis of the GPR signal is proposed. This methodology highlights that Ricker or Gaussian functions are not always the best solution for describing the amplitude spectrum of GPR traces and other functions should also be tested. The Equivalent Amplitude Spectrum (EAS) is introduced here, which can substitute the spectrum of the real GPR signal, since it reproduces the same attenuation characteristics. The EAS for 1200   MHz

Acknowledgments

We would like to thank Mr. Kleisthenis Dimitriadis and the company Geoservice (http://www.geoservice.gr/) for providing the "Field data".

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