NBSIR 88-3095

DIELECTRIC MIXING RULES FOR

BACKGROUND TEST SOILS

Richard G. Geyer

National Bureau of Standards

U.S. Department of Commerce

Boulder, Colorado 80303-3328

June 1988

oemm

Stimulating America's Progress 1913-1988

NBSIR 88-3095

DIELECTRIC MIXING RULES FOR

BACKGROUND TEST SOILS

Richard G. Geyer

Electromagnetic Fields Division

Center for Electronics and Electrical Engineering

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303-3328

June 1988

Sponsored by

U.S. Army Belvoir Research & Development Center

Fort Belvoir, Virginia 22060-5606

U.S. DEPARTMENT OF COMMERCE, C. William Verity, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

CONTENTS

Page

Abstract 1

1. INTRODUCTION 1

2. DIELECTRIC PROPERTIES OF PURE WATER. . . 3

3. SALINE WATER 4

HETEROGENEOUS SOIL MIXTURES 6

M.1 Function- Theoretic Rules 6

4.1.1 General Water-Dominated Dielectric Behavior

of Natural Soils 7

4.2 Generalized Heuristic Rules for Soil Mixtures 8

4.2.1 Dielectric Mixing Rule for Dry Soils 11

4.2.2 Dielectric Mixing Rule for Lossy, Fluid-Saturated Soils. 11

4. 2. 2.1 Partially Saturated Soil Mixtures 12

4. 2. 2. 2 Saturated Soil Mixtures 14

5. APPLICATION TO SOIL STANDARDS 15

6. CONCLUSIONS 16

iii

7.

REFERENCES 17

DIELECTRIC MIXING RULES FOR BACKGROUND

TEST SOILS

Richard G. Geyer

Electromagnetic Fields Division

National Bureau of Standards

Boulder, Co 80303

The bulk, or effective, dielectric constant of any background test

medium (whether naturally occurring or synthetic) determines the

electromagnetic visibility of buried objects. Heuristic mixing

rules are considered that allow the prediction of complex dielectric

behavior in linear, homogeneous, isotropic, and lossy multi-phase

soil mixtures. Measurement results in bioelectromagnetic and

microwave remote sensing suggest a refractive mixing model as that

being most suited for dry soils or soil-water mixtures.

Key words: dielectric simulation; mixing rules; multi-phase; soils.

1 . INTRODUCTION

Soils are mixtures of minerals that are the weathered by-products of

rocks. Usually, natural soils contain some water so that the way in which

dielectric constants combine is important in determining the bulk, or effective, dielectric constant of the soil at hand. The bulk dielectric

constant of any soil (whether natural or synthetic) determines the

electromagnetic visibility of buried land mines and, therefore, intrinsically

affects the performance of any detection system. Once a range of suitable

dielectric background test characteristics relatable to conditions actually

encountered in the field is accepted, mixing rule(s) provide the easiest and

most pragmatic approach to specification of "standard" test soils.

Geyer [1] has noted that some mixing rules have little broadband

applicability for soils since they are based on systems where little or no conduction takes place. For example, when one of the components in a composite dielectric is conductive, large (frequency-, temperature-, and

salinity-dependent) polarizations can occur that can be attributed to

1
interfacial polarizations at the boundaries of the conductive phase. A mixing

rule that does not account for these interfacial polarizations has little

broadband applicability. Despite the fact that most mixing rules fail in a broadband sense (since they do not account for all relaxation effects [1]), it

is nonetheless useful to be able to predict the effective electromagnetic

properties of soils of different lithologies and porosities even over narrower

frequency ranges—100 MHz to 2.0 GHz in this case—that affect the signal

levels measured by UHF land mine detection systems.

The purpose of a mixing rule is to allow estimation of the dielectric

properties of a soil (either test standard or soil encountered in the field)

from measurements of that soil’s physical properties only. Its usefulness

will be limited by its dependence on adjustable soil- and frequency-specific

parameters. An efficacious mixing rule, then, will provide a convenient means

for predicting a test soil’s dielectric behavior in microwave land mine

performance testing and in signal level determinations. It will also provide

a physically based mixing model that is dependent on measurable soil

parameters and can be used for subsequent development and research purposes.

Generally, all materials can be classified into one of three dielectric

groups. The first of these, to which pure water and ice belong, is homogenous

substances. A second group, in which ionic salts are dissolved in solution

(usually water) is electrolytic solutions. The third group, heterogeneous

mixtures, includes that of wet, lossy soils or multicomponent (lossy or nonlossy) media of interest here for test soil lanes. The merits of any

chosen background material (standard) for mine test lanes depend not only on correlation with actual field conditions likely to be encountered but also on

the ease with which its (complex) dielectric properties can be predicted and

controlled for the operational frequency range of interest. Before discussing

mixing rule(s) applicable to heterogeneous soil mixtures, it is necessary to

review fundamental dielectric behavior of pure and saline water.
2. DIELECTRIC PROPERTIES OF PURE WATER

The frequency dependence of the complex dielectric constant of pure water

for exp(j2TTfT) time dependence is well-known and is given by the Debye

equation [1,2]

^w ^W“

''' 1 + j2irf Tw

where

= bi^ frequency (or optical) limit of (dimensionless),

e^o = static dielectric constant of pure water (dimensionless),

= relaxation time of pure water (seconds), and

f = electromagnetic frequency (Hz).

Equation (1 ) may be simply written

e = e' - ie" = e’ (1 - jtan6 ) w w ^ w w ^ w

( 2 )

where tan6^ = e^/e^ is the loss tangent of water (temperature dependent).

Rationalization of eq (1) yields

£ “0

T _ WO

^W ^W” 1 + (27TfT )^

W

and

( 3 )

It EW

2TTfT (e - E 1 W ' WO W”

1 + l2mfTw

The magnitude of the high frequency dielectric constant

determined by Lane and Saxton [ 3 ] to be

(iJ)

e^oo has been

Ev^oo = 4.9 (b)

3
and is practically temperature independent. The relaxation frequency of pure

water, f^Q = 1/2-nT^, occurs in the microwave region and is temperature

dependent. At 0°C, = 9 GHz and at 20 °C, f^^o = It can be seen

from eqs (3) and (4) that has its maximum value at f = f^Q- A Cole-Cole

plot of e^ vs with f as a variable parameter, is shown in figure 1 for pure water at T = 0°C. This plot takes the shape of a semicircle with end

points defined by = e^q in the low-frequency limit and by " ^wTM the

high-frequency limit. The point on the circle at which is maximum

occurs at the relaxation frequency, f = f^^o* whose coordinates are simply

given by e' = (e + e )/2 and e" = fe - e 1/2. ® w ^ wo w«>'^ w ^ wo w«>^

The dielectric constant of nonconducti ve water, e^q, is a function of

temperature. Klein and Swift [6] have generated a regression fit for e^o (T)

from dielectric measurements conducted between 1 GHz and 3 GHz

ewo(T) = Cwo(T) = 88.045 - 0.4147 T + 0.0006295 T" (6)

where T is in °C.

3. SALINE WATER

Although the dielectric properties of pure water and ice obey the Debye

relaxation equations given above and are fairly well understood, ionic salts

dissolved in water produce an electrolytic solution whose microwave dielectric

properties may differ greatly from those of pure water. The salinity, S, of a solution is defined as the total mass of solid salt in grams dissolved in 1 kg

of solution. Thus, S is normally expressed in parts per thousand on a weight

basis. Little will be said about broadband dielectric characterization of

electrolytic solutions, except that the real and imaginary parts of the

dielectric constant of a saline water solution are given by [3,6]

0 “0

T _ SWO SW<” / J

N ^sw

” ^sw® ^

1 + ( 2-nf T ) ^ sw

4
and

2ttFt [e - e j o.

It _ sw ^ swo sw°° ^ 1 ^sw 1 + (2llfT 2 ji £ f

^ sw o where the subscript sw refers to saline water, is the ionic conductivity of

the aqueous solution in S/m, and Gq is the permittivity of free space (cq = 8,854 X 10

"'' 2 F/m). Note that the form of the complex permittivity for saline

water differs from the of pure water only in the loss term, e'g^, where the

added term due to ionic conductivity of the aqueous solution, 0 i/tjoeo> is

present. It is clear from eq ( 8 ) that the ionic conductivity of saline water

has marked effect on the loss factor e"g^ below 10 GHz. Therefore, it is

expected that hi^ soil salinities will significantly affect the dielectric

properties of wet soil. As Jedlicka [7] notes, few measurements and analyses

have been reported relating soil salinity to effective soil dielectric

constant. Consequently , the dependence to soil salinity to permittivity is

not well understood. We do know, however, that the salinity of (free) pore

water within a soil matrix depends directly on the cation exchange capacity of

the matrix material. This fact should provide a direct relationship between

soil type, amount of volumetric moisture poresent, and effective soil canplex

permittivity. Further work will enhance understanding between these physical

soil parameters and measured electromagnetic properties.

Stogryn [ 8 ] points out that there is no evidence to indicate that eg^^oo

depends on salinity; hence eg^^oo = Cyoo = 4.9 He also empirically

determines both the temperature and salinity dependence of saline water by

writing as a factorable product, i.e., Sq^q(T,S) = Cswo^’^i®) F(T,S).

Polynomial fits to the above relation have then been obtained [5,9] on measurements performed by Ho and Hall [10] and Ho, et. al. [11] for 4 < S ^ 35

to obtain the following functional dependence of the dielectric constant of

water with respect to salinity.

4wo = 4o(T) - 0.1556 - 0.00041 3 S (9)

+ 0.00000158 S"

and

£swotan6 g^Q = 5.66 + 0.00265 S - 0.0000045 S" ( 10 )

5
We note from eqs (9) and (10) that Cq^q is not an independent parameter.

Equations (6), (9) and (10) will be used in subsequent development relating

effective dielectric constant measurements (real part, e’, and loss tangent,

tan6) of a fluid-saturated lossy soil mixture to the in situ fluid dielectric

properties, as well as to the water-filled porosity of the soil mixture.

4. HETEROGENEOUS SOIL MIXTURES

4.1 Function-Theoretic Rules

In general, the average dielectric constant of a heterogeneous mixture

consisting of two or more substances is related to the dielectric constants of

the individual substances, their volume fractions, their spatial

distributions, and their orientations relative to the direction of the

incident electric field vector [12]. In order to determine the functional

dependence of the average dielectric constant of a mixture to these variables,

the average electric field within the mixture as a whole must be related to

the electric fields within the inclusions [4]. The problem is that if the

inclusions are randomly dispersed throughout the host medium, it is not

generally possible to derive an exact solution for the fields within the

inclusions since the mutual electromagnetic interactions of the inclusions are dependent on their positions with respect to each other. Tinga [13] gives a review of the various approximations that have been proposed for solving the

interaction problem. These approximations vary from ones ignoring short-range

interactions between inclusions (by restricting the validity of the dielectric

mixing model to only those mixtures characterized by a low concentration of

inclusions) to relations that account for first-order inclusion interactions

via the solution of Maxwell's equations and appropriate boundary conditions

[ 11 , 13 ]. In all cases, the dimensions of the inclusions are much smaller than

the propagation wavelength in the host medium. Bottcher [14] gives a comprehensive review of dielectric mixing models that includes both empirical

(or semi-empirical) formulations for specific mixtures as well as theoretical

models developed for highly specialized media that contain either ellipsoidal

particle inclusions (spheres, disks, needles) or confocal ellipsoidal

inclusions. A limitation of much of this work is its restricted applicability

to only specific mixtures and /or conditions.

6
4.1.1 General Water-Dominated Dielectric Behavior of Natural Soils

By definition, natural soils are mixtures of host matrix mineral(s), air,

and water. Generally, the effective relative permittivity, e^ff*

mixture rarely exceeds 8 in the microwave region—as long as there is no liquid water present within the mixture. Similarly, EQff usually does not

exceed 1 in the absence of liquid water. By way of comparison, we see from

figure 1 that of liquid water is one order of magnitude larger than the

relative permittivity of dry materials, whereas is two orders of

magnitude larger that e" of dry materials, particularly at frequencies less

than 2 GHz. Because of the large contrast between (complex) e of the pore

water and that of the host matrix in soils, the dielectric constant of the

mixture is generally dominated by the dielectric behavior of water. For this

reason, many investigators have generalized the Debye formulas given by eqs

(3) and (4) to mixtures in the following way.

^eff ^eff,»

^

p = ?Trf T eff eff

^eff,0

~ ^eff,- ^

1 +

[a

[27Tf "^eff^

eff ,0

1 + ('2^f T eff

eff

( 11 )

( 12 )

where Eeff,0» ^eff,“ ”^eff functions of the dielectric constant of

the matrix mineral(s), the water-volume fraction in the pore space of the

matrix, and shape and orientation of the water inclusions. The dielectric

constants of the matrix minerals are presumed to be nondispersive (frequency

independent or lossless) as well as independent of the applied direction

(polarization) of the incident electric field. The latter presumptions are borne out by many measurements so that the above formulas are often used in sea- ice and snow remote sensing [15,16]. However, caution must be exercised

in the use of eqs (11) and (12) for soil mixtures over a broad range in

frequency, since multiple relaxation phenomena not taken into account by thesDebye-type rules can occur [1].

7
4.2 Generalized Heuristic Rules for Soil Mixtures

In the previous section it was stated that natural soils are mixtures of

matrix minerals, air and water. As noted in [1], water in the pore spaces of

surface soils consists of two phases. One of these phases is the bulk (free)

pore water. The other is adsorbed water adjacent to the matrix grain surfaces

that is usually several molecular layers in thickness. This adsorbed water is

referred to as surface (or bound) water. The saturation level at which the

dielectric constant becomes less sensitive to water saturation is entirely a function of the amount of surface water in soil pore spaces, a fact which

explains the dependence of the dielectric constant on soil texture types

(particle size and shape distributions) as well as on the intrinsic porosity

of the soil mixture. Of course, the porosity is simply related to the bulk

density, and the degree of conductive loss responsible for electromagnetic

wave attenuation is dependent on the salinity of the pore water which, in

turn, depends quite naturally on both the matrix cation exchange capacity and

temperature. The fact that the electrical properties of water- saturated soils

are frequency dependent is also not physically surprising since we would

expect polarization, i.e., the orientation of polar molecules (molecules with

asymmetric charge distributions) to occur in an applied electric field. The

mobility of any polar molecule (such as water) will always depend on time rate

of variation of that field.

It is viell known that (bound) water adsorbed to a solid surface has a dielectric response significantly different from that of free water. This can

be attributed to the fact that the molecular mobility of the water molecules

has been reduced by physical bonding to the matrix grain surfaces [17,18,19].

Most of the measurement evidence to date seems to indicate that the restricted

mobility causes a reduction of the static dielectric constant of water

adsorbed to the surface from 80 for free water to about 6 for sorped water

[18], greater than an order of magnitude reduction. Furthermore,

surface-bound water exhibits a relaxation of about 10^ Hz instead of 100 GHz,

a relaxation frequency seven orders of magnitude lower than that of bulk water

[ 1 , 20 ].

8
Thus the most general form of a heuristic, predictive dielectric mixing

rule that might be used for soil specifications would separate the volumetric

percentages of bound and free water. The soil mixture is then described

electrically as a four- component system whose constituent components are linearly combined in terms of the respective volume fractions

a a a , a ^ a

e = V e + V e + v, e, + v^

soil mm a a bw bw fw fw (13)

where v represents volume fraction, the subscripts m, a, bw, and fw represent

soil matrix, air, bound water, and free water, respectively, and where a is a constant

.

Here we recognize that

= total porosity = ( Pm " Pb^^Pm = '' " Pb^Pm

where Pm, Pb denote the matrix and bulk density, respectively.

Vm = 1 -

(J) (14)

Vq = (p - Sw

Sw = Vbw + Vfw.

The two terms involving bound and free water are often combined into a single

term with an empirically determined multiplicative factor of the free water

permittivity in the soil [6]. That is,

a a ± a

V, e, + v„ e„ “ Sw e„ bw bw fw fw fw (15)

where the exponent, v, of total water saturation, Sw, is empirically derived.

Ct Substituting eqs (14) and (15) into (13) and recognizing that = 1

yields the following relation in terms of porosity and water saturation

9
( 16 ) 'soil

= (1 - (j)) e“ + - Sw + S^;; 6°^ m fw

In terms of the bulk and soil matrix densities, eq (16) may be written

Soil " Pb/Pm) ^ ^ ~ Pb/Pm + - Sw)

or

'soiln

-1 " (e“ - 1) * (sii; e“^ - Su

Pm m

(17)

where Pfe/pm = soil matrix volume fraction.

For a = 1, eq (17) is known as a linear model; for a = 1 /2 as a

1/ refractive model (since e ^ s n is the refractive index), and for a = 1/3 as the cubic model.

The results of over 500 measurements made by Dobson et al. [6] on five

differing soil types at nine frequencies (from 4.0 GHz to 18 GHz) and for

volumetric mositures, Sw, ranging from 0.01 to total saturation gave values of

V between 1.0 and 1.16 and suggested a refractive model (a = 1/2) as that

being most suited for soil-water mixtures. This was observed earlier by

Shutko and Reutov [21 ]. Hence and

: 1 * Ph

soil Pff]

^ m

1) t Sw (4^^ - 1). (18)

It has been noted [12] that combining the effects of bound and free water into

one term (eq (15)) reduces the implicit dependence of Cgon on soil type; this

is not surprising since clays are expected to have more bound water than, say,

sand grains. It should be noted that Csoil in eq (18) are in general

complex quantities, since attenuative loss due to electrolytic conduction is

fundamentally implicit in natural soils and therefore must be incorporated

into test lane soils for realistic performance testing. In fact, the loss

tangent of soil pore water, which depends on salinity (and temperature), is

essentially an in situ parameter and cannot be ascertained correctly by pore

fluid extraction. These complicating facts will be addressed.

10
4.2.1 Dielectric Mixing Rule for Dry Soils

For a dry soil mix eq (18) simplifies to

/a + Pji

[ - 1 ) soil Pin

^ matrix ‘

since Sw = 0. Or, in terms of the porosity p of the soil mix

( 19 )

'soil

= (1 - h

'soil

'mat ri

x

p eair

= (1 - p] matrix ^

(20)

y since e^ir = ^ ~ this case the soil mixture will have a real

dielectric constant (or exhibit no conductive losses). As such, essentially

no electromagnetic attenuation will be imposed on field behavior by the

background soil medium in the frequency range of interest and detection

systems operating at higher relative frequencies would be expected to perform

best, all other factors being equal [1]. Examples of dielectric, nonlossy

test soils are dry sands (Si02 or SiC). Frequency- domain measurements of the

dielectric constant on these soils have been reported previously [1].

4.2.2 Dielectric Mixing Rule for Lossy, Fluid-Saturated Soils

For lossy, fluid- saturated soils the dielectric mixing rule becomes more

complicated since both the bulk soil mix and the pore water become

electrically lossy and attenuate electromagnetic fields. In this case the

electromagnetic fields of a mine detection system operating at a higher

relative frequency would suffer greater attenuation, i.e., the mine detector

system would be characterized by a smaller (plane wave) skin depth. If the

effective skin depth is too small relative to the burial depth of a buried

mine, the detection system would perform more poorly than a system operating

at a lower frequency. There are two cases to consider: one where background

soils are only partially water saturated and the other where soils are fully

saturated.

11
4.2.2. 1 Partially Saturated Soil Mixtures

The complex dielectric constant of the soil may be written

where

'soil - (1 - $) +{({'- Sw) + Sw £ 'matrix

-^4 'air

4

water ( 21 )

= vV 'matrix matrix

4

(nonlossy)

air

f

= 1 (nonlossy)

^water ^^water ^ ^water^ (lossy) ( 22 )

= [e’ . M - j tan6 , )] ^ ,tan6 ,

'• water ^ water ^

’ water * _ water

'water

y, r

* . It ; ^soil ~ ^^soil ^ 'soil (lossy)

_ soil

= -1 [”1 “ j tan6 )] ^ tan6 - soil ^ ^ soil soil t 'soil

Use of the half-angle relation

tan6 = 2 tan 6/2

1 - tan^ 6/2

allows a complex dielectric constant e = e* 0 “ j tan6) to be written as

4e = /e’

[l - tan^

[l - tan^ - 2j tan |-]^2

A

1 - tan^

[[1 - j tan |)^] (23)

12
or

[l - j tan |] .

Use of eqs (23) and (22) in (21) then yields

soil

soil 'I y.

(l - j tan -^1^] = [l - (p) /P

4-2 soil 'I (1 - tan^ —5—

J

matrix + [({)- Sw]

Sw/e

water r. . , water 1 [1 - J tan 5—

J

[l - tanwater

Separating real and imaginary parts

[l - tan'

soil 'iK, ’^^matrix ^ ^^matrix^

Sw/

e

’ , water

(1 - tan^ ^iaterjy.

and

(2H)

Asoil tan

soil

Sw/e’ , tan 6 . /2 water water

(25)

6 '4 6 ^ 4

(1 - tan^ -^] (1 - tan^ J^ater

)

=

Both eqs (24) and (25) must be satisfied simultaneously. From measurements

^soil> tan6goii> ematrix known. The total porosity, (p, and the

water and air saturations, Sw, and b-Sw, respectively, may be determined by

using a value for the water salinity, S, which is based on the cation exchange

capacity of the matrix soil type. The dielectric constant of the pore water,

e^ater» is computed from eqs (6) and (9). The loss tangent of the pore

water is then calculated from eq (10). Substituting these values and measure!

^soil into eq (25) allows the determination of Sw from which

the total porosity is computed (eq (24)).

13
4. 2.2. 2 Saturated Soil Mixtures

A more expedient approach is to relate the complex dielectric constant of

the soil mixture to the water-filled porosity so that we may write

'soil 1 - c . . + matrix <P w water

Use of eqs (22) and (23) now yields

(26)

/c soil

6 .

,

(, - tan’

- (1 - * ^ ^w^ matrix

^w’^water

6 . y^ [l - tan’ -^f^]

(27)

and

6 soil

T tan „ soil 2

6 . , '4

(1 - tan’^)

^ water

(b y C j tSJl ^ ^w water 2

(28)

[l - tan

6 . 4

2 water -i ^

Again, Esoil> tan6goii, and known from measurements. A

value for the salinity of the pore water, S, is then taken. The real part of

the pore water permittivity, Cwater» temperature T (°C), is then

computed from

^water = ^wO^T) - 0.1556 - 0.000413 S + 0.00000158 S^ (29)

where

CwO(T) = 88.045 - 0.4147 T + 0.0006295 T^ (30)

Next the loss tangent of the pore water is calculated from

tan 6v^ater = [%aterl“'' [5.66 + 0.00265 S - 0.0000045 S^]. (31)

This initial value of tan6^ater ta substituted into eq (27) to determine

A corrected value of tanS^ater^^ is determined from eq (28) which is then used

to determine a new value for the water salinity and porosity, until they

converge to constant values. This approach is one commonly used in geophysics

and reservoir engineering to determine both the water-filled porosity and pore

water salinity of rocks from in situ dielectric measurements. For our purposes here, these are the fundamental parameters that allow us to predict.

14
based on a mixing relationship, how attenuative a background soil is. The

important point is that the complex permittivity (both nonlossy and lossy

parts) of the background test medium be the same in performance evaluations of

mine detector systems operating at the same frequency. While various

synthetic substances can be thought of that can simulate the real field

situation of water-saturated soils in tenns of the complex permittivity at a single frequency, there are few synthetics which, in combination, can simulate

the dielectric behavior of water-saturated soils over a broad range in

f requency

.

5. APPLICATION TO SOIL STANDARDS

As an application to dielectric property prediction of soil mixtures,

consider a two- phase mixture of air and dry sand, where sand consists of

washed quartz grains having diameters ranging from 0.027 and 0.60 mm. From eq

(19) we write

esoil

+ Pb. r/2

Pfjj

^ matrix

For this mixture, Geyer [1] and Jesch [22] have reported a measured mean

relative dielectric constant, Csoil» of 2.702 at 300 MHz and for a mean

bulk density, pj^, of 1.5^0 g/cc. Standard deviations for the relative

dielectric constant and mean bulk density were 0.0486 and 0.022 g/cc,

respectively. Bussey [23,24] reports e’of silica equal to 3.822, measured

at 9 GHz with the use of cavity resonators. Von Hippel [25] reports e' of

(fused) silica at 25°G and at 300 Mliz equal to 3.78. Von Hippel's results

show fused silica essentially dispersionless over the frequency range of 100

Hz to 25 GHz, with tan63 iiiQa = 0.5 x 10"^ at 300 MHz. Glark [26] and Morey

[27] give the matrix density of pure silica, prr), to be 2.203 g/cc.

In summary, use of the above two-phase refractive dielectric mixing r.i'< yields a predicted relative constant

15
y

2 ^soil, predicted = 0.699 [crnatrix “ 0]

= [l + 0.699 ( 3 . 780^" “ 1 )]^

^soil, predicted " 2.756.

This result differs by 2.1 percent from observed measurements using an open-ended transmission line with a vector automatic network analyzer [1,22].

This difference is probably due to impurities in the quartz sand, which would

affect both Pj^ and ^matrix*

6. CONCLUSIONS

Refractive dielectric mixing rules provide a convenient means for

predicting a (background) test soil’s dielectric behavior in land mine

performance testing. The test soil’s dielectric behavior implicitly affects

the electromagnetic visibility of a buried land mine. Although such mixing

rules allow specification of multicomponent heterogenous soils in terms of the

effective nonlossy and attenuative behavior of the mix, they do not obviate

the need for background media dielectric measurement. For lossy background

media it is preferable to measure both the relative dielectric constant and

the loss tangent in situ.

Additional research work should address possible in situ dielectric

measurement techniques, as well as the relation between cation exchange

capacities of the matrix materials in a fluid- saturated soil mixture, fluid

salinities, and corresponding test medium attenuative loss tangents affecting

mine detection system performance.

16
7. REFERENCES

[1]

Creyer, R. G. Experimental parameters for land mine detection

performance evaluations. Report, U. S. Army Bel voir Research and

Development Center, Fort Belvoir, VA (Proj. 7232457); 1987 November.

[2] 100 p.

Debye, P. Polar molecules. New York: Dover; 1929.

[3]

Lane, J. ; Saxton, J. Dielectric dispersion in pure polar liquids at very

high radio frequencies. III. The effect of electrolytes in solution.

Proc., Roy. Soc. 214(A); 1952. 531-545.

[4]

Hasted, J. B. Liquid water: dielectric properties. Chapter 7 Water

- a comprehensive treatise, I, The physics and chemistry of water. New

York: Plenum Press; 1972.

[5]

Klein, L. A.; Swift, C. T. An improved model for the dielectric constant

of sea water at microwave frequencies. IEEE Trans. Antennas Propag.

AP-25; 1977. 104-111.

[6]

Dobson, M. C.; Ulaby, F. T. ; Hallikainen, M. T. ; El-Rayes, M. A.

Microwave dielectric behavior of wet soil. Part II: dielectric mixing

models. IEEE Trans. Geosci. Remote Sensing. GE-23(1); 1985. 35-46.

[7]

Jedlicka, R. P. Saline soil dielectric measurements. M. S. Thesis New

Mexico State University, NM; 1978.

[8]

Stogryn, A. Equations for calculating the dielectric constant of saline

water. IEEE Trans. Microwave Theory Techn. MTT-19; 1971. 733-736.

[9]

1/Jharton, R. P. ; Hazen, G.A. ; Rau, R. N. ; Best, D. L. Electromagnetic

propagation logging: advances in technique and interpretation. SPE of

AIME Annual Technical Conference and Exhibition (Paper SPE 9267); 1980

September. 21-24.

[10]

Ho, VJ. ; Hall, W. F. Measurements of the dielectric properties of sea

water and NaCI solutions at 2.65 GHz. J. Geophys. Res. 78; 1973-

6301-6315.

[11]

Ho, W. W. ; Love, A. W. ; VanMelle, M. J. Measurements of the dielectric

properties of sea water at 1.43 GHz. NASA Contactor Report CR-2458. NASA

Langley Research Center, Langley, VA; 1974.

17
[12]

Ulaby, F. T. ; Moore, R. K.; Fung, A. K. Microwave remote sensing, Vol.

Ill: from theory to applications. London, England: Addison-Wesley

Publishing Co.; 1982.

[ 13

]

Tinga, W. R. Generalized approach to multiphase dielectric mixture

theory. J. Appl. Phys. 44; 1973- 3897 “3902. [14]

Bottcher, C. J. F. Theory of electric polarization. Amsterdam:

Elsevier; 1952.

[ 15

]

Hallikainen, M. Dielectric properties of sea ice at microwave

frequencies. Report S94. Helsinki University of Technology, Radio

Laboratory, Espoo, Finland; 1977.

[ 16

]

Hallikainen, M.; Ulaby, F. T. ; Abdelrazik, M. The dielectric behavior of

snow in the 3“ to 37“GHz range. IEEE International Geosci. Remote

Sensing Symp. Digest, Strasbourg, France; 1984 August 27“30. 169-176.

[ 17

]

Kurosaki , S. The dielectric behavior of water sorbed in silica gel. J. Phys. Chem. 58; 1954. 320-324.

[ 18

]

Bockris, J. ; Gileady, E. ; Muller, K. Dielectric relaxation in the

electric double layer. J. Chem. Physics. 44; 1966. 1445-1456.

[ 19

]

McCafferty, E. ; Zettlemayer, A. C. Adsorption of water vapor on cc-Fe 203 . Faraday Soc. Discussions, Vol. 52; 1971. 239-254.

[20]

Hasted, J. B. The dielectric properties of water Progress in

dielectrics Vol. 3. U. B. Birks and J. Hart, ed. New York: John Wiley &

Sons; 1961. 101-149.

[21]

Shutko, A. M. ; Reutov, E. M. Mixture formulas applied in estimation of

dielectric and radiative characteristics of soils and grounds at

microwave frequencies. IEEE Trans. Geosci. Remote Sensing. GE-20; 1982.

29-32.

[22]

Jesch, R. L. Dielectric measurements of five different soil textural

types as functions of frequency and moisture contenct. Nat. Bur. Stand.

(U.S.) NBSIR 78-896; 1978. 26 p.

[ 23

]

Bussey, H. E. International comparison of complex permittivity

measurement at 9 GHz. IEEE Trans. Instr. Meas. IM-23(3); 1974. 235-239.

18
[24]

Bussey, H. E. ; Gray, J. E. ; Bamberger, E. C.; Rushton, E. ; Russel, G.

;

Petley, B. W. ; Morris, D. International comparison of dielectric

measurements. IEEE Trans. Instr. Meas. IM-13; 1964. 305-311.

[25]

Von Hippel, A. R. Dielectric materials and applications. New York: The

Technology Press of M.I.T. and John Wiley & Sons; 1954. 438 p. [26]

Clark, S. P. Handbook of physical constants. Geol. Soc. Am. Memoir 97;

1966. 587 p. [27]

Morey, L. Properties of glass. Nevj York: Reinhold Press; 1954.

19
Figure 1

.

Cole-Cole Diagram for the dielectric constant of pure water at 0°C

(after Hasted [4]).

20
U.S. DEPT. OF COMM. 1. PUBLICATION OR

REPORT NO.

2. Performing Organ. Report No. 3. PubI ication Date BIBLIOGRAPHIC DATA

SHEET (See instructions) NBSIR 88-3095 June 1988

4. TITLE and subtitle

Dielectric Mixing Rules for Background Test Soils

5. AUTHOR(S)

Richard G. Geyer

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions) 7. Contract/Grant No.

national bureau of standards

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

8. Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City, State, ZIP)

U.S. Army Bel voir Research & Development Center

Fort Belvoir, Virginia 22060-5606

10.

SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11.

ABSTRACT ( A 200-word or less factual summary of most significant information. If document includes a significant

bi bliography or literature survey, mention it here)

The bulk, or effective dielectric constant of any background test medium

(whether naturally occurring or synthetic) determines the electromagnetic

visibility of buried objects. Heuristic mixing rules are considered that

allow the prediction of complex dielectric behavior in linear, homogeneous,

isotropic, and lossy multi-phase soil mixtures. Measurement results in bioelectromagnetic and microwave remote sensing suggest a refractive mixing model

as that being most suited for dry soils or soil-water mixtures.

12.

KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon - dielectric simulation; mixing rules; multi-phase; soils

13.

AVAILABILITY 14. NO. OF

PRINTED PAGES

[xj Uni imited

I I For Official Distribution. Do Not Release to NTIS

I I Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

28

15. Price

[Xj Order From National Technical Information Service (NTIS), Springfield, VA. 22161

u U.S. GOVERNMENT PRINTING OFFICE: 1988-576-865/85,244 REGION NO. 8