Radio frequency dielectric properties of limestone and sandstone from Ewekoro, Eastern Dahomey Basin

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1 Available online at Pelagia Reseach Libay Advances in Applied Science Reseach, 213, 4(6): ISSN: CODEN (USA): AASRFC Radio fequency dielectic popeties of limestone and sandstone fom Ewekoo, Easten Dahomey Basin 1 Olatinsu O. B., 1 Oloode D. O. and 2 Oyedele K. F. 1 Depatment of Physics, Faculty of Science, Univesity of Lagos, Lagos, Nigeia 2 Depatment of Geosciences, Faculty of Science, Univesity of Lagos, Lagos, Nigeia ABSTRACT The dielectic popeties of nine ock samples [limestone (8) and sandstone (4)] collected fom Ewekoo in Ogun State, Nigeia wee studied in the ange 1 khz 11 MHz unde ambient atmospheic conditions. It is found that ε ) values of the dy samples deceases with incease in fequency in the ange of dielectic constant ( measuement. Dielectic dispesion is elatively lage in almost all the samples. Conductivity dispesions followed the opposite tend inceasing in values with incease in fequency. Peaks ae moe ponounced in loss tangent (D) ε ) cuve. This is an indication that oveall electical esponse of these samples is cuve than in dielectic loss ( bette evealed by loss tangent vaiation than dielectic loss vaiation. All the studied samples ae govened by Cole-Cole dispesion which indicates a distibution of elaxation times which is common fo multicomponent systems. This is confimed by the value of the spead paamete which is below.5 fo all the samples. Keywods: Dielectic dispesion, elaxation fequency, limestone, sandstone. INTRODUCTION High-fequency electomagnetic waves tavel in the gound in analogous manne to seismic waves. Instead of being detemined by the elastic paametes the popagation of ada signals is dependent on the dielectic popeties of the subsuface ocks. Gound penetating ada (GPR) is a high esolution, nea suface, geophysical method that can be employed to image geological stuctues and mateials in the subsuface (Rust et al., 1999). Successful delineation of subsuface tagets using ada depends on electical conductivity, dielectic constant and magnetic pemeability. Howeve, most geological mateials ae geneally assumed to be non-magnetic and as a esult thei magnetic pemeability is negligible (Ngwenya and Sefaa, 29). The geneation of ada signal eflection is dependent on the significant diffeences in elative dielectic constant between ock fomations. Knowledge of the electical popeties of ocks in combination with the ada system is impotant fo pedicting the pefomance of ada in geological settings. Seveal electical/dielectic tools have been employed in the investigation of ock popeties. The efficient use of these tools depends on the undestanding of the mechanisms of dielectic behaviou of ocks (Knight, 1984a, b; Knight and Nu, 1987a, b; Gaouch and Shama, 1998; Gaouch, 1999). In this pesent study, dielectic popeties of limestone and sandstone samples fom Ewekoo have been epoted in the fequency ange 1 khz to 11 MHz. The pupose of this study is to undestand the complex dielectic dispesion and electochemical polaization behaviou of these ock types of diffeent chemical composition in suppot of ada investigation. Pelagia Reseach Libay 15

2 Olatinsu O. B. et al Adv. Appl. Sci. Res., 213, 4(6): MATERIALS AND METHODS 2.1 Mateials Samples of limestone ( ) and sandstone ( ) wee obtained fom Ewekoo in Ogun State, Nigeia. The samples along with thei physical chaacteistics and chemical compositions ae pesented in Table 1 and Table 2 espectively. Table 1: Physical chaacteistics of limestone and sandstone of Ewekoo Rock type Colou Textue Limestone Chalk white/light gey/gey/geenish. Fine coase gains. Sandstone Bown/eddish bown. Medium coase gains. Table 2: Chemical composition of limestone and sandstone of Ewekoo Popotion of Elemental Oxides (ppm) Sample SiO 2 Al 2O 3 Fe 2O 3 TiO 2 CaO P 2O 5 K 2O MnO MgO Na 2O LM= limestone; SA=sandstone 2.2 Sample pepaation fo dielectic measuements Peliminay sample pepaation involved cutting the samples into appoximately disc shape with the aid of a diamond saw electically opeated though a Siemens angle cutte. A ange of sizes in diamete and thickness wee obtained, depending on the size of the oiginal lump of sample. The disk-shaped sample sufaces wee late gound and polished using ginding machine to obtain as nealy as possible smooth, paallel faces. Sandstone samples due to poosity/poe spaces geneally etained some vey small degee of oughness. They wee then kept in polyethylene bags and late glass containes to avoid absobing moistue. 2.3 Dielectic measuements In this study, dielectic pemittivity and conductivity measuements wee caied out on dy samples of limestone and sandstone in the fequency ange of the applied field was fom 1 khz to 11 MHz. The dielectic measuing system consisted of a Pecision Impedance Analyze (Agilent 4294) and a test/measuement pobe (steel electode) specially fabicated fo paallel plate measuement at the Petophysics Laboatoy of the CSIRO Eath Science and Resouce Engineeing (CESRE) Unit of the Austalian Resouces Reseach Cente, Kensington, Westen Austalia. The output paametes fom the analyze ae the paallel capacitance C and the paallel esistance R, fom which both the eal pat of the elative dielectic pemittivity (dielectic constant) ε and the conductivity σ fom C( ω) d ε d ( ω) = and σ ( ω ) = espectively. The imaginay elative pemittivity (dielectic loss) ε ε A R( ω ) A was obtained using o ε and ε i.e. 1 σ ( ω) R ( ω) d ε ( ω) = o ε =. Also, the loss tangent D was computed fom the atio of ωε o ωε o A ε D =. Whee d is the distance between the electodes, A thei aea; Angula fequency ε ω = 2πf and ε o is the pemittivity of fee space. The diamete and thickness of the samples wee measued using an electonic digital callipe. Good electomagnetic shielding was implemented to the whole sample holde in ode to educe noise poblems that ae common, especially at low fequencies. The mateial was mounted in a sample cell between the paallel cicula electodes thus foming a sample capacito. The mateial placed in the capacito can be p p Pelagia Reseach Libay 151

3 Olatinsu O. B. et al Adv. Appl. Sci. Res., 213, 4(6): consideed as an equivalent electical cicuit which consists of a capacitance, C (ω), in paallel with a esistance, R (ω). These values ae the output of the dielectic analyze. RESULTS AND DISCUSSION 3.1 Cole-Cole Plots The Cole-Cole plot (Cole-Cole, 1941) was utilized as a quick way of obtaining insights into the polaization and conduction mechanisms in the ocks. The Debye esponse (Debye, 1929) has fequently been used to descibe dielectic dispesion in a system with a single elaxation time. Fo a Debye-type elaxation pocess in which a single elaxation time τ is assumed, this should poduce a semi-cicle with cente on the hoizontal axis. Howeve, many mateials, including ocks, deviate fom Debye behaviou, suggesting the pesence of a distibution of elaxation times. The plots fo the ocks in this study ae shown in Figues 1a and 1b. It is found that the dielectic dispesion of all the samples is govened by Cole-Cole elaxation behaviou due to oientation polaization pocess. This type of behaviou has been epoted fo geologic mateials by seveal wokes (Saint-Amant and Stangway, 197; Knight, 1984a; Knight and Nu 1987a; Sengwa and Soni, 25, 28). The Cole-Cole equation fo dielectic dispesion is * ε ( ω) ε ε = ε i ε = ε + 1 α 1+ ( iωτ ) whee ε is the low fequency limiting value of pemittivity o static dielectic constant, ε the high fequency limiting value of pemittivity, ω the angula fequency, τ the chaacteistic elaxation time of the dipole elaxation in the system and α the spead paamete which govens the boadness of the distibution ( < α < 1). The ε = ε ε, and α ae pesented in Table 3. Thee is evaluated values of ε, ε, dielectic stength significant vaiation in ε and ε fo the two sample types. ε vaies between and fo sandstone samples while fo limestone it vaies between and ε fo sandstone is in the ange while fo limestone the ange is Table 3 also show that the obseved α values of all the samples ae lowe than.5, which depicts a distibution of elaxations consistent with the multicomponent natue of these samples. 1a Dielectic Loss (F/m) Dielectic Constant (F/m) Pelagia Reseach Libay 152

4 Olatinsu O. B. et al Adv. Appl. Sci. Res., 213, 4(6): b 35 3 Dielectic Loss (F/m) Dielectic Constant (F/m) 3.2 Dielectic dispesion Figue 1: Cole-Cole plots fo the ock samples Table 3: Values of dielectic paametes of limestone and sandstone of Ewekoo Sample ε ε ε α ε ) values of dy limestone and sandstone samples as function of fequency ae The calculated pemittivity ( pesented in Figues 2a and 2b. These plots eveal dispesion, which is compaatively lage in almost all the samples. Table 2 shows the multicomponent natue of these ock samples in which the oveall dielectic behaviou ε. In eath mateials, dielectic of each is govened by contibutions fom each component having diffeing dispesion is due to polaization in the sample s bulk volume as a esult of chage build-up at gain boundaies of the components of the sample (Saint-Amant and Stangway, 197). Pelagia Reseach Libay 153

5 Olatinsu O. B. et al Adv. Appl. Sci. Res., 213, 4(6): a Dielectic Constant (F/m) b Dielectic Constant (F/m) Figue 2: Plots of dielectic constant vesus fequency fo the ock samples Pelagia Reseach Libay 154

6 Olatinsu O. B. et al Adv. Appl. Sci. Res., 213, 4(6): Dielectic Loss (F/m) 3a b 35 3 Dielectic Loss (F/m) Figue 3: Plots of dielectic loss vesus fequency fo the ock samples Pelagia Reseach Libay 155

7 Olatinsu O. B. et al Adv. Appl. Sci. Res., 213, 4(6): Dielectic Loss ε ) values of the samples ae plotted against log f in Figues 3a and 3b., The imaginay elative pemittivity ( and fo the sandstone samples show maximum absoption peaks with coesponding elaxation fequency 23.5 khz, 42.5 khz and 42.1 khz espectively. The elaxation fequency fo is pobably below 15 khz. Only two limestone samples, and show peaks in dielectic loss and the coesponding elaxation fequency ae 57.2 khz and 11.2 khz espectively. It is most likely that this fequency fo, and is below 5 KHz. 4a Conductivity (S/m) x1 7 4.x1 7 6.x1 7 8.x1 7 1.x x1 8 Fequency (Hz) 4b.6.5 Conductivity (S/m) x1 7 4.x1 7 6.x1 7 8.x1 7 1.x x1 8 Fequency (Hz) Figue 4: Plots of conductivity against fequency fo the ock samples Pelagia Reseach Libay 156

8 Olatinsu O. B. et al Adv. Appl. Sci. Res., 213, 4(6): Conductivity Figues 4a and 4b show the vaiation of A.C. conductivity of the studied samples. These all show incease in conductivity with fequency. This is in contast to dielectic dispesion which is moe stongly dependent on fequency, stating with high values at low fequencies and deceasing to asymptotic values at high fequencies. These chaacteistics have been intepeted as being caused by geometic o textual heteogeneities in the ock system (Sen, 1981; Sen and Chew, 1983). The simila popotion of elemental oxide composition (Table 2) account fo the closeness in conductivity values fo the sandstone samples. This tend is also obseved in the limestone samples except fo with compaatively lowe conductivity values. Loss Tangent a b Loss Tangent Figue 5: Plots of loss tangent against fequency fo the ock samples Pelagia Reseach Libay 157

9 Olatinsu O. B. et al Adv. Appl. Sci. Res., 213, 4(6): Loss Tangent The vaiation of loss tangent values with fequency fo the samples is shown in Figue 5a and 5b. Loss tangent peaks ae moe ponounced than maximum absoption peaks. This is found fo all the samples except fo which is low pobably less than 1 khz. The citical fequency vaies 21.8 khz to 569 khz fo the othe limestone samples while fo sandstone the ange is between 61.6 khz and 22 khz. CONCLUSION The esults of this study suggest that sample type and heteogeneity contibute to the dielectic behaviou of ocks. Chemical composition and natue of the two ock types studied clealy distinguish thei fequency dependent electical esponses. Simila to othe geologic mateials all the samples ae govened by Cole-Cole elaxation type which means a distibution of elaxation times. The detailed study of the diffeent ocks will assist significantly in adio fequency dielectic technique since ada imaging of the subsuface depends on the aveage dielectic constant of the ock types available in the aea of investigation. Futhemoe, the epoted values of dielectic paametes and thei intepetation can be applied to investigate the vaious existing fequency dependent empiical dielectic dispesion models of eath mateials. These empiical models ae often used to model and intepet induced polaization and gound-penetating ada data. Acknowledgements The authos wish to expess thei gatitude to CSIRO Eath Science and Resouce Engineeing (CESRE), Westen Austalia, fo taining and pemission to use Agilent 4294A fo data acquisition and pocessing. Ou special appeciation goes D. Ben Clennell and D. Matthew Josh fo endeing technical assistance to the fist autho duing his visit to CESRE. REFERENCES [1] K.S. Cole, R.H. Cole, J. of Chem Phys, 1941, 9, [2] P. Debye; Pola Molecules, Dove Publ., New Yok, [3] A.A. Gaouch, M.M. Shama, The Log Anal., 1998, 39, [4] A.A. Gaouch, The Log Anal., 1999, 4, [5] R.J. Knight, Ph.D. thesis, Stanfod Univesity (US, 1984). [6] R. Knight, J. Geomagn. Geoelect., 1984, 35, [7] R.J. Knight, A. Nu, Geophysics, 1987, 52, [8] R.J. Knight, A. Nu, The Log Anal., 1987, 28, [9] B, Ngwenya, M.T. Mafii, P.G. Sefaa, In: 11 th SAGA Biennial Technical Meeting and Exhibition (Swaziland, 29). [1] A.C. Rust, J.K. Russell, R.J. Knight, J. Vol. geo. es., 1999, 91, [11] M. Saint-Amant, D.W. Stangway, Geophysics, 197, 35, [12] P.N. Sen, Geophysics, 1981, 46, [13] P.N. Sen, W.C. Chew, J. Micowave and Powe, 1983, 18(1), [14] R.J. Sengwa, A. Soni, Indian J. adio & Space Physics, 25, 43, [15] R.J. Sengwa, A. Soni, Indian J. of adio & Space Physics, 28, 37, Pelagia Reseach Libay 158

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