ATTRIBUTE ANALYSES OF GPR DATA FOR HEAVY MINERALS EXPLORATION

Aycan Catakli Department of Applied Science University of Arkansas at Little

Rock, ETAS 101E, 2801 S. University Avenue, Little

Rock, AR, 72204 axcatakli@ualr.edu

Hanan Mahdi Arkansas Earthquake Center, GIT University of Arkansas at Little

Rock, ETAS 101C, 2801 S. University Avenue, Little

Rock, AR 72204 hhmahdi@ualr.edu

Haydar Al-Shukri Department of Applied Science University of Arkansas at Little

Rock, ETAS 300O, 2801 S. University Avenue, Little

Rock, AR 72204 hjalshukri@ualr.edu

Abstract—This study is a continuation for our previous work [1] depicting soil mineralogy using Texture Analysis (TA) of Ground Penetrating Radar (GPR) data. In addition to TA, Complex Trace Analysis (CTA), and Center Frequency Destitution (CFD) were applied to GPR data to predict the existence of buried heavy mineral deposits. CFD and CTA attribute were also used to determine the concentration of the buried heavy mineral deposits. The features of CTA are useful in showing changes of the potential energy components such as instantaneous energy. τ-parameter and Normal Distribution of Amplitude Spectra (NDoAS) were calculated from CTA to inspect the concentration of the buried samples and CFD was used to reveal energy allocations using spectral content of GPR data in time and frequency domain. GPR data collected from laboratory experiments using 1.5 GHz antenna were used in the study. The experiments were conducted using various heavy mineral samples with different concentrations.

Our previous study showed that buried minerals produced high entropy, contrast, correlation, standard deviation, and cluster, but these samples produced low energy, and homogeneity. Variance measure signifies edges of buried samples within host material. This study indicates that first and second derivatives of the envelope calculated from CTA emphasize the variation of the reflected energy and sharpen the reflection boundaries in the data. Instantaneous measures (energy and power) of envelope data reveal the existence of buried samples, while the frequency distribution of the data enables locating the contact of buried mineral. We found τ-parameter, NDoAS, and center-frequency proportionally increase with increased concentration of the mineral samples. The results from the three analyses, although in agreement with the previous work, they substantially improve the detection as well as quantifying the mineral concentration.

Keywords—Attribute Analyses; GPR; heavy minerals

I. INTRODUCTION This study is part of investigations funded by NASA to

explore the possibility of prospecting heavy minerals and predict areas with high concentration of those minerals on the Moon. High resolution images and detailed information of the nature of Moon’s subsurface are necessary. This requires investigating the Moon’s subsurface with high resolution techniques.

The main purpose of this study is to implement Ground Penetrating Radar (GPR) technology to explore heavy minerals of the Moon regolith. GPR method, a non-invasive technique based on the propagation of electromagnetic waves (EM), and its attributes have become attractive tools to investigate and map subsurface conditions. GPR method is a geophysical tool enabling high lateral and vertical resolution information about near-surface conditions. This method uses high frequency EM waves as a source to be transmitted underground. EM and Seismic waves are entirely analogous in their kinematic behaviors such as reflection and transmission at interfaces [2]. For this reason, data acquisition and processing procedures used in seismic method have been applied to GPR data.

Attribute analyses have been successfully used in seismic applications for many years, but its application to GPR is a new field. In this study, the attribute analyses of GPR data have been used to detect and identify heavy minerals within a host medium such as to the Moon regolith. We have applied these analyses to ground truth GPR data collected from several laboratory experiments. Laboratory data were used to calculate different features of these analyses. Details of the attribute analyses used in this study are given in the following section. The results are presented in Section IV.

II. ATTRIBUTE ANALYSES OF GPR DATA Attribute analysis has been used to emphasize the

information content of the data to enhance interpreter’s ability to determine, identify, and visualize detailed information of the subsurface. As a quantitative measure, attribute which has been calculated from the amplitude and frequency content of the EM signals can facilitate identification and interpretation of features in various fields such as geophysical applications. In addition to Texture Analysis (TA) that had been used in the previous study [1], Complex Trace Analysis (CTA), and Center Frequency Destitution (CFD) are applied to GPR data in this paper.

A. TEXTURE ANALYSIS (TA) Texture is one of the important attribute analyses that is

used for defining amplitude patterns by the magnitude and variation of neighboring amplitudes in the data. The analysis

supplies information regarding the spatial arrangements of pixels in the data. Gray-level co-occurrence matrix (GLCM) is very well-known tool, which is widely used to extract texture features. Reference [3] introduced the use of GLCM for definitions of textural features. GLCM represents co-occurrence numbers of the gray-level pairs and is characterized by the spatial distribution of intensity values of signals.

The analysis has been applied for different data sets such as synthetic aperture radar (SAR) data, medical images and infrared images. There are several studies dressing the application of texture analysis. Reference [4] investigated six statistical features of GLCM that are contrast, energy, variance, correlation, entropy, and inverse different moment. It emphasized that energy and contrast are the most efficient to discriminate different textural patterns. The new parameter was used to replace energy with contrast. It concluded that the computation of GLCM replaced the GLDH (Gray Level Difference Histogram) to benefit compromise texture measurement accuracy, computer storage, and computation time. Reference [5] used GLCM to single-date RADARSAT image and maximum likelihood supervised classifier was used for classification. The study concluded that wetland classification accuracy was improved using TA of a single-date RADARSAT image.

This analysis has been applied to seismic data in recent years. Reference [6] applied this analysis to 3D seismic data. They used GLCM to derive second-order statistics measures of TA. Application of this analysis to two 3D-data sets provided an enhanced picture of hydrocarbon bearing facies in reservoir. Reference [7] used statistical features of TA to seismic data to predict Mississippian limestone carbon potential. Their study concluded that this analysis is helpful to delineate hydrocarbon-bearing facies.

The application of TA to GPR data is a young field. Reference [8] used texture feature coding on GPR data to detect targets in 3D high resolution images. Reference [9] used geometric and texture attributes of 3D GPR data to visualize active faults. Reference [10] applied texture-based classification to GPR data to provide automated radar interpretation. Methodology of this analysis was presented in the previous paper (see Reference [1]).

B. CENTER FREQUENCY DESTITUTION (CFD) Spectral attributes are exciting research tools for

delineating frequency distribution of GPR data. CFD can improve the ability for characterizing and interpreting near-subsurface features. This attribute is used to quantify variations in frequency content. These variations can be associated with the presence of materials or structures having different physical and/or EM properties. This analysis can be used to reveal energy allocations using spectral content of the data in time and frequency domain. Spectral decomposition is an important method in reservoir and gas characterization and exploration [11]. This spectral information has also been used to exhibit low-frequency shadows that represent carbonate gas reservoirs. Low-frequency shadows, which are present in the data because of attenuation, have been used as direct hydrocarbon indicator [12]. Instead of the shadow idea, some authors also have been reported high frequency anomalies in

seismic data [12, 13, 14, 15]. These high frequency anomalies are related to thin-bed tuning which defines bed thickness being less than one-quarter of the wavelength. The reflection coefficients of these structures are larger than those in adjacent areas. Reference [16] used this analysis to calculate dispersion distribution of GPR data. The result of the study clearly illustrated that increased or decreased dispersion of GPR data correlates with high or low conductive structures of subsurface. Reference [17, 18] used this analysis to investigate the response of GPR data to thin sedimentary layers. They concluded that spectral shifts towards high frequency can be used as indicator of thin beds. Reference [19] used t-f analysis to obtain amplitude spectrum of the data. The spectrum information of GPR data was used to calculate Quality (Q) factor from frequency-shift method and then inverse-Q filter was applied to data to remove wavelet dispersion from GPR data to enhance data quality. Spectral characteristics are helpful to define average frequency content of the GPR data. Time-frequency (t-f) analysis methods especially improve attribute extraction. The estimation of spectral content should be conducted to quantitatively observe spectral changes within the data. There are some methods such as Fast Fourier Transformation (FFT) or wavelet transformation methods available to derive frequency changes versus time, but they are limited to resolve power spectrum [20]. In this paper, Stockwell (S) transform has been selected to calculate t-f representation of individual signals of the data.

The center frequency destitution was derived from center frequency equation [20, 21] using t-f representation of each signal obtained from S-transform,

1

1

( )

( )

N

ic N

i

fA ff

A f

=

=

=∑

∑ (1)

This analysis is notably able to allow observing frequency variations per signal.

B.1. Stockwell Transform (S-transform) To derive frequency content of the data versus time, S-

transform was applied to the data. This transform was used to characterize the data by transforming the data at each point in time with a series of windowed harmonics of various frequencies [19, 22]. Thus, it yields true measure of frequency content of the data. This transform is also defined as a hybrid of wavelet transform (WT). It has an advantage, because it can supply multi resolution analysis as preserving the absolute phase of each frequency [23] and window function has scalable length depends on frequency content of the window [24]. This transform is given as,

( ) ( )2

| |( , ) ( ) exp exp 222

ττ π

π

∞

−∞

⎛ ⎞−⎜ ⎟= − −⎜ ⎟⎝ ⎠

∫tfST f h t i ft dt (2)

where h(t) is the signal in time domain, τ is the translation parameter, first exponential term is the window and second exponential term represents harmonic functions.

C. COMPLEX TRACE ANALYSIS (CTA) Complex Trace Analysis has gained popularity as a

convenient display tool and been used to interpret data. Transformations are signal processing methods which convert the data from one form to another. For example Fourier Transform allows extracting average properties of signal from frequency content of the data; however, these methods do not allow examining local variations of data [25]. CTA, which is one of the seismic attributes used in oil/gas explorations, has been applied to identify the physical properties of the subsurface since 1970s. A complex trace is a series represents a combination of instantaneous amplitude and phase used to separate instantaneous amplitude (envelope) and phase information from each other. Instantaneous amplitude represents reflection strength and capable of draw differences in impedance, so it can give clearer images of lithology, hydrocarbons and thin-bed tuning. Also, instantaneous amplitude reduces the appearance of random signal in the data. Instantaneous phase is used to follow reflector continuity and to detect lateral changes in stratigraphy. Instantaneous frequency is also useful in specifying abnormal attenuation and thin bed-tuning [26].

The classic way of estimating instantaneous parameters of the signal is to use analytic signal. The real part of the analytic signal is the original signal and imaginary part of the signal is found from Hilbert transform (HT). HT is a rotator used to derive 900 of phase from GPR signal. As instantaneous amplitude represents maximum value of the amplitude of a signal, instantaneous phase is used to rotate the signal to maximum amplitude value. Instantaneous phase is found by comparing imaginary part with real part of the analytic signal and the instantaneous frequency is the time rate of change of the instantaneous phase angle [27]. The variations of these parameters are closely associated with geometry and physical properties of the medium where the signal propagates. All measures of the complex trace analysis are measured from envelope and phase by taking average, differentiation and combination [28].

Only a few studies discuss the application of the complex trace analysis to GPR data. Reference [29] used the instantaneous amplitude of GPR data to evaluate physical properties of the investigated subsurface by comparing Time Domain Reflectometry (TDR) data. CTA helped to improve the quality of GPR data and to map spatially soil electrical properties in the shallow-subsurface. Reference [30, 31] applied Complex Trace Analysis to GPR data to improve identification of gem-tourmaline-bearing pegmatites in Himalaya Mines, CA. Reference [32] used GPR data to detect Light Non-Aqueous Phase Liquid (LNAPL) floating on the water table. They used both the GPR data and some attributes of the complex trace analysis to detect hydrocarbons floating on the water table. Reference [33] integrated GPR data and micro gravimetric methods to map karstic features. In their study, they applied CTA to GPR data to obtain more confident interpretation of karstic cavities. They emphasized that the analysis is a helpful tool used to delineate and characterize the boundaries of cavities and to produce clearer images of changes that unexpectedly happen and reflections from complex subsurface systems in the data. Reference [34]

mapped archaeological features in urban area using GPR method. They created iso amplitude maps of instantaneous amplitude to visualize complex information on the data.

The complex trace analysis is one of the attributes which can be classified by instantaneous attributes. Those attributes have been calculated sample by sample and useful to define instantaneous parameters such as envelope and its derivatives, instantaneous frequency, and phase. Here, envelope data, first derivative, second derivative of the envelope data with respect to time, Instantaneous Energy, Instantaneous Power, τ parameter and Normal Distribution of amplitude Spectra (NDoAS) are calculated and the results of those instantaneous parameters are presented.

C.1 Methodology of the Analysis By using analytic signal, a GPR trace can be represented

by its envelope and phase component. If y(t) is the real signal (also called trace in this study),

( ) ( ) cos ( )y t a t tθ= (3)

and the imaginary part of the signal is given by,

( ) ( ) sin ( )y t a t tθ∗ = (4)

The real signal and Hilbert transform of the signal are used to derive analytic signal. y* (t) is given by Hilbert transform as

* 1 1( ) ( ) ( )y t y t y t dt tτ

τ τπ π

∞

=−∞

= ∗ = −∫ (5)

and analytic signal can be expressed as, ( )( ) ( ) ( ) ( ) j tY t y t jy t A t e θ∗= + = (6)

when real and imaginary parts of the analytic signal are known, instantaneous amplitude (or envelope) and phase can be calculated [25],

2 *2( ) ( ) ( ) ( )A t y t y t Y t= + = (7)

and

( )1 *( ) tan ( ) / ( )t y t y tθ −= (8)

Instantaneous energy is calculated from the square of envelope as instantaneous power is found by first derivation of the instantaneous energy relative to time. Instantaneous Energy and Instantaneous Power are given as [35],

2Instantaneous Energy=E ( )A t= (9)

Instantaneous Power dE dt= (10)

NDoAS is given as [36],

( )( )22 ( ) / 2 ( )dA t dt A tσ π= (11)

According to [37], first derivative of the is the time rate change of envelope, illustratesthe energy of reflected events. Second denvelope supplies the sharpness of the enveluseful to define reflecting interfaces. Rise timis defined as;

( )max

max

AdA dt

τ =

III. GPR LABORATORY EXPERIMENT PROCESSING

Several laboratory experiments were condGPR data using Geophysical Survey System 3000 system with 1.5 GHz central frequeantenna. Fig. 1 illustrates the GPR system usdata and the experiment box filled with quartzmineral sample was buried.

(a)

Figure 1. GPR system with 1.5 GHz antenna and experisand (a), a heavy mineral sample embedded i(b).

Two GPR data sets were used to produce attribute analyses in this paper. The first conducted by using ilmenite sample. Total samabout 98 gram. For the second experiment, a mixture of ilmenite and sand was embedded inlayer and the concentration of ilmenite waillustrates these samples used to conduct the ex

TABLE I. Heavy mineral samples embedded within the laboratory experiments.

GPR Data Heavy Mineral SLData1 Ilmenite LData2

Ilmenite-Soil

After data acquisition, data processing steto GPR data. Zero-time set was applied to mzero time. Background removal was appliedarrivals, which are air and ground waves, from

IV. RESULTS In this study, MATLAB was used to i

analyses and obtain the results. The followinresults obtained from these analyses.

envelope, which s the variation of erivative of the lope peak and is

me or τ-parameter

(12)

AND DATA

ducted to collect Inc. (GSSI) SIR

ency monostatic sed to collect the z-sand where the

(b)

iment box filled with inside the sand layer

the results of the experiment was mple weight was sample that was

nside a host sand as %17. Table I xperiments.

soil layer to conduct

Samples 98 gr

%17

eps were applied move start time to d to remove first m GPR data.

implement these ng part shows the

A. Results of TA A transformation of the gray

features of TA computed from GLthe calculations of TA. GPR data wgray-levels and 8 bit or 256 gray-lethe two cases did not yield significacalculated measures. We selected speed of calculations is increased decreased. Displacement is generaldata. In our calculations, we chose tand zero angle was used for aparameter used to define GLCM is the calculations, the size of the winAfter deciding on the parameters, tool to calculate the statistical featthus obtained various textural imaggiven in Fig. 2-13.

Figure 2. Processed LData

Figure 3. Autocorrelation texture attribute sdue to buried heavy mineral sampl

Figure 4. Cluster texture attribute; high cluheavy mineral sample.

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y levels of an image and LCM were implemented for were rescaled as 6 bit or 64 evels and it was found that antly different results in the 64 gray-levels so that the and the computing time is ly related to the size of the the displacement factor as 1 all calculations. The last the size of the window. For ndow was selected as 3×3. the GLCM was used as a

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a1 radar section.

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Figure 5. Contrast measure of TA shows high values are associated with buried heavy mineral sample.

Figure 6. Correlation texture measure of high values due to buried heavy mineral sample.

Figure 7. Dissimilarity texture measure: high dissimilarity values due to

buried heavy mineral sample.

Figure 8. Texture energy; Low values of the energy measure correspond to the

buried heavy mineral sample.

Figure 9. Entropy texture measure defining the buried sample with high entropy values.

Figure 10. Homogeneity texture measure of low values around buried heavy mineral sample.

Figure 11. Maximum probability measure showing the buried sample with low

values of maximum probability.

Figure 12. Standard deviation measure of TA shows buried heavy mineral

samples with high values.

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Figure 13. Variance texture attribute showing the edges of the anomaly.

B. Results of CTA B.1. Results of Instantaneous Parameters The features of CTA have been calculated to detect and

estimate the concentration of the heavy minerals embedded within host medium. In here, first derivative of the envelope, which is the time rate of change of envelope, was used to recognize possible absorption effects and second derivative of the envelope was applied to detect reflecting interfaces. Instantaneous energy and power parameters were also calculated. Fig. 14-19 illustrate results of CTA features.

Figure 14. Processed LData1 GPR section.

Figure 15. Envelope of the GPR LData1.

Figure 16 1st derivation of envelope data with respect to time showing most

energy variation around the buried heavy mineral sample.

Figure 17. 2nd derivation of envelope data with respect to time indicating the

reflecting boundary.

Figure 18. Instantaneous Energy measure of CTA clearly showing the buried

sample.

Figure 19. Instantaneous Power measure section clearly defining the buried

sample.

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B.2. Results of τ-parameter and NDoAS parameter NDoAS and τ-parameter measured from CTA have been

used to estimate qualitatively the concentration/weight of heavy mineral samples. The results of these parameters are illustrated in Fig. 20-23. The same color scales were used in order to compare the calculated values of these parameters.

Figure 20. τ-parameter section obtained from CTA for LData1.

Figure 21. τ-parameter section obtained from CTA for LData2.

Figure 22. NDoAS measure of CTA for LData1.

Figure 23. NDoAS measure of CTA for LData2.

C. Results of CFD The goal of this section is to show the detection ability of

CFD analysis to buried heavy minerals and to find a correlation between frequency distribution and the concentration of the heavy minerals. The power of spectral analysis is that the analysis allows the transforming of GPR data into its individual frequency content. Background removal, which is one of the basic data processing technique used to remove first arrivals that is air and direct ground waves, was not applied to the data. Some applications of data processing steps showed that this technique changes spectral content of the data. Thus, first arrivals were not removed from the data to preserve the original frequency content. The spectrum variations of the data were estimated trace by trace in order to derive spectral information. Fig. 24-27 illustrate the results of center frequency destitution of the data sets derived from the analysis.

Figure 24. 1.5 GHz Raw LData1 radar section.

Figure 25. Center frequency distribution section of LData1.

Figure 26. 1.5 GHz Raw LData2 radar section.

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Figure 27. Center frequency distribution section of LData2.

V. CONCLUSIONS In this study, we have presented the applications of the

attribute analyses to GPR data for exploration of heavy minerals embedded within a background medium. The findings of the study can be summarized as;

1. The results of texture analysis show that buried heavy minerals cause high entropy, contrast, correlation, autocorrelation, standard deviation, dissimilarity and cluster. The buried sample produces low energy, maximum probability, and homogeneity. The results presented in this paper show that variance is able to detect edges of the anomalies. Contrast, autocorrelation, correlation, dissimilarity, and standard deviation enables emphasizing the contrast between buried heavy mineral samples and host medium. In addition, these features are able to locate buried sample inside the background medium. Cluster can visualize more clearly reflections caused by buried samples.

2. CTA can be used as a tool to predict buried heavy mineral samples embedded within the soil layer. The results of the measurements of the analysis prove that first derivative of the envelope indicates variation of the reflected energy around buried sample and second derivative of the envelope can identify the reflecting interface in the data. Instantaneous energy and power measures of envelope data are able to reveal the presence of buried samples.

3. CFD may be used to improve detection of buried mineral samples. The results clearly indicate that the frequency distribution of the data enables locating the contact of buried mineral samples. CFD analysis can detect thin mineral layers as high-frequency anomalies.

4. The results of τ-parameter and NDoAS calculated from CTA as well as center-frequency from CFD show a relation between the calculated values and the amount of the heavy minerals. The results of this study point out that these parameters increases with increasing concentration of the mineral samples.

ACKNOWLEDGMENT The work was supported by a NASA EPSCOR grant. The

authors wish to thank Hussein Khalefa Chlaib, Julien Szumilas, Sebastien Maganuco, and Giovanni Fontaine for lab assistance.

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[4] A. Baraldi., 1995. An investigation of the textural Characteristics associated with grey level co-occurrence matrix statistical parameters. IEEE Transactions on Geoscience and Remote Sensing, vol. 33, p. 293-304.

[5] S. Arzandeh, and J. Wang., 2002. Texture Evaluation of RADARSAT imagery for wetland mapping. Canadian Journal of Remote Sensing, vol.28, p. 653-666.

[6] S. Chopra and V. Alexeev., 2006. Applications of texture attribute analysis to 3D seismic data. The Leading Edge, vol. 25, p. 934-940.

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[10] S. R. Moysey, J. Knight. and H. M. Jol., 2006. Texture-based classification of ground-penetrating radar images, Geophysics, v. 71, n.6, K111-K118.

[11] G. Chen., G. Matteucci., B. Fahmy, and C.Finn., 2008. Spectral decomposition response to reservoir fluids from a deepwater West Africa reservoir. Geophysics, vol. 73, no. 6, p. C23-C30.

[12] Y. Li., X. Zheng, and Y. Zhang., 2011. High-frequency Anomalies in Carbonate Reservoir Characterization Using Spectral Decomposition. Geophysics, vol. 76, no. 3, p. V47-V57.

[13] A. Chakraborty, and D. Okaya., 1995. Frequency-time decomposition of seismic data using wavelet based methods. Geophysics, vol.60, no. 6, p.1906-1916.

[14] H. Chung, and D. C. Lawton., 1995. Frequency Characteristics of Seismic Reflections from Thin-beds. Canadian Journal of Exploration Geophysics. Vol. 31, p. 32-37.

[15] M D. Burnett., J. P. Castagna., E. Mendez-Hernandez., G. Z. Rodriguez., L. F. Garzia., J. T. M. Vazquez., M. T. Aviles, and R. V. Villasenor., 2003. Application of Spectral decomposition to gas basins in Mexico. The Leading Edge, vol.22, p.1130-1134.

[16] J. H. Bradford., 2007. Frequency-dependent attenuation analysis of ground-penetrating radar. Geophysics, vol.72, p.J7-J16.

[17] S. Guha., S. Kruse, and P. Wang., 2008. Joint time-frequency Analysis of GRP data over layered sequences. The Leading Edge, p.1454-1460.

[18] S. Guha., S. E.Kruse., E. E. Wright, and U. E. Kruse., 2005. Spectral Analysis of Ground Penetrating Radar

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