Dielectric behaviour of shale and calcareous sandstone of Jodhpur region
R 1 Sengwa1, A Soni1 & B Ram2
1Microwave Research Laboratory, Department of Physics J NV University, Jodhpur 342 005, Rajasthan, India
2Department of Mines and Geology, Government of Rajasthan Jodhpur 342 005, Rajasthan, India
Received 23 July 2003; revised 29 September 2003; accepted 29 April 2004
Dielectric permittivity e' and loss £" of dry and water saturated shale, sandy sandstone (sandy shale) and calcareous sandstone of Jodhpur region were studied at room temperature in the frequency range from 100Hz to 100kHz and also at 10.1 GHz. It is observed that thee' values of these samples decrease with increase in frequency. The complex plane plots(£"
versus e') of these geological materials are Cole-Cole arcs. The low frequency limiting dielectric constant £0 , high frequency limiting dielectric constant £~, dielectric relaxation time T and distribution parameter a of these samples have been determined from these Cole-Cole plots. The ac conductivity of dry and water-saturated samples has also been reported. The large enhancement in the permittivity value of water-saturated samples was found due to electrochemical polarization.
Further it is observed that the increase in e' value of water saturated shale and sandy sandstone is proportional to the volume fraction of water absorbed in the samples. The effect of the density, porosity, grain sizes and chemical composition on the frequency dependent dielectric permittivity of these samples has been explored.
Keywords: Dielectric permittivity, Dielectric relaxation time, Cole-Cole plots, Sandstone, Conductivity PACS No: 77.22 Gm; 84.40 Xb
1 Introduction
The complex dielectric constant E*(CD)
=
E' - j£"spectrum of geological materials is of considerable theoretical and practical interest. The dielectric permittivity E' is indicative of the materials capability for storing energy in the electric field (electrical polarization) whereas dielectric loss E" is indicative of that material's capability for absorbing energy from the alternating electric field. In these materials, energy loss (dissipation) results from the conversion of electrical energy to thermal energy (Joule heating) through momentum transfer during collisions as the charge move.
The measurements of frequency dependent values of
E' and E" of geologic materials help in planning ground penetrating radar (GPR) surveys1-3, applications to microwave remote sensing4-11
, to understand the behaviour of induced-polarization 12 and their use in time domain reflectometry (TOR) measurements13'14
. In rocks and sediments, dielectric properties3·12
are primarily a function of mineralogy, porosity <j>, density d, frequency f, water saturation, which in tum depend on the rock lithology, component geometries and electrochemical interactions. Earlier studies15-18
confirmed that the dry geological rocks and minerals show the dielectric dispersion in low frequency region i.e. from 10-3 to 106
Hz. Further, it is also confu-med that the values of E' of dry rocks and minerals4'19
-21
in microwave frequency region are almost independent of the value of frequency. The presence of water in the pores of geological materials highly influences the dielectric constant at low frequencies and the behaviour is also anomalous. But at
· fr • 22-24 h a] f I ·
microwave equenctes , t e v ue o E mcreases proportional to the percentage of water concentration in the sample.
In the present paper, the systematic frequency dependent values of E' and E" of dry and water saturated samples of two different shale, one sample of sandy sandstone and one sample of calcareous sandstone of Jodhpur region have been reported. The physical parameters and mineralogical composition with their locations of these samples are recorded in Table 1. Shale occurs in two forms, i.e. massive shale or mudstone and laminated shale. The studied samples of Jodhpur region are laminated shale. These are composed of alternate laminations of clay-rich and quartz-rich material. Iron oxide is found as finely dispersed reddish brown to opaque tiny grains within the clay mass. Sandy sandstone (also called sandy shale) of Jodhpur region occurs at the base of main Jodhpur sandstone throughout in Marwar super group
330 INDIAN J RADIO & SPACE PHYS, OCTOBER 2004
Table !- Physical parameters and mineralogical composition of the samples
Sample Location Colour Density Porosity
d %
(glee) <I>
Shale (I) Bhopalgarh Maroon 2.02 9.72
Shale (2) Ganeshdungari Red 1.97 19.41
Sandy Bhopalgarh Reddish 1.77 13.79
sandstone
Calcareous Shastri- Greyish 2.04 14.38
sandstone naoar Brown
of rocks. The studied calcareous sandstone is a coarse grained sandstone, mainly comprising quartz and matrix of carbonate material (calcite). Geologically it belongs to quaternary formation and formed by reworking of earlier deposited sandstone. Calcareous sandstone is an excellent ground aquifer for ground water in the Jodhpur region.
2 Experimental details
2.1 Sample preparation
The samples were cut by a diamond wheel cutter and polished to obtain thin plates of thickness ""' 1.4 mm. Silver plated brass plates of area 180.6 mm2 were used for the fabrication of parallel plate capacitors with samples as dielectric to study the frequency dependent dielectric response in the frequency range from 100 Hz to 100 kHz. For microwave frequency dielectric measurements, portions of the same samples were cut and polished to fit in the X-band sample holder of width 0.9" and height 0.4". Two samples of different lengths of each material were prepared for the determination of the dielectric constants at 10.1 GHz.
2.2 Dielectric measurements
In the frequency range from 100 Hz to 100 kHz, the frequency dependent values of£' and £" were determined by measuring the capacitance and dissipation factor of prepared parallel plate capacitor with sample as dielecttic using automatic Keithley LCZ meter (model 3330). The values of E' and £" at 10.1 GHz were canied out using a short-circuited slotted rectangular wave-guide operating in TE10 mode. The sample length variation method (two- point method) 8·25•26 was used for the measurement of the shift in minimum with reference to the short without sample and voltage standing wave ratio in presence of
Grain size % % % % %Feldspar
(mm) Si02 Chert AlzOi Fe203 NaAISiP8/
volcanic/ CaO/ KAISi308/
clatic MgO/ CaAI2SizOs
sand Clay
0.03-0.001 68 7 13 12
0.015-0.001 69 7 14 14
0.5-0.05 78 6 10 10
0.6-0.03 81 16 3
48·0
40·0
32·0
·w 24·0
16·0
8·0
0·0
2·0 5·0
log 11Hz
Fig. 1--c' versus log f plots of dry samples [(0) Shale (1); (~) Shale (2); (e) Sandy sandstone and (A) Calcareous sandstone]
the sample. For the measurement of permittivity and loss of water-saturated samples, the prepared samples were immersed in distilled water for 3 days. These water- saturated samples were used for the dielechic measurements after removing the surface water with the help of tissue paper. The volume and weight of each dry and water saturated sample was determined and used for the evaluation of the porosity </>. All these measurements were made at room temperature.
3 Results and discussion
3.1 Dielectric behaviour (100Hz to 100kHz)
3.1.1 Dry samples--Frequency dependent£' values of two different shales, sandy sandstone and calcareous sandstone denoted by 1, 2, 3 and 4, respectively, are
depicted in Fig. I. The same numbers are also used to represent dielectric parameters of these samples in Figs 2-6. It is found that the value of £' decreases with the increase in frequency for all these samples. The decrease in£' with the increase in frequency in the range from 100 Hz to 100 kHz is the common characteristic of the geological matetials15·16
·18
•27
. Table 1 shows that the shale samples (1) and (2) have nearly equal mineralogical composition, but the observed £' values of shale (2) is smaller than the £' values of shale (1). This difference may be due to the variation in the grain size of shale (1) and shale (2). Cervelle and Jin-Kai5 also reported £' values of shale in the frequency range from 1 kHz to 1 MHz. But the shale mineralogical composition is not given. Therefore, it is not possible to COLTelate these £' data with the earlier repmted £'values of the shale5.
Recently, Lesmes and Morgan 12 using physiochemical model confirmed that the complex dielectric response of sandstones is governed by the grain-size and grain- volume distribution. They also suggested that the dielectric response below 2 kHz is primarily controlled by the macroscopic grain fraction (mainly quartz grains), whereas the frequency response above 2 kHz by the clay size grains and smface roughness. In low frequency region the polarization of the dty samples depends on the grain-size and grain-volume distribution12 and hence the grain size is imp01tant. For water saturated samples, the porosity is also impOitant along with grain size, because the volume of the water held by the sample depend on the size of the grains, as also on its geometty.
Comparative £' values of these samples show that the sandy sandstone has smaller £' values in the frequency range from 100Hz to 100kHz. The quartz percentage in sandy sandstone is higher than the shale and it is larger in calcareous sandstone (Table 1). The £' values of these samples confirm that the low frequency dielectric permittivity is not governed by the percentage of quartz in the sample. In case of calcareous sandstone, it seems that the £' values are significantly influenced by the presence of feldspar in the sample. The anomalous variation in £' values with quartz percentage of these samples also shows that the low frequency permittivity is affected by the grain volume distribution as suggested by Lesmes and Morgan 12•
Figure 2 shows the vruiation of loss tangent (tan 8
=
£" /£') against frequency of these dry samples. The maximum value of tan 8 is found to be === 0.4. In case of shale (1) and calcareous sandstone, a peak in the loss tangent curves is observed near 10 kHz, but it seems that
the maximum tan 8 peak for shale (2) and sandy sandstone is above 100 kHz. It is difficult here to correlate the physical and mineralogical composition of these samples with their observed tan 8 peak values. The a.c. conductivity (cr) of these dry samples against
0·40
2
0·30
3
<JJ
c 4
~ 0·20
0·10
2·0 3·0 4·0 5·0
log t, Hz
Fig. 2 -Tan
o
versus logf plots of dry samples [(0) Shale (I); (6.) Shale (2); (e) Sandy sandstone and(..&.) Calcareous sandstone]-7·0
I
e
u -S·O~ b -9·0
"'
2 -10·0
-11·0
2·0 3·0 4·0 5·0
log t, Hz
Fig. 3---Log a versus log f plots of dry samples [(0) Shale (I);
(6.) Shale (2); (e) Sandy sandstone and (..&.) Calcareous sandstone]
332 INDIAN J RADIO & SPACE PHYS, OCTOBER 2004
frequency is depicted in Fig. 3. For all these samples, a linear behaviour is observed between log cr and logf
The complex plane plots of the dry shale, sandy sandstone and calcareous sandstone are shown in Fig. 4.
These plots are governed by Cole-Cole equation28
, . , E0 - E
E*(m)=E-JE =E
+
~~ 1 +(jw-r)l-a
where E0 is the low frequency limiting value of permittivity, ~ the high frequency limiting value of permittivity,
w
the angular frequency, -r the macroscopic15r---,
10 5
0~--~---L----~----~--~----~~
6 4
2
0~--~~--~----~----~----~--~~
3 2
10 5
0~--~~--~----~----~--~~--~~
0
€'
Fig. 4---Cole-Cole plots of dry samples [(0) Shale(!); (~) Shale (2); (e) Sandy sandstone and (.A.) Calcareous sandstone]
relaxation time and
a
the distribution parameter. The evaluated values of E0 , E~, a, '! and dielectric relaxation strength ~E=
E0 - ~ are recorded in Table 2. The values of E0 and E~ were obtained by extrapolation of the Cole- Cole plots corresponding to low frequency region and high frequency region on the real axis, respectively. The relaxation time '! is evaluated29 from the relation v/u = ((JJ't)1-a. Here, u and v are the distance from the experimental points of Cole-Cole diagram to ~ and Eo, respectively on the permittivity axis. The Cole-Cole type behaviour of several geological materials is also reported by earlier investigators 12'16.3°.31•
Table 2 shows that the E0 value of these samples varies over a wide range. The variation in the values of Eo indicates that the mechanism involved in dielectric polarization of these samples is significantly different.
Value of ~E of sandy sandstone was found to be very small in compru.ison to ~E values of other samples. All these samples have large values of a. The finding of the non-zero
a
indicates a distribution of relaxations, which is consistent with the inhomogeneous structure of these samples. Taherian etat?
also drew similar conclusions for many sedimentary rocks having non-zero value of a.Table 2 shows that the observed a value increases from shale to sandy sandstone and also from sandy sandstone to calcareous sandstone. Although there is large difference in the Eo values of the shale samples, the observed value of
a
is the same, which is interesting. The '! values of these dry samples were found of the order of 11s. In case of shale (2), the observed -r value is very small in comparison to the -r value of shale (1). Nearly equal -r values were found in the case of shale (2) and sandy sandstone. Further, comparatively very high '! value is observed in case of calcareous sandstone (Table 3).Earlier12 for geological materials, it is suggested that the value of'! depends upon the particle radius by the relation -r
=
R2 I 2D, where R is particle radius and Dis diffusion coefficient of counterions in fixed layer. The comparative -r values of the studied samples also show that the Table 2- Values of static dielectric constant E0, high frequency limiting dielectric constant E~,dielectric relaxation strength ~E, distribution parameter a and relaxation time "C of the dry samples
Sample Eo E~ ~E a "C ()J.S)
Shale (I) 49.0 8.3 40.7 0.45 49.2
Shale (2) 20.7 3.7 17.0 0.45 4.1
Sandy sandstone 16.3 5.6 10.7 0.47 3.2
Calcareous sandstone 52 10.5 41.5 0.56 126.0
Table 3--Values of dielectric constants at 10.1 GHz
Sample Dr~ samEles
E' E"
Shale (1) 3.88 0.33
Shale (2) 3.51 0.11
Sandy sandstone 3.27 0.34 Calcareous sandstone 4.33 0.18
4·50
3 4·00
3·50
3·00
_.,
w
01
~ 2·50
2·00
1·50
1·00
2·0 3·0 4·0 5·0
logt,Hz
Fig. 5--Log E', versus logfplots of water saturated samples [(0) Shale (1); (L1) Shale (2); (e) Sandy sandstone and (.6.) Calcareous sandstone]
relaxation mechanism is governed by the particles of different radius.
3.1.2 Water-saturated samples-Theoretical models12 (and refs. therein) confirmed that the complex dielectric response of the water saturated geologic materials is a function of pmticle radius and it is proportional to the surface charge density in the fixed layer and the electric double layer (EDL). Both the fixed and diffuse parts of the EDL are polarized when subject to an external electric field. The frequency dependent permittivity of wetted samples is given by the relation E's
=
eR4 I kT(l +uh2), where e is the electronic charge, T the absolute temperature, k the Boltzmann's constant, w the angular frequency, R the particle radius, and4
the surface charge carrier density in the fixed layer (i.e.Water saturated samEles
E', Ens ~E'=E',-E' E', (theo)
9.92 3.93 6.04 9.63
18.25 0.95 14.74 15.05
12.56 0.73 9.29 11.51
9.72 0.89 5.39 12.78
14·0
12·0
10·0
8·0 co
c:
2
6·0
4·0
2·0
0·0
2·0 3·0 4·0 5·0
log 11Hz
Fig. 6--Tan 0 versus log f plots of water saturated samples [(0) Shale (I); (L1) Shale (2); (e) Sandy sandstone and (.6.) Calcareous sandstone]
number of chm·ges per squm·e meter). The frequency dependent observed permittivity E's values of shale (1 and 2), sandy sandstone and calcareous sandstone are shown in Fig. 5. It is observed tqat there is large enhancement in
E's values of water-saturated samples in comparison to the£' values of the dry samples (Fig. 1). This is due to the increase in surface charge carrier density in presence of water molecules in the pores of the samples. The frequency dependent comparative E's values of water saturated shale and dry shale show that the anomalous variation in the valt.le of permittivity of water-saturated shale is highly influenced by the grain-size distribution in the wetted sample. The water absorption capacity of the geologic materials depends on their porosity. Because of the nearly unity density of water at room temperature, the
334 INDIAN 1 RADIO & SPACE PHYS, OCTOBER 2004
absorbed volumetric water content in the sample is equal to its porosity. Figure 5 shows that the increase in E's
values of these samples is not directly proportional to the volumetric water content in the sample. This suggests that the interactions of water molecules with grain size of these samples changes significantly with the frequency of a.c. electric field.
The loss tangent (tan 8 = c:"/c:') versus log
f
plots of these water-saturated samples is presented in Fig. 6. For shale and sandy sandstone one loss peak is observed in the frequency range from 100Hz to 100kHz. The value of corresponding loss peak frequency increases from the shale (1) to shale (2) and also from shale (2) to sandy sandstone. But in case of calcareous sandstone, it seems that the loss peak frequency is below 100Hz.The a.c. conductivity cr of water-saturated shale was found almost independent of the frequency, in the range from 100Hz to 100kHz. The a.c. conductivity of shale
(1) <J = 1.26 X 10-6 (Q cmr' is slightly higher than the
a.c. conductivity value of shale (2) cr = 6.03 x 10-7 (Q cmr'. For sandy sandstone, (J value varies from 6.76 X 10-7 to 7.24 X 10--{\ (Q cmr'. Around 3kHz, the variation in (J value from 7.24 X 10--{\ to 6.76 X 10-7 (Q cmr' is observed for sandy stone. The variation in cr value for calcareous sandstone is from 10-7 tO 1.26 X 10--{) (Q cmr'. The observed values of a.c. conductivity of water saturated shale, sandy sandstone and calcareous sandstones were found lower than the conductivity of water32 (<J = 17.03 X 10-5 (Q cmr') at room temperature.
The high conductivity of wetted samples shows that there are some conductive paths or segments through the sample matrix, which can be short-circuited by the conductive fluid at low frequencies and hence the conductivity of these water saturated samples increases up to nearly the conductivity of water.
3.2 Microwave dielectric constant
3.2.1 Dry samples-It is known4·'9-21 that the c:' values of dry geological materials remain independent of the frequency in the microwave frequency region. Therefore the single frequency measurement in the microwave region is significant to correlate the c:' values of dry geological materials with their physical parameters and also with the mineralogical composition. Table 3 shows that the c:' value of dry shale (1) is higher than the c:' value of dry shale (2) at 10.1 GHz. Further the c:' value of dry sandy sandstone is found smaller than the c:' values of both the shale samples.
The comparative variation in c:' value of these samples at 10.1 GHz also follows the trend in the variation of c:'
values of these dry samples in the range from 100 Hz to 100kHz (Fig. 1). The c:' value of calcareous sandstone is found higher than the c:' values of other samples at 10.1 GHz (Table 3). In low frequency region, initially the value of c:' of calcareous sandstone is smaller than the c:' value of shale (1), but above 10kHz its c:' value exceeds the c:' value of shale (1) (Fig. 1) and hence the observed value of calcareous sandstone is found higher at microwave frequency. From Tables 1 and 3 it seems that the variation in c:' value at microwave frequency is according to the density variation of these samples, i.e.
the c:' values increases with increase in the value of sample density. The density dependent values of c:' of dry rocks at microwave frequencies had been confirmed by earlier workers4• 19• Further the c:' values of these samples at 10.1 GHz were found smaller than the corresponding values of E.x, determined from the Cole-Cole plots. The
c:" values of these dry samples at 10.1 GHz are found in
the range from 0.11 to 0.34.
3.2.2 Water-saturated samples-Table 3 shows that the observed values of permittivity c:'s of water saturated shale and sandy sandstone (sandy shale) samples at 10.1 GHz are proportional to their porosity. This confirms that at 10.1 GHz the volumetric water content in the sample governs dielectric permittivity of the shale. In case of water saturated calcareous sandstone, although the c:', increases, an increase in permittivity value is not equal to an increase in permittivity value of sandy sandstone of equal porosity. This may be due to different kinds of water interactions with their mineralogical composition
;n microwave frequency region. The dielectric loss E"s is found much higher for shale (1) in comparison to the values of E"s of other samples at 10.1 GHz. This suggests that these water-saturated samples have different frequency ranges of dielectric dispersion.
The values of permittivity of these water saturated samples were also determined theoretically using the mixing equation22: E's (theo)
=
<!> E'w + (1 - <!>) £'. Here c:' w and c:' are the permittivity values of water and dry sample at 10.1 GHz, respectively. Also, <!> is the porosity of the sample. These theoretically evaluated values33 using E'w=
63 at 10.1 GHz are recorded in Table 3. Only in case of shale (1) the practical and theoretical permittivity values are found to be same, but for other samples there is significant difference in these values. Therefore, from these results it is inferred that the simple mixing equation is not valid for all types of geological materials.4 Conclusions
The relationship of mixing model given by Lang22 is not suitable for these water saturated samples. Only in case of shale (2) the observed practical and theoretical values are equal. The objective of this paper is to report the dielectric data of dry and water saturated samples over wide frequency range. There are different mixing models like Complex Refractive Index method (CRIM), etc. All models have their limitations. Different m1xmg models represent dielectric data of different geological materials.
Presently the authors are working on dielectric measurements of shale, various types of Jodhpur sandstones, different grades of limestone, marbles and granites in dry and water saturated state.
For dry samples, Cole-Cole plots (Fig. 4) were drawn and relaxation time evaluated. In case of water- saturated samples, the dielectric data in the frequency range 10-100 MHz is needed. Due to the limitation in the range of frequency of LCZ meter, measurements were made up to 100 kHz. After dielectric study of several different types of geological materials, we will evaluate the penetration depth in dry and wet rocks using the measured values of 10 GHz dielectric data and all the comparative data will be published simultaneously in future. It will be more significant to compare the theoretically evaluated penetration depth with experimentally measured values using Ground Penetration Radar (GPR), which facility will be acquired by the Institute in the near future.
Acknowledgement
The authors are grateful to the Department of Science and Technology, Government of Rajasthan, Jaipur, for financial assistance.
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