Texture Analysis of GPR Data as a Tool for Depicting Soil Mineralogy

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—For the past decade, texture analysis has become one of the quantitative attributes used extensively in seismic studies for target detection and interpretation of subsurface anomalies, such as moisture content and landmines in inhomogeneous soil. The application of this analysis has been limited to other geophysical techniques, such as Ground Penetrating Radar (GPR). GPR is a non-invasive method based on the propagation of electromagnetic waves to derive a model for the subsurface. In general, interpreting GPR data is primarily qualitative and depends on the expertise of the analysts. The goal of this study is to verify the ability of texture analysis technique to differentiate soil mineralogy.

We have developed and tested a Matlab code that derives various texture measures such as energy, homogeneity, contrast, and entropy. Those statistical measures are generated using a gray-level co-occurrence matrix (GLCM). The measures supply different information about the data, such as uniformity or complexity; thus, they can produce different features in the GPR data when they are used together. We tested the texture analysis code on synthetic GPR data sets that have been derived for two different models with two different heavy minerals, ilmenite and spodumene embedded inside a host medium. To obtain synthetic data, we used GPRMax2D software which applies the Finite-Difference Time-Domain method (FDTD) to simulate various subsurface scenarios. In addition to the synthetic data, real GPR data that had been collected from a prototype laboratory experiment were used.

The calculated statistical features and results show that ilmenite has higher entropy, dissipation, and contrast measures than spodumene. On the other hand, spodumene shows higher energy and homogeneity features than ilmenite. Based on the synthetic data results, the combination of the texture-based analysis measures can be used as an enhanced interpretation tool that clearly brings out the distinction between minerals. The texture results computed from ground-truth GPR data show that heavy mineral bodies can be identified due to their high contrast, entropy, correlation, standard deviation, and low energy and homogeneity. Variance measure of texture analysis can help to

highlight the edge of the buried samples. Cluster indicator is more effective in visualizing the anomaly than the raw data.

Keywords-component; Texture analysis; GLCM; GPR; heavy minerals

I. INTRODUCTION Attribute analysis has been used to emphasize the

information content of the data. Thus, the analysis can enhance interpreter’s ability to determine, identify and visualize detailed information. As a quantitative measure, attribute which has been calculated from the amplitudes of the signals can facilitate identification and interpretation of features in various field such as geophysical applications. Texture is one of the important attribute analysis which was firstly introduced by [9] for image processing. Reference [8] describes that texture as ‘an everyday term relating to touch that includes such concepts as rough, silky, and bumpy. When a texture is rough to touch, the surface exhibits sharp differences in elevation [15]. Texture analysis can be mathematically described as the statistical measures of amplitude values in the data. In the analysis, amplitude patterns are defined by the magnitude and variation of neighboring amplitudes in the data. Gray-level co-occurrence matrices (GLCMs) are used to estimate second-order statistics, such as energy, and contrast. The GLCMs are well-known and widely used to extract texture features and represent the probability of occurrence of grey-levels with a pre-determined offset in the data.

Texture analysis has been commonly used to increase classification accuracy in remote sensing. The analysis has been applied to different data sets such as synthetic aperture radar (SAR) data, and infrared images. There are several studies relating to the application of texture analysis. For example, Reference [1] used the analysis to assess correlations between texture measurers as a function of segmentation scale while mapping rangeland vegetation structure groups using 5-cm resolution true-color aerial photography. Reference [13]

used the texture analysis for mapping sea ice-patterns. Available texture measures were evaluated to determine the best parameter values and to create representations for mapping sea ice texture.

In seismic method, various attributes have been used to map geologic features that are associated with reservoir, migration and interpretation since 1930s [3]. Texture attribute analysis has been extensively used and applied to 3D surface seismic data in petroleum industry. In seismic studies, texture analysis was introduced by [10] who used the analysis to draw patterns of seismic signal character. Recently, seismic method has used statistical measures to identify and classify patterns by using GLCMs [6], [16]. Some of the statistical measures that have been used are energy, which represents textural homogeneity; entropy, which indicates disorder or complexity; and contrast, which shows local image variations.

In this study, we applied texture analysis to GPR data to identify mineralogy. GPR method is a geophysical tool enabling high lateral and vertical resolution information about near-subsurface and its application is similar to seismic reflection method. Application of the texture analysis in the GPR field is fairly new which resembles its application to seismic data. Reference [4] used texture feature coding on GPR data to detect targets in 3D high resolution images. Reference [11] used geometric and texture attributes of 3D GPR data to visualize active faults. Reference [12] applied texture-based classification to GPR data to provide automated radar interpretation, thus provides quantitative criteria as a helpful tool in the classification of GPR data.

The aim of application of the analysis is to depict heavy minerals embedded within the host layer. Heavy minerals are characterized by high specific gravity and tend to accumulate in the deposits at river channels or along coastal shorelines. Most important concentration of minerals would be found in the beach-sand deposits. These deposits include the titanium minerals of ilmenite, leucoxene and rutile. Heavy minerals are primary sources used to manufacture some materials such as paint, varnish and plastics.

We have tested various statistical measures of texture analysis as indicating to the presence of heavy minerals. The analysis was applied to synthetic data as well as ground truth GPR data. GprMax was used to simulate 2D subsurface configuration and calculate synthetic GPR data. The aim was to show the effect of different mineralogy by using texture analysis. In the modeling study, we assumed two kinds of heavy minerals, ilmenite and spodumene, buried in soil layer. In laboratory experiments, we used heavy mineral samples buried within quartz-sand and we used this prototype experiment to collect numerous GPR profiles. Then the synthetic and laboratory data were used to calculate different statistical measures such as energy, entropy, homogeneity and variance.

II. METHODOLOGY Reference [9] introduced the texture analysis used in

identification of the objects in various images like a satellite image, aerial photograph, or a photomicrograph. They suggested 14 textural measures, which can be calculated from

GLCMs. The matrix, also called Gray-level Dependency matrix, provides a second-order method that generates various textural features by using different radius and orientation. The matrix is identified as a histogram of grey levels which shows how many times a pair of pixels appears in the matrix. Radius or displacement is generally chosen as 1. Some studies illustrate that the value of the displacement changes from 1 or 2 to 10. Large displacement would produce GLCMs which can’t represent detailed textural information [5]. In GLCMs, an angle between the pixel of interest and its neighbor has four options which are 00, 450, 900 and 1350. Offsets corresponding to every angle is given as [0 d], [-d d], [-d 0] and [-d -d] where d is displacement. In a chosen window, every pixel has eight neighbors for angle, which are 00, 450, 900, 1350, 1800, 2250, 2700, and 3150. Co-occurrence pairs would have the similar value for 00 and 1800, 450 and 2250 so on. Thus, given four options above can be enough for selection of an angle. A GLCM is a square matrix that its size is determined by gray levels. Gray levels mean the dynamic range of the data. Rescaled data would be 4-bit (matrix size is 16×16) or 6-bit (256×256 matrix). Reference [2] suggests that different gray-levels don’t produce any significant results of texture measures in practice. On the other side, Reference [5] mentioned that more levels can produce more accurate results of texture measures. It seems that there is not any single option to choose the value of gray-levels.

Most of the texture measures are included in four statistical measures, which are energy, entropy, homogeneity and contrast. Those are most useful texture properties to produce the desired discrimination between different reflections patterns in the data [2], [11], [15]. Energy, which is called uniformity, is a measure that gives information on texture uniformity. High energy value happens when distribution of gray-level is a constant. Homogeneity, is also called inverse difference moment, represents similarity of pixels and is used to indicate smoothness of the amplitude [6] and has high value for GLCM with elements distributed near the diagonal. Energy and homogeneity are helpful to draw reflector continuity [11], [2]. Contrast gives local variations and differences between neighboring amplitudes. When there is a large amount of local variation exists in the data, GLCMs elements are scattered from diagonal and the measure has high value [9], [11]. The measure is the spatial frequency of an image and is also called difference moment of GLCM. Entropy is a statistical measure of the texture analysis and gives disorder or complexity of the data. The measure has large value for non-uniform data which generally produce low GLCM values. It means that complex textures tend to have high entropy value. Entropy is inversely related to energy measure of texture attribute. Correlation indicator measures correlation between the pixels of GLCMs. If data has high correlation, it means that data is complex. The other indicator is the cluster which reflects data symmetry. If the measure has high value, it indicates that data is not symmetric. Variance indicator is a measure of heterogeneity and has high values when the gray-level values are different from their mean [5].

Equations used to define the GLCMs-based statistical measures are given by the following formulas [9], [13].

∑∑= =

=g gN

i

N

jjiPEnergy

1 1

2, (1)

∑∑= =

−=g gN

i

N

jjiji PPEntropy

1 1,, log

(2)

ji

N

i

N

jP

jiyHomogeneit

g g

,1 1

2)(11∑∑

= = −+= (3)

ji

N

i

N

jPjiContrast

g g

,1 1

2)(∑∑= =

−= (4)

∑∑= =

−−=

g gN

i

N

j yx

jiyx PjinCorrelatio

1 1

,))((σσ

μμ (5)

ji

N

i

N

jPjiityDissimilar

g g

,1 1

||∑∑= =

−= (6)

( ) ( )( ) ji

N

i

N

jji PjideClusterSha

g g

,

3

1 1∑∑= =

−+−= μμ (7)

( ) ( ) xyy

N

i

N

jx PjPiVariance

g g2

1 1

2 μμ −−= ∑∑= =

(8)

Pij, μx, μy , σx and σy are (i,j)th element of GLCM, means and standard deviations or row and column sums, respectively. Px and Py are obtained by summing rows and columns of the elements of GLCMs. Ng is the number of gray-levels.

III. APPLICATION OF TEXTURE ANALYSIS TO GPR DATA

In this study, a transformation of the gray levels of an image, and some features computed from the matrix were implemented in Matlab. Gray-level elements are stored as an array of bits. GPR data were rescaled as 6 bit or 64 gray-levels and 8 bit or 256 gray-levels and it was found that the two cases did not yield significantly different results in the calculated measures. We selected 64 gray-levels so that the speed of calculations is increased, and the computing time is decreased. The other factors used in the computations are displacement and angle. Displacement is generally related to the size of the

data. In our calculations, we chose the factor as 1. As for the angle, we found that the results obtained by using different angles did not produce important differences in the computed properties, so zero angle was used for all calculations. The last thing is the size of the window. For all calculated images, the size of the window was selected as 3×3. After deciding on the parameters, the GLCMs was used as a tool to calculate the statistical features at each window, and thus obtained various textural images.

A. Application for Synthetic Data Numerical modeling of GPR is a useful tool to help

understanding GPR method’s detection mechanism. Synthetic models were derived in order to be used for texture analysis. This was the first step in our study in order to assess the possibility of depicting heavy minerals buried inside soil layer by using texture analysis. GprMax software was used to simulate subsurface configuration. The software uses Finite Difference Time Domain (FDTD) method which was pioneered by [14] and widely used to simulate subsurface. The method provides numerical solution of Maxwell’s equations in time domain [7].

The dimension of the synthetic model used to texture analysis was 2×1.5 m (Fig.1) and source signal used was Ricker pulse centered at 750 MHz. In our models, two kinds of heavy minerals were separately embedded inside a soil layer that has a dielectric constant, εs, of 1.7. One of these minerals is ilmenite and the other is spodumene. A dielectric constant, εi, of 4.05 and electrical conductivity, σ, of almost zero S/m was used for ilmenite and a dielectric constant, εi, of 2.28 and electric conductivity, σ, of almost zero S/m was used for spodumene.

(a)

(b)

Figure 1. (a) Synthetic modeling of GPR Data, (b) Synthetic GPR section corresponding to the configuration

B. GPR Laboratory Experiment and Data Processing Several laboratory experiments were conducted to collect

GPR data using Geophysical Survey System Inc. (GSSI) SIR 3000 system with 1.5 GHz central frequency monostatic antenna. Fig.2 illustrates the GPR system used to collect the data and the experiment box filled with sand where the mineral sample to be buried. For the sake of brevity, we present five data sets and computed features corresponding to each one. For the first experiment, a mixture of sand and AR River at Little Rock heavy mineral (HM AR) was placed a depth of 20-25 cm within the sand. Total weight of the sample was 69 gram and the concentration of the mineral was about 45%. For the second experiment, ilmenite sample of weighting 32 gram was used. Its concentration was 83%. For the third experiment, ilmenite sample having mass of about 50 gram was embedded inside the host layer (sand). To conduct the fourth experiment, a sample composed of rutile with a mass of 140.8 gram was placed within the host layer. The fifth sample of the last experiment was pure HM AR and was buried inside the host layer. Total weight of the sample was 96 gram. We buried heavy mineral samples about 20-25 cm depth inside the host layer.

After data acquisition, data processing steps were applied to GPR data. Zero-time set was applied to move start time to zero in time direction. Subtracting average and background removal were applied to remove first arrivals, which represent air and ground reflections, from GPR data.

Figure 2. GPR system with 1.5 GHz antenna and experiment box filled with

sand (left), a sample buried inside the host layer (right).

IV. RESULTS As indicated earlier, MATLAB was used to implement co-

occurrence matrix and the textural features

A. Synthetic Data Results Numerical solution of the subsurface configuration

calculated by GprMax was obtained in time domain. Synthetic data were utilized to observe differentiation between two different mineralogy, ilmenite and spodumene, by using various features of the texture analysis.

Fig.3 shows entropy results for ilmenite and spodumene. The same color scale was used to visualize entropy between two mineral cases. Table.1 presents computed statistical features for whole profile. The statistical results of texture features show that ilmenite has higher entropy, dissipation, and contrast measures than spodumene. On the other hand, spodumene shows higher energy and homogeneity features than ilmenite

(a)

(b)

Figure 3. (a) The result of entropy measure for ilmenite, and (b) spodumene

TABLE I. THE RESULTS OF DIFFERENT STATISTICAL FEATURES CALCULATED FROM WHOLE PROFILE

Measures Ilmenite Model Spodumene Model Contrast 0.5037 0.0618

Dissipation 0.2709 0.0611 Energy 0.5540 0.7906 Entropy 1.3806 0.5108

Homogeneity 0.8951 0.9696

B. Ground-truth GPR Data Results Some of the data sets and their textural features are

illustrated in the following figures. Fig.4.a represents GPR data collected from the survey which sand and HM AR sample were mixed with concentration of 55% and 45%, respectively and buried inside sand layer. Fig.4.b-f show energy, standard deviation, contrast, variance and homogeneity features, respectively. Fig.5.a represents the GPR data collected from the experiment which ilmenite was embedded within the host layer and concentration of the ilmenite was 83%. Fig.5.b-f illustrate entropy, energy, contrast, standard deviation and homogeneity features. Fig.6.a shows the next data collected from the experiment which ilmenite was embedded inside the host layer and the mass of the ilmenite was about 50 gram. The results of measures of radar texture that are entropy, energy, contrast, standard deviation, and correlation, are given in Fig.6.b-f, respectively. Fig.7.a shows another data obtained from the laboratory experiment that rutile with a mass of 140.8 gram was buried inside the host layer. Fig.7.b-f represent cluster, variance, contrast, homogeneity and entropy measures. Fig.8.a illustrate the GPR data collected from the last experiment that pure sample of HM AR was buried inside sand layer and the

weight of the buried sample was 96 gram. Cluster, variance, contrast, homogeneity and standard deviation features computed from the data shown in Fig.8.a. are illustrated in Fig.8.b-f.

The results show that buried samples inside host layer caused high entropy, contrast, correlation and standard deviation than the host medium. On the other side, buried samples have lower energy and homogeneity measure than the host medium. It can be seen from the figures, contrast, standard deviation, and correlation features especially emphasize the feature associated with the buried samples than the other features. Standard deviation measure can draw a contrast between the samples and host media. The results of variance feature allow better detection to the edge of the samples and can be very useful to map out buried samples. For GPR data shown in Fig.4.a, variance feature illustrated in Fig.4.e indicates the same trend with data, but it is not easy to make a decision by using the other measures such as standard deviation, contrast. However, all these measures were very helpful to locating and depicting the heavy mineral samples.

V. CONCLUSION The aim of this study is to analyze the application of the

texture attribute analysis to GPR data for prospecting of heavy minerals. The calculated statistical features and results of synthetic data show that ilmenite has higher entropy, dissipation, and contrast measures than spodumene. On the other hand, spodumene shows higher energy and homogeneity features than ilmenite.

Based on the results of the analysis computed from laboratory data, we find that buried heavy minerals cause high entropy, contrast, correlation, standard deviation, and cluster and low energy and homogeneity. The results of texture indicators show that variance allow edge detection and highlight of buried samples within host material. Contrast, correlation and standard deviation may emphasize the contrast between buried samples and background and can mark the location of buried sample inside the host layer. Cluster can visualize more clearly anomalies caused by buried sample than the data. All results obtained in the study clearly conclude that use of various texture measures is the best way to evaluate the results and make more realistic interpretations.

ACKNOWLEDGMENT We wish to thank Hussein Khalefa Chlaib, Mert Su, Julien

Szumilas, Sebastien Maganuco and Giovanni Fontaine for lab assistance. We would like to thank Engin Mendi for his contribution to Matlab programming. Also our thanks go to Dr. Tito Viswanathan for allowing us to use Triple Beam Balance system to measure our samples. The work was supported by the NASA EPSCOR grant.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 4. (a) Processed GPR data from the survey which is mixed of sand

and HM AR sample buried inside host layer and concentration of heavy minerals is 45%; (b) Energy, (c) Standard deviation, (d) Contrast, (e) Variance, (f) Homogeneity.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 5. (a) Processed GPR data from the survey which is mixed of soil

and ilmenite sample buried inside sand layer and concentration of ilmenite is 83%; (b) Entropy, (c) Energy, (d) Contrast, (e) Standard deviation, (f) Homogeneity.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 6. (a) Processed GPR data from the survey which is ilmenite and

weight of the sample was about 50 gram, (b) Entropy, (c) Energy, (d) Contrast, (e) Standard deviation, (f) Correlation.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 7. (a) Processed GPR data from the survey that rutile pieces

embedded inside host layer and weight of the sample was 140.8 gram, (b) Cluster, (c) Variance, (d) Contrast, (e) Homogeneity, (f) Entropy.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 8. (a) Processed GPR data from the survey that HM AR mineral was

embedded inside host layer and weight of the sample was 96 gram, (b) Cluster, (c) Variance, (d) Contrast , (e) Homogeneity, (f) Standard deviation.

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